Octet baryon masses and sigma terms in covariant baryon chiral perturbation theory
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International Journal of Modern Physics: Conference Seriesc (cid:13)
World Scientific Publishing Company
OCTET BARYON MASSES AND SIGMA TERMS IN COVARIANTBARYON CHIRAL PERTURBATION THEORY
XIU-LEI REN
School of Physics and Nuclear Energy Engineering and International Research Center forNuclei and Particles in the Cosmos, Beihang University, Beijing, 100191, [email protected]
LI-SHENG GENG
School of Physics and Nuclear Energy Engineering and International Research Center forNuclei and Particles in the Cosmos, Beihang University, Beijing, 100191, [email protected]
JIE MENG
School of Physics and Nuclear Energy Engineering and International Research Center forNuclei and Particles in the Cosmos, Beihang University, Beijing, 100191, ChinaState Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University,Beijing, 100871, ChinaDepartment of Physics, University of Stellenbosch, Stellenbosch, 7602, South [email protected]
Received Day Month YearRevised Day Month YearWe report an analysis of the octet baryon masses using the covariant baryon chiral per-turbation theory up to next-to-next-to-next-to-leading order with and without the virtualdecuplet contributions. Particular attention is paid to the finite-volume corrections andthe finite lattice spacing effects on the baryon masses. A reasonable description of allthe publicly available n f = 2 + 1 lattice QCD data is achieved. Utilyzing the Feynman-Hellmann theorem, we determine the nucleon sigma terms as σ πN = 55(1)(4) MeV and σ sN = 27(27)(4) MeV. Keywords : Chiral Lagrangians; Lattice QCD calculations; Baryon resonancesPACS numbers: 12.39.Fe, 12.38.Gc, 14.20.Gk
1. Introduction
Recently, the lowest-lying octet baryon masses have been studied on the lattice with n f = 2 + 1 configurations 1 , , , , , , , ,
9. Because the limitation of the computa-tional resources, most lattice quantum chromodynamics (LQCD) simulations stillhave to employ larger than physical light-quark masses, finite lattice volume andfinite lattice spacing. Chiral perturbation theory (ChPT) 10, as an effective fieldtheory of low-energy QCD, plays an important role in performing the multiple ex- une 27, 2018 18:54 WSPC/INSTRUCTION FILE EOMSmasses XIU-LEI REN et al. trapolations needed to extrapolate LQCD results (chiral extrapolations 11 , , , ,
16, and continuum extrapolations 17 ,
18) to thephysical world.In this work we report on the first systematic study of the ground-state octetbaryon masses in the covariant baryon chiral perturbation theory (BChPT) with theextended-on-mass-shell (EOMS) scheme up to next-to-next-to-next-to-leading order(N LO). The virtual decuplet contributions to the octet baryon masses and finitelattice volume and lattice spacing effects on the lattice data are studied. Finally,the octet baryon sigma terms are predicted using the Feynman-Hellmann theorem.
2. Theoretical Framework
Up to N LO, the octet baryon masses with the virtual decuplet contributions canbe written as m B = m + m (2) B + m (3) B + m (4) B + m ( D ) B , (1)where m is the chiral limit octet baryon mass, m (2) B , m (3) B , and m (4) B correspondto the O ( p ), O ( p ), and O ( p ) contributions from the octet-only EOMS BChPT,respectively. The last term m ( D ) B denotes the contributions of the virtual decupletresonances up to N LO. Their explicit expressions and the corresponding FVCs canbe found in Refs. 19 , ,
22. In Ref. 23, weconstructed the corresponding chiral Lagrangians up to O ( a ) to study the finitelattice spacing effects on the octet baryon masses, which can be written as m ( a ) B = m O ( a ) B + m O ( am q ) B + m O ( a ) B . (2)Here we want to mention that there are 19 unknown LECs ( m , b , b D , b F , b , ··· , , d , ··· , , , ) needed to be fixed in the EOMS BChPT at O ( p ). Furthermore,including the finite lattice spacing effects (Eq. (2)), one has to introduce 4 morecombinations of the unknown LECs 23.
