JHEP11(2020)037
Published for SISSA by Springer
Received: September 29, 2020 Accepted: October 1, 2020 Published:November 10, 2020
Addendum: Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD
Gunnar S. Bali,
a,bVladimir M. Braun,
aSimon Bürger,
aMeinulf Göckeler,
aMichael Gruber,
aFabian Hutzler,
aPiotr Korcyl,
cAndreas Schäfer,
aAndré Sternbeck
dand Philipp Wein
aon behalf of the RQCD collaboration
aInstitut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany
bDepartment of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
cMarian Smoluchowski Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland
dTheoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany
E-mail: gunnar.bali@ur.de, vladimir.braun@ur.de, simon.buerger@ur.de, meinulf.goeckeler@ur.de, michael1.gruber@ur.de, fabian.hutzler@ur.de, piotr.korcyl@uj.edu.pl, andreas.schaefer@ur.de,
andre.sternbeck@uni-jena.de, philipp.wein@ur.de Addendum to: JHEP08(2019)065
Abstract: We update our lattice determination of the two lowest Gegenbauer moments of the leading-twist pion and kaon light-cone distribution amplitudes [1] using the recently calculated three-loop matching factors for the conversion from the RI
0/SMOM to the MS scheme [2, 3]. We find a
π2= 0.116
+19−20for the pion, a
K1= 0.0525
+31−33and a
K2= 0.106
+15−16for the kaon. Updated plots can be found in the appendix in the arXiv submission.
ArXiv ePrint: 1903.08038
We have rerun our analysis [1] using the newly available three-loop matching (N
3LO) for the conversion from the RI
0/SMOM to the MS scheme [2, 3]. The results can be taken from table 1, which is an updated version of table 3 in the main article [1]. As one can see, the errors of the renormalization procedure are reduced considerably. The new N
3LO results for a
π2and a
K2are slightly larger, but are still consistent with the previous NNLO result within errors. Considering the first moment of the kaon distribution amplitude, where we can compare results using RI
0/SMOM or RI
0/MOM as intermediate schemes, it
Open Access, cThe Authors.
Article funded by SCOAP3. https://doi.org/10.1007/JHEP11(2020)037
JHEP11(2020)037
M RI0 order hξ2iM aM2
π SMOM N3LO 0.240+6−6(2)r(3)a(2)m 0.116+16−17(4)r(9)a(5)m
π SMOM NNLO 0.234+6−6(4)r(4)a(2)m 0.101+17−17(12)r(10)a(5)m π SMOM NLO 0.227+6−6(5)r(5)a(2)m 0.078+18−19(16)r(13)a(5)m
K SMOM N3LO 0.236+3−4(1)r(3)a(1)m 0.106+10−12(4)r(9)a(4)m
K SMOM NNLO 0.231+4−4(4)r(4)a(1)m 0.090+10−12(11)r(11)a(4)m K SMOM NLO 0.223+4−5(5)r(5)a(2)m 0.067+11−13(16)r(14)a(5)m
η8 SMOM N3LO 0.235+3−4(1)r(3)a(1)m 0.103+10−13(4)r(9)a(4)m η8 SMOM NNLO 0.230+4−4(4)r(4)a(1)m 0.087+10−13(11)r(11)a(4)m
η8 SMOM NLO 0.222+4−5(6)r(5)a(2)m 0.063+11−14(16)r(14)a(5)m
M RI0 order hξ1iM aM1
K SMOM N3LO 0.0315+10−11(2)r(12)a(10)m 0.0525+17−19(3)r(20)a(17)m
K SMOM NNLO 0.0320+11−12(3)r(13)a(11)m 0.0533+18−19(6)r(22)a(18)m K SMOM NLO 0.0327+11−12(6)r(14)a(11)m 0.0545+18−20(9)r(23)a(18)m
K MOM N3LO 0.0315+11−11(1)r(11)a(10)m 0.0525+18−19(2)r(19)a(17)m
K MOM NNLO 0.0319+11−12(1)r(11)a(10)m 0.0531+18−19(2)r(18)a(17)m
Table 1. Continuum limit extrapolated values for the first two moments of the octet mesons. The results have been converted to the MS scheme at µ= 2 GeV using intermediate RI0 schemes and different loop orders in the perturbative matching. The statistical error given as sub- and superscript reflects the errors of the data after extrapolation. The numbers in parentheses give estimates of the systematic uncertainties due to the nonperturbative renormalization (r) as described in section 2.3 of ref. [1], the continuum extrapolation (a), and the chiral extrapolation (m). As discussed in section 3.1 of ref. [1], finite volume effects are negligible in our setting.
is encouraging to see that the final results in the MS scheme agree perfectly, if one uses three-loop matching in both cases.
Adding all errors in quadrature we obtain with three-loop matching
a
π2= 0.116
+19−20, a
K1= 0.0525
+31−33, a
K2= 0.106
+15−16.
We include updates of the figures of ref. [1], using the new, slightly shifted values as an appendix in the arXiv submission.
Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
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JHEP11(2020)037
References
[1] G.S. Bali et al.,Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD, JHEP 08(2019) 065[arXiv:1903.08038] [INSPIRE].
[2] B.A. Kniehl and O.L. Veretin,Bilinear quark operators in the RI/SMOM scheme at three loops,Phys. Lett. B804(2020) 135398 [arXiv:2002.10894] [INSPIRE].
[3] B.A. Kniehl and O.L. Veretin,MomentsN = 2 andN = 3of the Wilson twist-two operators at three loops in the RI0/SMOM scheme,arXiv:2009.11325[INSPIRE].
