Pion and kaon $⟨x^3⟩$ from lattice QCD and PDF reconstruction from Mellin moments

Journal Article · Fri Sep 10 00:00:00 EDT 2021 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.104.054504· OSTI ID:1819467

Alexandrou, Constantia; Bacchio, Simone; Cloët, Ian; Constantinou, Martha ; Hadjiyiannakou, Kyriakos; Koutsou, Giannis; Lauer, Colin

We present a calculation of the pion and kaon Mellin moment < x³ > extracted directly in lattice QCD using a three-derivative local operator. We use one ensemble of gauge configurations with two degenerate light, a strange and a charm quark (N_f = 2 + 1 + 1) of maximally twisted mass fermions with clover improvement. The ensemble reproduces a pion mass ~260 MeV, and a kaon mass ~530 MeV. Excited-states contamination is evaluated using four values of the source-sink time separation within the range of 1.12–1.67 fm. We use an operator that is free of mixing, and apply a multiplicative renormalization function calculated nonperturbatively. Our results are converted to the MS¯ scheme and evolved at a scale of 2 GeV, using three-loop expressions in perturbation theory. The final values are < x³ >$$^{u+}_{π}$$ = 0.024(18)_stat(2)_syst, < x³ >$$^{u+}_{K}$$ = 0.035(6)_stat(3)_syst, and < x³ >$$^{s+}_{K}$$ = 0.075(5)_stat(1)_syst, where the systematic error is the uncertainty due to excited state contamination. We combine < x³ > with the two lower moments, namely < x > and < x² >, to obtain the ratios < x³ >/< x > and < x³ >/< x² >, as well as < x³ >$$^{u+}_{K}$$/< x³ >$$^{u+}_{π}$$ and < x³ >$$^{u+}_{K}$$/< x³ >$$^{u+}_{π}$$. In addition, we reconstruct the x-dependence of the pion and kaon PDFs via 2- and 3-parameter fits to our results. We find that the reconstruction is feasible and that our lattice data favor a large x-dependence that falls as (1–x)² for both the pion and kaon PDFs. We integrate the reconstructed PDFs to extract the higher moments with 4 ≤ n ≤ 6. Finally, we compare the pion and kaon PDFs, as well as the ratios of their moments, to address the effect of SU(3) flavor symmetry breaking.

• Research Organization: Argonne National Lab. (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Nuclear Physics (NP)
• Contributing Organization: ETM Collaboration
• Grant/Contract Number: SC0020405; AC02-06CH11357
• OSTI ID: 1819467
• Alternate ID(s): OSTI ID: 1828878
• Journal Information: Physical Review D, Journal Name: Physical Review D Vol. 104 Journal Issue: 5; ISSN 2470-0010
• Publisher: American Physical Society
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Lattice QCD