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Register a new userComplete flavor decomposition of the spin and momentum fraction of the proton using lattice QCD simulations at physical pion mass
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C. Alexandrou
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We evaluate the gluon and quark contributions to the spin of the proton using an ensemble of gauge configuration generated at physical pion mass. We compute all valence and sea quark contributions to high accuracy. We perform a non-perturbative renormalization for both quark and gluon matrix elements. We find that the contribution of the up, down, strange and charm quarks to the proton intrinsic spin is $frac{1}{2}sum_{q=u,d,s,c}DeltaSigma^{q^+}=0.191(15)$ and to the total spin $sum_{q=u,d,s,c}J^{q^+}=0.285(45)$. The gluon contribution to the spin is $J^g=0.187(46)$ yielding $J=J^q+J^g=0.473(71)$ confirming the spin sum. The momentum fraction carried by quarks in the proton is found to be $0.618(60)$ and by gluons $0.427(92)$, the sum of which gives $1.045(118)$ confirming the momentum sum rule. All scale and scheme dependent quantities are given in the $mathrm{ overline{MS}}$ scheme at 2 GeV.
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We determine within lattice QCD, the nucleon spin carried by valence and sea quarks, and gluons. The calculation is performed using an ensemble of gauge configurations with two degenerate light quarks with mass fixed to approximately reproduce the physical pion mass. We find that the total angular momentum carried by the quarks in the nucleon is $J_{u+d+s}{=}0.408(61)_{rm stat.}(48)_{rm syst.}$ and the gluon contribution is $J_g {=}0.133(11)_{rm stat.}(14)_{rm syst.}$ giving a total of $J_N{=}0.54(6)_{rm stat.}(5)_{rm syst.}$ consistent with the spin sum. For the quark intrinsic spin contribution we obtain $frac{1}{2}Delta Sigma_{u+d+s}{=}0.201(17)_{rm stat.}(5)_{rm syst.}$. All quantities are given in the $overline{textrm{MS}}$ scheme at 2~GeV. The quark and gluon momentum fractions are also computed and add up to $langle xrangle_{u+d+s}+langle xrangle_g{=}0.804(121)_{rm stat.}(95)_{rm syst.}+0.267(12)_{rm stat.}(10)_{rm syst.}{=}1.07(12)_{rm stat.}(10)_{rm syst.}$ satisfying the momentum sum.
We present the first nonperturbatively-renormalized determination of the glue momentum fraction $langle x rangle_g$ in the nucleon, based on lattice-QCD simulations at physical pion mass using the cluster-decomposition error reduction (CDER) technique. We provide the first practical strategy to renormalize the glue energy-momentum tensor (EMT) nonperturbatively in the RI/MOM scheme, and convert the results to the $overline{textrm{MS}}$ scheme with 1-loop matching. The simulation results show that the CDER technique can reduce the statistical uncertainty of its renormalization constant by a factor of ${cal O}$(300) in calculations using typical state-of-the-art lattice volume, and the nonperturbatively-renormalized $langle x rangle_g$ is shown to be independent of the lattice definitions of the glue EMT up to discretization errors. We determine the renormalized $langle x rangle_g^{overline{textrm{MS}}}(2textrm{ GeV})$ to be 0.47(4)(11) at physical pion mass, which is consistent with the experimentally-determined value.
We present results for the moments of nucleon isovector vector and axial generalised parton distribution functions computed within lattice QCD. Three ensembles of maximally twisted mass clover-improved fermions simulated with a physical value of the pion mass are analyzed. Two of these ensembles are generated using two degenerate light quarks. A third ensemble is used having, in addition to the light quarks, strange and charm quarks in the sea. A careful analysis of the convergence to the ground state is carried out that is shown to be essential for extracting the correct nucleon matrix elements. This allows a controlled determination of the unpolarised, helicity and tensor second Mellin moments. The vector and axial-vector generalised form factors are also computed as a function of the momentum transfer square up to about 1 GeV$^2$. The three ensembles allow us to check for unquenching effects and to assess lattice finite volume effects.
We present a state-of-the-art calculation of the isovector quark helicity Bjorken-$x$ distribution in the proton using lattice-QCD ensembles at the physical pion mass. We compute quasi-distributions at proton momenta $P_z in {2.2, 2.6, 3.0}$~GeV on the lattice, and match them systematically to the physical parton distribution using large-momentum effective theory (LaMET). We reach an unprecedented precision through high statistics in simulations, large-momentum proton matrix elements, and control of excited-state contamination. The resulting distribution with combined statistical and systematic errors is in agreement with the latest phenomenological analysis of the spin-dependent experimental data; in particular, $Delta bar{u}(x)>Delta bar{d}(x)$.
We present results on the nucleon scalar, axial and tensor charges as well as on the momentum fraction, and the helicity and transversity moments. The pion momentum fraction is also presented. The computation of these key observables is carried out using lattice QCD simulations at a physical value of the pion mass. The evaluation is based on gauge configurations generated with two degenerate sea quarks of twisted mass fermions with a clover term. We investigate excited states contributions with the nucleon quantum numbers by analyzing three sink-source time separations. We find that, for the scalar charge, excited states contribute significantly and to a less degree to the nucleon momentum fraction and helicity moment. Our analysis yields a value for the nucleon axial charge agrees with the experimental value and we predict a value of 1.027(62) in the $overline{text{MS}}$ scheme at 2 GeV for the isovector nucleon tensor charge directly at the physical point. The pion momentum fraction is found to be $langle xrangle_{u-d}^{pi^pm}=0.214(15)(^{+12}_{-9})$ in the $overline{rm MS}$ at 2 GeV.
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