Theory of hadronic B decays
Dan Pirjol\index{DP}
I give an overview of the theory of hadronic nonleptonic B decays into two light mesons. Using the soft-collinear effective theory (SCET), a factorization theorem for these processes has been proven to leading order in $1/m_b$. The phenomenological implications of this factorization relation for $B\to \pi\pi$ decays are discussed, together with the prospects for determining $\alpha$ from these modes.
fpcp04-macro.tex
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%%  Useful macros for FPCP 2003
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%%  basic formatting macros:
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%%  single-line equations:

\def\beq{\begin{equation}}
\def\eeq#1{\label{#1}\end{equation}}
\def\eeqn{\end{equation}}

%%  multiple-line equations  (use \CR as the carriage return):

\def\beqa{\begin{eqnarray}}
\def\eeqa#1{\label{#1}\end{eqnarray}}
\def\eeqan{\end{eqnarray}}
\def\CR{\nonumber \\ }

%%  reference to an equation number:

\def\leqn#1{(\ref{#1})}

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%%  bibliographic entries   (use this or the SPIRES LaTeX output)

\def\Journal#1#2#3#4{{#1} {\bf #2}, #3 (#4)}
\def\add#1#2#3{{\bf #1}, #2 (#3)}

%%   Journal or bibliographic formatting macros are obsolete!
%%   The SLAC/SPIRES database supplies properly formatted citations;
%%      click on  LaTeX(US) or LaTeX(EU)   

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%%  sizing and bars

\def\st{\scriptstyle}
\def\sst{\scriptscriptstyle}

\def\overbar#1{\overline{#1}}
\let\littlebar=\bar
\let\bar=\overbar

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%  text-mode macros:

\def\etal{{\it et al.}}
\def\ie{{\it i.e.}}
\def\eg{{\it e.g.}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%  expectation values:

\def\VEV#1{\left\langle{ #1} \right\rangle}
\def\bra#1{\left\langle{ #1} \right|}
\def\ket#1{\left| {#1} \right\rangle}
\def\vev#1{\langle #1 \rangle}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%  caligraphic letters (for matrix elements, luminosity, etc.)

\def\cD{{\cal D}}
\def\cL{{\cal L}}
\def\cM{{\cal M}}
\def\cO{{\cal O}}
\def\cW{{\cal W}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%  matrix operations and fractions:

\def\One{{\bf 1}}
\def\hc{{\mbox{\rm h.c.}}}
\def\tr{{\mbox{\rm tr}}}
\def\half{\frac{1}{2}}
\def\thalf{\frac{3}{2}}
\def\third{\frac{1}{3}}
\def\tthird{\frac{2}{3}}

\def\Dslash{\not{\hbox{\kern-4pt $D$}}}
\def\dslash{\not{\hbox{\kern-2pt $\del$}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%  high-energy physics terminology:

\def\Pl{{\mbox{\scriptsize Pl}}}
\def\eff{{\mbox{\scriptsize eff}}}
\def\CM{{\mbox{\scriptsize CM}}}
%% \def\BR{\mbox{\rm BR}}
\def\eepm{e^+e^-}
\def\sstw{\sin^2\theta_w}
\def\cstw{\cos^2\theta_w}
\def\mz{m_Z}
\def\gz{\Gamma_Z}
\def\mw{m_W}
\def\mt{m_t}
\def\gt{\Gamma_t}
\def\mh{m_h}
\def\gmu{G_\mu}
\def\GF{G_F}
\def\alphas{\alpha_s}
\def\msb{{\bar{\ssstyle M \kern -1pt S}}}
\def\lmsb{\Lambda_{\msb}}
\def\ELER{e^-_Le^+_R}
\def\EREL{e^-_Re^+_L}
\def\ELEL{e^-_Le^+_L}
\def\ERER{e^-_Re^+_R}
\def\epsi{\epsilon}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%  supersymmetry:

\def\ch#1{\widetilde\chi^+_{#1}}
\def\chm#1{\widetilde\chi^-_{#1}}
\def\neu#1{\widetilde\chi^0_{#1}}
\def\s#1{\widetilde{#1}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\vckm{V_{\rm CKM}}

\newcommand{\lsime} {\buildrel < \over {_\sim}}
\newcommand{\gsime} {\buildrel > \over {_\sim}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\BB0bar{B^0 {\overline B}^0}
\def\BB0dbar{B_d^0 {\overline B}_d^0}
\def\BB0sbar{B_s^0 {\overline B}_s^0}
\def\rhobara{\bar \rho}
\def\etabara{\bar \eta}
\def\rhoeta{\rhobara-\etabara}
\def\rar{\rightarrow}
\def\stb{\sin 2\beta}
\def\sta{\sin 2\alpha}
\def\dmd{\Delta m_d}
\def\dms{\Delta m_s}
\def\Cpipi{C_{\pi\pi}}
\def\Spipi{S_{\pi\pi}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
%%%%%   Standard symbols for use in BABAR papers and BAD Notes
%%%%%
%%%%%   Revised   05/22/01 P. Dauncey     Added \hepex, etc. and clean up a bit
%%%%%   Revised   12/07/00 D. Hitlin      Added features of D. Kirkby's HEP.sty
%%%%%   Revised   07/13/00 R. Waldi       Corrected \Kbar, \Bbar ... macros
%%%%%   Revised   07/13/00 D. MacFarlane  Replaced incorrect \chic1 symbols
%%%%%   Revised   07/05/00 P. Dauncey     Added \mes, \mec, removed \O
%%%%%   Revised   07/04/00 D. MacFarlane  Added scalable version of BABAR
%%%%%   Revised   07/01/00 D. MacFarlane
%%%%%   Revised   06/21/00 D. Hitlin
%%%%%   Original  06/10/00 D. Hitlin
%%%%%   Revision of TDR and Physics Book symbol file
%%%%%

\RequirePackage{xspace}

%%%%%%%%%%%%%%%%%%%% BABAR ... THE NAME OF THE COLLABORATION %%%%

% Huge boldface
\def\hbabar{\mbox{{\huge\bf\sl B}\hspace{-0.1em}{\LARGE\bf\sl A}\hspace{-0.03em}{\huge\bf\sl B}\hspace{-0.1em}{\LARGE\bf\sl A\hspace{-0.03em}R}}}
% LARGE
\def\Lbabar{\mbox{{\LARGE\sl B}\hspace{-0.15em}{\Large\sl A}\hspace{-0.07em}{\LARGE\sl B}\hspace{-0.15em}{\Large\sl A\hspace{-0.02em}R}}}
% Large
\def\lbabar{\mbox{{\large\sl B}\hspace{-0.4em} {\normalsize\sl A}\hspace{-0.03em}{\large\sl B}\hspace{-0.4em} {\normalsize\sl A\hspace{-0.02em}R}}}
% normal size
%\def\babar{\mbox{\sl B\hspace{-0.4em} {\small\sl A}\hspace{-0.37em} \sl B\hspace{-0.4em} {\small\sl A\hspace{-0.02em}R}}}
% replace normalsize with scalable version       dbm 7/4/00
\usepackage{relsize}
\def\babar{\mbox{\slshape B\kern-0.1em{\smaller A}\kern-0.1em
    B\kern-0.1em{\smaller A\kern-0.2em R}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%   LEPTONS   %%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\let\emi\en
\def\electron   {\ensuremath{e}\xspace}
\def\en         {\ensuremath{e^-}\xspace}   % electron negative (\em is taken)
\def\ep         {\ensuremath{e^+}\xspace}
\def\epm        {\ensuremath{e^\pm}\xspace} 
\def\epem       {\ensuremath{e^+e^-}\xspace}
\def\ee         {\ensuremath{e^-e^-}\xspace}

\def\mmu        {\ensuremath{\mu}\xspace}
\def\mup        {\ensuremath{\mu^+}\xspace}
\def\mun        {\ensuremath{\mu^-}\xspace} % muon negative (\mum is taken)
\def\mumu       {\ensuremath{\mu^+\mu^-}\xspace}
\def\mtau       {\ensuremath{\tau}\xspace}

\def\taup       {\ensuremath{\tau^+}\xspace}
\def\taum       {\ensuremath{\tau^-}\xspace}
\def\tautau     {\ensuremath{\tau^+\tau^-}\xspace}

\def\ellm       {\ensuremath{\ell^-}\xspace}
\def\ellp       {\ensuremath{\ell^+}\xspace}
\def\ellell     {\ensuremath{\ell^+ \ell^-}\xspace}

\def\nub        {\ensuremath{\overline{\nu}}\xspace}
\def\nunub      {\ensuremath{\nu{\overline{\nu}}}\xspace}
\def\nub        {\ensuremath{\overline{\nu}}\xspace}
\def\nunub      {\ensuremath{\nu{\overline{\nu}}}\xspace}
\def\nue        {\ensuremath{\nu_e}\xspace}
\def\nueb       {\ensuremath{\nub_e}\xspace}
\def\nuenueb    {\ensuremath{\nue\nueb}\xspace}
\def\num        {\ensuremath{\nu_\mu}\xspace}
\def\numb       {\ensuremath{\nub_\mu}\xspace}
\def\numnumb    {\ensuremath{\num\numb}\xspace}
\def\nut        {\ensuremath{\nu_\tau}\xspace}
\def\nutb       {\ensuremath{\nub_\tau}\xspace}
\def\nutnutb    {\ensuremath{\nut\nutb}\xspace}
\def\nul        {\ensuremath{\nu_\ell}\xspace}
\def\nulb       {\ensuremath{\nub_\ell}\xspace}
\def\nulnulb    {\ensuremath{\nul\nulb}\xspace}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%  PHOTONS  %%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\g     {\ensuremath{\gamma}\xspace}
\def\gaga  {\ensuremath{\gamma\gamma}\xspace}  %% changed from \gg, which is >>
\def\ggstar{\ensuremath{\gamma\gamma^*}\xspace}

\def\ega    {\ensuremath{e\gamma}\xspace}
\def\game   {\ensuremath{\gamma e^-}\xspace}
\def\epemg  {\ensuremath{e^+e^-\gamma}\xspace}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%  Other GAUGE BOSONS  %%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\H      {\ensuremath{H^0}\xspace}
\def\Hp     {\ensuremath{H^+}\xspace}
\def\Hm     {\ensuremath{H^-}\xspace}
\def\Hpm    {\ensuremath{H^\pm}\xspace}
\def\W      {\ensuremath{W}\xspace}
\def\Wp     {\ensuremath{W^+}\xspace}
\def\Wm     {\ensuremath{W^-}\xspace}
\def\Wpm    {\ensuremath{W^\pm}\xspace}
\def\Z      {\ensuremath{Z^0}\xspace}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%   QUARKS   %%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\q     {\ensuremath{q}\xspace}
\def\qbar  {\ensuremath{\overline q}\xspace}
\def\qqbar {\ensuremath{q\overline q}\xspace}
\def\u     {\ensuremath{u}\xspace}
\def\ubar  {\ensuremath{\overline u}\xspace}
\def\uubar {\ensuremath{u\overline u}\xspace}
\def\d     {\ensuremath{d}\xspace}
\def\dbar  {\ensuremath{\overline d}\xspace}
\def\ddbar {\ensuremath{d\overline d}\xspace}
\def\s     {\ensuremath{s}\xspace}
\def\sbar  {\ensuremath{\overline s}\xspace}
\def\ssbar {\ensuremath{s\overline s}\xspace}
\def\cq     {\ensuremath{c}\xspace}
\def\cbar  {\ensuremath{\overline c}\xspace}
\def\ccbar {\ensuremath{c\overline c}\xspace}
\def\b     {\ensuremath{b}\xspace}
\def\bbar  {\ensuremath{\overline b}\xspace}
\def\bbbar {\ensuremath{b\overline b}\xspace}
\def\t     {\ensuremath{t}\xspace}
\def\tbar  {\ensuremath{\overline t}\xspace}
\def\tbar  {\ensuremath{\overline t}\xspace}
\def\ttbar {\ensuremath{t\overline t}\xspace}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%% LIGHT MESONS  %%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\piz   {\ensuremath{\pi^0}\xspace}
\def\pizs  {\ensuremath{\pi^0\mbox\,\rm{s}}\xspace}
\def\ppz   {\ensuremath{\pi^0\pi^0}\xspace}
\def\pip   {\ensuremath{\pi^+}\xspace}
\def\pim   {\ensuremath{\pi^-}\xspace}
\def\pipi  {\ensuremath{\pi^+\pi^-}\xspace}
\def\pipm  {\ensuremath{\pi^\pm}\xspace}
\def\pimp  {\ensuremath{\pi^\mp}\xspace}

\def\kaon  {\ensuremath{K}\xspace}
%%% do NOT use ensuremath here
\def\Kbar  {\kern 0.2em\overline{\kern -0.2em K}{}\xspace}
\def\Kb    {\ensuremath{\Kbar}\xspace}
\def\Kz    {\ensuremath{K^0}\xspace}
\def\Kzb   {\ensuremath{\Kbar^0}\xspace}
\def\KzKzb {\ensuremath{\Kz \kern -0.16em \Kzb}\xspace}
\def\Kp    {\ensuremath{K^+}\xspace}
\def\Km    {\ensuremath{K^-}\xspace}
\def\Kpm   {\ensuremath{K^\pm}\xspace}
\def\Kmp   {\ensuremath{K^\mp}\xspace}
\def\KpKm  {\ensuremath{\Kp \kern -0.16em \Km}\xspace}
\def\KS    {\ensuremath{K^0_{\scriptscriptstyle S}}\xspace} 
\def\KL    {\ensuremath{K^0_{\scriptscriptstyle L}}\xspace} 
\def\Kstarz  {\ensuremath{K^{*0}}\xspace}
\def\Kstarzb {\ensuremath{\Kbar^{*0}}\xspace}
\def\Kstar   {\ensuremath{K^*}\xspace}
\def\Kstarb  {\ensuremath{\Kbar^*}\xspace}
\def\Kstarp  {\ensuremath{K^{*+}}\xspace}
\def\Kstarm  {\ensuremath{K^{*-}}\xspace}
\def\Kstarpm {\ensuremath{K^{*\pm}}\xspace}
\def\Kstarmp {\ensuremath{K^{*\mp}}\xspace}

