Michele Della Morte\thanks{Support by the European %%Community's Human Potential Programme under contract RTN1-1999-00246 %%is acknowledged.}
%% DESY-Zeuthen
Platanenallee 6
D-15738
Zeuthen
Germany
%%Non-perturbative lattice studies of QCD in the chiral %%thermodynamic regime, where chiral symmetry is spontaneously broken, %%require to deal with almost quark zero modes in a theoretically %%clean and computationally efficient way. We discuss the basic %%features and some realistic tests of a formulation, known as %%lattice tmQCD, that fulfills these requirements. %%
web_tm2001synth.tex
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\begin{flushright}
MS-TP-01-16\\
Bicocca-FT-01-25
\end{flushright}

\vskip 1 cm
\begin{center}

{\Large\bf A lattice approach to QCD in the chiral regime}

\end{center}
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\vbox{
\centerline{
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\begin{center}
{\large
Michele Della Morte$^{\scriptscriptstyle a}$\footnote{Support by the European
Community's Human Potential Programme under contract RTN1-1999-00246
is acknowledged.},
Roberto Frezzotti$^{\scriptscriptstyle b}$\footnote{I acknowledge
        support and warm hospitality by the Theory Division of CERN
        for the time when the work presented in this contribution was done.} 
and 
Jochen Heitger$^{\scriptscriptstyle c}$
}
\vskip 1.5cm
%
$^{\scriptstyle a}$
DESY-Zeuthen,\\
Platanenallee 6, D-15738, Zeuthen, Germany
\vskip 2.5ex
$^{\scriptstyle b}$
Universit\`a di Milano-Bicocca, Dipartimento di Fisica,\\
Piazza della Scienza 3, I-20126 Milano, Italy
\vskip 2.5ex
$^{\scriptstyle c}$
Westf\"alische Wilhelms-Universit\"at M\"unster,
Institut f\"ur Theoretische Physik,\\
Wilhelm-Klemm-Strasse 9, D-48149 M\"unster, Germany
\vskip 1.5cm
{\bf Abstract}
\vskip 0.7ex
\end{center}

Non-perturbative lattice studies of QCD in the chiral
thermodynamic regime, where chiral symmetry is spontaneously broken,
require to deal with almost quark zero modes in a theoretically
clean and computationally efficient way. We discuss the basic
features and some realistic tests of a formulation, known as
lattice tmQCD, that fulfills these requirements.

\vskip 1.5ex
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\begin{center}
November 2001
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%%\author{Michele Della Morte\thanks{Support by the European
%%Community's Human Potential Programme under contract RTN1-1999-00246
%%is acknowledged.}\\
%%        DESY-Zeuthen, Platanenallee 6, D-15738, Zeuthen, Germany}
%%
%%\author{\speaker{Roberto Frezzotti}\thanks{I acknowledge 
%%        support and warm hospitality by the Theory Division of CERN 
%%        for the time when the work presented in this contribution was done.} \\
%%        Univ. of Milano Bicocca, Dip. di Fisica, 
%%        Piazza della Scienza 3, I-20126, Italy                           
%%       }                       
%%
%%\author{ Jochen Heitger \\
%%        WWU M\"unster,
%%                 Institut f\"ur Theoretische Physik,
%%         Wilhelm-Klemm-Str. 9, \\ D-48149 M\"unster, Germany}
%%              
%%
%%\abstract{
%%Non-perturbative lattice studies of QCD in the chiral 
%%thermodynamic regime, where chiral symmetry is spontaneously broken, 
%%require to deal with almost quark zero modes in a theoretically
%%clean and computationally efficient way. We discuss the basic
%%features and some realistic tests of a formulation, known as
%%lattice tmQCD, that fulfills these requirements.
%%}
%%
%%
%%\begin{document}
%%

\input{sect1}
\input{sect2}
\input{sect3}
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\section{Conclusions}

Lattice tmQCD is well suited to perform non-perturbative studies of QCD
in the chiral (thermodynamic or finite-volume) regime for all
cases where it is technically sufficient to recover chiral
symmetry in the continuum limit. The framework has been successfully
tested in the quenched approximation and can straightforwardly be
extended beyond it.

The tmQCD project is part of the ALPHA
Collaboration research programme. We acknowledge the very pleasant
collaboration with P.A.~Grassi, S.~Sint and P.~Weisz, as well as
fruitful discussions
with M.~L\"uscher, G.C.~Rossi and R.~Sommer.


