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Register a new userCurrent Status toward the Proton Mass Calculation in Lattice QCD
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Authors
Yoshinobu Kuramashi
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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.
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We use the infinite volume reconstruction method to calculate the charged/neutral pion mass difference. The hadronic tensor is calculated on lattice QCD and then combined with an analytic photon propagator, and the mass splitting is calculated with exponentially-suppressed finite volume errors. The calculation is performed using six gauge ensembles generated with $2+1$-flavor domain wall fermions, and five ensembles are at the physical pion mass. Both Feynman and Coulomb gauge are adopted in the calculation and result in a good agreement when the lattice spacing approaches zero. After performing the continuum extrapolation and examining the residual finite-volume effects, we obtain the pion mass splitting $Delta m_pi = 4.534(42)(43)~mathrm{MeV}$, which agrees well with experimental measurements.
Lattice QCD calculations of hadron structure are a valuable complement to many experimental programs as well as an indispensable tool to understand the dynamics of QCD. I present a focused review of a few representative topics chosen to illustrate both the challenges and advances of our community: the momentum fraction, axial charge and charge radius of the nucleon. I will discuss the current status of these calculations and speculate on the prospects for accurate calculations of hadron structure from lattice QCD.
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.
This an English translation of a review of finite-density lattice QCD. The original version in Japanese appeared in Soryushiron Kenkyu Vol 31 (2020) No. 1.
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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