\newcommand{\etapr}{\ensuremath{\eta^{\prime}}\xspace}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%% HEAVY MESONS  %%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% do NOT use ensuremath here
\def\Dbar    {\kern 0.2em\overline{\kern -0.2em D}{}\xspace}
\def\Db      {\ensuremath{\Dbar}\xspace}
\def\Dz      {\ensuremath{D^0}\xspace}
\def\Dzb     {\ensuremath{\Dbar^0}\xspace}
\def\DzDzb   {\ensuremath{\Dz {\kern -0.16em \Dzb}}\xspace}
\def\Dp      {\ensuremath{D^+}\xspace}
\def\Dm      {\ensuremath{D^-}\xspace}
\def\Dpm     {\ensuremath{D^\pm}\xspace}
\def\Dmp     {\ensuremath{D^\mp}\xspace}
\def\DpDm    {\ensuremath{\Dp {\kern -0.16em \Dm}}\xspace}
\def\Dstar   {\ensuremath{D^*}\xspace}
\def\Dstarb  {\ensuremath{\Dbar^*}\xspace}
\def\Dstarz  {\ensuremath{D^{*0}}\xspace}
\def\Dstarzb {\ensuremath{\Dbar^{*0}}\xspace}
\def\Dstarp  {\ensuremath{D^{*+}}\xspace}
\def\Dstarm  {\ensuremath{D^{*-}}\xspace}
\def\Dstarpm {\ensuremath{D^{*\pm}}\xspace}
\def\Dstarmp {\ensuremath{D^{*\mp}}\xspace}
\def\Ds      {\ensuremath{D^+_s}\xspace}
\def\Dsb     {\ensuremath{\Dbar^+_s}\xspace}
\def\Dss     {\ensuremath{D^{*+}_s}\xspace}

% Obsolete
\newcommand{\dstr}{\ensuremath{\Dstar}\xspace}
\newcommand{\dstrstr}{\ensuremath{D^{**}}\xspace}
\newcommand{\dsp}{\ensuremath{\Dstarp}\xspace}
\newcommand{\dsm}{\ensuremath{\Dstarm}\xspace}
\newcommand{\dsz}{\ensuremath{\Dstarz}\xspace}


\def\B       {\ensuremath{B}\xspace}
%%% do NOT use ensuremath here
\def\Bbar    {\kern 0.18em\overline{\kern -0.18em B}{}\xspace}
\def\Bb      {\ensuremath{\Bbar}\xspace}
\def\BB      {\ensuremath{B\Bbar}\xspace} 
\def\Bz      {\ensuremath{B^0}\xspace}
\def\Bzb     {\ensuremath{\Bbar^0}\xspace}
\def\BzBzb   {\ensuremath{\Bz {\kern -0.16em \Bzb}}\xspace}
\def\Bu      {\ensuremath{B^+}\xspace}
\def\Bub     {\ensuremath{B^-}\xspace}
\def\Bp      {\ensuremath{\Bu}\xspace}
\def\Bm      {\ensuremath{\Bub}\xspace}
\def\Bpm     {\ensuremath{B^\pm}\xspace}
\def\Bmp     {\ensuremath{B^\mp}\xspace}
\def\BpBm    {\ensuremath{\Bu {\kern -0.16em \Bub}}\xspace}
\def\Bs      {\ensuremath{B_s}\xspace}
\def\Bsb     {\ensuremath{\Bbar_s}\xspace}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%% ONIA %%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\jpsi     {\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace}
\def\psitwos  {\ensuremath{\psi{(2S)}}\xspace}
\def\psiprpr  {\ensuremath{\psi(3770)}\xspace}
\def\etac     {\ensuremath{\eta_c}\xspace}
\def\chiczero {\ensuremath{\chi_{c0}}\xspace}
\def\chicone  {\ensuremath{\chi_{c1}}\xspace}
\def\chictwo  {\ensuremath{\chi_{c2}}\xspace}
\mathchardef\Upsilon="7107
\def\Y#1S{\ensuremath{\Upsilon{(#1S)}}\xspace}% no space before {...}!
\def\OneS  {\Y1S}
\def\TwoS  {\Y2S}
\def\ThreeS{\Y3S}
\def\FourS {\Y4S}
\def\FiveS {\Y5S}

%\def\chic1{\ensuremath{\chi_{c1}}}
%\def\chic2{\ensuremath{\chi_{c2}}}
%\def\chic3{\ensuremath{\chi_{c3}}}
\def\chic#1{\ensuremath{\chi_{c#1}}\xspace} % dbm


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%% BARYONS %%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\proton      {\ensuremath{p}\xspace}
\def\antiproton  {\ensuremath{\overline p}\xspace}
\def\neutron     {\ensuremath{n}\xspace}
\def\antineutron {\ensuremath{\overline n}\xspace}

\mathchardef\Deltares="7101
\mathchardef\Xi="7104
\mathchardef\Lambda="7103
\mathchardef\Sigma="7106
\mathchardef\Omega="710A

%%% do NOT use ensuremath here
\def\Deltabar{\kern 0.25em\overline{\kern -0.25em \Deltares}{}\xspace}
\def\Lbar{\kern 0.2em\overline{\kern -0.2em\Lambda\kern 0.05em}\kern-0.05em{}\xspace}
\def\Sigbar{\kern 0.2em\overline{\kern -0.2em \Sigma}{}\xspace}
\def\Xibar{\kern 0.2em\overline{\kern -0.2em \Xi}{}\xspace}
\def\Obar{\kern 0.2em\overline{\kern -0.2em \Omega}{}\xspace}
\def\Nbar{\kern 0.2em\overline{\kern -0.2em N}{}\xspace}
\def\Xb{\kern 0.2em\overline{\kern -0.2em X}{}\xspace}

\def\X {\ensuremath{X}\xspace}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% TAU BRANCHING FRACTIONS %%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\BR         {{\ensuremath{\cal B}\xspace}}
\def\BRtauptoe  {\ensuremath{\BR(\taup \to \ep)}\xspace}
\def\BRtaumtoe  {\ensuremath{\BR(\taum \to \en)}\xspace}
\def\BRtauptomu {\ensuremath{\BR(\taup \to \mup)}\xspace}
\def\BRtaumtomu {\ensuremath{\BR(\taum \to \mun)}\xspace}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%  LIGHT HADRON DECAYS %%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\etaprepp}{\ensuremath{\etapr \to \eta \pipi}\xspace}
\newcommand{\etaprrg} {\ensuremath{\etapr \to \rho^0 \g}\xspace}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%  B DECAYS   %%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\bpsiks     {\ensuremath{\Bz \to \jpsi \KS}\xspace}
\def\bpsikst    {\ensuremath{\Bz \to \jpsi \Kstar}\xspace}
\def\bpsikl     {\ensuremath{\Bz \to \jpsi \KL}\xspace}
\def\bpsikzeropi{\ensuremath{\Bz \to \jpsi \Kstarz (\to \KL \piz)}\xspace}
\def\bpsikpluspi{\ensuremath{\Bu \to \jpsi \Kstarp (\to \KL \pip)}\xspace}
\def\bpsikpi    {\ensuremath{\Bz/\Bzb \to \jpsi (\to \mumu) \Kpm \pimp}\xspace}
\def\bupsik     {\ensuremath{\Bpm \to \jpsi (\to \mumu) \Kpm}\xspace}
\def\bpsiX      {\ensuremath{\Bz \to \jpsi \X}\xspace}

\def\Bzbtomu    {\ensuremath{\Bzb \to \mu \X}\xspace}
\def\Bzbtox     {\ensuremath{\Bzb \to \X}\xspace}
\def\Bztopipi   {\ensuremath{\Bz \to \pipi}\xspace}
\def\Bztokpi    {\ensuremath{\Bz \to \Kpm \pimp}\xspace}
\def\Bztorhopi  {\ensuremath{\Bz \to \rho^+ \pim}\xspace}
\def\Bztorhorho {\ensuremath{\Bz \to \rho \rho}\xspace}
\def\Bztokrho   {\ensuremath{\Bz \to K \rho}\xspace}
\def\Bztokstpi  {\ensuremath{\Bz \to \Kstar \pi}\xspace}
\def\Bztoapi    {\ensuremath{\Bz \to a_1 \pi}\xspace}
\def\Bztodd     {\ensuremath{\Bz \to \DpDm}\xspace}
\def\Bztodstd   {\ensuremath{\Bz \to \Dstarp \Dm}\xspace}
\def\Bztodstdst {\ensuremath{\Bz \to \Dstarp \Dstarm}\xspace}

\def\BtoDK      {\ensuremath{B \to DK}\xspace}
\def\Btodstlnu  {\ensuremath{B \to \Dstar \ell \nu}\xspace}
\def\Btodstdlnu {\ensuremath{B \to \Dstar(D) \ell \nu}\xspace}
\def\Btorholnu  {\ensuremath{B \to \rho \ell \nu}\xspace}
\def\Btopilnu   {\ensuremath{B \to \pi \ell \nu}\xspace}

\def\Btoetah    {\ensuremath{B \to \eta h}\xspace}
\def\Btoetaph   {\ensuremath{B \to \etapr h}\xspace}

\newcommand{\Betaprks}{\ensuremath{\Bz \to \etapr \KS}\xspace}
\newcommand{\Betaprkz}{\ensuremath{\Bz \to \etapr \Kz}\xspace}

\def\btosgam    {\ensuremath{b \to s \g}\xspace}
\def\btodgam    {\ensuremath{b \to d \g}\xspace}
\def\btosll     {\ensuremath{b \to s \ellell}\xspace}
\def\btosnunu   {\ensuremath{b \to s \nunub}\xspace}
\def\btosgaga   {\ensuremath{b \to s \gaga}\xspace}
\def\btosglue   {\ensuremath{b \to s g}\xspace}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%  Y(4S) DECAYS   %%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\upsbb   {\ensuremath{\FourS \to \BB}\xspace}
\def\upsbzbz {\ensuremath{\FourS \to \BzBzb}\xspace}
\def\upsbpbm {\ensuremath{\FourS \to \BpBm}\xspace}
\def\upspsikl{\ensuremath{\FourS \to (\bpsikl) (\Bzbtox)}\xspace}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%  TAU DECAYS   %%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\tauptoe    {\ensuremath{\taup \to \ep \nunub}\xspace}
\def\taumtoe    {\ensuremath{\taum \to \en \nunub}\xspace}
\def\tauptomu   {\ensuremath{\taup \to \mup \nunub}\xspace}
\def\taumtomu   {\ensuremath{\taum \to \mun \nunub}\xspace}
\def\tauptopi   {\ensuremath{\taup \to \pip \nub}\xspace}
\def\taumtopi   {\ensuremath{\taum \to \pim \nu}\xspace}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%% GAMMA-GAMMA REACTIONS %%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\ggtopi     {\ensuremath{\gaga \to \pipi}\xspace}
\def\ggtopiz    {\ensuremath{\gaga \to \ppz}\xspace}
\def\ggstox     {\ensuremath{\ggstar \to \X(1420) \to \kaon \kaon \pi}\xspace}
\def\ggstoeta   {\ensuremath{\ggstar \to \eta(550) \to \pipi \piz}\xspace}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%   KINEMATICS    %%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\ptot       {\mbox{$p$}\xspace}
%\def\pxy        {\mbox{$p_{\rm t}$}
\def\pxy        {\mbox{$p_T$}\xspace}
%\def\pt         {\mbox{$p_{\rm t}$}\xspace}
\def\pt         {\mbox{$p_T$}\xspace}
\def\mes        {\mbox{$m_{\rm ES}$}\xspace}
\def\mec        {\mbox{$m_{\rm EC}$}\xspace}
\def\DeltaE     {\mbox{$\Delta E$}\xspace}

\def\pbcm {\ensuremath{p^*_{\Bz}}\xspace}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%   GEOMETRY    %%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\mphi       {\mbox{$\phi$}\xspace}
\def\mtheta     {\mbox{$\theta$}\xspace}
\def\ctheta     {\mbox{$\cos\theta$}\xspace}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%% ENERGY AND MOMENTUM %%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\tev}{\ensuremath{\mathrm{\,Te\kern -0.1em V}}\xspace}
\newcommand{\gev}{\ensuremath{\mathrm{\,Ge\kern -0.1em V}}\xspace}
\newcommand{\mev}{\ensuremath{\mathrm{\,Me\kern -0.1em V}}\xspace}
\newcommand{\kev}{\ensuremath{\mathrm{\,ke\kern -0.1em V}}\xspace}
\newcommand{\ev}{\ensuremath{\mathrm{\,e\kern -0.1em V}}\xspace}
\newcommand{\gevc}{\ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c}}\xspace}
\newcommand{\mevc}{\ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c}}\xspace}
\newcommand{\gevcc}{\ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c^2}}\xspace}
\newcommand{\mevcc}{\ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c^2}}\xspace}
%\def\ev   {\ensuremath{\rm \,e\kern -0.08em V}}
%\def\kev  {\ensuremath{\rm \,ke\kern -0.08em V}} 
%\def\mev  {\ensuremath{\rm \,Me\kern -0.08em V}} 
%\def\gev  {\ensuremath{\rm \,Ge\kern -0.08em V}} 
%\def\gevc {\ensuremath{\rm \,Ge\kern -0.08em V\!/c}} 
%\def\gevc {\ensuremath{{\rm \,Ge\kern -0.08em V\!/}c}} 
%\def\tev  {\ensuremath{\rm \,Te\kern -0.08em V}}
%\def\mevc {\ensuremath{\rm \,Me\kern -0.08em V\!/c}} 
%\def\mevc {\ensuremath{{\rm \,Me\kern -0.08em V\!/}c}} 
%\def\gevcc{\ensuremath{\rm \,Ge\kern -0.08em V\!/c^2}} 
%\def\mevcc{\ensuremath{\rm \,Me\kern -0.08em V\!/c^2}} 
%\def\gevcc{\ensuremath{{\rm \,Ge\kern -0.08em V\!/}c^2}} 
%\def\mevcc{\ensuremath{{\rm \,Me\kern -0.08em V\!/}c^2}} 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%% DISTANCE AND AREA %%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\syin {\ensuremath{^{\prime\prime}}\xspace}
\def\inch   {\ensuremath{\rm \,in}\xspace} % \in is taken
\def\ft   {\ensuremath{\rm \,ft}\xspace}
\def\km   {\ensuremath{\rm \,km}\xspace}
\def\m    {\ensuremath{\rm \,m}\xspace}
\def\cm   {\ensuremath{\rm \,cm}\xspace}
\def\cma  {\ensuremath{{\rm \,cm}^2}\xspace}
\def\mm   {\ensuremath{\rm \,mm}\xspace}
\def\mma  {\ensuremath{{\rm \,mm}^2}\xspace}
%\def\mum  {\ensuremath{\rm \,\mum}\xspace}
\def\mum  {\ensuremath{\,\mu\rm m}\xspace}%% mu meter 
%\def\muma {\ensuremath{\rm \,\mum}^2\xspace}
\def\muma       {\ensuremath{\,\mu\rm m^2}\xspace}
\def\nm   {\ensuremath{\rm \,nm}\xspace}
\def\fm   {\ensuremath{\rm \,fm}\xspace}
\def\nm         {\ensuremath{\rm \,nm}\xspace}   %% nanometer
\def\nb         {\ensuremath{\rm \,nb}\xspace}
%
\def\barn{\ensuremath{\rm \,b}\xspace}
\def\barnhyph{\ensuremath{\rm -b}\xspace}
\def\mbarn{\ensuremath{\rm \,mb}\xspace}
\def\mbarnhyph{\ensuremath{\rm -mb}\xspace}
\def\pb {\ensuremath{\rm \,pb}\xspace}
\def\invpb {\ensuremath{\mbox{\,pb}^{-1}}\xspace}
\def\fb   {\ensuremath{\mbox{\,fb}}\xspace}
\def\invfb   {\ensuremath{\mbox{\,fb}^{-1}}\xspace}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%% TIME AND MASS  %%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\mus  {\ensuremath{\rm \,\mus}\xspace}
\def\ns   {\ensuremath{\rm \,ns}\xspace}
\def\ps   {\ensuremath{\rm \,ps}\xspace}
\def\fs   {\ensuremath{\rm \,fs}\xspace}
\def\gm   {\ensuremath{\rm \,g}\xspace}

