document: the standard model of elementary particles ( sm ) has been very successful in describing the nature at the electroweak ( ew ) scale . 
   recently , the atlas and cms collaborations at the large hadron collider ( lhc ) have discovered a new particle  @xcite , which is consistent with the sm higgs boson . 
   this discovery also strengthens the correctness of the sm . 
   so far , no explicit evidence of physics beyond the sm has been reported from the lhc . 
   several groups , however , have reported an anomaly of the muon anomalous magnetic moment @xmath9 ( muon g-2 ) , which has been precisely measured experimentally  @xcite and compared with state - of - the - art theoretical predictions ( for example , see @xcite and references therein ) . 
   the estimated discrepancies between the sm predictions and the measured value are consistently more than @xmath10 , as listed in table  [ tab : g-2 ] .    although it is too early to conclude that this anomaly is evidence of new physics beyond the sm , we expect new particles and interactions related with the muon sector once we regard it as a hint of new physics . 
   gauge interactions have been playing a central role to construct fundamental models in particle physics history . following this line , in this paper 
   , we purse the possibility that the muon has a new gauge interaction beyond the sm . 
   .measured muon g-2 ( @xmath11 ) and the estimated differences ( @xmath12 ) from the recent sm predictions in several references . [ cols="^,^",options="header " , ]     from the charge assignments , renormalizable terms in a lagrangian which contribute to the lepton masses are given by @xmath13 here , @xmath14 are the yukawa couplings of the charged leptons and not related to the neutrino mass . the neutrino mass is determined from yukawa couplings @xmath15 , majorana masses @xmath16 and @xmath17 , and yukawa couplings @xmath18 and @xmath19 . 
   note that the mass terms between the left and right - handed neutrinos are diagonal . 
   therefore , the neutrino mixing is obtained by mixing among the right - handed neutrinos . if the majorana masses @xmath20 and @xmath21 are of the same order , the seesaw mechanism  @xcite provides the observed order one neutrino mixing . from the seesaw formula , a relation between the parameters is given by @xmath22 where @xmath23 gev is the vacuum expectation value of the sm higgs , and @xmath24 is the difference between the mass squared of the left - handed neutrinos . @xmath25 and @xmath26 denote @xmath27 and @xmath20 and @xmath21 collectively 
   .      interactions given by eq . 
   ( [ eq : mass terms ] ) break the lepton symmetry . 
   on the other hand , @xmath28 symmetry is broken by the anomaly against the @xmath29 gauge interaction , whose effect is efficient at the early universe by the sphaleron process in the finite temperature  @xcite . 
   therefore , the baryon asymmetry is washed out if both effects are important simultaneously . 
   let us calculate a condition such that the washout does not occur . 
   first of all , the sphaleron process is efficient only at the temperature above the ew scale . 
   therefore , if the baryon asymmetry is generated below the ew scale , the washout does not occur . in the following , we assume that the baryon asymmetry is produced above the ew scale and calculate the constraint on the parameters in eq . 
   ( [ eq : mass terms ] ) . 
   let us consider two possibilities in which the washout does not occur .    1 . 
   @xmath30 is small , 2 . 
   @xmath16 and @xmath17 are small . 
   if any of the two conditions are satisfied , the lepton number is effectively conserved . 
   therefore , one should adopt the weakest condition among them . 
   let us discuss the two cases in detail .      in the limit @xmath31 , the lepton symmetry is restored for each flavors . 
   therefore , if the interaction by @xmath30 is inefficient , the washout of the baryon asymmetry does not occur . 
   the most efficient interaction is shown in figure  [ fig : lambda ] and its rate is given by @xmath32 where @xmath33 , @xmath34 , @xmath35 , @xmath36 are the cross section of the process , the number density of related particles , the velocity of related particles , and the yukawa coupling of the top quark , respectively . 
   @xmath37 denotes the thermal average . by requiring that the rate is smaller than the hubble scale for @xmath38 gev 
   , we obtain the bound @xmath39    .,width=264 ]          if both majorana masses vanish , @xmath40 symmetry is restored . the most efficient interaction which induces the symmetry violation by the majorana masses 
   is shown in figure  [ fig : m ] . 
   its rate is given by @xmath41 this rate is smaller than the hubble scale for @xmath38 gev if @xmath42    from the relation ( [ eq : seesaw ] ) , one can see that the condition ( [ eq : constraint - m ] ) is severer than the condition ( [ eq : constraint - l ] ) . 
   therefore , it is enough to satisfy the condition ( [ eq : constraint - l ] ) in order for the washout not to occur . with the relation ( [ eq : seesaw ] ) , the condition is interpreted as @xmath43    since the right - handed neutrinos are light and weakly coupled , it is necessary to consider whether they are long - lived . if they are long - lived , they might over - close the universe , or destroy the success of the big - bang nucleosynthesis ( bbn ) . 
   the most important decay channel is given by the diagram shown in figure . 
