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Register a new userQED effects in the pseudoscalar meson sector
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We present results on the pseudoscalar meson masses from a fully dynamical simulation of QCD+QED. We concentrate particularly on violations of isospin symmetry. We calculate the $pi^+$-$pi^0$ splitting and also look at other isospin violating mass differences. We have presented results for these isospin splittings in arXiv:1508.06401 [hep-lat]. In this paper we give more details of the techniques employed, discussing in particular the question of how much of the symmetry violation is due to QCD, arising from the different masses of the $u$ and $d$ quarks, and how much is due to QED, arising from the different charges of the quarks. This decomposition is not unique, it depends on the renormalisation scheme and scale. We suggest a renormalisation scheme in which Dashens theorem for neutral mesons holds, so that the electromagnetic self-energies of the neutral mesons are zero, and discuss how the self-energies change when we transform to a scheme such as $bar{MS}$, in which Dashens theorem for neutral mesons is violated.
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The SU(3) flavour symmetry breaking expansion in up, down and strange quark masses is extended from hadron masses to meson decay constants. This allows a determination of the ratio of kaon to pion decay constants in QCD. Furthermore when using partially quenched valence quarks the expansion is such that SU(2) isospin breaking effects can also be determined. It is found that the lowest order SU(3) flavour symmetry breaking expansion (or Gell-Mann-Okubo expansion) works very well. Simulations are performed for 2+1 flavours of clover fermions at four lattice spacings.
Hadron masses are subject to few MeV corrections arising from QED interactions, almost entirely arising from the electric charge of the valence quarks. The QED effects include both self-energy contributions and interactions between the valence quarks/anti-quarks. By combining results from different signs of the valence quark electric charge we are able to isolate the interaction term which is dominated by the Coulomb piece, $langle alpha_{mathrm{QED}}e_{q_1}e_{overline{q}_2}/r rangle$, in the nonrelativistic limit. We study this for $D_s$, $eta_c$ and $J/psi$ mesons, working in lattice QCD plus quenched QED. We use gluon field configurations that include up, down, strange and charm quarks in the sea at multiple values of the lattice spacing. Our results, including also values for mesons with quarks heavier than charm, can be used to improve phenomenological models for the QED contributions. The QED interaction term carries information about meson structure; we derive effective sizes $langle 1/r_{mathrm{eff}} rangle^{-1}$ for $eta_c$, $J/psi$ and $D_s$ of 0.206(8) fm, 0.321(14) fm and 0.307(31) fm respectively.
Lattice QCD simulations are now reaching a precision where isospin breaking effects become important. Previously, we have developed a program to systematically investigate the pattern of flavor symmetry beaking within QCD and successfully applied it to meson and baryon masses involving up, down and strange quarks. In this Letter we extend the calculations to QCD + QED and present our first results on isospin splittings in the pseudoscalar meson and baryon octets. In particular, we obtain the nucleon mass difference of $M_n-M_p=1.35(18)(8),mbox{MeV}$ and the electromagnetic contribution to the pion splitting $M_{pi^+}-M_{pi^0}=4.60(20),mbox{MeV}$. Further we report first determination of the separation between strong and electromagnetic contributions in the $bar{MS}$ scheme.
We present preliminary results for light, strange and charmed pseudoscalar meson physics from simulations using four flavors of dynamical quarks with the highly improved staggered quark (HISQ) action. These simulations include lattice spacings ranging from 0.15 to 0.06 fm, and sea-quark masses both above and at their physical value. The major results are charm meson decay constants f_D, f_{D_s} and f_{D_s}/f_D and ratios of quark masses. This talk will focus on our procedures for finding the decay constants on each ensemble, the continuum extrapolation, and estimates of systematic error.
Based on lattice simulations with two flavours of dynamical, O(a)-improved Wilson fermions we present results for the first two moments of the distribution amplitudes of pseudoscalar mesons at several values of the valence quark masses. By extrapolating our results to the physical masses of up/down and strange quarks, we find the first two moments of the K^+ distribution amplitude and the second moment of the pi^+ distribution amplitude. We use nonperturbatively determined renormalisation coefficients to obtain results in the MSbar scheme. At a scale of 4 GeV^2 we find a_2^pi=0.201(114) for the second Gegenbauer moment of the pions distribution amplitude, while for the kaon, a_1^K=0.0453(9)(29) and a_2^K=0.175(18)(47).
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