%%\def\s{\ensuremath{\rm {\,s}}} %% second - this displays nothing  - why?
\def\sec{\ensuremath{\rm {\,s}}\xspace}       %% second - this works - jw 4/19
\def\ms         {\ensuremath{{\rm \,ms}}\xspace}     %% millisecond
\def\mus        {\ensuremath{\,\mu{\rm s}}\xspace}    %% microsecond
\def\ns         {\ensuremath{{\rm \,ns}}\xspace}      %% nanosecond
\def\ps         {\ensuremath{{\rm \,ps}}\xspace}  %% picosecond


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%   MISCELLANEOUS %%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\Xrad {\ensuremath{X_0}\xspace}
\def\NIL{\ensuremath{\lambda_{int}}\xspace}
\let\dgr\degrees


%\def\m          {\ensuremath{\rm \,m}}    %% meter
%\def\ma         {\ensuremath{\rm \,m}^2}  %% meter squared
%\def\cm         {\ensuremath{\rm \,cm}}   %% centimeter
%\def\cma        {\ensuremath{\rm \,cm}^2} %% centimeter squared
\def\cms         {\ensuremath{{\rm \,cm}^{-2} {\rm s}^{-1}}\xspace}
%\def\mm         {\ensuremath{\rm \,mm}}   %% millimeter
%\def\mma        {\ensuremath{\rm \,mm}^2} %% millimeter squared
%\def\mum        {\ensuremath{\,\mu\rm m}} %% mu meter
%\def\muma       {\ensuremath{\,\mu\rm m^2}}


\def\mic  {\ensuremath{\,\mu{\rm C}}\xspace}
\def\krad {\ensuremath{\rm \,krad}\xspace}
\def\cmc  {\ensuremath{{\rm \,cm}^3}\xspace}
\def\yr   {\ensuremath{\rm \,yr}\xspace}
\def\hr   {\ensuremath{\rm \,hr}\xspace}
\def\degc {\ensuremath{^\circ}{C}\xspace}
\def\degk {\ensuremath {\rm K}\xspace}
\def\degrees{\ensuremath{^{\circ}}\xspace}
\def\mrad{\ensuremath{\rm \,mrad}\xspace}               %% milliradian
\def\rad{\ensuremath{\rm \,rad}\xspace}
\def\mradhyph{\ensuremath{\rm -mr}\xspace}
%
\def\sx    {\ensuremath{\sigma_x}\xspace}    
\def\sy    {\ensuremath{\sigma_y}\xspace}   
\def\sz    {\ensuremath{\sigma_z}\xspace}    

%\renewcommand{\bar}[1]{\overline{#1}}  

% Some more (from Helen)
%\def\O{{\ensuremath{\cal O}}}  !!! This is a predefined LaTeX symbol !!!
\def\order{{\ensuremath{\cal O}}\xspace}
\def\L{{\ensuremath{\cal L}}\xspace}
\def\calL{{\ensuremath{\cal L}}\xspace}
%\def\S{{\ensuremath{\cal S}}}  !!! This is a predefined LaTeX symbol !!!
\def\calS{{\ensuremath{\cal S}}\xspace}
\def\calA{{\ensuremath{\cal A}}\xspace}
\def\calD{{\ensuremath{\cal D}}\xspace}
\def\calR{{\ensuremath{\cal R}}\xspace}

%% Arrows:
\def\ra                 {\ensuremath{\rightarrow}\xspace}
\def\to                 {\ensuremath{\rightarrow}\xspace}


\newcommand{\stat}{\ensuremath{\mathrm{(stat)}}\xspace}
\newcommand{\syst}{\ensuremath{\mathrm{(syst)}}\xspace}


\def\pep2{PEP-II}
\def\BF{$B$ Factory}
\def\abf {asymmetric \BF}
\def\sx    {\ensuremath{\sigma_x}\xspace}     
\def\sy    {\ensuremath{\sigma_y}\xspace}   
\def\sz    {\ensuremath{\sigma_z}\xspace}


\newcommand{\inverse}{\ensuremath{^{-1}}\xspace}
\newcommand{\dedx}{\ensuremath{\mathrm{d}\hspace{-0.1em}E/\mathrm{d}x}\xspace}
\newcommand{\chisq}{\ensuremath{\chi^2}\xspace}
\newcommand{\delm}{\ensuremath{m_{\dstr}-m_{\dz}}\xspace}
\newcommand{\lum} {\ensuremath{\mathcal{L}}\xspace}

\def\gsim{{~\raise.15em\hbox{$>$}\kern-.85em
          \lower.35em\hbox{$\sim$}~}\xspace}
\def\lsim{{~\raise.15em\hbox{$<$}\kern-.85em
          \lower.35em\hbox{$\sim$}~}\xspace}

\def\qsq                {\ensuremath{q^2}\xspace}


% Data processing
\def\kbytes     {\ensuremath{{\rm \,kbytes}}\xspace}
\def\kbsps      {\ensuremath{{\rm \,kbytes/s}}\xspace}
\def\kbits      {\ensuremath{{\rm \,kbits}}\xspace}
\def\kbsps      {\ensuremath{{\rm \,kbits/s}}\xspace}
\def\mbsps      {\ensuremath{{\rm \,Mbits/s}}\xspace}
\def\mbytes     {\ensuremath{{\rm \,Mbytes}}\xspace}
\def\mbps       {\ensuremath{{\rm \,Mbyte/s}}\xspace}
\def\mbsps      {\ensuremath{{\rm \,Mbytes/s}}\xspace}
\def\gbsps      {\ensuremath{{\rm \,Gbits/s}}\xspace}
\def\gbytes     {\ensuremath{{\rm \,Gbytes}}\xspace}
\def\gbsps      {\ensuremath{{\rm \,Gbytes/s}}\xspace}
\def\tbytes     {\ensuremath{{\rm \,Tbytes}}\xspace}
\def\tbpy       {\ensuremath{{\rm \,Tbytes/yr}}\xspace}
%




% QCD parameters

\newcommand{\as}{\ensuremath{\alpha_{\scriptscriptstyle S}}\xspace}
\newcommand{\MSb}{\ensuremath{\overline{\mathrm{MS}}}\xspace}
\newcommand{\LMSb}{%
  \ensuremath{\Lambda_{\overline{\scriptscriptstyle\mathrm{MS}}}}\xspace
}

% Electroweak parameters

\newcommand{\tw}{\ensuremath{\theta_{\scriptscriptstyle W}}\xspace}
\newcommand{\twb}{%
  \ensuremath{\overline{\theta}_{\scriptscriptstyle W}}\xspace
}
\newcommand{\Afb}[1]{{\ensuremath{A_{\scriptscriptstyle FB}^{#1}}}\xspace}
\newcommand{\gv}[1]{{\ensuremath{g_{\scriptscriptstyle V}^{#1}}}\xspace}
\newcommand{\ga}[1]{{\ensuremath{g_{\scriptscriptstyle A}^{#1}}}\xspace}
\newcommand{\gvb}[1]{{\ensuremath{\overline{g}_{\scriptscriptstyle V}^{#1}}}\xspace}
\newcommand{\gab}[1]{{\ensuremath{\overline{g}_{\scriptscriptstyle A}^{#1}}}\xspace}


% CKM, CP violation

\def\eps{\varepsilon\xspace}
\def\epsK{\varepsilon_K\xspace}
\def\epsB{\varepsilon_B\xspace}
\def\epsp{\varepsilon^\prime_K\xspace}

\def\CP                {\ensuremath{C\!P}\xspace}
%\def\CPT               {\ensuremath{C\!P\!T}\xspace}
\def\CPT               {\ensuremath{C\!PT}\xspace} % Looks better without \!

\def\epstag  {\ensuremath{\varepsilon_{\rm tag}}\xspace}
\def\tagfac  {\ensuremath{\epstag(1-2w)^2}\xspace}

\def\rhobar {\ensuremath{\overline \rho}\xspace}
\def\etabar {\ensuremath{\overline \eta}\xspace}
%\def\paramest {\ensuremath{{\hat A}, {\hat \rho}, {\hat \eta} }}
%\def\ssparamest {\ensuremath{{\hat A}, {\hat {\sin 2 \alpha}}, 
%{\hat {\sin 2 \beta}} }}
\def\meas {\ensuremath{|V_{cb}|, |\frac{V_{ub}}{V_{cb}}|, 
|\varepsilon_K|, \Delta m_{B_d}}\xspace}

\def\Vud  {\ensuremath{|V_{ud}|}\xspace}
\def\Vcd  {\ensuremath{|V_{cd}|}\xspace}
\def\Vtd  {\ensuremath{|V_{td}|}\xspace}
\def\Vus  {\ensuremath{|V_{us}|}\xspace}
\def\Vcs  {\ensuremath{|V_{cs}|}\xspace}
\def\Vts  {\ensuremath{|V_{ts}|}\xspace}
\def\Vub  {\ensuremath{|V_{ub}|}\xspace}
\def\Vcb  {\ensuremath{|V_{cb}|}\xspace}
\def\Vtb  {\ensuremath{|V_{tb}|}\xspace}

%\def\sa{${\sin\! 2 \alpha  }$\xspace}
%\def\sb{${\sin\! 2 \beta   }$\xspace}
%\def\sg{${\sin\! 2 \gamma  }$\xspace}

% added by Gautier for tagging, tagmix, and sin2beta
\def\stwoa{\ensuremath{\sin\! 2 \alpha  }\xspace}
\def\stwob{\ensuremath{\sin\! 2 \beta   }\xspace}
\def\stwog{\ensuremath{\sin\! 2 \gamma  }\xspace}
\def\mistag{\ensuremath{w}\xspace}
\def\dilution{\ensuremath{\cal D}\xspace}
\def\deltaz{\ensuremath{{\rm \Delta}z}\xspace}
\def\deltat{\ensuremath{{\rm \Delta}t}\xspace}
\def\deltamd{\ensuremath{{\rm \Delta}m_d}\xspace}

\newcommand{\fsubd}{\ensuremath{f_D}}\xspace
\newcommand{\fds}{\ensuremath{f_{D_s}}\xspace}
\newcommand{\fsubb}{\ensuremath{f_B}\xspace}
\newcommand{\fbd}{\ensuremath{f_{B_d}}\xspace}
\newcommand{\fbs}{\ensuremath{f_{B_s}}\xspace}
\newcommand{\bsubb}{\ensuremath{B_B}\xspace}
\newcommand{\bbd}{\ensuremath{B_{B_d}}\xspace}
\newcommand{\bbs}{\ensuremath{B_{B_s}}\xspace}
\newcommand{\rgbb}{\ensuremath{\hat{B}_B}\xspace}
\newcommand{\rgbbd}{\ensuremath{\hat{B}_{B_d}}\xspace}
\newcommand{\rgbbs}{\ensuremath{\hat{B}_{B_s}}\xspace}
\newcommand{\rgbk}{\ensuremath{\hat{B}_K}\xspace}
\newcommand{\lqcd}{\ensuremath{\Lambda_{\mathrm{QCD}}}\xspace}

%\newcommand{\eqref}[1]{Eq.~(\ref{eq:#1})}
\newcommand{\secref}[1]{Section~\ref{sec:#1}}
\newcommand{\subsecref}[1]{Section~\ref{subsec:#1}}
\newcommand{\figref}[1]{Figure~\ref{fig:#1}}
\newcommand{\tabref}[1]{Table~\ref{tab:#1}}






% Journal References

% These bases are useful for ``submitted to'' when no volume is needed
\newcommand{\epjBase}        {Eur.\ Phys.\ Jour.\xspace}
\newcommand{\jprlBase}       {Phys.\ Rev.\ Lett.\xspace}
\newcommand{\jprBase}        {Phys.\ Rev.\xspace}
\newcommand{\jplBase}        {Phys.\ Lett.\xspace}
\newcommand{\nimBaseA}       {Nucl.\ Instr.\ Meth.\xspace}
\newcommand{\nimBaseB}       {Nucl.\ Instr.\ and Meth.\xspace}
\newcommand{\nimBaseC}       {Nucl.\ Instr.\ and Methods\xspace}
\newcommand{\nimBaseD}       {Nucl.\ Instrum.\ Methods\xspace}
\newcommand{\npBase}         {Nucl.\ Phys.\xspace}
\newcommand{\zpBase}         {Z.\ Phys.\xspace}


