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MILC Collaboration: S. Basak
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For some time, the MILC Collaboration has been studying electromagnetic effects on light mesons. These calculations use fully dynamical QCD, but only quenched photons, which suffices to NLO in XPT. That is, the sea quarks are electrically neutral, while the valence quarks carry charge. For the photons we use the non-compact formalism. We have new results with lattice spacing as small as 0.045 fm and a large range of volumes. We consider how well chiral perturbation theory describes these results and the implications for light quark masses
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The MILC Collaboration has completed production running of electromagnetic effects on light mesons using asqtad improved staggered quarks. In these calculations, we use quenched photons in the noncompact formalism. We study four lattice spacings from $approx!0.12:$fm to $approx!0.045:$fm. To study finite-volume effects, we used six spatial lattice sizes $L/a=12$, 16, 20, 28, 40, and 48, at $a!approx!0.12:$fm. We update our preliminary values for the correction to Dashens theorem ($epsilon$) and the quark-mass ratio $m_u/m_d$.
Properties of QCD matter change significantly around the chiral crossover temperature, and the effects on $U(1)_A$ and topological susceptibilities, as well as the meson spectrum have been studied with much care. Baryons and the effect of parity doubling in this temperature range have been analyzed previously by various other groups employing different setups. Here we construct suitable operators to investigate chiral and axial $U(1)_A$ symmetries in the baryon spectrum. Measurements for different volumes and quark-masses are done with two flavors of chirally symmetric domain-wall fermions at temperatures above the critical one. The possibility of emergent $SU(4)$ and $SU(2)_{CS}$ symmetries is discussed.
At the precision reached in current lattice QCD calculations, electromagnetic effects are becoming numerically relevant. We will present preliminary results for electromagnetic corrections to light hadron masses, based on simulations in which a $mathrm{U}(1)$ degree of freedom is superimposed on $N_f=2+1$ QCD configurations from the BMW collaboration.
The quenched hadron spectrum in the continuum obtained with the Wilson quark action in recent simulations on the CP-PACS is presented. Results for the light quark masses and the QCD scale parameter are reported.
In order to reduce the current hadronic uncertainties in the theory prediction for the anomalous magnetic moment of the muon, lattice calculations need to reach sub-percent accuracy on the hadronic-vacuum-polarization contribution. This requires the inclusion of $mathcal{O}(alpha)$ electromagnetic corrections. The inclusion of electromagnetic interactions in lattice simulations is known to generate potentially large finite-size effects suppressed only by powers of the inverse spatial extent. In this paper we derive an analytic expression for the $mathrm{QED}_{mathrm{L}}$ finite-volume corrections to the two-pion contribution to the hadronic vacuum polarization at next-to-leading order in the electromagnetic coupling in scalar QED. The leading term is found to be of order $1/L^{3}$ where $L$ is the spatial extent. A $1/L^{2}$ term is absent since the current is neutral and a photon far away thus sees no charge and we show that this result is universal. Our analytical results agree with results from the numerical evaluation of loop integrals as well as simulations of lattice scalar $U(1)$ gauge theory with stochastically generated photon fields. In the latter case the agreement is up to exponentially suppressed finite-volume effects. For completeness we also calculate the hadronic vacuum polarization in infinite volume using a basis of 2-loop master integrals.
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