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 uþdþs ¼ 0.408ð61Þ stat ð48Þ syst and the gluon contribution is J g ¼ 0.133ð11Þ stat ð14Þ syst , giving a total of J N ¼ 0.54ð6Þ stat ð5Þ syst that is consistent with the spin sum. For the quark intrinsic spin contribution, we obtain 1 2 ΔΣ uþdþs ¼ 0.201ð17Þ stat ð5Þ syst . All quantities are given in the modified minimal subtraction scheme at 2 GeV. The quark and gluon momentum fractions are also computed and add up to hxi uþdþs þ hxi g ¼ 0.804ð121Þ stat ð95Þ syst þ 0.267ð12Þ stat ð10Þ syst ¼ 1.07ð12Þ stat ð10Þ syst , thus satisfying the momentum sum. DOI: 10.1103/PhysRevLett.119.142002 Introduction.-The distribution of the proton spin among its constituent quarks and gluons has been a long-standing puzzle ever since the European Muon Collaboration showed in 1987 that only a fraction of the proton spin is carried by the quarks [1,2]. This was in sharp contrast to what one expected based on the quark model. This socalled proton spin crisis triggered rich experimental and theoretical activity. Recent experiments show that only 30% of the proton spin is carried by the quarks [3], while experiments at RHIC [4,5] on the determination of the gluon polarization in the proton point to a nonzero contribution [6]. A global fit to the most recent experimental data that includes the combined set of inclusive deep-inelastic scattering data from HERA and Drell-Yan data from Tevatron and LHC led to an improved determination of the valence quark distributions and the flavor separation of the up and down quarks [7]. The combined HERA data also provide improved constraints on the gluon distributions, but large uncertainties remain [7]. Obtaining the quark and gluon contributions to the nucleon spin and momentum fraction within lattice quantum chromodynamics (QCD) provides an independent input that is extremely crucial, but the computation is very challenging. This is because a complete determination must include, besides the valence, sea quark and gluon contributions that exhibit a large noise-to-signal ratio and are computationally very demanding. A first computation of the gluon spin was performed recently via the evaluation of the gluon helicity in a mixed action approach of overlap valence quarks on N f ¼ 2 þ 1 domain wall fermions that included an ensemble with pion mass 139 MeV [8]. In this Letter, we evaluate

The masses of the low lying baryons are evaluated using a total of ten ensembles of dynamical twisted mass fermion gauge configurations. The simulations are performed using two degenerate flavors of light quarks, and a strange and a charm quark fixed to approximately their physical values. The light sea quarks correspond to pseudo scalar masses in the range of about 210 MeV to 430 MeV. We use the Iwasaki improved gluonic action at three values of the coupling constant corresponding to lattice spacing a = 0.094 fm, 0.082 fm and 0.065 fm determined from the nucleon mass. We check for both finite volume and cut-off effects on the baryon masses. We examine the issue of isospin symmetry breaking for the octet and decuplet baryons and its dependence on the lattice spacing. We show that in the continuum limit isospin breaking is consistent with zero, as expected. We performed a chiral extrapolation of the forty baryon masses using SU(2) χPT. After taking the continuum limit and extrapolating to the physical pion mass our results are in good agreement with experiment. We provide predictions for the mass of the doubly charmed Ξ * cc , as well as of the doubly and triply charmed Ωs that have not yet been determined experimentally.

We present results on the axial and the electromagnetic form factors of the nucleon, as well as, on the first moments of the nucleon generalized parton distributions using maximally twisted mass fermions. We analyze two N f =2+1+1 ensembles having pion masses of 213 MeV and 373 MeV each at a different value of the lattice spacing. The lattice scale is determined using the nucleon mass computed on a total of 17 N f =2+1+1 ensembles generated at three values of the lattice spacing, a. The renormalization constants are evaluated non-perturbatively with a perturbative subtraction of O(a 2 )-terms. The moments of the generalized parton distributions are given in the MS scheme at a scale of µ = 2 GeV. We compare with recent results obtained using different discretization schemes. The implications on the spin content of the nucleon are also discussed.

No abstract