\newcommand{\apas}      [1]  {{Acta Phys.\ Austr.\ Suppl.\ {\bf #1}}}
\newcommand{\app}       [1]  {{Acta Phys.\ Polon.\ {\bf #1}}}
\newcommand{\ace}       [1]  {{Adv.\ Cry.\ Eng.\ {\bf #1}}}
\newcommand{\anp}       [1]  {{Adv.\ Nucl.\ Phys.\ {\bf #1}}}
\newcommand{\annp}      [1]  {{Ann.\ Phys.\ {\bf #1}}}
\newcommand{\araa}      [1]  {{Ann.\ Rev.\ Astr.\ Ap.\ {\bf #1}}}
\newcommand{\arnps}     [1]  {{Ann.\ Rev.\ Nucl.\ Part.\ Sci.\ {\bf #1}}}
\newcommand{\arns}      [1]  {{Ann.\ Rev.\ Nucl.\ Sci.\ {\bf #1}}}
\newcommand{\appopt}    [1]  {{Appl.\ Opt.\ {\bf #1}}}
\newcommand{\japj}      [1]  {{Astro.\ Phys.\ J.\ {\bf #1}}}
\newcommand{\baps}      [1]  {{Bull.\ Am.\ Phys.\ Soc.\ {\bf #1}}}
\newcommand{\seis}      [1]  {{Bull.\ Seismological Soc.\ of Am.\ {\bf #1}}}
\newcommand{\cmp}       [1]  {{Commun.\ Math.\ Phys.\ {\bf #1}}}
\newcommand{\cnpp}      [1]  {{Comm.\ Nucl.\ Part.\ Phys.\ {\bf #1}}}
\newcommand{\cpc}       [1]  {{Comput.\ Phys.\ Commun.\ {\bf #1}}}
\newcommand{\epj}       [1]  {\epjBase\ {\bf #1}}
%\newcommand{\epjc}      [1]  {{Eur.\ Phys.\ Jour.\ C~{\bf #1}}}
\newcommand{\epjc}      [1]  {\epjBase\ C~{\bf #1}}
\newcommand{\fizika}    [1]  {{Fizika~{\bf #1}}}
\newcommand{\fp}        [1]  {{Fortschr.\ Phys.\ {\bf #1}}}
\newcommand{\ited}      [1]  {{IEEE Trans.\ Electron.\ Devices~{\bf #1}}}
\newcommand{\itns}      [1]  {{IEEE Trans.\ Nucl.\ Sci.\ {\bf #1}}}
\newcommand{\ijqe}      [1]  {{IEEE J.\ Quantum Electron.\ {\bf #1}}}
\newcommand{\ijmp}      [1]  {{Int.\ Jour.\ Mod.\ Phys.\ {\bf #1}}}
\newcommand{\ijmpa}     [1]  {{Int.\ J.\ Mod.\ Phys.\ {\bf A{\bf #1}}}}
\newcommand{\jl}        [1]  {{JETP Lett.\ {\bf #1}}}
\newcommand{\jetp}      [1]  {{JETP~{\bf #1}}}
\newcommand{\jpg}       [1]  {{J.\ Phys.\ {\bf G{\bf #1}}}}
\newcommand{\jap}       [1]  {{J.\ Appl.\ Phys.\ {\bf #1}}}
\newcommand{\jmp}       [1]  {{J.\ Math.\ Phys.\ {\bf #1}}}
\newcommand{\jmes}      [1]  {{J.\ Micro.\ Elec.\ Sys.\ {\bf #1}}}
%\newcommand{\josa}      [1]  {{J.\ Opt.\ Soc.\ Am.\ {\bf #1}}}
\newcommand{\mpl}       [1]  {{Mod.\ Phys.\ Lett.\ {\bf #1}}}

%\newcommand{\nim}       [1]  {{Nucl.\ Instr.\ and Methods~{\bf #1}}}
\newcommand{\nim}       [1]  {\nimBaseC~{\bf #1}}
%\newcommand{\nima}      [1]  {{Nucl.\ Instr.\ Methods~{\bf A{\bf #1}}}}
\newcommand{\nima}      [1]  {\nimBaseC~A~{\bf #1}}

%\newcommand{\np}        [1]  {{Nucl.\ Phys.\ {\bf #1}}}
\newcommand{\np}        [1]  {\npBase\ {\bf #1}}
%\newcommand{\npb}       [1]  {{Nucl.\ Phys.\ {\bf B{\bf #1}}}}
\newcommand{\npb}       [1]  {\npBase\ B~{\bf #1}}
\newcommand{\npps}      [1]  {{Nucl.\ Phys.\ Proc.\ Suppl.\ {\bf #1}}}
\newcommand{\npaps}     [1]  {{Nucl.\ Phys.\ A~Proc.\ Suppl.\ {\bf #1}}}
\newcommand{\npbps}     [1]  {{Nucl.\ Phys.\ B~Proc.\ Suppl.\ {\bf #1}}}

\newcommand{\ncim}      [1]  {{Nuo.\ Cim.\ {\bf #1}}}
\newcommand{\optl}      [1]  {{Opt.\ Lett.\ {\bf #1}}}
\newcommand{\optcom}    [1]  {{Opt.\ Commun.\ {\bf #1}}}
\newcommand{\partacc}   [1]  {{Particle Acclerators~{\bf #1}}}
\newcommand{\pan}       [1]  {{Phys.\ Atom.\ Nuclei~{\bf #1}}}
\newcommand{\pflu}      [1]  {{Physics of Fluids~{\bf #1}}}
\newcommand{\ptoday}    [1]  {{Physics Today~{\bf #1}}}

%\newcommand{\jpl}       [1]  {{Phys.\ Lett.\ {\bf #1}}}      % dbm
\newcommand{\jpl}       [1]  {\jplBase\ {\bf #1}}
%\newcommand{\plb}       [1]  {{Phys.\ Lett.\ B~{\bf #1}}}   % dbm
\newcommand{\plb}       [1]  {\jplBase\ B~{\bf #1}}
\newcommand{\prep}      [1]  {{Phys.\ Rep.\ {\bf #1}}}
%\newcommand{\jprl}      [1]  {{Phys.\ Rev.\ Lett.\ {\bf #1}}} % dbm
\newcommand{\jprl}      [1]  {\jprlBase\ {\bf #1}}
%\newcommand{\pr}        [1]  {{Phys.\ Rev.\ {\bf #1}}}
\newcommand{\pr}        [1]  {\jprBase\ {\bf #1}}
%\newcommand{\jpra}      [1]  {{Phys.\ Rev.\ A~{\bf #1}}}
\newcommand{\jpra}      [1]  {\jprBase\ A~{\bf #1}}
%\newcommand{\jprd}      [1]  {{Phys.\ Rev.\ D~{\bf #1}}}
\newcommand{\jprd}      [1]  {\jprBase\ D~{\bf #1}}
%\newcommand{\jpre}      [1]  {{Phys.\ Rev.\ E~{\bf #1}}}
\newcommand{\jpre}      [1]  {\jprBase\ E~{\bf #1}}

\newcommand{\prsl}      [1]  {{Proc.\ Roy.\ Soc.\ Lond.\ {\bf #1}}}
\newcommand{\ppnp}      [1]  {{Prog.\ Part.\ Nucl.\ Phys.\ {\bf #1}}}
\newcommand{\progtp}    [1]  {{Prog.\ Th.\ Phys.\ {\bf #1}}}
\newcommand{\rpp}       [1]  {{Rep.\ Prog.\ Phys.\ {\bf #1}}}
\newcommand{\jrmp}      [1]  {{Rev.\ Mod.\ Phys.\ {\bf #1}}}  % dbm
\newcommand{\rsi}       [1]  {{Rev.\ Sci.\ Instr.\ {\bf #1}}}
\newcommand{\sci}       [1]  {{Science~{\bf #1}}}
\newcommand{\sjnp}      [1]  {{Sov.\ J.\ Nucl.\ Phys.\ {\bf #1}}}
\newcommand{\spd}       [1]  {{Sov.\ Phys.\ Dokl.\ {\bf #1}}}
\newcommand{\spu}       [1]  {{Sov.\ Phys.\ Usp.\ {\bf #1}}}
\newcommand{\tmf}       [1]  {{Teor.\ Mat.\ Fiz.\ {\bf #1}}}
\newcommand{\yf}        [1]  {{Yad.\ Fiz.\ {\bf #1}}}
%\newcommand{\zp}        [1]  {{Z.\ Phys.\ {\bf #1}}}
\newcommand{\zp}        [1]  {\zpBase\ {\bf #1}}
%\newcommand{\zpc}       [1]  {{Z.\ Phys.\ C~{\bf #1}}}
\newcommand{\zpc}       [1]  {\zpBase\ C~{\bf #1}}
\newcommand{\zpr}       [1]  {{ZhETF Pis.\ Red.\ {\bf #1}}}

\newcommand{\hepex}     [1]  {hep-ex/{#1}}
\newcommand{\hepph}     [1]  {hep-ph/{#1}}
\newcommand{\hepth}     [1]  {hep-th/{#1}}


%%%%%%%%%%%%%%%%%%%% SOFTWARE PACKAGES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\aslund     {\mbox{\tt Aslund}\xspace}
\def\bbsim      {\mbox{\tt BBsim}\xspace}
\def\beast      {\mbox{\tt Beast}\xspace}
\def\beget      {\mbox{\tt Beget}\xspace}
\def\Bta        {\mbox{\tt Beta}\xspace}
\def\betakfit   {\mbox{\tt BetaKfit}\xspace}
\def\cornelius  {\mbox{\tt Cornelius}\xspace}
\def\evtgen     {\mbox{\tt EvtGen}\xspace}
\def\euclid     {\mbox{\tt Euclid}\xspace}
\def\fitver     {\mbox{\tt FitVer}\xspace}
\def\fluka      {\mbox{\tt Fluka}\xspace}
\def\fortran    {\mbox{\tt Fortran}\xspace}
\def\gcalor     {\mbox{\tt GCalor}\xspace}
\def\geant      {\mbox{\tt GEANT}\xspace}
\def\gheisha    {\mbox{\tt Gheisha}\xspace}
\def\hemicosm   {\mbox{\tt HemiCosm}\xspace}
\def\hepevt     {\mbox{\tt{/HepEvt/}}\xspace}
\def\jetset74   {\mbox{\tt Jetset \hspace{-0.5em}7.\hspace{-0.2em}4}\xspace}
%\def\jetset     {\mbox{\tt Jetset \hspace{-0.5em}7.\hspace{-0.2em}4}}
\def\koralb     {\mbox{\tt KoralB}\xspace}
\def\minuit     {\mbox{\tt Minuit}\xspace}
\def\objegs     {\mbox{\tt Objegs}\xspace}
\def\paw        {\mbox{\tt Paw}\xspace}
\def\Root       {\mbox{\tt Root}\xspace}
\def\squaw      {\mbox{\tt Squaw}\xspace}
\def\stdhep     {\mbox{\tt StdHep}\xspace}
\def\trackerr   {\mbox{\tt TrackErr}\xspace}
\def\turtle     {\mbox{\tt Decay~Turtle}\xspace}

%%% Local Variables: 
%%% mode: plain-tex
%%% TeX-master: t
%%% End: 

fpcp04.tex
%%    TEMPLATE for articles submitted to FPCP 2004 proceedings
%%
%%
%%     Please do not remove lines commented out with %+
%%           these are for the editors' use.
%%           Replace title and author's name by yours
%%
%%     Questions?  Send email to :  cskim@yonsei.ac.kr
%%
\documentclass[12pt]{article}
\usepackage{epsfig,graphicx}
\usepackage{fpcp04}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  Do not change the page dimension defined in fpcp04.sty

%%  Adjust these for your printer:

\hoffset=-5mm
\voffset=0mm


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  personal abbreviations and macros
%    the following package contains macros used in this document:
%    Try to not use others ...

\input fpcp04-macro
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  To include an item in the INDEX of the conference volume,
%           flag it with    \index{<item name>}
%  The use of this macro is illustrated in the text.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\Slash#1{{#1\!\!\!\slash}}
\def\Aslash{A\!\!\!\!\slash}
\def\Bslash{B\!\!\!\!\slash}
\def\Dslash{D\!\!\!\!\slash}
\def\Eslash{E\!\!\!\slash}
\def\Mslash{M\!\!\!\!\!\slash}
\def\SppP{{\cal {P\!\!\!\!\hspace{0.04cm}\slash}}_\perp}
\def\ppslash{p^{\,\prime}\!\!\!\!\!\slash}
\def\nslash{n\!\!\!\slash}
\def\bnslash{\bar n\!\!\!\slash}
\def\pslash{p\!\!\!\slash}
\def\qslash{q\!\!\!\slash}
\def\ellslash{\ell\!\!\!\slash}
\def\lslash{l\!\!\!\slash}
\def\dslash{\partial\!\!\!\slash}
\def\Aslash{A\!\!\!\slash}
\def\epslash{\epsilon\!\!\!\slash}
\def\vslash{v\!\!\!\slash}
\def\OMIT#1{}

\newcommand{\CH}[2]{\chi_{#1,#2}}
\newcommand{\CHp}[3]{\chi_{#1,#2}^{#3}}
\newcommand{\bCH}[2]{\overline\chi_{#1,#2}}
\newcommand{\bCHp}[3]{\overline\chi_{#1,#2}^{#3}}

\newcommand{\nn}{\nonumber} 
\newcommand{\lc}{\lowercase}
\newcommand{\bn}{{\bar n}}
\newcommand{\bea}{\begin{eqnarray}}
\newcommand{\eea}{\end{eqnarray}}
\newcommand{\mcdot}{\!\cdot\!}


\newcommand{\SCETa}{\mbox{${\rm SCET}_{\rm I}$ }}
\newcommand{\SCETb}{\mbox{${\rm SCET}_{\rm II}$ }}

\newcommand{\DgppPl}{\,\overleftarrow D{}_{\!c\,\alpha}^{\perp}}
\newcommand{\DgppPr}{\,\overrightarrow D{}_{\!c\,\alpha}^{\perp}}

\def\lqcd{\Lambda_{\rm QCD}}
\begin{document}


\Title{Theory of hadronic B decays}
\bigskip

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\label{PirjolStart}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Your name
%
\author{ Dan Pirjol\index{DP} }

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Your address
%
\address{Center for Theoretical Physics, MIT\\
77 Massachusetts Avenue, Cambridge, MA 02139\\
}

\makeauthor\abstracts{
I give an overview of the theory of hadronic nonleptonic B decays into
two light mesons. Using the soft-collinear effective theory (SCET), a 
factorization theorem for these processes has been proven to leading
order in $1/m_b$. The phenomenological implications of this
factorization relation for $B\to \pi\pi$ decays are discussed, together
with the prospects for determining $\alpha$ from these modes. 
}

\section{Introduction}

The hadronic decays of B mesons provide a unique source of information
about the flavor structure of the Standard Model. Due to the peculiar
hierarchy structure of the CKM matrix, CP violation is an order unity effect 
in $B$ decays. After several years of data taking from the B factories 
BABAR and BELLE, we are now in a position to perform precision tests of the 
CKM mechanism for CP violation.


It is therefore of considerable interest to have a better theoretical 
understanding of the hadronic dynamics of B decays. Two main approaches are 
widely followed:
a) flavor symmetry methods \cite{GHLR,BuFl}, where isospin or 
SU(3) flavor symmetry are used to reduce the number of independent hadronic amplitudes.
b) dynamical approaches, based on the $1/m_b$ expansion and factorization
theorems. Several such methods have been proposed and used extensively over
the past few years, known as `QCD factorization' (QCDF) 
\cite{BBNS} and `pQCD' \cite{pQCD}. Recently, an effective theory
approach based on the Soft-Collinear Effective Theory (SCET) \cite{SCET} has been
used to study these decays.
The flavor symmetry approach is covered at this conference in the talk of
J. Zupan \cite{zupan-fpcp04} and some aspects of the second approach in the 
talk of H.~Y.~Cheng \cite{cheng-fpcp04}. I will discuss here
recent progress on hadronic decays using the SCET.