   [ fig : decay of n ] . here , we have assumed that @xmath33 is heavier than the right - handed neutrinos and hence the decay mode @xmath44 is closed . 
   the decay rate is given by @xmath45 the decay of the right - handed neutrinos is efficient around the temperature @xmath46 therefore , the right - handed neutrinos decay before the bbn begins and does not affect it . 
   passarino - veltman functions  @xcite are defined by @xmath47 \left[(k+p)^2-m_b^2+i \epsilon\right]},\nonumber \\ 
   p^\mu b_1(a , b;p ) & = & 16\pi^2 \mu^{2\epsilon } \int \frac{d^n k}{i(2\pi)^n}\frac{k^\mu } { \left[k^2-m_a^2+i\epsilon\right]\left[(k+p)^2-m_b^2+i\epsilon\right ] } , \nonumber \\ 
   p^\mu p^\nu b_{21}(a , b;p)&+&g^{\mu \nu}b_{22}(a , b;p ) \nonumber \\ & = & 16\pi^2 \mu^{2\epsilon } \int \frac{d^n k}{i(2\pi)^n } \frac{k^\mu k^\nu } { \left[k^2-m_a^2+i\epsilon\right]\left[(k+p)^2-m_b^2+i\epsilon\right ] } , \ ] ] @xmath48[(k+p_1)^2-m_b^2+i\epsilon][(k+p_1+p_2)^2-m_c^2+i\epsilon ] } , \nonumber   \\ & & \left ( p_1^\mu c_{11}+p_2^\mu c_{12 } \right)(a , b , c;p_1,p_2 ) \nonumber \\ & = & 16\pi^2 \mu^{2\epsilon } \int \frac{d^n k}{i(2\pi)^n}\frac{k^\mu } { [ k^2-m_a^2+i\epsilon][(k+p_1)^2-m_b^2+i\epsilon][(k+p_1+p_2)^2-m_c^2+i\epsilon ] } , \nonumber   \\ & & \left\{(p_1^\mu p_1^\nu c_{21 } + p_2^\mu p_2^\nu c_{22}+(p_1^\mu p_2^\nu+p_1^\nu p_2^\mu)c_{23 } + g^{\mu \nu}c_{24 } \right\ } ( a , b , c;p_1,p_2 ) \nonumber \\ & = & 16\pi^2 \mu^{2\epsilon } \int \frac{d^n k}{i(2\pi)^n}\frac{k^\mu k^\nu } { [ k^2-m_a^2+i\epsilon][(k+p_1)^2-m_b^2+i\epsilon][(k+p_1+p_2)^2-m_c^2+i\epsilon ] } , \nonumber   \\\end{aligned}\ ] ] where we use dimensional regularization in @xmath49 dimensions , and @xmath50 is a renormalization scale .      99 g.  aad _ et al . _ [ atlas collaboration ] , phys . 
   b * 716 * , 1 ( 2012 ) . 
   s.  chatrchyan _ et al . 
   _ [ cms collaboration ] , phys . 
   b * 716 * , 30 ( 2012 ) . 
   j.  beringer _ 
   [ particle data group collaboration ] , phys . 
   d * 86 * , 010001 ( 2012 ) and 2013 partial update for the 2014 edition . 
   t.  aoyama , m.  hayakawa , t.  kinoshita and m.  nio , phys .  rev 
   .  lett . 
   * 109 * , 111808 ( 2012 ) [ arxiv:1205.5370 [ hep - ph ] ] . 
   a.  czarnecki , w.  j.  marciano and a.  vainshtein , phys . 
   d * 67 * , 073006 ( 2003 ) [ erratum - ibid . 
   d * 73 * , 119901 ( 2006 ) ] . 
   k.  hagiwara , r.  liao , a.  d.  martin , d.  nomura and t.  teubner , j.  phys . 
   g * 38 * , 085003 ( 2011 ) [ arxiv:1105.3149 [ hep - ph ] ] . 
   t.  teubner , k.  hagiwara , r.  liao , a.  d.  martin and d.  nomura , chin . 
   c * 34 * , 728 ( 2010 ) [ arxiv:1001.5401 [ hep - ph ] ] . 
   m.  benayoun , p.  david , l.  delbuono and f.  jegerlehner , eur . 
   j.  c * 72 * , 1848 ( 2012 ) [ arxiv:1106.1315 [ hep - ph ] ] . 
   f.  jegerlehner and r.  szafron , eur . 
   j.  c * 71 * , 1632 ( 2011 ) [ arxiv:1101.2872 [ hep - ph ] ] . f.  jegerlehner and a.  nyffeler , phys . 