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\begin{thebibliography}{99}
%  \bibitem{...} ....          % Use JHEP shortcuts to get hyperlinks!
%\bibitem{Luscher_LH97} For reviews see: M.~L\"uscher,
%hep-lat/9802029; S.~Sint, 
%Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 94} (2001) 79.
  
\bibitem{wilson74} K.G.~Wilson, Phys. Rev. D10 (1974) 2445.

\bibitem{GW_rediscov} P.H.~Ginsparg and K.G.~Wilson, Phys. Rev. D25
(1982) 2649. P.~Hasenfratz, Nucl.~Phys. B525 (1998) 401. H.~Neuberger,
Phys.~Lett. B417 (1998) 141. M.~L\"uscher, Phys. Lett. B428 (1998) 342.
Y.~Kikukawa and T.~Noguchi, hep-lat/9902022. 

\bibitem{bmmrt} M. Bochicchio et al. , Nucl.~Phys. B262 (1985) 331.
%L.~Maiani, G.~Martinelli, G.C.~Rossi
%and M.~Testa, Nucl.~Phys. B262 (1985) 331.

\bibitem{O(a)_impr} 
M. L\"uscher, S. Sint, R. Sommer and P. Weisz,
Nucl. Phys. B478 (1996) 365. 

\bibitem{BeGo} C.W. Bernard and M.F.L.~Golterman, 
Phys.~Rev. D46 (1992) 853; Phys.Rev. D49 (1994) 486.
G.~Colangelo and E.~Pallante, Nucl.~Phys. B520 (1998) 433.

\bibitem{CaBa} 
T.~Banks and A.~Casher, Nucl.~Phys. B169 (1980) 103.
%%%S.~Chandrasekharan, Phys.~Rev. D60 (1999) 074503.

\bibitem{CPPACS_hadspe} S.~Aoki et al. [CP-PACS Collaboration], 
Phys.Rev.Lett. 84 (2000) 238, and references therein. 

\bibitem{ShaSho}
S.~R.~Sharpe and N.~Shoresh, Phys.~Rev. D62 (2000) 094503.

\bibitem{paper1}
R.~Frezzotti, P.~A.~Grassi, S.~Sint and P.~Weisz,
Nucl.~Phys.~B (Proc. Suppl.) 83 (2000) 941;
JHEP 0108 (2001) 058.

\bibitem{FS01}
R.~Frezzotti and S.~Sint, hep-lat/0110140.

\bibitem{BK01}
M.~Guagnelli, J.~Heitger, C.~Pena, S.~Sint and A.~Vladikas, hep-lat/0110097.

\bibitem{Bardeen_et_al}
W.~Bardeen, A.~Duncan, E.~Eichten and H.~Thacker,
Phys.~Rev. D59 (1999) 014507.

\bibitem{pq_exceptionals}
A.~C.~Irving et al. , Phys.~Lett. B518 (2001) 243.

\bibitem{unq_exceptionals}
B.~Joo  [UKQCD Collaboration], hep-lat/0110047.
 
\bibitem{AoGo} S.~Aoki and A. Gocksch, Phys.~Rev.~Lett 63 (1989) 1125.

\bibitem{Aoki_phase} S.~Aoki, Phys. Rev. D30 (1984) 2653. 
S.R.~Sharpe and R.L.~Singleton, Phys.~Rev. D58 (1998) 074501.

\bibitem{RFnotes} R.~Frezzotti, unpublished notes.

\bibitem{paper2} 
R.~Frezzotti, S.~Sint and P.~Weisz, JHEP 0107 (2001) 048.

\bibitem{paper3}
M.~Della Morte, R.~Frezzotti, J.~Heitger and S.~Sint,
hep-lat/0108019.

\bibitem{paper4}
M.~Della Morte, R.~Frezzotti and J.~Heitger, hep-lat/0110166
and work in preparation.

\bibitem{sommer_r_0} R.~Sommer, Nucl.~Phys. B411 (1994) 839.

\bibitem{CPPACS_B_K} A.~Ali~Khan et al. [CP-PACS Collaboration],
hep-lat/0105020.

\bibitem{garden} J.~Garden, J.~Heitger, R.~Sommer and H.~Wittig,
Nucl.~Phys. B571 (2000) 237.

\bibitem{UK_tmQCD} C.~McNeile and C.~Michael,
hep-lat/0110108.