\section{SCET factorization relation}

The weak Hamiltonian mediating non-leptonic $B$ decays is given by
\begin{eqnarray} \label{HW}
 H_W = \frac{G_F}{\sqrt{2}}\sum_{f=d,s} \left[ V_{ub} V_{uf}^*
 \left( C_1 O_1^u + C_2 O_2^u  \right) +
V_{cb} V_{cf}^*
 \left( C_1 O_1^c + C_2 O_2^c  \right)
  - V_{tb} V_{tf}^* \sum_{i=3}^{10}\!\! C_i O_i^f \Big) \right],\nn
\end{eqnarray}
where $f=d,s$ for $\Delta S = 0,1$
transitions, respectively.  The tree operators $O_{1,2}^q$ are defined as
\begin{eqnarray}\label{O12}
 O_1^q \!\! &=&\!\! (\bar q b)_{V\!-\!A}
  (\bar f q)_{V\!-\!A}, \ \
 O_2^q = (\bar q_{\beta} b_{\alpha})_{V\!-\!A}
  (\bar f_{\alpha} q_{\beta})_{V\!-\!A}, \nonumber 
\end{eqnarray}
while $O_{3-6}$ are the so-called QCD penguin operators, and $O_{7-10}$
are the electroweak (EW) penguins.
The Hamiltonian Eq.~(\ref{HW}) is matched onto \SCETa
at the scale $Q\sim m_b$ 
\begin{eqnarray} \label{SCETeff}
 H_W  &=  & \frac{2G_F}{\sqrt{2}} \sum_{n,\bn} \bigg\{ 
  \sum_i \int [d\omega_{j}]_{j=1}^{3}
       c_i(\omega_j)  Q_{i}^{(0)}(\omega_j)
  + \sum_i \int [d\omega_{j}]_{j=1}^{4}  b_i(\omega_j) 
  Q_{i}^{(1)}(\omega_j) 
  + {\cal Q}_{c\bar c} + \ldots \bigg\} 
\end{eqnarray}
where $c_i^{(f)}(\omega_j)$ and $b_i^{(f)}(\omega_j)$ are Wilson coefficients, the ellipses
denote color-octet operators which do not contribute at leading order and higher order terms 
in $\lqcd/Q$, $Q=\{m_b,E\}$, and ${\cal Q}_{c\bar c}$
denotes operators containing a $c \bar c$ pair. Their precise form is not required
in the following. We omit the dependence of the Wilson coefficients on the labels 
$\omega_j$. The SCET operators appearing here are defined as ($q=u,d,s$)
\begin{eqnarray} \nn
\begin{array}{cc}
O(\lambda^0) &  O(\lambda) \\
\hline
  Q_{1}^{(0)} =  \big[ \bar u_{n,\omega_1} \bnslash P_L b_v\big]
  \big[ \bar f_{\bn,\omega_2}  \nslash P_L u_{\bn,\omega_3} \big]
  & 
  Q_{1}^{(1)} = \frac{-2}{m_b} 
     \big[ \bar u_{n,\omega_1}\, ig\,\slash\!\!\!\!{\cal B}^\perp_{n,\omega_4} 
     P_L b_v\big]
     \big[ \bar f_{\bn,\omega_2}  \nslash P_L u_{\bn,\omega_3} \big] \\
  Q_{2,3}^{(0)} =  \big[ \bar f_{n,\omega_1} \bnslash P_L b_v \big]
  \big[ \bar u_{\bn,\omega_2} \nslash P_{L,R} u_{\bn,\omega_3} \big]
  &
  Q_{2,3}^{(1)} =  \frac{-2}{m_b}  
     \big[ \bar f_{n,\omega_1} \, ig\,\slash\!\!\!\!{\cal B}^\perp_{n,\omega_4} 
     P_L b_v \big]
     \big[ \bar u_{\bn,\omega_2} \nslash P_{L,R} u_{\bn,\omega_3} \big] \\
  Q_{4}^{(0)} =  \big[ \bar q_{n,\omega_1} \bnslash P_L b_v \big]
  \big[ \bar f_{\bn,\omega_2} \nslash P_{L}\, q_{\bn,\omega_3} \big]
  & 
  Q_{4}^{(1)} =  \frac{-2}{m_b} 
     \big[ \bar q_{n,\omega_1} \, ig\,\slash\!\!\!\!{\cal B}^\perp_{n,\omega_4} 
     P_L b_v \big]
     \big[ \bar f_{\bn,\omega_2} \nslash P_{L}\, q_{\bn,\omega_3} \big] \\
\hline
\end{array} 
\end{eqnarray}
where we have omitted operators which give rise to flavor-singlet light mesons. 
The operators $Q_3$ receive contributions only from electroweak penguins. 
The effective theory operators contain collinear fields along both $n$ and $\bn$
directions \cite{nbn}.


It is convenient to write the Wilson coefficients of the SCET operators 
in a form which separates the contributions from different operators in the 
full theory Hamiltonian
\begin{eqnarray}
c_i &=& \lambda_u^{(f)} c_{iu} + 
\lambda_t^{(f)} \left[c_{it}^{\rm p} + c_{it}^{\rm ew} \right] \,,\qquad
b_i = \lambda_u^{(f)} c_{iu} + 
\lambda_t^{(f)} \left[b_{it}^{\rm p} + b_{it}^{\rm ew} \right] \,.
\end{eqnarray}
The Wilson coefficients of the $O(\lambda^0)$ operators are known to 
$O(\alpha_s(Q))$ \cite{BBNS}, but those of the $O(\lambda^0)$ operators only to 
tree level. The dominant contributions of the EWPs to the SCET
Wilson coefficients
$c_{it}^{\rm ew}$ and $b_{it}^{\rm ew}$ come from $Q_{9,10}$ and
are fixed by SU(3) symmetry to all orders in terms of the coefficients 
of the tree operators $c_{1,2u}$ and $b_{1,2u}$ \cite{BaPi}.

The nonleptonic B decay amplitudes are obtained by taking the
matrix elements of the SCET effective Hamiltonian Eq.~(\ref{SCETeff})
with subleading terms in the usoft-collinear Lagrangian \cite{position}.
The procedure is completely analogous to that followed in deriving
factorization relations for the heavy-to-light form factors \cite{Bauer:2002aj}.
The main result for the $\bar B\to M_n M_\bn$ nonleptonic decay amplitude 
at leading order in $\Lambda/m_b$ can be written in a schematic form as
\begin{eqnarray}\label{fact}
A = c(u) \star \phi_\bn(u) \zeta^{BM_n} + b(x,z,u) \star \phi_n(x) \star \phi_\bn(u) 
\star J(x,z,k_+) \star \phi_B(k_+) + (n \leftrightarrow \bn) +
\langle {\cal Q}_{c\bar c}\rangle
\end{eqnarray}
with $c,b$ Wilson coefficients, $J(x,z,k_+)$ a jet function, $\zeta^{BM_n}$ is a 
nonperturbative soft function and $\phi_n(x), \phi_\bn(u), 
\phi_B(k_+)$ are light-cone wavefunctions for the light mesons and the B meson respectively. 
The corrections to this formula are suppressed by one power of $\Lambda/m_b$.

The main features of this factorization formula are:

\begin{itemize}

\item The soft function $\zeta^{BM}$ is the same as that appearing in the
heavy-to-light form factor $B\to M$ at large recoil \cite{Bauer:2002aj}.

\item Jet universality. The jet function is the same as that 
entering the factorization relation for $B\to P, V_\parallel$
form factors.

\end{itemize}

These points show an unexpected relation between semileptonic 
and nonleptonic decays. This connection can be made more transparent
by defining a new nonperturbative amplitude $\zeta_J^{BM_n}(u,z) \equiv
\phi_n(x) \star J(x,z,k_+) \star \phi_B(k_+)$, which has the same
scaling in $1/m_b$ as $\zeta^{BM_n}$. In the following we will take as independent
nonperturbative parameters $\zeta,\zeta_J(u,z)$, which effectively 
includes perturbative corrections at the collinear scale $\mu^2= Q\Lambda$
to all orders. 

\section{$B\to \pi\pi$ decays}

As an application of the formalism described above we discuss the nonleptonic
$B\to \pi\pi$ decays. The amplitudes can be written 
in a compact form  as
\begin{eqnarray}\label{Apipi}
 A(\bar B^0\to \pi^+\pi^- ) &=& 
\lambda_u^{(d)} (-T-P_{u}) + \lambda_c^{(d)}(-P_c) + \lambda_t^{(d)} (-P_{t})
\equiv
\lambda_u^{(d)} T_c ( 1 + r_c e^{i\delta_c} e^{i\phi}) \\
\sqrt2 A(\bar B^0\to \pi^0 \pi^0) &=& 
\lambda_u^{(d)} (-C +P_u) +  \lambda_c^{(d)} P_c +
\lambda_t^{(d)} P_t \equiv
\lambda_u^{(d)} T_n (1 + r_n e^{i\delta_n} e^{i\phi})\nonumber \\
\sqrt2 A(B^-\to \pi^- \pi^0) &=&
\lambda_u^{(d)} (T + C) \nn
\end{eqnarray}
We neglected here small contributions from electroweak penguins, which can be
included in a model-independent way using isospin symmetry. The amplitudes
on the rhs are defined as $T_c = - T - P_u + P_t, T_n = -C+P_u-P_t$ and
$\phi = \gamma$.

The $B\to \pi\pi$ data is shown in Table 1 \cite{pipiexp}.
This includes the branching ratios and the time-dependent CP violation
parameters $S_{\pi\pi}, C_{\pi\pi}$ in $B^0(t)\to \pi^+\pi^-$. 
The relevant branching ratio information is contained in the two ratios
\begin{eqnarray}
R_c = \frac{Br(B^0\to \pi^+\pi^-)}{2 Br(B^-\to \pi^0\pi^-)}\frac{\tau_{B^+}}{\tau^{B^0}}
= 0.445 \pm 0.062\,,\quad
R_n = \frac{Br(B^0\to \pi^0\pi^0)}{Br(B^-\to \pi^0\pi^-)}\frac{\tau_{B^+}}{\tau^{B^0}}
= 0.292 \pm 0.063
\end{eqnarray}
We show in Table I also $C_{\pi^0\pi^0}$, the direct CP asymmetry
in $B^0\to \pi^0\pi^0$, which was recently measured by the Babar and BELLE Collaborations.

\subsection{Isospin analysis}

For a given $\gamma$, the data on $S_{\pi\pi}, C_{\pi\pi}, R_c, R_n$
allows the determination
of the amplitude parameters $T,C,P$ in Eqs.~(\ref{Apipi}). 
Adding in also $C_{\pi^0\pi^0}$, the weak phase $\alpha = \pi -\beta-\gamma$ 
can be determined with a four-fold ambiguity. This is the well-known isospin
analysis of Gronau and London \cite{GL}. We present first the isospin
analysis for fixed $\gamma$, and then compare
the results with the SCET predictions. We discuss the 
prospects for a $\gamma$ (or $\alpha$) determination in Sec.~4.

We will present the results of the isospin analysis in terms of the
parameters $(r_c, \delta_c, u, v)$, where $t = (u,v)$ are the coordinates
of the apex of the
triangle of isospin amplitudes $1 + t_n = t$. We defined here
$t = T/T_c, t_n = T_n/T_c$. The measurable parameters are given by
\begin{eqnarray}
S_{\pi\pi} &=& 
\frac{-\sin(2\beta+2\gamma) - 2r_c \cos\delta_c \sin(2\beta+\gamma)-
r_c^2\sin 2\beta}{1+2r_c \cos\delta_c \cos\gamma + r_c^2}\\
C_{\pi\pi} &=& 
\frac{2r_c \sin\delta_c \sin\gamma }
{1+2r_c \cos\delta_c \cos\gamma + r_c^2}\\
R_c &=& \frac{1}{t^2}[1 + r_c^2 + 2r_c \cos\delta_c \cos\gamma]\,,\quad
R_n = \frac{1}{t^2}[t_n^2 + r_c^2 - 2
r_c (\cos\delta_c (u-1) + \sin\delta_c v) \cos\gamma]
\end{eqnarray}
with $t^2 = u^2+v^2, t_n^2=(u-1)^2+v^2$. The direct CP asymmetry in the
$B^0\to \pi^0\pi^0$ mode is
\begin{eqnarray}
C_{\pi^0\pi^0} = -
\frac{2[r_c \sin\delta_c(u-1) - r_c\cos\delta_c v] \sin\gamma }
{t_n^2 - 2[r_c \cos\delta_c (u-1) + r_c \sin\delta_c v] \cos\gamma + r_c^2}
\end{eqnarray}

We show in Table 2 the results for the amplitude parameters extracted 
from the data corresponding to several values of $\gamma$.
For each given value of $\gamma$, there are four solutions for the
parameters $(r_c,\delta_c,u,v)$, which fall into two sets with common
values of $(r_c,\delta_c)$. We select only the physical solution corresponding
to $r_c \leq 1$, which gives the 2 solutions for the 
amplitudes $T_c, T_n$ shown in Table 2.
For each of these solutions we show also predictions for the
direct CP asymmetry in the neutral pions channel $C_{\pi^0\pi^0}$.
%Comparison with data in Table 1 favors larger values of the angle $\gamma$.
Similar analyses have been presented in \cite{BuFl,pheno}.


\begin{table}
\begin{center}
\scriptsize
\begin{tabular}{|c|ccc|} 
\hline
 & BABAR & Belle & Avg. \\
\hline
$Br(B^+\to \pi^+ \pi^0)$                    & %         Mode
$5.8\pm 0.6\pm 0.4$                         & %   [18]  BABAR
$5.0\pm 1.2\pm 0.5$                         & %   [46]  Belle
$5.61\pm 0.61$                              \\ % Avg

$Br(B^0\to \pi^0 \pi^0)$                    & %         Mode
$1.17\pm 0.32 \pm 0.10$                     & %   [18]  BABAR
$2.32^{+0.44+0.22}_{-0.48-0.18}$            & %   [44]  Belle
$1.51\pm 0.28$                              \\ %         WA

$Br(B^+\to \pi^+ \pi^-)$                    & %         Mode
$4.7\pm 0.6\pm 0.2$                         & %   [18]  BABAR
$4.4\pm 0.6 \pm 0.3$                        & %   [46]  Belle
$4.6\pm 0.4$                                \\ % Avg
% & & & \\

\hline


$S_{\pi \pi}$                               & %         Mode
$-0.30\pm 0.17\pm 0.03$                     & %   [18]  BABAR
$-1.00\pm 0.22$                             & %   [46]  Belle
$-0.608\pm 0.135$                           \\ % Avg

$C_{\pi \pi}$                               & %         Mode
$-0.09\pm 0.15\pm 0.04$                     & %   [18]  BABAR
$-0.58\pm 0.17$                             & %   [46]  Belle
$-0.368\pm 0.112$                           \\ % Avg
\hline