   * 477 * , 1 ( 2009 ) [ arxiv:0902.3360 [ hep - ph ] ] . 
   m.  davier , a.  hoecker , b.  malaescu and z.  zhang , eur . 
   j.  c * 71 * , 1515 ( 2011 ) [ erratum - ibid . 
   c * 72 * , 1874 ( 2012 ) ] . 
   t.  moroi , phys .  rev . 
   d * 53 * , 6565 ( 1996 ) [ erratum - ibid . 
   d * 56 * , 4424 ( 1997 ) ] . 
   for example , see t.  hambye , k.  kannike , e.  ma and m.  raidal , phys . 
   d * 75 * , 095003 ( 2007 ) [ hep - ph/0609228 ] ; s.  kanemitsu and k.  tobe , phys . 
   d * 86 * , 095025 ( 2012 ) [ arxiv:1207.1313 [ hep - ph ] ] . 
   g.  abbiendi _ et al . _ 
   [ opal collaboration ] , eur . 
   j.  c * 33 * , 173 ( 2004 ) [ hep - ex/0309053 ] . 
   j.  abdallah _ et al . 
   _ [ delphi collaboration ] , eur . 
   j.  c * 45 * , 589 ( 2006 ) [ hep - ex/0512012 ] . 
   t.  aaltonen _ et al . _ 
   [ cdf collaboration ] , phys . 
   lett .   * 
   102 * , 091805 ( 2009 ) [ arxiv:0811.0053 [ hep - ex ] ] . 
   v.  m.  abazov _ et al . _ 
   [ d0 collaboration ] , phys . 
   b * 695 * , 88 ( 2011 ) . 
   g.  aad _ et al . 
   _ [ atlas collaboration ] , jhep * 1211 * , 138 ( 2012 ) [ arxiv:1209.2535 [ hep - ex ] ] . 
   s.  chatrchyan _ et al . _ 
   [ cms collaboration ] , phys . 
   b * 720 * , 63 ( 2013 ) [ arxiv:1212.6175 [ hep - ex ] ] . 
   fayet , phys . 
   d * 75 * , 115017 ( 2007 ) [ hep - ph/0702176 [ hep - ph ] ] 
   . m.  pospelov , phys .  rev . 
   d * 80 * , 095002 ( 2009 ) [ arxiv:0811.1030 [ hep - ph ] ] . 
   m.  endo , k.  hamaguchi and g.  mishima , phys . 
   d * 86 * , 095029 ( 2012 ) [ arxiv:1209.2558 [ hep - ph ] ] . 
   h.  davoudiasl , h.  -s . 
   lee and w.  j.  marciano , phys . 
   d * 86 * , 095009 ( 2012 ) [ arxiv:1208.2973 [ hep - ph ] ] . 
   x.  -g . 
   he , g.  c.  joshi , h.  lew and r.  r.  volkas , phys .  rev . 
   d * 44 * , 2118 ( 1991 ) . 
   s.  baek , n.  g.  deshpande , x.  g.  he and p.  ko , phys . 
   d * 64 * , 055006 ( 2001 ) [ hep - ph/0104141 ] . 
   e.  ma , d.  p.  roy and s.  roy , phys .  lett . 
   b * 525 * , 101 ( 2002 ) [ hep - ph/0110146 ] . 
   e.  salvioni , a.  strumia , g.  villadoro and f.  zwirner , jhep * 1003 * , 010 ( 2010 ) . j.  heeck and w.  rodejohann , phys . 
   d * 84 * , 075007 ( 2011 ) [ arxiv:1107.5238 [ hep - ph ] ] . c.  d.  carone and h.  murayama , phys . 
   lett .   * 74 * , 3122 ( 1995 ) [ hep - ph/9411256 ] ; phys . 
   * d52 * , 484 ( 1995 ) [ hep - ph/9504393 ] . g.  -c . 
   cho _ et al . 
