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Register a new userA percent-level determination of the nucleon axial coupling from Quantum Chromodynamics
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The $textit{axial coupling of the nucleon}$, $g_A$, is the strength of its coupling to the $textit{weak}$ axial current of the Standard Model of particle physics, in much the same way as the electric charge is the strength of the coupling to the electromagnetic current. This axial coupling dictates the rate at which neutrons decay to protons, the strength of the attractive long-range force between nucleons and other features of nuclear physics. Precision tests of the Standard Model in nuclear environments require a quantitative understanding of nuclear physics rooted in Quantum Chromodynamics, a pillar of the Standard Model. The prominence of $g_A$ makes it a benchmark quantity to determine theoretically - a difficult task because quantum chromodynamics is non-perturbative, precluding known analytical methods. Lattice Quantum Chromodynamics provides a rigorous, non-perturbative definition of quantum chromodynamics that can be implemented numerically. It has been estimated that a precision of two percent would be possible by 2020 if two challenges are overcome: contamination of $g_A$ from excited states must be controlled in the calculations and statistical precision must be improved markedly. Here we report a calculation of $g_A^{QCD} = 1.271pm0.013$, using an unconventional method inspired by the Feynman-Hellmann theorem that overcomes these challenges.
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In this study, we present a determination of the unpolarized gluon Ioffe-time distribution in the nucleon from a first principles lattice quantum chromodynamics calculation. We carry out the lattice calculation on a $32^3times 64$ ensemble with a pion mass of $358$ MeV and lattice spacing of $0.094$ fm. We construct the nucleon interpolating fields using the distillation technique, flow the gauge fields using the gradient flow, and solve the summed generalized eigenvalue problem to determine the glounic matrix elements. Combining these techniques allows us to provide a statistically well-controlled Ioffe-time distribution and unpolarized gluon PDF. We obtain the flow time independent reduced Ioffe-time pseudo-distribution, and calculate the light-cone Ioffe-time distribution and unpolarized gluon distribution function in the $overline{rm MS}$ scheme at $mu = 2$ GeV, neglecting the mixing of the gluon operator with the quark singlet sector. Finally, we compare our results to phenomenological determinations.
We present state-of-the-art results from a lattice QCD calculation of the nucleon axial coupling, $g_A$, using Mobius Domain-Wall fermions solved on the dynamical $N_f = 2 + 1 + 1$ HISQ ensembles after they are smeared using the gradient-flow algorithm. Relevant three-point correlation functions are calculated using a method inspired by the Feynman-Hellmann theorem, and demonstrate significant improvement in signal for fixed stochastic samples. The calculation is performed at five pion masses of $m_pisim {400, 350, 310, 220, 130}$~MeV, three lattice spacings of $asim{0.15, 0.12, 0.09}$~fm, and we do a dedicated volume study with $m_pi Lsim{3.22, 4.29, 5.36}$. Control over all relevant sources of systematic uncertainty are demonstrated and quantified. We achieve a preliminary value of $g_A = 1.285(17)$, with a relative uncertainty of 1.33%.
The low-energy neutron-Sigma^- interactions determine, in part, the role of the strange quark in dense matter, such as that found in astrophysical environments. The scattering phase shifts for this system are obtained from a numerical evaluation of the QCD path integral using the technique of Lattice QCD. Our calculations, performed at a pion mass of m_pi ~ 389 MeV in two large lattice volumes, and at one lattice spacing, are extrapolated to the physical pion mass using effective field theory. The interactions determined from QCD are consistent with those extracted from hyperon-nucleon experimental data within uncertainties, and strengthen theoretical arguments that the strange quark is a crucial component of dense nuclear matter.
We present a new analysis method that allows one to understand and model excited state contributions in observables that are dominated by a pion pole. We apply this method to extract axial and (induced) pseudoscalar nucleon isovector form factors, which satisfy the constraints due to the partial conservation of the axial current up to expected discretization effects. Effective field theory predicts that the leading contribution to the (induced) pseudoscalar form factor originates from an exchange of a virtual pion, and thus exhibits pion pole dominance. Using our new method, we can recover this behavior directly from lattice data. The numerical analysis is based on a large set of ensembles generated by the CLS effort, including physical pion masses, large volumes (with up to $96^3 times 192$ sites and $L m_pi = 6.4$), and lattice spacings down to $0.039 , text{fm}$, which allows us to take all the relevant limits. We find that some observables are much more sensitive to the choice of parametrization of the form factors than others. On the one hand, the $z$-expansion leads to significantly smaller values for the axial dipole mass than the dipole ansatz ($M_A^{text{$z$-exp}}=1.02(10) , text{GeV}$ versus $M_A^{text{dipole}} = 1.31(8) , text{GeV}$). On the other hand, we find that the result for the induced pseudoscalar coupling at the muon capture point is almost independent of the choice of parametrization ($g_P^{star text{$z$-exp}} = 8.68(45)$ and $g_P^{star text{dipole}} = 8.30(24)$), and is in good agreement with both, chiral perturbation theory predictions and experimental measurement via ordinary muon capture. We also determine the axial coupling constant $g_A$.
We determine the nucleon axial, scalar and tensor charges within lattice Quantum Chromodynamics including all contributions from valence and sea quarks. We analyze three gauge ensembles simulated within the twisted mass formulation at approximately physical value of the pion mass. Two of these ensembles are simulated with two dynamical light quarks and lattice spacing $a=0.094$~fm and the third with $a=0.08$~fm includes in addition the strange and charm quarks in the sea. After comparing the results among these three ensembles, we quote as final values our most accurate analysis using the latter ensemble. For the nucleon isovector axial charge we find $1.286(23)$ in agreement with the experimental value. We provide the flavor decomposition of the intrinsic spin $frac{1}{2}DeltaSigma^q$ carried by quarks in the nucleon obtaining for the up, down, strange and charm quarks $frac{1}{2}DeltaSigma^{u}=0.431(8)$, $frac{1}{2}DeltaSigma^{d}=-0.212(8)$, $frac{1}{2}DeltaSigma^{s}=-0.023(4)$ and $frac{1}{2}DeltaSigma^{c}=-0.005(2)$, respectively. The corresponding values of the tensor and scalar charges for each quark flavor are also evaluated providing valuable input for experimental searches for beyond the standard model physics. In addition, we extract the nucleon $sigma$-terms and find for the light quark content $sigma_{pi N}=41.6(3.8)$~MeV and for the strange $sigma_{s}=45.6(6.2)$~MeV. The y-parameter that is used in phenomenological studies we find $y=0.078(7)$.
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