Moments of nucleon isovector structure functions in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>-flavor QCD
Santanu Mondal, Rajan Gupta, Sungwoo Park, Boram Yoon, Tanmoy Bhattacharya, Huey-Wen Lin
Abstract
We present results on the isovector momentum fraction, $⟨x{⟩}_{u\ensuremath{-}d}$, helicity moment, $⟨x{⟩}_{\mathrm{\ensuremath{\Delta}}u\ensuremath{-}\mathrm{\ensuremath{\Delta}}d}$, and the transversity moment, $⟨x{⟩}_{\ensuremath{\delta}u\ensuremath{-}\ensuremath{\delta}d}$, 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. 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 ${\mathrm{RI}}^{\ensuremath{'}}\text{\ensuremath{-}}\text{MOM}$ scheme. The data have been collected at lattice spacings $a\ensuremath{\approx}0.15$, 0.12, 0.09, and 0.06 fm and ${M}_{\ensuremath{\pi}}\ensuremath{\approx}310$, 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 $\overline{\mathrm{MS}}$ scheme at 2 GeV, are $⟨x{⟩}_{u\ensuremath{-}d}=0.173(14)(07)$, $⟨x{⟩}_{\mathrm{\ensuremath{\Delta}}u\ensuremath{-}\mathrm{\ensuremath{\Delta}}d}=0.213(15)(22)$, and $⟨x{⟩}_{\ensuremath{\delta}u\ensuremath{-}\ensuremath{\delta}d}=0.208(19)(24)$, 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.