   _ , jhep * 1111 * , 068 ( 2011 ) [ arxiv:1104.1769 ] . 
   g.  -c . 
   cho and k.  hagiwara , nucl . 
   b * 574 * , 623 ( 2000 ) [ hep - ph/9912260 ] . 
   k.  hagiwara _ et al . 
   _ , z.  phys . 
   c * 64 * , 559 ( 1994 ) [ erratum - ibid . 
   c * 68 * , 352 ( 1995 ) ] [ hep - ph/9409380 ] . 
   s.  schael _ et al . _ 
   [ aleph and delphi and l3 and opal and sld and lep electroweak working group and sld electroweak group and sld heavy flavour group collaborations ] , phys . 
   rept .   * 427 * , 257 ( 2006 ) [ hep - ex/0509008 ] . 
   a.  belyaev , n.  d.  christensen and a.  pukhov , comput . 
   commun . 
   * 184 * , 1729 ( 2013 ) [ arxiv:1207.6082 [ hep - ph ] ] . 
   t.  sjostrand , s.  mrenna and p.  z.  skands , jhep * 0605 * , 026 ( 2006 ) [ hep - ph/0603175 ] . 
   s.  ovyn , x.  rouby and v.  lemaitre , arxiv:0903.2225 [ hep - ph ] . 
   s.  chatrchyan _ et al . 
   _ [ cms collaboration ] , jhep * 1212 * , 034 ( 2012 ) [ arxiv:1210.3844 [ hep - ex ] ] . 
   atlas collaboration , `` atlas measurements of the 7 and 8 tev cross sections for @xmath53 in pp collisions '' , atlas - conf-2013 - 055 ( may 27 , 2013 ) .        p.  nason , jhep * 0411 * , 040 ( 2004 ) ; s.  frixione , p.  nason and c.  oleari , jhep * 0711 * , 070 ( 2007 ) ; s.  alioli , p.  nason , c.  oleari and e.  re , jhep * 1006 * , 043 ( 2010 ) ; t.  melia , p.  nason , r.  rontsch and g.  zanderighi , jhep * 1111 * , 078 ( 2011 ) . 
   t.  yanagida , in `` proceedings of the workshop on unified theory and baryon number of the universe , '' eds ; o. sawada and a. sugamoto ( kek , 1979 ) p.95 ; m. gell- mann , p. ramond and r. slansky , in `` supergravity , '' eds . ; p. van niewwenhuizen and d. freedman ( north holland , amsterdam , 1979 ) . 
   see also p.  minkowski , phys . 
   * b67 * , 421 ( 1977 ) .
summary: in this paper , we consider phenomenology of a model with an @xmath0 gauge symmetry . since the muon couples to the @xmath0 gauge boson ( called @xmath1 boson ) , its contribution to the muon anomalous magnetic moment ( muon g-2 ) can account for the discrepancy between the standard model prediction and the experimental measurements . on the other hand , 
   the @xmath1 boson does not interact with the electron and quarks , and hence there are no strong constraints from collider experiments even if the @xmath1 boson mass is of the order of the electroweak scale . 
   we show an allowed region of a parameter space in the @xmath0 symmetric model , taking into account consistency with the electroweak precision measurements as well as the muon g-2 . 
   we study the large hadron collider ( lhc ) phenomenology , and show that the current and future data would probe the interesting parameter space for this model . 
   # 1    .75 in     * muon g-2 and lhc phenomenology in the @xmath0 gauge symmetric model * .75 in    keisuke harigaya@xmath2 , takafumi igari@xmath3 , mihoko m. nojiri@xmath4 , + michihisa takeuchi@xmath5 , and kazuhiro tobe@xmath6    0.25 in    _ @xmath2kavli ipmu ( wpi ) , todias , university of tokyo , chiba , kashiwa , 277 - 8583 , japan _ 
   _ @xmath3department of physics , nagoya university , aichi , nagoya 464 - 8602 , japan _    _ @xmath7theory center , kek , tsukuba , ibaraki 305 - 0801 , japan _    _ 
   @xmath5theoretical particle physics and cosmology group , department of physics , king s college london , london wc2r 2ls , uk _    _ @xmath8kobayashi - maskawa institute for the origin of particles and the universe , + nagoya university , aichi , nagoya 464 - 8602 , japan _ 
   .5 in    kcl - ph - th/2013-*37 *    kek - th-1684    ipmu 13 - 0213