$C_{\pi^0 \pi^0}$                           & %         Mode
$-0.12\pm 0.56 \pm 0.06$                    & %   [18]  BABAR
$-0.43\pm 0.51^{0.16}_{-0.17}$              & %   [46]  Belle
$-0.28\pm 0.39$                             \\ % Avg
\hline
\end{tabular}
\end{center}
{\caption{Data on $B\to \pi\pi$ decays after ICHEP 2004,  Beijing \cite{HFAG,pipiexp}. 
The CP-averaged branching ratios are
quoted in units of $10^{-6}$. }}
\end{table}




\begin{table}
\begin{center}
\scriptsize

\begin{tabular}{|c|c|c||c|}
\hline
\hline
$\gamma$ & $(r_c,\delta_c)$ & $(u,v)$ & 
$C_{\pi^0\pi^0}$ \\
\hline
$54^\circ$ & $(0.32\pm 0.11\,, -1.12\pm 0.40)$ &  
\begin{tabular}{c}
$(1.36\pm 0.21\,, -1.00\pm 0.17)$ \\ 
$(1.60\pm 0.22\,, 0.53\pm 0.21)$ \\
\end{tabular}
 & 
\begin{tabular}{c}
$-0.07\pm 0.29$ \\
$0.48\pm 0.21$ \\
\end{tabular} \\
\hline
$64^\circ$ & $(0.49\pm 0.14\,, -0.71\pm 0.27)$ &  
\begin{tabular}{c}    
$(1.63\pm 0.27\,, -0.92\pm 0.21)$ \\
$(1.80\pm 0.27\,, 0.51\pm 0.30)$  \\
\end{tabular}
&
\begin{tabular}{c}
$-0.24\pm 0.34$ \\
$0.78\pm 0.21$ \\
\end{tabular} \\
\hline
$74^\circ$ & $(0.68\pm 0.15\,, -0.53\pm 0.20)$  & 
\begin{tabular}{c}
$(1.95\pm 0.41\,, -0.43\pm 1.03)$ \\
$(2.00\pm 0.27\,, 0.11\pm 1.12)$ \\
\end{tabular}
  & 
\begin{tabular}{c}
$0.12\pm 1.10$ \\ 
$0.67\pm 0.84$ \\
\end{tabular} \\
\hline
\hline
\end{tabular}
\end{center}
{\caption{Amplitude parameters in $B\to \pi\pi$ for several
input values for $\gamma$, together with the prediction for the
CP asymmetry in $B\to \pi^0\pi^0$. For each value of $\gamma$ there are
two solutions for the tree amplitudes.}
\label{amps:pipi} }
\end{table}

The absolute magnitudes of the amplitudes are set by
%\begin{eqnarray}
$|T_c+T_n| = N_\pi (0.296 \pm 0.016)$ GeV, which can be extracted from 
Br$(B^- \to \pi^-\pi^0)$. [We denoted here
$N_\pi = G_F/\sqrt2 m_B^2 f_\pi$ and used $|V_{ub}|=0.0039$.]

\subsection{SCET analysis}

The analysis discussed above used only isospin symmetry.
Next we examine the predictions from the SCET factorization formula.

1. {\em Predicting $Br(B^0\to \pi^0\pi^0)$.}
At tree level in matching, the strong phases of the tree amplitudes
vanish Arg$(T_n/T_c) \sim O(\alpha_s(Q), \Lambda/Q)$. This fixes
one hadronic parameter $(v\to 0)$, such that 
%$v\sim O(\alpha_s(Q), \Lambda/Q)$ is suppressed, which gives that 
$R_c, R_n$ and $C_{\pi^0\pi^0}$ are not independent quantities, but are related as
\begin{eqnarray}\label{RnSCET}
R_n = \frac{1}{t}[(t-1)(1 - t R_c) + r_c^2]\,,\qquad
C_{\pi^0\pi^0}  = - (t-1)\frac{R_c}{R_n} C_{\pi^+\pi^-}
\end{eqnarray}
This allows predictions for $R_n(\alpha)$ and $C_{\pi^0\pi^0}(\alpha)$ to be made
using only data on $R_c, S_{\pi\pi}, C_{\pi\pi}$. We show in Fig. 1 (a) the 
prediction for $R_n(\alpha)$ from Eq.~(\ref{RnSCET}) as a function of $\alpha$.
%For example, at $\gamma = 64^\circ$ one finds $R_n = 0.205\pm 0.067\,,
%C_{\pi^0\pi^0} = 0.49$. 
%which are in reasonable agreement with data.

2. {\em Determining the SCET nonperturbative parameters.}
The LO factorization relation for $T$ and $T_c$ expresses these amplitudes
in terms of SCET Wilson coefficients and the 
nonperturbative parameters $\zeta, \zeta_J(x)$. 
Working at tree level in matching, one finds
%the strong phase between $T$ and $T_c$ is predicted to be 
%$\sim O(\alpha_s(m_b))$, which is well satisfied by data. 
\begin{eqnarray}\label{SCETLO}
\left. \zeta^{B \pi} \right|_{\gamma = 64^\circ} =
(0.08 \pm 0.03) \left( \frac{3.9 \times 10^{-3}}{|V_{ub}|} \right) \,,\qquad
%(0.067 \pm 0.025) \left( \frac{4.7 \times 10^{-3}}{|V_{ub}|} \right) \nn\\
\left. \zeta_J^{B \pi} \right|_{\gamma = 64^\circ} =
(0.10 \pm 0.02) \left( \frac{3.9 \times 10^{-3}}{|V_{ub}|} \right) \,,
%(0.083 \pm 0.017) \left( \frac{4.7 \times 10^{-3}}{|V_{ub}|} \right) \,,
\end{eqnarray}
which does not include any theoretical uncertainties.
These values can be used to predict the $B\to \pi$ form factor $f_+(0)$
at $q^2=0$ as
\begin{eqnarray}
&&f_+(0)= \zeta^{B\pi} + \zeta_J^{B\pi} = \nn
(0.18 \pm 0.05) \left( \frac{3.9 \times 10^{-3}}{|V_{ub}|} \right) 
\end{eqnarray}
which is somewhat lower than recents results from QCD sum rules
$f_+(0)= 0.26\pm 0.03$ \cite{QCDSR}. 
The result for $\zeta_J^{B\pi}$ in Eq.~(\ref{SCETLO}) is slightly higher than
the values obtained in perturbation theory working at tree level in the
jet function in Eq.~(\ref{fact}) 
\begin{eqnarray}
\zeta_J^{B\pi} = \frac{\pi\alpha_s C_F}{N_c} \frac{f_B f_\pi}{m_B}
\langle \bar x^{-1}\rangle_\pi
\langle k_+^{-1}\rangle_B \sim 0.02 - 0.05
\end{eqnarray}
where we took $ \langle \bar x^{-1}\rangle_\pi=
3(1+a_2^\pi)$ with $a_2^\pi = 0.2\pm 0.2$, $f_B = 200$  MeV, $f_\pi =131$ MeV
and $\langle k_+^{-1}\rangle_B = 1/\lambda_B$ with 
$\lambda_B =(350\pm 150)$ MeV \cite{BBNS}. [The $O(\alpha_s^2(m_b \Lambda))$
corrections to this result have been recently obtained in \cite{jetoneloop}.]
Conceivable explanations for this discrepancy 
are experimental errors in the $B\to \pi\pi$ data, or neglected power corrections
to the factorization formula.
A detailed analysis using the QCDF approach
\cite{comparison} shows that power corrections are small in the tree amplitudes 
$T,T_c$ and thus do not affect significantly this determination of 
$\zeta_J^{B\pi}$. 

\section{Prospects for determining $\alpha$ }

The main motivation for the experimental study of the $\Delta S = 0$ decays
such as $B\to \pi^+\pi^-$ is
in connection with the determination of the angle $\alpha$. 
In fact what is measured is the combination $\beta+\gamma = \pi - \alpha$,
which taken together with the precise value of $\beta$ known from
charmonium modes, can be translated into a value of $\gamma$.

The measurements are usually expressed in terms of an effective
angle $\alpha_{\rm eff}$ defined by $\sin 2\alpha_{\rm eff} =
S_{\pi\pi}/\sqrt{1-C^2_{\pi\pi}}$. This is related to the physical
angle by $\alpha_{\rm eff} = \alpha - \theta$ with 
$\theta = Arg(A_{\pi^+\pi^-}/\bar A_{\pi^+\pi^-})$. Using only data on 
$R_c,R_n,C$, only bounds on $\theta$ can be obtained. 
These bounds can be turned into a determination provided that 
$C_{\pi^0\pi^0}$ is also measured \cite{GL}.

Several  bounds on $\theta$ using only isospin have been given in 
Refs.~\cite{bounds,GLSS}, of which the most restrictive one is
the GLSS bound \cite{GLSS}
\begin{eqnarray}\label{glss}
\cos 2\theta \geq \frac{1}{2R_c \sqrt{1-C^2_{\pi\pi}}}
[(R_c+1-R_n)^2-2R_c]
\end{eqnarray}
With the present data in Table I these bounds constrain $\alpha$
to lie within 4 windows of width $2\theta$
with $\theta = 29.0^\circ$
centered on $\alpha_{\rm eff} = 1/2 \arcsin(S_{\pi\pi}/\sqrt{1-C^2_{\pi\pi}})$. 
The window corresponding to the physically preferred solution has
$\alpha_{\rm eff}^{\rm I} = 110.41^\circ$.
%$90^\circ - \alpha_{\rm eff}^{\rm I}, 270^\circ - \alpha_eff^{\rm I}$.
These can be translated into bounds on $\beta+\gamma$ 
%by using $\beta = 23.5^\circ$, 
which gives $40.6^\circ = 69.6^\circ - \theta \leq
\gamma + \beta \leq 69.6^\circ + \theta = 98.6^\circ$.

These bounds can be turned into a determination of $\alpha$ provided that
$C_{\pi^0\pi^0}$ is known, which is equivalent to performing the full
isospin analysis. In the absence of this information, one can restrict
the ranges of the bound by adding in dynamical information about the
amplitudes $T,P,C$. Several such ``constrained'' bounds exist, of which 
we mention only two.

\begin{itemize}

\item The Buchalla-Safir bound \cite{BuSa}. This assumes that
$|\delta_c | \leq \pi/2$, which leads to a lower bound on $\bar \eta$
as a function of $S_{\pi\pi}$.

\item The SCET constraint \cite{Bauer:2004tj,scetgamma}. The dynamical
input here is the smallness of the relative strong phase of $T_c$ and $T_n$.
\begin{eqnarray}\label{corr}
Arg(T/T_c) \sim Arg(T_n/T_c) \sim O(\alpha_s(m_b), \Lambda/m_b)
\end{eqnarray}
\end{itemize}



\begin{figure}[t!]
 \centerline{
\epsfysize=6truecm \hbox{\epsfbox{alpha_rnflat.eps}} 
\raisebox{-1cm}
{\epsfysize=7truecm \hbox{\epsfbox{alpha_pipi.eps}}}  
} 
\hspace{3cm}(a) \hspace{8cm} (b)
%\vskip -0.2cm
{\caption[1]{(a) Constraint on the weak phase $\alpha$ 
following from a small relative strong phase between the tree amplitudes $T,T_c$. 
The light band shows the $1\sigma$ prediction for $R_n(\alpha)$ as a function
of the weak phase $\alpha$ following from Eq.~(\ref{RnSCET}); the horizontal 
band
shows the measured value $R_n=0.292\pm 0.063$. 
The solid line denotes the GLSS bound 
$R_n \geq R^{GLSS}_n(\alpha, R_c, S_{\pi\pi}, C_{\pi\pi})$ for central values
of the parameters.
(b) constraints on $\alpha$ from charmless $B$ decays \cite{ZICHEP}.}
\label{fig:CKMf} }
\vskip -0.3cm
\end{figure}


We will discuss here in some detail the SCET constraint.
We show in Fig.~1 (a) the constraints on $\alpha$ from comparing
the prediction for $R_n(\alpha)$ from requiring a flat tree triangle Eq.~(\ref{RnSCET})
with the measured value of this parameter $R_n = 0.292 \pm 0.063$. One additional
constraint is introduced by the GLSS bound (\ref{glss}) which bounds
$R_n$ from below $R_n \geq R_n^{GLSS}(\alpha,R_c,C_{\pi\pi})$.
 Taking into 
account all these constraints, the plot in Fig.~1 (a) allows the range for $\alpha$
\begin{eqnarray}
73^\circ \leq \alpha \leq 95^\circ
\end{eqnarray}
which includes only the experimental uncertainties. This result is in 
agreement with present constraints on $\alpha$ from $\Delta S=0$
modes (see Fig.~1(b)) and with a general constraint combining
$B\to \pi\pi, \rho\pi, \rho\rho$ modes \cite{alphacons}.

A method for determining $\gamma$ based on this constraint was proposed in
Ref.~\cite{scetgamma}, where it was argued that theoretical 
uncertainties to the 
condition Eq.~(\ref{corr}) from radiative corrections and power corrections 
of canonical size introduce a very small theoretical error on $\alpha$ of 
$\pm 2^\circ$ (for the present central values of the data). 
More detailed theoretical computations of the correction to Eq.~(\ref{corr}) 
would be welcome. 
With improved data the SCET constraint Eq.~(\ref{corr}) can 
be expected to give useful information on $\alpha$, complementing alternative 
determinations of this weak phase.




\subsection{Acknowledgments}
I would like to thank the organizers for an enjoyable conference. 
This work has been supported by the U.S.\ Department of Energy under cooperative
research agreement 
DOE-FC02-94ER40818.




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A.~J.~Buras, R.~Fleischer, S.~Recksiegel and F.~Schwab,
%``The B $\to$ pi K puzzle and its relation to rare B and K decays,''
Eur.\ Phys.\ J.\ C {\bf 32}, 45 (2003);
%[arXiv:hep-ph/0309012].

