Mellin moments $\langle x \rangle$ and $\langle x^2 \rangle$ for the pion and kaon from lattice QCD - INSPIRE

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Mellin moments $\langle x \rangle$ and $\langle x^2 \rangle$ for the pion and kaon from lattice QCD

ETM

Collaboration

•

Constantia Alexandrou
(
- Cyprus U. and
- Cyprus Inst.
)

Oct 7, 2020

17 pages

Published in:

Phys.Rev.D 103 (2021) 1, 014508

Published: Jan 13, 2021

e-Print:

2010.03495 [hep-lat]

DOI:

10.1103/PhysRevD.103.014508

View in:

ADS Abstract Service

reference search21 citations

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Abstract: (APS)

We present a calculation of the pion quark momentum fraction, ⟨x⟩, and its third Mellin moment ⟨x2⟩. We also obtain directly, for the first time, ⟨x⟩ and ⟨x2⟩ for the kaon using local operators. We use an ensemble of two degenerate light, a strange, and a charm quark (Nf=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-state contributions. The necessary renormalization functions are calculated nonperturbatively in the RI′ scheme and are converted to the modified minimal subtraction scheme at a scale of 2 GeV. The final values for the momentum fraction are ⟨x⟩u+π=0.261(3)stat(6)syst, ⟨x⟩u+K=0.246(2)stat(2)syst, and ⟨x⟩s+K=0.317(2)stat(1)syst. For the third Mellin moments, we find ⟨x2⟩u+π=0.082(21)stat(17)syst, ⟨x2⟩u+K=0.093(5)stat(3)syst, and ⟨x2⟩s+K=0.134(5)stat(2)syst. The reported systematic uncertainties are due to excited-state contamination. We also give the ratio ⟨x2⟩/⟨x⟩ which is an indication of how quickly the parton distribution functions lose support at large x.

Note:

21 pages, 10 figures

Lattice field theories, lattice QCD
quark: mass
pi: mass
K: mass
fermion: mass: twist
quark: momentum
excited state
lattice
lattice field theory
renormalization

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