\end{thebibliography}

\end{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



hep-lat0111048.extracted_bib
\begin{thebibliography}{99}
%  \bibitem{...} ....          % Use JHEP shortcuts to get hyperlinks!
%\bibitem{Luscher_LH97} For reviews see: M.~L\"uscher,
%hep-lat/9802029; S.~Sint, 
%Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 94} (2001) 79.
  
\bibitem{wilson74} K.G.~Wilson, Phys. Rev. D10 (1974) 2445.

\bibitem{GW_rediscov} P.H.~Ginsparg and K.G.~Wilson, Phys. Rev. D25
(1982) 2649. P.~Hasenfratz, Nucl.~Phys. B525 (1998) 401. H.~Neuberger,
Phys.~Lett. B417 (1998) 141. M.~L\"uscher, Phys. Lett. B428 (1998) 342.
Y.~Kikukawa and T.~Noguchi, hep-lat/9902022. 

\bibitem{bmmrt} M. Bochicchio et al. , Nucl.~Phys. B262 (1985) 331.
%L.~Maiani, G.~Martinelli, G.C.~Rossi
%and M.~Testa, Nucl.~Phys. B262 (1985) 331.

\bibitem{O(a)_impr} 
M. L\"uscher, S. Sint, R. Sommer and P. Weisz,
Nucl. Phys. B478 (1996) 365. 

\bibitem{BeGo} C.W. Bernard and M.F.L.~Golterman, 
Phys.~Rev. D46 (1992) 853; Phys.Rev. D49 (1994) 486.
G.~Colangelo and E.~Pallante, Nucl.~Phys. B520 (1998) 433.

\bibitem{CaBa} 
T.~Banks and A.~Casher, Nucl.~Phys. B169 (1980) 103.
%%%S.~Chandrasekharan, Phys.~Rev. D60 (1999) 074503.

\bibitem{CPPACS_hadspe} S.~Aoki et al. [CP-PACS Collaboration], 
Phys.Rev.Lett. 84 (2000) 238, and references therein. 

\bibitem{ShaSho}
S.~R.~Sharpe and N.~Shoresh, Phys.~Rev. D62 (2000) 094503.

\bibitem{paper1}
R.~Frezzotti, P.~A.~Grassi, S.~Sint and P.~Weisz,
Nucl.~Phys.~B (Proc. Suppl.) 83 (2000) 941;
JHEP 0108 (2001) 058.

\bibitem{FS01}
R.~Frezzotti and S.~Sint, hep-lat/0110140.

\bibitem{BK01}
M.~Guagnelli, J.~Heitger, C.~Pena, S.~Sint and A.~Vladikas, hep-lat/0110097.

\bibitem{Bardeen_et_al}
W.~Bardeen, A.~Duncan, E.~Eichten and H.~Thacker,
Phys.~Rev. D59 (1999) 014507.

\bibitem{pq_exceptionals}
A.~C.~Irving et al. , Phys.~Lett. B518 (2001) 243.

\bibitem{unq_exceptionals}
B.~Joo  [UKQCD Collaboration], hep-lat/0110047.
 
\bibitem{AoGo} S.~Aoki and A. Gocksch, Phys.~Rev.~Lett 63 (1989) 1125.

\bibitem{Aoki_phase} S.~Aoki, Phys. Rev. D30 (1984) 2653. 
S.R.~Sharpe and R.L.~Singleton, Phys.~Rev. D58 (1998) 074501.

\bibitem{RFnotes} R.~Frezzotti, unpublished notes.

\bibitem{paper2} 
R.~Frezzotti, S.~Sint and P.~Weisz, JHEP 0107 (2001) 048.

\bibitem{paper3}
M.~Della Morte, R.~Frezzotti, J.~Heitger and S.~Sint,
hep-lat/0108019.

\bibitem{paper4}
M.~Della Morte, R.~Frezzotti and J.~Heitger, hep-lat/0110166
and work in preparation.

\bibitem{sommer_r_0} R.~Sommer, Nucl.~Phys. B411 (1994) 839.

\bibitem{CPPACS_B_K} A.~Ali~Khan et al. [CP-PACS Collaboration],
hep-lat/0105020.

\bibitem{garden} J.~Garden, J.~Heitger, R.~Sommer and H.~Wittig,
Nucl.~Phys. B571 (2000) 237.

\bibitem{UK_tmQCD} C.~McNeile and C.~Michael,
hep-lat/0110108.


\end{thebibliography}