\bibitem{zupan-fpcp04}
J. Zupan, {\em Determining $\alpha$ and $\gamma$ - theory},
[arXiv:hep-ph/0410371].
%%CITATION = HEP-PH 0410371;%%


\bibitem{cheng-fpcp04} 
H.~Y.~Cheng,
{\em Direct CP violation and final state interactions in hadronic B decays},
[arXiv:hep-ph/0411340].
%%CITATION = HEP-PH 0411340;%%


%\cite{Beneke:1999br}
\bibitem{BBNS}
M.~Beneke, G.~Buchalla, M.~Neubert and C.~T.~Sachrajda,
%``{QCD} factorization for B $\to$ pi pi decays: Strong phases and CP  violation
%in the heavy quark limit,''
Phys.\ Rev.\ Lett.\  {\bf 83}, 1914 (1999);
%[arXiv:hep-ph/9905312].
%%CITATION = HEP-PH 9905312;%%
%\cite{Beneke:2001ev}
%\bibitem{Beneke:2001ev}
%M.~Beneke, G.~Buchalla, M.~Neubert and C.~T.~Sachrajda,
%``QCD factorization in B $\to$ pi K, pi pi decays and extraction of
%Wolfenstein parameters,''
Nucl.\ Phys.\ B {\bf 606}, 245 (2001);
%[arXiv:hep-ph/0104110].
%%CITATION = HEP-PH 0104110;%%
%\bibitem{Beneke:2003zv}
M.~Beneke and M.~Neubert,
%``QCD factorization for B $\to$ P P and B $\to$ P V decays,''
Nucl.\ Phys.\ B {\bf 675}, 333 (2003).
%[arXiv:hep-ph/0308039].
%%CITATION = HEP-PH 0308039;%%

%\cite{Keum:2000wi}
\bibitem{pQCD}
Y.~Y.~Keum, H.~N.~Li and A.~I.~Sanda,
%``Penguin enhancement and B $\to$ K pi decays in perturbative QCD,''
Phys.\ Rev.\ D {\bf 63}, 054008 (2001);
%[arXiv:hep-ph/0004173].
%%CITATION = HEP-PH 0004173;%%
%\bibitem{Chen:2001pr}
C.~H.~Chen, Y.~Y.~Keum and H.~n.~Li,
%``Perturbative QCD analysis of B $\to$ Phi K decays,''
Phys.\ Rev.\ D {\bf 64}, 112002 (2001);
%[arXiv:hep-ph/0107165].
%%CITATION = HEP-PH 0107165;%%
H.~Y.~Cheng, C.~K.~Chua and A.~Soni,
%``Final state interactions in hadronic B decays,''
arXiv:hep-ph/0409317.
%%CITATION = HEP-PH 0409317;%%



\bibitem{SCET}
C.~W.~Bauer, S.~Fleming and M.~E.~Luke,
%``Summing Sudakov logarithms in B $\to$ X/s gamma in effective field  theory,''
Phys.\ Rev.\ D {\bf 63}, 014006 (2001);
%[arXiv:hep-ph/0005275].
%%CITATION = HEP-PH 0005275;%%
C.~W.~Bauer, S.~Fleming, D.~Pirjol and I.~W.~Stewart,
%``An effective field theory for collinear and soft gluons: Heavy to light
%decays,''
Phys.\ Rev.\ D {\bf 63}, 114020 (2001);
%[arXiv:hep-ph/0011336].
%%CITATION = HEP-PH 0011336;%%
C.~W.~Bauer and I.~W.~Stewart,
%``Invariant operators in collinear effective theory,''
Phys.\ Lett.\ B {\bf 516}, 134 (2001);
%[arXiv:hep-ph/0107001].
%%CITATION = HEP-PH 0107001;%%
%``Soft-collinear factorization in effective field theory,''
Phys.\ Rev.\ D {\bf 65}, 054022 (2002).
%[arXiv:hep-ph/0109045].
%%CITATION = HEP-PH 0109045;%%

\bibitem{nbn}
C.~W.~Bauer, S.~Fleming, D.~Pirjol, I.~Z.~Rothstein and I.~W.~Stewart,
Phys.\ Rev.\ D {\bf 66}, 014017 (2002).
%%CITATION = HEP-PH 0202088; %%


%\cite{Chay:2003zp}
\bibitem{Chay:2003zp}
J.~g.~Chay and C.~Kim,
%``Factorization of B decays into two light mesons in soft-collinear  effective
%theory,''
Phys.\ Rev.\ D {\bf 68}, 071502 (2003);
%[arXiv:hep-ph/0301055].
%%CITATION = HEP-PH 0301055;%%
%\cite{Chay:2003ju}
%\bibitem{Chay:2003ju}
%J.~Chay and C.~Kim,
%``Nonleptonic B decays into two light mesons in soft-collinear effective
%theory,''
Nucl.\ Phys.\ B {\bf 680}, 302 (2004).
%[arXiv:hep-ph/0301262].
%%CITATION = HEP-PH 0301262;%%


%\cite{Bauer:2002aj}
\bibitem{Bauer:2002aj}
C.~W.~Bauer, D.~Pirjol and I.~W.~Stewart,
%``Factorization and endpoint singularities in heavy-to-light decays,''
Phys.\ Rev.\ D {\bf 67}, 071502 (2003);
%[arXiv:hep-ph/0211069].
%%CITATION = HEP-PH 0211069;%%
D.~Pirjol and I.~W.~Stewart,
%``A complete basis for power suppressed collinear-ultrasoft operators,''
Phys.\ Rev.\ D {\bf 67}, 094005 (2003)
[Erratum-ibid.\ D {\bf 69}, 019903 (2004)];
%[arXiv:hep-ph/0211251].
%%CITATION = HEP-PH 0211251;%%
D.~Pirjol and I.~W.~Stewart,
%``The phenomenology of rare and semileptonic B decays,''
eConf {\bf C030603}, MEC04 (2003)
[arXiv:hep-ph/0309053].
%%CITATION = HEP-PH 0309053;%%

%\cite{Bauer:2004tj}
\bibitem{Bauer:2004tj}
C.~W.~Bauer, D.~Pirjol, I.~Z.~Rothstein and I.~W.~Stewart,
%``B $\to$ M(1) M(2): Factorization, charming penguins, strong phases, and
%polarization,''
Phys.\ Rev.\ D {\bf 70}, 054015 (2004).
%[arXiv:hep-ph/0401188].
%%CITATION = HEP-PH 0401188;%%


\bibitem{BaPi}
C.~W.~Bauer and D.~Pirjol,
%``Graphical amplitudes from SCET,''
Phys.\ Lett.\ B {\bf 604}, 183 (2004)
%[arXiv:hep-ph/0408161].
%%CITATION = HEP-PH 0408161;%%



\bibitem{position}
M.~Beneke, A.~P.~Chapovsky, M.~Diehl and T.~Feldmann,
%``Soft-collinear effective theory and heavy-to-light currents 
%power,''
Nucl.\ Phys.\ B {\bf 643}, 431 (2002);
%[arXiv:hep-ph/0206152].
%%CITATION = HEP-PH 0206152;%%
M.~Beneke and T.~Feldmann,
%``Multipole-expanded soft-collinear effective theory with 
%symmetry,''
Phys.\ Lett.\ B {\bf 553}, 267 (2003)
%[arXiv:hep-ph/0211358].
%%CITATION = HEP-PH 0211358;%%

\bibitem{HFAG} 
The Heavy Flavor Averaging Group, 
%\begin{verbatim} 
http://www.slac.stanford.edu/xorg/hfag/
%\end{verbatim}

\bibitem{pipiexp}
B.~Aubert  [BABAR Collaboration],
%``Branching fractions and CP asymmetries in B0 $\to$ pi0 pi0, B+ $\to$ pi+ pi0
%and B+ $\to$ K+ pi0 decays and isospin analysis of the B $\to$ pi pi system,''
arXiv:hep-ex/0412037;
%%CITATION = HEP-EX 0412037;%%
K.~Abe {\it et al.}  [Belle Collaboration],
%``Observation of B0 $\to$ pi0 pi0,''
arXiv:hep-ex/0408101.
%%CITATION = HEP-EX 0408101;%%
B.~Aubert  [BABAR Collaboration],
arXiv:hep-ex/0501071.


\bibitem{EWP} M. Neubert and J.L. Rosner,
Phys. Lett. B {\bf 441}, 403 (1998);
A.~J.~Buras and R.~Fleischer, Eur. Phys. J. C {\bf 11}, 93 (1999).
%%CITATION = HEP-PH 9810260;%%
M.~Gronau, D.~Pirjol and T.~M.~Yan,
%``Model-independent electroweak penguins in B decays to two  pseudoscalars,''
Phys.\ Rev.\ D {\bf 60}, 034021 (1999);
[Erratum-ibid.\ D {\bf 69}, 119901 (2004)].
%[arXiv:hep-ph/9810482].
%%CITATION = HEP-PH 9810482;%%

\bibitem{GL}
M.~Gronau and D.~London,
%``Isospin Analysis Of CP Asymmetries In B Decays,''
Phys.\ Rev.\ Lett.\  {\bf 65}, 3381 (1990).
%%CITATION = PRLTA,65,3381;%%

\bibitem{pheno}
C.~W.~Chiang, M.~Gronau, Z.~Luo, J.~L.~Rosner and D.~A.~Suprun,
%``Charmless B $\to$ V P decays using flavor SU(3) symmetry,''
Phys.\ Rev.\ D {\bf 69}, 034001 (2004);
%[arXiv:hep-ph/0307395].
%%CITATION = HEP-PH 0307395;%%
%C.~W.~Chiang, M.~Gronau, J.~L.~Rosner and D.~A.~Suprun,
%``Charmless B $\to$ P P decays using flavor SU(3) symmetry,''
(ibid) arXiv:hep-ph/0404073;
%%CITATION = HEP-PH 0309012;%%
%%CITATION = HEP-PH 0404073;%%
A.~Ali, E.~Lunghi and A.~Y.~Parkhomenko,
%``An analysis of the time-dependent CP asymmetry in B $\to$ pi pi decays in
%the standard model,''
Eur.\ Phys.\ J.\ C {\bf 36}, 183 (2004);
%[arXiv:hep-ph/0403275].
%%CITATION = HEP-PH 0403275;%%
J.~Charles {\it et al.}  [CKMfitter Group Collaboration],
%``CP violation and the CKM matrix: Assessing the impact of the asymmetric B
%factories,''
arXiv:hep-ph/0406184.
%%CITATION = HEP-PH 0406184;%%

\bibitem{jetoneloop}
R.~J.~Hill, T.~Becher, S.~J.~Lee and M.~Neubert,
%``Sudakov resummation for subleading SCET currents and heavy-to-light form
%factors,''
JHEP {\bf 0407}, 081 (2004)
%[arXiv:hep-ph/0404217].
%%CITATION = HEP-PH 0404217;%%

\bibitem{comparison}
C.~W.~Bauer, D.~Pirjol, I.~Z.~Rothstein and I.~W.~Stewart,
%``On Differences Between SCET and QCDF for B->pi pi Decays,''
arXiv:hep-ph/0502094.
%%CITATION = HEP-PH 0502094;%%

\bibitem{bounds}
Y.~Grossman and H.~R.~Quinn,
%``Bounding the effect of penguin diagrams in a(CP)(B0 $\to$ pi+ pi-),''
Phys.\ Rev.\ D {\bf 58}, 017504 (1998);
%[arXiv:hep-ph/9712306].
%%CITATION = HEP-PH 9712306;%
J.~Charles,
%``Taming the penguin in the B/d0(t) $\to$ pi+ pi- CP-asymmetry:  Observables
%and minimal theoretical input,''
Phys.\ Rev.\ D {\bf 59}, 054007 (1999);
%[arXiv:hep-ph/9806468].
%%CITATION = HEP-PH 9806468;%%

\bibitem{GLSS}
M.~Gronau, D.~London, N.~Sinha and R.~Sinha,
%``Improving bounds on penguin pollution in B $\to$ pi pi,''
Phys.\ Lett.\ B {\bf 514}, 315 (2001).
%[arXiv:hep-ph/0105308].
%%CITATION = HEP-PH 0105308;%%

\bibitem{su3bounds}
D.~Pirjol,
%``Bounding the penguin effects in determinations of alpha from  B0(t) $\to$
%pi+ pi-,''
Phys.\ Rev.\ D {\bf 60}, 054020 (1999);
%%CITATION = HEP-PH 9903447;%%
R.~Fleischer,
%``New strategies to extract beta and gamma from B/d $\to$ pi+ pi- and  B/s
%$\to$ K+ K-,''
Phys.\ Lett.\ B {\bf 459}, 306 (1999).
%%CITATION = HEP-PH 9903456;%

\bibitem{BuSa}
G.~Buchalla and A.~S.~Safir,
%``Model independent bound on the unitarity triangle from CP violation in B
%$\to$ pi+ pi- and B $\to$ psi K(S),''
Phys.\ Rev.\ Lett.\  {\bf 93}, 021801 (2004).
%[arXiv:hep-ph/0310218].
%%CITATION = HEP-PH 0310218;%%

\bibitem{QCDSR}
P.~Ball and R.~Zwicky,
%``Improved analysis of B $\to$ pi e nu from QCD sum rules on the
%light-cone,''
JHEP {\bf 0110}, 019 (2001);
%[arXiv:hep-ph/0110115].
%%CITATION = HEP-PH 0110115;%%
P.~Ball and R.~Zwicky,
%``New results on B $\to$ pi, K, eta decay formfactors from light-cone sum
%rules,''
arXiv:hep-ph/0406232.
%%CITATION = HEP-PH 0406232;%

\bibitem{ZICHEP}
Z.~Ligeti,
%``The CKM matrix and CP violation,''
arXiv:hep-ph/0408267.
%%CITATION = HEP-PH 0408267;%%


\bibitem{scetgamma}
C.~W.~Bauer, I.~Z.~Rothstein and I.~W.~Stewart,
%``A new method for determining gamma from B $\to$ pi pi decays,''
arXiv:hep-ph/0412120.
%%CITATION = HEP-PH 0412120;%%

\bibitem{alphacons}
M.~Gronau, E.~Lunghi and D.~Wyler,
%``Reducing the error on alpha in B $\to$ pi pi, rho rho, rho pi,''
Phys.\ Lett.\ B {\bf 606}, 95 (2005)
[arXiv:hep-ph/0410170].
%%CITATION = HEP-PH 0410170;%%

%\bibitem{tough}
%M.~Pivk and F.~R.~Le Diberder,
%``Isospin constraints from / on B $\to$ pi pi,''
%arXiv:hep-ph/0406263.
%%CITATION = HEP-PH 0406263;%%

\end{thebibliography}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Label to flag the last page of your contribution
% Replace Perret by your name starting with a capital letter
%
\label{PirjolEnd}

\end{document}



hep-ph0502141.extracted_bib
\begin{thebibliography}{99}

%\cite{Gronau:1994rj}
\bibitem{GHLR}
M.~Gronau, O.~F.~Hernandez, D.~London and J.~L.~Rosner,
%``Decays of B mesons to two light pseudoscalars,''
Phys.\ Rev.\ D {\bf 50}, 4529 (1994);
%[arXiv:hep-ph/9404283].
%%CITATION = HEP-PH 9404283;%%
%M.~Gronau, O.~F.~Hernandez, D.~London and J.~L.~Rosner,
%``Electroweak penguins and two-body B decays,''
Phys.\ Rev.\ D {\bf 52}, 6374 (1995).
%[arXiv:hep-ph/9504327].
%%CITATION = HEP-PH 9504327;%%

\bibitem{BuFl}
A.~J.~Buras, R.~Fleischer, S.~Recksiegel and F.~Schwab,
%``Anatomy of prominent B and K decays and signatures of CP-violating new
%physics in the electroweak penguin sector,''
arXiv:hep-ph/0402112;
%%CITATION = HEP-PH 0402112;%%
A.~J.~Buras, R.~Fleischer, S.~Recksiegel and F.~Schwab,
%``The B $\to$ pi K puzzle and its relation to rare B and K decays,''
Eur.\ Phys.\ J.\ C {\bf 32}, 45 (2003);
%[arXiv:hep-ph/0309012].

