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Register a new userUp-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD
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We calculate the up-, down-, strange-, charm-, and bottom-quark masses using the MILC highly improved staggered-quark ensembles with four flavors of dynamical quarks. We use ensembles at six lattice spacings ranging from $aapprox0.15$~fm to $0.03$~fm and with both physical and unphysical values of the two light and the strange sea-quark masses. We use a new method based on heavy-quark effective theory (HQET) to extract quark masses from heavy-light pseudoscalar meson masses. Combining our analysis with our separate determination of ratios of light-quark masses we present masses of the up, down, strange, charm, and bottom quarks. Our results for the $overline{text{MS}}$-renormalized masses are $m_u(2~text{GeV}) = 2.130(41)$~MeV, $m_d(2~text{GeV}) = 4.675(56)$~MeV, $m_s(2~text{GeV}) = 92.47(69)$~MeV, $m_c(3~text{GeV}) = 983.7(5.6)$~MeV, and $m_c(m_c) = 1273(10)$~MeV, with four active flavors; and $m_b(m_b) = 4195(14)$~MeV with five active flavors. We also obtain ratios of quark masses $m_c/m_s = 11.783(25)$, $m_b/m_s = 53.94(12)$, and $m_b/m_c = 4.578(8)$. The result for $m_c$ matches the precision of the most precise calculation to date, and the other masses and all quoted ratios are the most precise to date. Moreover, these results are the first with a perturbative accuracy of $alpha_s^4$. As byproducts of our method, we obtain the matrix elements of HQET operators with dimension 4 and 5: $overline{Lambda}_text{MRS}=555(31)$~MeV in the minimal renormalon-subtracted (MRS) scheme, $mu_pi^2 = 0.05(22)~text{GeV}^2$, and $mu_G^2(m_b)=0.38(2)~text{GeV}^2$. The MRS scheme [Phys. Rev. D97, 034503 (2018), arXiv:1712.04983 [hep-ph]] is the key new aspect of our method.
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We present a lattice QCD calculation of the up, down, strange and charm quark masses performed using the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values. The simulations are based on a unitary setup for the two light quarks and on a mixed action approach for the strange and charm quarks. The analysis uses data at three values of the lattice spacing and pion masses in the range 210 - 450 MeV, allowing for accurate continuum limit and controlled chiral extrapolation. The quark mass renormalization is carried out non-perturbatively using the RI-MOM method. The results for the quark masses converted to the bar{MS} scheme are: mud(2 GeV) = 3.70(17) MeV, ms(2 GeV) = 99.6(4.3) MeV and mc(mc) = 1.348(46) GeV. We obtain also the quark mass ratios ms/mud = 26.66(32) and mc/ms = 11.62(16). By studying the mass splitting between the neutral and charged kaons and using available lattice results for the electromagnetic contributions, we evaluate mu/md = 0.470(56), leading to mu = 2.36(24) MeV and md = 5.03(26) MeV.
Lattice determinations of quark mass have made significant progress in the last few years. I will review recent advances in calculations of charm and bottom mass, which are near to achieving percent-level precision and with fully controlled systematics. Precise knowledge of these parameters is of particular interest for precision Higgs studies at future accelerators.
We report a calculation of the nucleon axial form factors $G_A^q(Q^2)$ and $G_P^q(Q^2)$ for all three light quark flavors $qin{u,d,s}$ in the range $0leq Q^2lesssim 1.2text{ GeV}^2$ using lattice QCD. This work was done using a single ensemble with pion mass 317 MeV and made use of the hierarchical probing technique to efficiently evaluate the required disconnected loops. We perform nonperturbative renormalization of the axial current, including a nonperturbative treatment of the mixing between light and strange currents due to the singlet-nonsinglet difference caused by the axial anomaly. The form factor shapes are fit using the model-independent $z$ expansion. From $G_A^q(Q^2)$, we determine the quark contributions to the nucleon spin and axial radii. By extrapolating the isovector $G_P^{u-d}(Q^2)$, we obtain the induced pseudoscalar coupling relevant for ordinary muon capture and the pion-nucleon coupling constant. We find that the disconnected contributions to $G_P$ form factors are large, and give an interpretation based on the dominant influence of the pseudoscalar poles in these form factors.
In a previous letter (arXiv:1306.2287) we determined the isospin mass splittings of the baryon octet from a lattice calculation based on quenched QED and $N_f{=}2{+}1$ QCD simulations with 5 lattice spacings down to $0.054~mathrm{fm}$, lattice sizes up to $6~mathrm{fm}$ and average up-down quark masses all the way down to their physical value. Using the same data we determine here the corrections to Dashens theorem and the individual up and down quark masses. For the parameter which quantifies violations to Dashenss theorem, we obtain $epsilon=0.73(2)(5)(17)$, where the first error is statistical, the second is systematic, and the third is an estimate of the QED quenching error. For the light quark masses we obtain, $m_u=2.27(6)(5)(4)~mathrm{MeV}$ and $m_d=4.67(6)(5)(4)~mathrm{MeV}$ in the $bar{mathrm{MS}}$ scheme at $2~mathrm{GeV}$ and the isospin breaking ratios $m_u/m_d=0.485(11)(8)(14)$, $R=38.2(1.1)(0.8)(1.4)$ and $Q=23.4(0.4)(0.3)(0.4)$. Our results exclude the $m_u=0$ solution to the strong CP problem by more than $24$ standard deviations.
We use overlap fermions as valence quarks to calculate meson masses in a wide quark mass range on the $2+1$-flavor domain-wall fermion gauge configurations generated by the RBC and UKQCD Collaborations. The well-defined quark masses in the overlap fermion formalism and the clear valence quark mass dependence of meson masses observed from the calculation facilitate a direct derivation of physical current quark masses through a global fit to the lattice data, which incorporates $O(a^2)$ and $O(m_c^4a^4)$ corrections, chiral extrapolation, and quark mass interpolation. Using the physical masses of $D_s$, $D_s^*$ and $J/psi$ as inputs, Sommers scale parameter $r_0$ and the masses of charm quark and strange quark in the $overline{rm MS}$ scheme are determined to be $r_0=0.465(4)(9)$ fm, $m_c^{overline{rm MS}}(2,{rm GeV})=1.118(6)(24)$ GeV (or $m_c^{overline{rm MS}}(m_c)=1.304(5)(20)$ GeV), and $m_s^{overline{rm MS}}(2,{rm GeV})=0.101(3)(6),{rm GeV}$, respectively. Furthermore, we observe that the mass difference of the vector meson and the pseudoscalar meson with the same valence quark content is proportional to the reciprocal of the square root of the valence quark masses. The hyperfine splitting of charmonium, $M_{J/psi}-M_{eta_c}$, is determined to be 119(2)(7) MeV, which is in good agreement with the experimental value. We also predict the decay constant of $D_s$ to be $f_{D_s}=254(2)(4)$ MeV. The masses of charmonium $P$-wave states $chi_{c0}, chi_{c1}$ and $h_c$ are also in good agreement with experiments.
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