We report on the first lattice calculation of the QCD phase transition using chiral fermions at physical values of the quark masses. This calculation uses 2+1 quark flavors, spatial volumes between (4 fm$)^3$ and (11 fm$)^3$ and temperatures between
139 and 196 MeV . Each temperature was calculated using a single lattice spacing corresponding to a temporal Euclidean extent of $N_t=8$. The disconnected chiral susceptibility, $chi_{rm disc}$ shows a pronounced peak whose position and height depend sensitively on the quark mass. We find no metastability in the region of the peak and a peak height which does not change when a 5 fm spatial extent is increased to 10 fm. Each result is strong evidence that the QCD ``phase transition is not first order but a continuous cross-over for $m_pi=135$ MeV. The peak location determines a pseudo-critical temperature $T_c = 155(1)(8)$ MeV. Chiral $SU(2)_Ltimes SU(2)_R$ symmetry is fully restored above 164 MeV, but anomalous $U(1)_A$ symmetry breaking is non-zero above $T_c$ and vanishes as $T$ is increased to 196 MeV.
The real and imaginary parts of the $K_L-K_S$ mixing matrix receive contributions from all three charge-2/3 quarks: up, charm and top. These give both short- and long-distance contributions which are accessible through a combination of perturbative a
nd lattice methods. We will discuss a strategy to compute both the mass difference, $Delta M_K$ and $epsilon_K$ to sub-percent accuracy, looking in detail at the contributions from each of the three CKM matrix element products $V_{id}^*V_{is}$ for $i=u, c$ and $t$ as described in Ref. [1]
We present a systematic study of the effectiveness of light quark mass reweighting. This method allows a single lattice QCD ensemble, generated with a specific value of the dynamical light quark mass, to be used to determine results for other, nearby
light dynamical quark masses. We study two gauge field ensembles generated with 2+1 flavors of dynamical domain wall fermions with light quark masses m_l=0.02 (m_pi=620 MeV) and m_l=0.01 (m_pi=420 MeV). We reweight each ensemble to determine results which could be computed directly from the other and check the consistency of the reweighted results with the direct results. The large difference between the 0.02 and 0.01 light quark masses suggests that this is an aggressive application of reweighting as can be seen from fluctuations in the magnitude of the reweighting factor by four orders of magnitude. Never-the-less, a comparison of the reweighed topological charge, average plaquette, residual mass, pion mass, pion decay constant, and scalar correlator between these two ensembles shows agreement well described by the statistical errors. The issues of the effective number of configurations and finite sample size bias are discussed. An examination of the topological charge distribution implies that it is more favorable to reweight from heavier mass to lighter quark mass.
The largest contribution to the CP violating K_L-K_S mixing parameter epsilon_K comes from second order weak interactions at short distances and can be accurately determined by a combination of electroweak perturbation theory and the calculation of t
he parameter B_K from lattice QCD. However, there is an additional long distance contribution to epsilon_K which is estimated to be of order 5%. Here recently introduced lattice techniques for computing the long-distance component of the K_L-K_S mass difference are generalized to this long-distance contribution to epsilon_K.
We review the current status of calculations of the two pion decays of the kaon using the first-principles methods of lattice gauge theory and the significant challenges that these calculations pose. While a calculation with controlled errors at even
the 10-20% level has not yet been performed, present results suggest that such a calculation of the real and imaginary parts of the Delta I = 3/2 amplitude should be accomplished within the next two years. The more difficult Delta I = 1/2 amplitude may also be now within reach.
We present a calculation of the renormalization coefficients of the quark bilinear operators and the K-Kbar mixing parameter B_K. The coefficients relating the bare lattice operators to those in the RI/MOM scheme are computed non-perturbatively and t
hen matched perturbatively to the MSbar scheme. The coefficients are calculated on the RBC/UKQCD 2+1 flavor dynamical lattice configurations. Specifically we use a 16^3 x 32 lattice volume, the Iwasaki gauge action at beta=2.13 and domain wall fermions with L_s=16.