\bibitem{zupan-fpcp04}
J. Zupan, {\em Determining $\alpha$ and $\gamma$ - theory},
[arXiv:hep-ph/0410371].
%%CITATION = HEP-PH 0410371;%%


\bibitem{cheng-fpcp04} 
H.~Y.~Cheng,
{\em Direct CP violation and final state interactions in hadronic B decays},
[arXiv:hep-ph/0411340].
%%CITATION = HEP-PH 0411340;%%


%\cite{Beneke:1999br}
\bibitem{BBNS}
M.~Beneke, G.~Buchalla, M.~Neubert and C.~T.~Sachrajda,
%``{QCD} factorization for B $\to$ pi pi decays: Strong phases and CP  violation
%in the heavy quark limit,''
Phys.\ Rev.\ Lett.\  {\bf 83}, 1914 (1999);
%[arXiv:hep-ph/9905312].
%%CITATION = HEP-PH 9905312;%%
%\cite{Beneke:2001ev}
%\bibitem{Beneke:2001ev}
%M.~Beneke, G.~Buchalla, M.~Neubert and C.~T.~Sachrajda,
%``QCD factorization in B $\to$ pi K, pi pi decays and extraction of
%Wolfenstein parameters,''
Nucl.\ Phys.\ B {\bf 606}, 245 (2001);
%[arXiv:hep-ph/0104110].
%%CITATION = HEP-PH 0104110;%%
%\bibitem{Beneke:2003zv}
M.~Beneke and M.~Neubert,
%``QCD factorization for B $\to$ P P and B $\to$ P V decays,''
Nucl.\ Phys.\ B {\bf 675}, 333 (2003).
%[arXiv:hep-ph/0308039].
%%CITATION = HEP-PH 0308039;%%

%\cite{Keum:2000wi}
\bibitem{pQCD}
Y.~Y.~Keum, H.~N.~Li and A.~I.~Sanda,
%``Penguin enhancement and B $\to$ K pi decays in perturbative QCD,''
Phys.\ Rev.\ D {\bf 63}, 054008 (2001);
%[arXiv:hep-ph/0004173].
%%CITATION = HEP-PH 0004173;%%
%\bibitem{Chen:2001pr}
C.~H.~Chen, Y.~Y.~Keum and H.~n.~Li,
%``Perturbative QCD analysis of B $\to$ Phi K decays,''
Phys.\ Rev.\ D {\bf 64}, 112002 (2001);
%[arXiv:hep-ph/0107165].
%%CITATION = HEP-PH 0107165;%%
H.~Y.~Cheng, C.~K.~Chua and A.~Soni,
%``Final state interactions in hadronic B decays,''
arXiv:hep-ph/0409317.
%%CITATION = HEP-PH 0409317;%%



\bibitem{SCET}
C.~W.~Bauer, S.~Fleming and M.~E.~Luke,
%``Summing Sudakov logarithms in B $\to$ X/s gamma in effective field  theory,''
Phys.\ Rev.\ D {\bf 63}, 014006 (2001);
%[arXiv:hep-ph/0005275].
%%CITATION = HEP-PH 0005275;%%
C.~W.~Bauer, S.~Fleming, D.~Pirjol and I.~W.~Stewart,
%``An effective field theory for collinear and soft gluons: Heavy to light
%decays,''
Phys.\ Rev.\ D {\bf 63}, 114020 (2001);
%[arXiv:hep-ph/0011336].
%%CITATION = HEP-PH 0011336;%%
C.~W.~Bauer and I.~W.~Stewart,
%``Invariant operators in collinear effective theory,''
Phys.\ Lett.\ B {\bf 516}, 134 (2001);
%[arXiv:hep-ph/0107001].
%%CITATION = HEP-PH 0107001;%%
%``Soft-collinear factorization in effective field theory,''
Phys.\ Rev.\ D {\bf 65}, 054022 (2002).
%[arXiv:hep-ph/0109045].
%%CITATION = HEP-PH 0109045;%%

\bibitem{nbn}
C.~W.~Bauer, S.~Fleming, D.~Pirjol, I.~Z.~Rothstein and I.~W.~Stewart,
Phys.\ Rev.\ D {\bf 66}, 014017 (2002).
%%CITATION = HEP-PH 0202088; %%


%\cite{Chay:2003zp}
\bibitem{Chay:2003zp}
J.~g.~Chay and C.~Kim,
%``Factorization of B decays into two light mesons in soft-collinear  effective
%theory,''
Phys.\ Rev.\ D {\bf 68}, 071502 (2003);
%[arXiv:hep-ph/0301055].
%%CITATION = HEP-PH 0301055;%%
%\cite{Chay:2003ju}
%\bibitem{Chay:2003ju}
%J.~Chay and C.~Kim,
%``Nonleptonic B decays into two light mesons in soft-collinear effective
%theory,''
Nucl.\ Phys.\ B {\bf 680}, 302 (2004).
%[arXiv:hep-ph/0301262].
%%CITATION = HEP-PH 0301262;%%


%\cite{Bauer:2002aj}
\bibitem{Bauer:2002aj}
C.~W.~Bauer, D.~Pirjol and I.~W.~Stewart,
%``Factorization and endpoint singularities in heavy-to-light decays,''
Phys.\ Rev.\ D {\bf 67}, 071502 (2003);
%[arXiv:hep-ph/0211069].
%%CITATION = HEP-PH 0211069;%%
D.~Pirjol and I.~W.~Stewart,
%``A complete basis for power suppressed collinear-ultrasoft operators,''
Phys.\ Rev.\ D {\bf 67}, 094005 (2003)
[Erratum-ibid.\ D {\bf 69}, 019903 (2004)];
%[arXiv:hep-ph/0211251].
%%CITATION = HEP-PH 0211251;%%
D.~Pirjol and I.~W.~Stewart,
%``The phenomenology of rare and semileptonic B decays,''
eConf {\bf C030603}, MEC04 (2003)
[arXiv:hep-ph/0309053].
%%CITATION = HEP-PH 0309053;%%

%\cite{Bauer:2004tj}
\bibitem{Bauer:2004tj}
C.~W.~Bauer, D.~Pirjol, I.~Z.~Rothstein and I.~W.~Stewart,
%``B $\to$ M(1) M(2): Factorization, charming penguins, strong phases, and
%polarization,''
Phys.\ Rev.\ D {\bf 70}, 054015 (2004).
%[arXiv:hep-ph/0401188].
%%CITATION = HEP-PH 0401188;%%


\bibitem{BaPi}
C.~W.~Bauer and D.~Pirjol,
%``Graphical amplitudes from SCET,''
Phys.\ Lett.\ B {\bf 604}, 183 (2004)
%[arXiv:hep-ph/0408161].
%%CITATION = HEP-PH 0408161;%%



\bibitem{position}
M.~Beneke, A.~P.~Chapovsky, M.~Diehl and T.~Feldmann,
%``Soft-collinear effective theory and heavy-to-light currents 
%power,''
Nucl.\ Phys.\ B {\bf 643}, 431 (2002);
%[arXiv:hep-ph/0206152].
%%CITATION = HEP-PH 0206152;%%
M.~Beneke and T.~Feldmann,
%``Multipole-expanded soft-collinear effective theory with 
%symmetry,''
Phys.\ Lett.\ B {\bf 553}, 267 (2003)
%[arXiv:hep-ph/0211358].
%%CITATION = HEP-PH 0211358;%%

\bibitem{HFAG} 
The Heavy Flavor Averaging Group, 
%\begin{verbatim} 
http://www.slac.stanford.edu/xorg/hfag/
%\end{verbatim}

\bibitem{pipiexp}
B.~Aubert  [BABAR Collaboration],
%``Branching fractions and CP asymmetries in B0 $\to$ pi0 pi0, B+ $\to$ pi+ pi0
%and B+ $\to$ K+ pi0 decays and isospin analysis of the B $\to$ pi pi system,''
arXiv:hep-ex/0412037;
%%CITATION = HEP-EX 0412037;%%
K.~Abe {\it et al.}  [Belle Collaboration],
%``Observation of B0 $\to$ pi0 pi0,''
arXiv:hep-ex/0408101.
%%CITATION = HEP-EX 0408101;%%
B.~Aubert  [BABAR Collaboration],
arXiv:hep-ex/0501071.


\bibitem{EWP} M. Neubert and J.L. Rosner,
Phys. Lett. B {\bf 441}, 403 (1998);
A.~J.~Buras and R.~Fleischer, Eur. Phys. J. C {\bf 11}, 93 (1999).
%%CITATION = HEP-PH 9810260;%%
M.~Gronau, D.~Pirjol and T.~M.~Yan,
%``Model-independent electroweak penguins in B decays to two  pseudoscalars,''
Phys.\ Rev.\ D {\bf 60}, 034021 (1999);
[Erratum-ibid.\ D {\bf 69}, 119901 (2004)].
%[arXiv:hep-ph/9810482].
%%CITATION = HEP-PH 9810482;%%

\bibitem{GL}
M.~Gronau and D.~London,
%``Isospin Analysis Of CP Asymmetries In B Decays,''
Phys.\ Rev.\ Lett.\  {\bf 65}, 3381 (1990).
%%CITATION = PRLTA,65,3381;%%

\bibitem{pheno}
C.~W.~Chiang, M.~Gronau, Z.~Luo, J.~L.~Rosner and D.~A.~Suprun,
%``Charmless B $\to$ V P decays using flavor SU(3) symmetry,''
Phys.\ Rev.\ D {\bf 69}, 034001 (2004);
%[arXiv:hep-ph/0307395].
%%CITATION = HEP-PH 0307395;%%
%C.~W.~Chiang, M.~Gronau, J.~L.~Rosner and D.~A.~Suprun,
%``Charmless B $\to$ P P decays using flavor SU(3) symmetry,''
(ibid) arXiv:hep-ph/0404073;
%%CITATION = HEP-PH 0309012;%%
%%CITATION = HEP-PH 0404073;%%
A.~Ali, E.~Lunghi and A.~Y.~Parkhomenko,
%``An analysis of the time-dependent CP asymmetry in B $\to$ pi pi decays in
%the standard model,''
Eur.\ Phys.\ J.\ C {\bf 36}, 183 (2004);
%[arXiv:hep-ph/0403275].
%%CITATION = HEP-PH 0403275;%%
J.~Charles {\it et al.}  [CKMfitter Group Collaboration],
%``CP violation and the CKM matrix: Assessing the impact of the asymmetric B
%factories,''
arXiv:hep-ph/0406184.
%%CITATION = HEP-PH 0406184;%%

\bibitem{jetoneloop}
R.~J.~Hill, T.~Becher, S.~J.~Lee and M.~Neubert,
%``Sudakov resummation for subleading SCET currents and heavy-to-light form
%factors,''
JHEP {\bf 0407}, 081 (2004)
%[arXiv:hep-ph/0404217].
%%CITATION = HEP-PH 0404217;%%

\bibitem{comparison}
C.~W.~Bauer, D.~Pirjol, I.~Z.~Rothstein and I.~W.~Stewart,
%``On Differences Between SCET and QCDF for B->pi pi Decays,''
arXiv:hep-ph/0502094.
%%CITATION = HEP-PH 0502094;%%

\bibitem{bounds}
Y.~Grossman and H.~R.~Quinn,
%``Bounding the effect of penguin diagrams in a(CP)(B0 $\to$ pi+ pi-),''
Phys.\ Rev.\ D {\bf 58}, 017504 (1998);
%[arXiv:hep-ph/9712306].
%%CITATION = HEP-PH 9712306;%
J.~Charles,
%``Taming the penguin in the B/d0(t) $\to$ pi+ pi- CP-asymmetry:  Observables
%and minimal theoretical input,''
Phys.\ Rev.\ D {\bf 59}, 054007 (1999);
%[arXiv:hep-ph/9806468].
%%CITATION = HEP-PH 9806468;%%

\bibitem{GLSS}
M.~Gronau, D.~London, N.~Sinha and R.~Sinha,
%``Improving bounds on penguin pollution in B $\to$ pi pi,''
Phys.\ Lett.\ B {\bf 514}, 315 (2001).
%[arXiv:hep-ph/0105308].
%%CITATION = HEP-PH 0105308;%%

\bibitem{su3bounds}
D.~Pirjol,
%``Bounding the penguin effects in determinations of alpha from  B0(t) $\to$
%pi+ pi-,''
Phys.\ Rev.\ D {\bf 60}, 054020 (1999);
%%CITATION = HEP-PH 9903447;%%
R.~Fleischer,
%``New strategies to extract beta and gamma from B/d $\to$ pi+ pi- and  B/s
%$\to$ K+ K-,''
Phys.\ Lett.\ B {\bf 459}, 306 (1999).
%%CITATION = HEP-PH 9903456;%

\bibitem{BuSa}
G.~Buchalla and A.~S.~Safir,
%``Model independent bound on the unitarity triangle from CP violation in B
%$\to$ pi+ pi- and B $\to$ psi K(S),''
Phys.\ Rev.\ Lett.\  {\bf 93}, 021801 (2004).
%[arXiv:hep-ph/0310218].
%%CITATION = HEP-PH 0310218;%%

\bibitem{QCDSR}
P.~Ball and R.~Zwicky,
%``Improved analysis of B $\to$ pi e nu from QCD sum rules on the
%light-cone,''
JHEP {\bf 0110}, 019 (2001);
%[arXiv:hep-ph/0110115].
%%CITATION = HEP-PH 0110115;%%
P.~Ball and R.~Zwicky,
%``New results on B $\to$ pi, K, eta decay formfactors from light-cone sum
%rules,''
arXiv:hep-ph/0406232.
%%CITATION = HEP-PH 0406232;%

\bibitem{ZICHEP}
Z.~Ligeti,
%``The CKM matrix and CP violation,''
arXiv:hep-ph/0408267.
%%CITATION = HEP-PH 0408267;%%


\bibitem{scetgamma}
C.~W.~Bauer, I.~Z.~Rothstein and I.~W.~Stewart,
%``A new method for determining gamma from B $\to$ pi pi decays,''
arXiv:hep-ph/0412120.
%%CITATION = HEP-PH 0412120;%%

\bibitem{alphacons}
M.~Gronau, E.~Lunghi and D.~Wyler,
%``Reducing the error on alpha in B $\to$ pi pi, rho rho, rho pi,''
Phys.\ Lett.\ B {\bf 606}, 95 (2005)
[arXiv:hep-ph/0410170].
%%CITATION = HEP-PH 0410170;%%

%\bibitem{tough}
%M.~Pivk and F.~R.~Le Diberder,
%``Isospin constraints from / on B $\to$ pi pi,''
%arXiv:hep-ph/0406263.
%%CITATION = HEP-PH 0406263;%%

\end{thebibliography}