3. Results and Discussions
The details of the studies can be found in Refs. 19 , , ,
24. Here we only brieflysummarize the main results.In order to determine all the LECs and test the consistency of the currentLQCD simulations, we perform a simultaneous fit to all the publicly available n f =2 + 1 LQCD data from the PACS-CS 3, LHPC 5, QCDSF-UKQCD 8, HSC 6,and NPLQCD 9 Collaborations. To ensure that the N LO BChPT stays in itsapplicability range, fitted LQCD data are limited to those satisfying M π < . and M φ L > ,
20, we found that the octet-only EOMS BChPT shows a good de-scription of the LQCD and experimental data with order-by-order improvement.une 27, 2018 18:54 WSPC/INSTRUCTION FILE EOMSmasses
OCTET BARYON MASSES ...... Up to N LO, the χ / d . o . f . is about 1 .
0, which indicates that the lattice simulationsfrom these five collaborations are consistent with each other a , although their setupsare very different. In addition, we showed that the explicit inclusion of the virtualdecuplet baryons does not change the description of the LQCD data in any signif-icant way, at least at O ( p ). This implies that using only the octet baryon massdata, one can not disentangle the virtual decuplet contributions from those of thevirtual octet baryons and tree-level diagrams. On the other hand, we notice that theexplicit inclusion of the virtual decuplet baryons does seem to improve slightly thedescription of the FVCs, especially for the LQCD data with small M φ L . Therefore,the virtual decuplet contributions to the octet baryon masses are not taken intoaccount in our following studies.To study discretization effects on the ground-state octet baryon masses, weconstructed the relevant chiral Lagrangians up to O ( a ) in Ref. 23. By analyzing thelatest n f = 2 + 1 O ( a )-improved LQCD data of the PACS-CS, QCDSF-UKQCD,HSC and NPLQCD Collaborations, we found that the finite lattice spacing effectsare at the order of 1 −
2% for lattice spacings up to 0 .
15 fm and the pion mass upto 500 MeV, which is in agreement with other LQCD studies.Finally, the octet baryon sigma terms are predicted using the Feynman-Hellmanntheorem. In order to obtain an accurate determination of sigma terms, a careful ex-amination of the LQCD data is essential, since not all of them are of the samequality though they are largely consistent with each other. In Ref. 24, we only em-ployed the PACS-CS, LHPC and QCDSF-UKQCD data. We also took into accountthe scale setting effects of the LQCD simulations and studied systematic uncer-tainties from truncating chiral expansions. Furthermore, strong-interaction isospinbreaking effects to the baryon masses were for the first time employed to betterconstrain the relevant LECs up to N LO. We predict the nucleon sigma terms as σ πN = 55(1)(4) MeV and σ sN = 27(27)(4) MeV, which are consistent with recentLQCD and BChPT studies.
4. Conclusions
We have studied the lowest-lying octet baryon masses in the EOMS BChPT up toN LO. The unknown low-energy constants are determined by a simultaneous fit tothe latest n f = 2 + 1 LQCD simulations, and it is shown that the LQCD results areconsistent with each other, though their setups are quite different. The contributionsof virtual decuplet resonances are explicitly included and we find that their effectson the octet baryon masses are small, especially for the chiral extrapolations.We have studied finite-volume corrections and finite lattice spacing effects onthe LQCD baryon masses as well. We find that their effects are of similar size butfinite volume corrections are more important to better constrain the LECs and to a This does not seem to be the case for the LQCD simulations of the ground-state decuplet baryonmasses 25. une 27, 2018 18:54 WSPC/INSTRUCTION FILE EOMSmasses XIU-LEI REN et al. reduce the χ / d . o . f . .Using the Feynman-Hellmann theorem, we have performed an accurate deter-mination of the nucleon sigma terms, focusing on the uncertainties from the latticescale setting method and chiral expansions. Our predictions are σ πN = 55(1)(4)MeV and σ sN = 27(27)(4) MeV, which are consistent with most of the recent LQCDand BChPT studies. However, further LQCD simulations are needed to reduce theuncertainty of the nucleon strangeness-sigma term. Acknowledgments
X.-L.R acknowledges the Innovation Foundation of Beihang University for Ph.D.Graduates. This work was partly supported by the National Natural Science Foun-dation of China under Grants No. 11005007, No. 11375024, and No. 11175002, andthe New Century Excellent Talents in University Program of Ministry of Educationof China under Grant No. NCET-10-0029, the Fundamental Research Funds for theCentral Universities, and the Research Fund for the Doctoral Program of HigherEducation under Grant No. 20110001110087.
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