Lutz, M. F. M.

Semke, A.

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Chiral extrapolations of baryon massesM.F.M. Lutz and A. Semke, GSI, Darmstadt, GermanyWe consider the chiral extrapolation of the baryonmasses to unphysical quark masses assuming exact isospinsymmetry. The dependence on the light quark massesmay be traded against a dependence on the pion and kaonmasses, where we assume a quark-mass dependence of themeson masses as predicted by χPT at the next-to-leadingorder with parameters as recalled in [2]. The ’physical’strange quark mass is determined such that at the physi-cal pion mass the empirical kaon mass is reproduced. Thebaryon masses are computed at N3LO where we use phys-ical baryon and meson masses in the one-loop contribu-tions to the baryon self energies and assume systematicallylarge-Nc sum rules for the parameter set. Our approach isdetailed in [1, 2]. Initially we adjusted the parameter set tothe physical masses of the baryon octet and decuplet statesand to the results for the pion-mass dependence of the nu-cleon and omega masses as predicted by the BMW group[2]. That initial parameter set was further slightly adjustedin [3] to achieve consistency with recent lattice results ofthe LHPC and PACS-CS groups. Insisting on a simulta-neous description of the BMW and PACS-CS data we un-ambiguously recover the unﬁtted results of the HSC andQCDSF-UKQCD groups with an amazing accuracy [4].We also explored the role of the axial coupling constants Fand D, which we found to be accurately determined froma simultaneous ﬁt of the lattice data [4]. In Fig. 1 we showthe baryon masses for our favored parameter set as a func-tion of the linear pion mass [3]. It is a striking phenomenathat for pion masses larger than 300 MeV there appears tobe an approximate linear dependence for all baryon masses.Note however, that given our approach the linear depen-dence is signiﬁcantly and systematically altered at smallerpion masses. Our results are confronted against the lat-tice data from the HSC groups (open circles), which pro-vide data for an almost physical strange quark mass. In or-der to provide a quantitative comparison, we compute thebaryon masses for the pion and kaon masses as predictedby the HSC group. The grey ﬁlled circles show our results.The distance of the ﬁlled circles to the solid lines measuresthe importance of taking the precise physical strange quarkmass in the computation of the baryon masses. In Fig. 1we also confront our approach with the simulation data ofthe PACS-CS (open squares) and QCDSF-UKQCD (opendiamonds) groups. Since the later groups use strange quarkmasses that are signiﬁcantly off the physical value, the datapoints are typically quite distant from the solid line. Againour results, green squares and red diamonds, are quite closeto their corresponding lattice points, open squares and dia-monds. Note that all lattice points are shown with statisti-cal errors only, where we assume the central values of thelattice spacing as provided by the various lattice groups.	        !  	      !!"  Figure 1: Baryon masses as a function of the pion mass asexplained in the text.References[1] A. Semke, M. F. M. Lutz, Baryon self energies in the chiralloop expansion, Nucl. Phys. A778 (2006) 153.[2] A. Semke, M. F. M. Lutz, Quark-mass dependence of thebaryon ground-state masses, Phys. Rev. D85 (2012) 034001.[3] A. Semke, M. F. M. Lutz, Strangeness in the baryon groundstates, Phys. Lett. B717 (2012) 242.[4] M. F. M. Lutz, A. Semke, On the consistency of recent QCDlattice data of the baryon ground-state masses, Phys. Rev.D86 (2012) 091502.PHN-HSD-THEORY-02 GSI SCIENTIFIC REPORT 201224

Chiral extrapolations of baryon masses

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Chiral extrapolations of baryon masses

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