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Register a new userMoments of nucleon isovector structure functions in $2+1+1$-flavor QCD
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We present results on the isovector momentum fraction, $langle x rangle_{u-d}$, helicity moment, $langle x rangle_{Delta u-Delta d}$, and the transversity moment, $langle x rangle_{delta u-delta d}$, of the nucleon obtained using nine ensembles of gauge configurations generated by the MILC collaboration using $2+1+1$-flavors of dynamical highly improved staggered quarks (HISQ). The correlation functions are calculated using the Wilson-Clover action and the renormalization of the three operators is carried out nonperturbatively on the lattice in the RI${}^prime$-MOM scheme. The data have been collected at lattice spacings $a approx 0.15, 0.12, 0.09,$ and 0.06 fm and $M_pi approx 310, 220$ and 135 MeV, which are used to obtain the physical values using a simultaneous chiral-continuum-finite-volume fit. The final results, in the $overline{MS}$ scheme at 2 GeV, are $langle x rangle_{u-d} = 0.173(14)(07)$, $langle x rangle_{Delta u-Delta d} = 0.213(15)(22)$ and $langle x rangle_{delta u-delta d} = 0.208(19)(24)$, where the first error is the overall analysis uncertainty and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with other recent lattice calculations and phenomenological global fit values.
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We present high-statistics results for the isovector and flavor diagonal charges of the proton using 11 ensembles of 2+1+1 flavor HISQ fermions. In the isospin symmetric limit, results for the neutron are given by the $u leftrightarrow d$ interchange. A chiral-continuum fit with leading order corrections was made to extract the connected and disconnected contributions in the continuum limit and at $M_pi=135$ MeV. All results are given in the $overline{MS}$ scheme at 2 GeV. The isovector charges, $g_A^{u-d} = 1.218(25)(30)$, $g_S^{u-d} = 1.022(80)(60) $ and $g_T^{u-d} = 0.989(32)(10)$, are used to obtain low-energy constraints on novel scalar and tensor interactions, $epsilon_{S}$ and $epsilon_{T}$, at the TeV scale. The flavor diagonal axial charges are: $g_A^u equiv Delta u equiv langle 1 rangle_{Delta u^+} = 0.777(25)(30)$, $g_A^d equiv Delta d equiv langle 1 rangle_{Delta d^+} = -0.438(18)(30)$, and $g_A^s equiv Delta s equiv langle 1 rangle_{Delta s^+} = -0.053(8)$. Their sum gives the total quark contribution to the proton spin, $sum_{q=u,d,s} (frac{1}{2} Delta q) = 0.143(31)(36)$. This result is in good agreement with the recent COMPASS analysis $0.13 < frac{1}{2} Delta Sigma < 0.18$. Implications of results for the flavor diagonal tensor charges, $g_T^u = 0.784(28)(10)$, $g_T^d = -0.204(11)(10)$ and $g_T^s = -0.0027(16)$ for constraining the quark electric dipole moments and their contributions to the neutron electric dipole moment are discussed. These flavor diagonal charges also give the strength of the interaction of dark matter with nucleons via axial and tensor mediators.
Nucleon-structure calculations of isovector vector- and axialvector-current form factors, transversity and scalar charge, and quark momentum and helicity fractions are reported from two recent 2+1-flavor dynamical domain-wall fermions lattice-QCD ensembles generated jointly by the RIKEN-BNL-Columbia and UKQCD Collaborations with Iwasaki $times$ dislocation-suppressing-determinatn-ratio gauge action at inverse lattice spacing of 1.378(7) GeV and pion mass values of 249.4(3) and 172.3(3) MeV.
We present results on the axial, scalar and tensor isovector-couplings of the nucleon from 2+1 flavor lattice QCD with physical light quarks ($m_pi$ = 135 MeV) in large spatial volume of (10.8 fm)$^3$. The calculations are carried out with the PACS10 gauge configurations generated by the PACS Collaboration with the stout-smeared $mathcal{O}(a)$ improved Wilson fermions and Iwasaki gauge action at $beta=1.82$ corresponding to the lattice spacing of 0.084 fm. For the renormalization, we use the RI/SMOM scheme, a variant of Rome-Southampton RI/MOM scheme with reduced systematic errors, as the intermediate scheme. We then evaluate our final results in the $overline{rm MS}$ scheme at a scale of 2 GeV, using the continuum perturbation theory for the matching scale of RI/SMOM and $overline{rm MS}$ schemes and running.
We report lattice-volume independence of low moments of nucleon structure functions from the coarse RIKEN-BNL-Columbia (RBC) and UKQCD joint dynamical (2+1)-flavor domain-wall fermions (DWF) ensembles at the lattice cut off of (a^{-1}sim1.7) GeV. The isovector quark momentum fraction, (< x >_{u-d}), and helicity fraction, (< x >_{Delta u - Delta d}), both fully non-perturbatively renormalized are studied on two spatial volumes of ((sim {rm 2.7 fm})^3) and ((sim {rm 1.8 fm})^3). Their naturally renormalized ratio, (< x >_{u-d}/< x >_{Delta u - Delta d}), is not affected by any finite-size effect. It does not depend strongly on light quark mass and does agree well with the experiment. The respective absolute values, fully non-perturbatively renormalized, do not show any finite-size effect either. They show trending toward the respective experimental values at the lightest up- and down-quark mass. This trending down to the experimental values appears to be a real physical effect driven by lighter quarks. The observations are in contrast to the huge finite-size effect seen in the axial-current form factors.
The current status of the LHP and RBC joint calculations of the nucleon isovector form factors and low moments of structure functions with a 2+1-flavor dynamical domain-wall fermion (DWF) lattice-QCD ensemble at the physical pion mass generated by RBC and UKQCD Collaborations with a momentum cutoff of 1.730(4) GeV and lattice spatial extent of 5.476(12) fm is reported. About ten percent of the statistics reported in Lattice 2014 were found with an incorrect boundary condition in time but correcting for it resulted in less than one-percent difference.
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