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Register a new userFlavour breaking effects in the pseudoscalar meson decay constants
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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.
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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.
We compute the leptonic decay constants $f_{D^+}$, $f_{D_s}$, and $f_{K^+}$, and the quark-mass ratios $m_c/m_s$ and $m_s/m_l$ in unquenched lattice QCD. We use the MILC highly improved staggered quark (HISQ) ensembles with four dynamical quark flavors. Our primary results are $f_{D^+} = 212.6(0.4)({}^{+1.0}_{-1.2}) mathrm{MeV}$, $f_{D_s} = 249.0(0.3)({}^{+1.1}_{-1.5}) mathrm{MeV}$, and $f_{D_s}/f_{D^+} = 1.1712(10)({}^{+29}_{-32})$, where the errors are statistical and total systematic, respectively. We also obtain $f_{K^+}/f_{pi^+} = 1.1956(10)({}^{+26}_{-18})$, updating our previous result, and determine the quark-mass ratios $m_s/m_l = 27.35(5)({}^{+10}_{-7})$ and $m_c/m_s = 11.747(19)({}^{+59}_{-43})$. When combined with experimental measurements of the decay rates, our results lead to precise determinations of the CKM matrix elements $|V_{us}| = 0.22487(51) (29)(20)(5)$, $|V_{cd}|=0.217(1) (5)(1)$ and $|V_{cs}|= 1.010(5)(18)(6)$, where the errors are from this calculation of the decay constants, the uncertainty in the experimental decay rates, structure-dependent electromagnetic corrections, and, in the case of $|V_{us}|$, the uncertainty in $|V_{ud}|$, respectively.
We present an update of our calculations of the decay constants of the D, D_s, B, and B_s mesons in unquenched 2+1 flavor QCD. We use the MILC library of improved staggered gauge ensembles at lattice spacings 0.09, 0.12, and 0.15 fm, clover heavy quarks with the Fermilab normalizations, and improved staggered light valence quarks.
We evaluate the $pi N!N$, $piSigmaSigma$, $piLambdaSigma$, $KLambda N$ and $K Sigma N $ coupling constants and the corresponding monopole masses in lattice QCD with two flavors of dynamical quarks. The parameters representing the SU(3)-flavor symmetry are computed at the point where the three quark flavors are degenerate at the physical $s$-quark mass. In particular, we obtain $alphaequiv F/(F+D)=0.395(6)$. The quark-mass dependences of the coupling constants are obtained by changing the $u$- and the $d$-quark masses. We find that the SU(3)-flavor parameters have weak quark-mass dependence and thus the SU(3)-flavor symmetry is broken by only a few percent at each quark-mass point we consider.
We compute the leptonic decay constants $f_{D^+}$, $f_{D_s}$, and $f_{K^+}$, and the quark-mass ratios $m_c/m_s$ and $m_s/m_l$ in unquenched lattice QCD using the experimentally determined value of $f_{pi^+}$ for normalization. We use the MILC highly improved staggered quark (HISQ) ensembles with four dynamical quark flavors---up, down, strange, and charm---and with both physical and unphysical values of the light sea-quark masses. The use of physical pions removes the need for a chiral extrapolation, thereby eliminating a significant source of uncertainty in previous calculations. Four different lattice spacings ranging from $aapprox 0.06$ fm to $0.15$ fm are included in the analysis to control the extrapolation to the continuum limit. Our primary results are $f_{D^+} = 212.6(0.4)({}^{+1.0}_{-1.2}) mathrm{MeV}$, $f_{D_s} = 249.0(0.3)({}^{+1.1}_{-1.5}) mathrm{MeV}$, and $f_{D_s}/f_{D^+} = 1.1712(10)({}^{+29}_{-32})$, where the errors are statistical and total systematic, respectively. The errors on our results for the charm decay constants and their ratio are approximately two to four times smaller than those of the most precise previous lattice calculations. We also obtain $f_{K^+}/f_{pi^+} = 1.1956(10)({}^{+26}_{-18})$, updating our previous result, and determine the quark-mass ratios $m_s/m_l = 27.35(5)({}^{+10}_{-7})$ and $m_c/m_s = 11.747(19)({}^{+59}_{-43})$. When combined with experimental measurements of the decay rates, our results lead to precise determinations of the CKM matrix elements $|V_{us}| = 0.22487(51) (29)(20)(5)$, $|V_{cd}|=0.217(1) (5)(1)$ and $|V_{cs}|= 1.010(5)(18)(6)$, where the errors are from this calculation of the decay constants, the uncertainty in the experimental decay rates, structure-dependent electromagnetic corrections, and, in the case of $|V_{us}|$, the uncertainty in $|V_{ud}|$, respectively.
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