The Mellin moments $⟨x⟩$ and $⟨x^2⟩$ for the pion and kaon from lattice QCD

Abstract

We present a calculation of the pion quark momentum fraction, $⟨x⟩$, and its third Mellin moment $⟨x^2⟩$. We also obtain directly, for the first time, $⟨x⟩$ and $⟨x^2⟩$ for the kaon using local operators. We use an ensemble of two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with clover improvement. The quark masses are chosen so that they reproduce a pion mass of about 260 MeV, and a kaon mass of 530 MeV. The lattice spacing of the ensemble is 0.093 fm and the lattice has a spatial extent of 3 fm. We analyze several values of the source-sink time separation within the range of $1.12-2.23$ fm to study and eliminate excited-states contributions. The necessary renormalization functions are calculated non-perturbatively in the RI${}^{\prime }$ scheme, and are converted to the $\overline{\mathrm{MS}}$ scheme at a scale of 2 GeV. The final values for the momentum fraction are $⟨x{⟩}_{u^{+}}^{\pi }=0.261(3{)}_{\mathrm{stat}}(6{)}_{\mathrm{syst}}$, $⟨x{⟩}_{u^{+}}^K=0.246(2{)}_{\mathrm{stat}}(2{)}_{\mathrm{syst}}$, and $⟨x{⟩}_{s^{+}}^K=0.317(2{)}_{\mathrm{stat}}(1{)}_{\mathrm{syst}}$. For the third Mellin moments we find $⟨x^2{⟩}_{u^{+}}^{\pi }=0.082(21{)}_{\mathrm{stat}}(17{)}_{\mathrm{syst}}$, $⟨x^2{⟩}_{u^{+}}^K=0.093(5{)}_{\mathrm{stat}}(3{)}_{\mathrm{syst}}$, and $⟨x^2{⟩}_{s^{+}}^K=0.134(5{)}_{\mathrm{stat}}(2{)}_{\mathrm{syst}}$. The reported systematic uncertainties are due to excited-state contamination. We also give the ratio $⟨x^2⟩/⟨x⟩$ which is an indication of how quickly the PDFs lose support at large $x$.

21 pages, 10 figures

References in corpus (15)

• Exploring hadrons' partonic structure using ab initio lattice QCD calculations
• Exclusive processes in position space and the pion distribution amplitude
• Pion Valence Quark Distribution from Matrix Element Calculated in Lattice QCD
• Nonperturbative Evolution of Parton Quasi-Distributions
• Valence parton distribution of pion from lattice QCD: Approaching continuum
• Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to Neural Networks
• Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point
• The pion form factor from lattice QCD with two dynamical flavours
• Parton Distribution Functions from Ioffe Time Pseudodistributions from Lattice Calculations: Approaching the Physical Point
• Renormalization constants for 2-twist operators in twisted mass QCD
• New insights on proton structure from lattice QCD: the twist-3 parton distribution function $g_T(x)$
• Light Meson Form Factors at near Physical Masses
• Renormalization of local quark-bilinear operators for Nf=3 flavors of SLiNC fermions
• QCD Factorization and PDFs from Lattice QCD Calculation
• Dressed Quark Mass Dependence of Pion and Kaon Form Factors

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