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We determine the second Mellin moment of the isovector quark parton distribution function <x>_{u-d} from lattice QCD with N_f=2 sea quark flavours, employing the non-perturbatively improved Wilson-Sheikholeslami-Wohlert action at a pseudoscalar mass of 157(6) MeV. The result is converted non-perturbatively to the RI-MOM scheme and then perturbatively to the MSbar scheme at a scale mu = 2 GeV. As the quark mass is reduced we find the lattice prediction to approach the value extracted from experiments.
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The exclusive semileptonic decay $B rightarrow pi ell u$ is a key process for the determination of the Cabibbo-Kobayashi-Maskawa matrix element $V_{ub}$ from the comparison of experimental rates as a function of $q^2$ with theoretically determined form factors. The sensitivity of the form factors to the $u/d$ quark mass has meant significant systematic uncertainties in lattice QCD calculations at unphysically heavy pion masses. Here we give the first lattice QCD calculations of this process for u/d quark masses going down to their physical values, calculating the $f_0$ form factor at zero recoil to 3%. We are able to resolve a long-standing controversy by showing that the soft-pion theorem result $f_0(q^2_{max}) = f_B/f_{pi}$ does hold as $m_{pi} rightarrow 0$. We use the Highly Improved Staggered Quark formalism for the light quarks and show that staggered chiral perturbation theory for the $m_{pi}$ dependence is almost identical to continuum chiral perturbation theory for $f_0$, $f_B$ and $f_{pi}$. We also give results for other processes such as $B_s rightarrow K ell u$.
The quark flavor sector of the Standard Model is a fertile ground to look for new physics effects through a unitarity test of the Cabbibo-Kobayashi-Maskawa (CKM) matrix. We present a lattice QCD calculation of the scalar and the vector form factors (over a large $q^2$ region including $q^2 = 0$) associated with the $D rightarrow Kl{ u}$ semi-leptonic decay. This calculation will then allow us to determine the central CKM matrix element, $V_{cs}$ in the Standard Model, by comparing the lattice QCD results for the form factors and the experimental decay rate. This form factor calculation has been performed on the $N_f =2+1+1$ MILC HISQ ensembles with the physical light quark masses.
Working with a pion mass $m_pi approx 150$ MeV, we study $pipi$ and $Kpi$ scattering using two flavours of non-perturbatively improved Wilson fermions at a lattice spacing $aapprox 0.071$ fm. Employing two lattice volumes with linear spatial extents of $N_s=48$ and $N_s=64$ points and moving frames, we extract the phase shifts for p-wave $pipi$ and $Kpi$ scattering near the $rho$ and $K^*$ resonances.Comparing our results to those of previous lattice studies, that used pion masses ranging from about 200 MeV up to 470 MeV, we find that the coupling $g_{rhopipi}$ appears to be remarkably constant as a function of $m_{pi}$.
Over the past few years new physics methods and algorithms as well as the latest supercomputers have enabled the study of the QCD thermodynamic phase transition using lattice gauge theory numerical simulations with unprecedented control over systematic errors. This is largely a consequence of the ability to perform continuum extrapolations with physical quark masses. Here we review recent progress in lattice QCD thermodynamics, focussing mainly on results that benefit from the use of physical quark masses: the crossover temperature, the equation of state, and fluctuations of the quark number susceptibilities. In addition, we place a special emphasis on calculations that are directly relevant to the study of relativistic heavy ion collisions at RHIC and the LHC.
We present the latest lattice QCD results for baryon interactions obtained at nearly physical quark masses. $N_f = 2+1$ nonperturbatively ${cal O}(a)$-improved Wilson quark action with stout smearing and Iwasaki gauge action are employed on the lattice of $(96a)^4 simeq (8.1mbox{fm})^4$ with $a^{-1} simeq 2.3$ GeV, where $m_pi simeq 146$ MeV and $m_K simeq 525$ MeV. In this report, we study the two-nucleon systems and two-$Xi$ systems in $^1S_0$ channel and $^3S_1$-$^3D_1$ coupled channel, and extract central and tensor interactions by the HAL QCD method. We also present the results for the $NOmega$ interaction in $^5S_2$ channel which is relevant to the $NOmega$ pair-momentum correlation in heavy-ion collision experiments.
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