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Register a new userFlavor decomposition of the nucleon unpolarized, helicity and transversity parton distribution functions from lattice QCD simulations
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Constantia Alexandrou
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We present results on the quark unpolarized, helicity and transversity parton distributions functions of the nucleon. We use the quasi-parton distribution approach within the lattice QCD framework and perform the computation using an ensemble of twisted mass fermions with the strange and charm quark masses tuned to approximately their physical values and light quark masses giving pion mass of 260 MeV. We use hierarchical probing to evaluate the disconnected quark loops. We discuss identification of ground state dominance, the Fourier transform procedure and convergence with the momentum boost. We find non-zero results for the disconnected isoscalar and strange quark distributions. The determination of the quark parton distribution and in particular the strange quark contributions that are poorly known provide valuable input to the structure of the nucleon.
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We present, for the first time, an textit{ab initio} calculation of the individual up, down and strange quark helicity parton distribution functions for the proton. The calculation is performed within the twisted mass clover-improved fermion formulation of lattice QCD using one ensemble of dynamical up, down, strange and charm quarks with a pion mass of 260 MeV. The lattice matrix elements are non-perturbatively renormalized and the final results are presented in the $overline{ rm MS}$ scheme at a scale of 2 GeV. We give results on the $Delta u^+(x)$ and $Delta d^+(x)$, including disconnected quark loop contributions, as well as on the $Delta s^+(x)$. For the latter we achieve unprecedented precision compared to the phenomenological estimates.
We present the first direct calculation of the transversity parton distribution function within the nucleon from lattice QCD. The calculation is performed using simulations with the light quark mass fixed to its physical value and at one value of the lattice spacing. Novel elements of the calculations are non-perturbative renormalization and extraction of a formula for the matching to light-cone PDFs. Final results are presented in the $overline{rm MS}$ scheme at a scale of $sqrt{2}$ GeV.
We present the first lattice-QCD calculation of the nucleon isovector unpolarized parton distribution functions (PDFs) at the physical-continuum limit using Large-Momentum Effective Theory (LaMET). The lattice results are calculated using ensembles with multiple sea pion masses with the lightest one around 135~MeV, 3 lattice spacings $ain[0.06,0.12]$~fm, and multiple volumes with $M_pi L$ ranging 3.3 to 5.5. We perform a simultaneous chiral-continuum extrapolation to obtain RI/MOM renormalized nucleon matrix elements with various Wilson-link displacements in the continuum limit at physical pion mass. Then, we apply one-loop perturbative matching to the quasi-PDFs to obtain the lightcone PDFs. We find the lattice-spacing dependence to be much larger than the dependence on pion mass and lattice volume for these LaMET matrix elements. Our physical-continuum limit unpolarized isovector nucleon PDFs are found to be consistent with global-PDF results.
High statistics results for the isovector momentum fraction, $langle x rangle_{u-d}$, helicity moment, $langle x rangle_{Delta u-Delta d}$, and the transversity moment, $langle xrangle_{delta u-delta d}$, of the nucleon are presented using seven ensembles of gauge configurations generated by the JLab/W&M/LANL/MIT collaborations using $2+1$-flavors of dynamical Wilson-clover quarks. Attention is given to understanding and controlling the contributions of excited states. The final results are obtained using a simultaneous fit in the lattice spacing $a$, pion mass $M_pi$ and the finite volume parameter $M_pi L$ keeping leading order corrections. The data show no significant dependence on the lattice spacing and some evidence for finite-volume corrections. The main variation is with $M_pi$, whose magnitude depends on the mass gap of the first excited state used in the analysis. Our final results, in the $overline{rm MS}$ scheme at 2 GeV, are $langle x rangle_{u-d} = 0.160(16)(20)$, $langle x rangle_{Delta u-Delta d} = 0.192(13)(20)$ and $langle x rangle_{delta u-delta d} = 0.215(17)(20)$, where the first error is the overall analysis uncertainty assuming excited-state contributions have been removed, 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.
We report a state-of-the-art lattice calculation of the isovector quark transversity distribution of the proton at the physical pion mass. Within the framework of large-momentum effective theory (LaMET), we compute the transversity quasi-distributions using clover valence fermions on 2+1+1-flavor (up/down, strange, charm) HISQ-lattice configurations with boosted proton momenta as large as 3.0~GeV. The relevant lattice matrix elements are nonperturbatively renormalized in regularization-independent momentum-subtraction (RI/MOM) scheme and systematically matched to the physical transversity distribution. With high statistics, large proton momenta and meticulous control of excited-state contamination, we provide the best theoretical prediction for the large-$x$ isovector quark transversity distribution, with better precision than the most recent global analyses of experimental data. Our result also shows that the sea quark asymmetry in the proton transversity distribution is consistent with zero, which has been assumed in all current global analyses.
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