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The charge radius of the proton has been measured in scattering and spectroscopy experiments using both electronic and muonic probes. The electronic and muonic measurements are discrepant at $5sigma$, giving rise to what is known as the proton radius puzzle. With the goal of resolving this, we introduce a novel method of using lattice QCD to determine the isovector charge radius -- defined as the slope of the electric form factor at zero four-momentum transfer -- by introducing a mass splitting between the up and down quarks. This allows us to access timelike four-momentum transfers as well as spacelike ones, leading to potentially higher accuracy in determining the form factor slope at $Q^2 = 0$ by interpolation. In this preliminary study, we find a Dirac isovector radius squared of $0.320 pm 0.074$ fm$^2$ at quark masses corresponding to $m_pi = 450$ MeV. We compare the feasibility of this method with other approaches of determining the proton charge radius from lattice QCD.
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Protons and neutrons have a rich structure in terms of their constituents, the quarks and gluons. Understanding this structure requires solving Quantum Chromodynamics (QCD). However QCD is extremely complicated, so we must numerically solve the equations of QCD using a method known as lattice QCD. Here we describe a typical lattice QCD calculation by examining our recent computation of the nucleon axial charge.
The proton mass calculation is still a tough challenge for lattice QCD. We discuss the current status and difficulties based on the recent PACS-CS results for the hadron spectrum in 2+1 flavor QCD.
We report on a lattice QCD calculation of the nucleon axial charge, $g_A$, using M{o}bius Domain-Wall fermions solved on the dynamical $N_f=2+1+1$ HISQ ensembles after they are smeared using the gradient-flow algorithm. The calculation is performed with three pion masses, $m_pisim{310,220,130}$ MeV. Three lattice spacings ($asim{0.15,0.12,0.09}$ fm) are used with the heaviest pion mass, while the coarsest two spacings are used on the middle pion mass and only the coarsest spacing is used with the near physical pion mass. On the $m_pisim220$ MeV, $asim0.12$ fm point, a dedicated volume study is performed with $m_pi L sim {3.22,4.29,5.36}$. Using a new strategy motivated by the Feynman-Hellmann Theorem, we achieve a precise determination of $g_A$ with relatively low statistics, and demonstrable control over the excited state, continuum, infinite volume and chiral extrapolation systematic uncertainties, the latter of which remains the dominant uncertainty. Our final determination at 2.6% total uncertainty is $g_A = 1.278(21)(26)$, with the first uncertainty including statistical and systematic uncertainties from fitting and the second including model selection systematics related to the chiral and continuum extrapolation. The largest reduction of the second uncertainty will come from a greater number of pion mass points as well as more precise lattice QCD results near the physical pion mass.
We present a quenched lattice QCD calculation of the alpha and beta parameters of the proton decay matrix element. The simulation is carried out using the Wilson quark action at three values of the lattice spacing in the range aapprox 0.1-0.064 fm to study the scaling violation effect. We find only mild scaling violation when the lattice scale is determined by the nucleon mass. We obtain in the continuum limit, |alpha(NDR,2GeV)|=0.0090(09)(^{+5}_{-19})GeV^3 and |beta(NDR,2GeV)|=0.0096(09)(^{+6}_{-20})GeV^3 with alpha and beta in a relatively opposite sign, where the first error is statistical and the second is due to the uncertainty in the determination of the physical scale.
We present results for the isovector electromagnetic form factors of the nucleon computed on the CLS ensembles with $N_f=2+1$ flavors of $mathcal{O}(a)$-improved Wilson fermions and an $mathcal{O}(a)$-improved vector current. The analysis includes ensembles with four lattice spacings and pion masses ranging from 130 MeV up to 350 MeV and mainly targets the low-$Q^2$ region. In order to remove any bias from unsuppressed excited-state contributions, we investigate several source-sink separations between 1.0 fm and 1.5 fm and apply the summation method as well as explicit two-state fits. The chiral interpolation is performed by applying covariant chiral perturbation theory including vector mesons directly to our form factor data, thus avoiding an auxiliary parametrization of the $Q^2$ dependence. At the physical point, we obtain $mu=4.71(11)_{mathrm{stat}}(13)_{mathrm{sys}}$ for the nucleon isovector magnetic moment, in good agreement with the experimental value and $langle r_mathrm{M}^2rangle~=~0.661(30)_{mathrm{stat}}(11)_{mathrm{sys}},~mathrm{fm}^2$ for the corresponding square-radius, again in good agreement with the value inferred from the $ep$-scattering determination [Bernauer et~al., Phys. Rev. Lett., 105, 242001 (2010)] of the proton radius. Our estimate for the isovector electric charge radius, $langle r_mathrm{E}^2rangle = 0.800(25)_{mathrm{stat}}(22)_{mathrm{sys}},~mathrm{fm}^2$, however, is in slight tension with the larger value inferred from the aforementioned $ep$-scattering data, while being in agreement with the value derived from the 2018 CODATA average for the proton charge radius.
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