We compute the static-light baryon spectrum with N_f = 2 flavors of sea
quarks using Wilson twisted mass lattice QCD. As light valence quarks we
consider quarks, which have the same mass as the sea quarks with corresponding
pion masses in the range 340 MeV < m_PS < 525 MeV, as well as partially
quenched quarks, which have the mass of the physical s quark. We extract masses
of states with isospin I = 0, 1/2, 1, with strangeness S = 0, -1, -2, with
angular momentum of the light degrees of freedom j = 0, 1 and with parity P =
+, -. We present a preliminary extrapolation in the light u/d and an
interpolation in the heavy b quark mass to the physical point and compare with
available experimental results.Comment: 7 pages, 2 figures, talk given at the XXVIII International Symposium
  on Lattice Field Theory (Lattice 2010), June 14-19 2010, Villasimius, Ital

Wagner, Marc

Wiese, Christian

English

arXiv

We compute the static-light baryon spectrum with Nf = 2 flavors of sea quarks using Wilson twisted mass lattice QCD. As light valence quarks we consider quarks, which have the same mass as the sea quarks with corresponding pion masses in the range 340MeV<∼ mPS<∼ 525MeV, as well as partially quenched quarks, which have the mass of the physical s quark. We extract masses of states with isospin I = 0,1/2,1, with strangeness S = 0,−1,−2, with angular momentum of the light degrees of freedom j = 0,1 and with parity P = +,−. We present a preliminary extrapolation in the light u/d and an interpolation in the heavy b quark mass to the physical point and compare with available experimental results

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PoS(Lattice 2010)130The spectrum of static-light baryons in twistedmass lattice QCDMarc Wagner, Christian Wiese∗Humboldt-Universität zu Berlin, Institut für Physik, Newtonstraße 15, D-12489 Berlin, GermanyE-mail: mcwagner@physik.hu-berlin.deE-mail: wiese@physik.hu-berlin.deWe compute the static-light baryon spectrum with Nf = 2 ﬂavors of sea quarks using Wilsontwisted mass lattice QCD. As light valence quarks we consider quarks, which have the same massas the sea quarks with correspondingpion masses in the range 340MeV<∼mPS <∼525MeV, as wellas partially quenched quarks, which have the mass of the physical s quark. We extract massesof states with isospin I = 0,1/2,1, with strangeness S = 0,−1,−2, with angular momentumof the light degrees of freedom j = 0,1 and with parity P = +,−. We present a preliminaryextrapolation in the light u/d and an interpolation in the heavy b quark mass to the physical pointand compare with available experimental results.The XXVIII International Symposium on Lattice Field Theory, Lattice2010June 14-19, 2010Villasimius, Italy∗Speaker.c ￿ Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/PoS(Lattice 2010)130The spectrum of static-light baryons in twisted mass lattice QCD Christian Wiese1. IntroductionA systematic way to study bottom baryons from ﬁrst principles is lattice QCD. Since amb > 1for currently available lattice spacings for large volume simulations, one needs to use for the bquark a formalism such as Heavy Quark Effective Theory (HQET). In this paper we considerthe leading order of HQET, which is the static limit. The spectrum of static-light baryons hasbeen studied by lattice methods in the quenched approximation [1, 2, 3] and recently also withdynamical sea quarks [4, 5, 6]. Here we use Nf = 2 ﬂavors of dynamical Wilson twisted massquarks. Our intention is to explore the static-light baryon spectrum as fully as possible. Besides theexperimentally known states L0b, Sb/S∗b, X−b and W−b we also predict a number of not yet measuredstates, mainly of negative parity.2. Simulation setupWe use 243×48 gauge ﬁeld conﬁgurations generated by the European Twisted Mass Collab-oration (ETMC). The fermion action is Nf = 2 Wilson twisted mass [7, 8] tuned to maximal twist,where static-light mass differences are automatically O(a) improved [9]. The gauge action is tree-level Symanzik improved [10] with b = 3.9 corresponding to a lattice spacing a = 0.079(3)fm[11]. At the moment we have considered three different values of the twisted mass mq with corre-sponding pion masses listed in Table 1. For details regarding these gauge ﬁeld conﬁgurations werefer to [12, 13].In the valence sector we use light quarks, which have the same mass as the sea quarks (corre-sponding to u/d quarks), as well as partially quenched quarks with a mass mq,val = 0.0220, whichis around the mass of the physical s quark [14, 15].mq mPS in MeV number of gauge ﬁeld conﬁgurations0.0040 340(13) 2000.0064 423(16) 400.0100 525(20) 30Table 1: twisted masses mq, corresponding pion masses mPS and number of gauge ﬁeld conﬁgurationsconsidered.3. Static-light baryon creation operatorsTo create static-light baryons, we use operatorsOtwistedG = eabcQa￿(cb,(1))TCGtwistedcc,(2)￿, (3.1)where Q is a static quark operator and c(n) are light quark operators in the so-called twisted basis.The upper indices a, b and c are color indices, C =g0g2 is the charge conjugation matrix and Gtwistedis an appropriately chosen combination of g matrices.2PoS(Lattice 2010)130The spectrum of static-light baryons in twisted mass lattice QCD Christian WieseWhen discussing quantum numbers of static-light baryons, it is more convenient to ﬁrst trans-form the operators (3.1) into the physical basis, in which they have the same structure, i.e.OphysicalG = eabcQa￿(yb,(1))TCGphysicalyc,(2)￿. (3.2)In the continuum the relation between the physical and the twisted basis is given by the twistrotation y = exp(ig5t3w/2)c, where the twist angle w = p/2 at maximal twist. At ﬁnite latticespacing, however, issues are more complicated: the twist rotation only holds for renormalizedoperators and the QCDsymmetries isospin and parity are explicitely broken by O(a). Nevertheless,it is possible to unambiguously interpret states obtained from correlation functions of twisted basisoperators in terms of QCD quantum numbers. The method has successfully been applied in thecontext of static-light mesons [16] and is explained in detail for kaons and D mesons in [17]. Fordetails regarding its application to static-light baryons we refer to an upcoming publication [18].Since there are no interactions involving the static quark spin, it is appropriate to label static-light baryons by angular momentum j and parity P of the light degrees of freedom, which aredetermined by Gphysical. Consequently, j = 1 states correspond to degenerate pairs of states withtotal angular momentum J = 1/2 and J = 3/2 respectively.To access all possible isospin and strangeness combinations, we consider light quark ﬂavorsy(1)y(2) = ud −du (corresponding to I = 0, S = 0), y(1)y(2) ∈ {uu, dd, ud +du} (correspond-ing to I = 1, S = 0), y(1)y(2) ∈ {us, ds} (corresponding to I = 1/2, S = −1) and y(1)y(2) = ss(corresponding to I = 0, S = −2).The operators we have considered and their associated quantum numbers are collected in Ta-ble 2.Gphysical jP J I S name I S name I S nameg5 0+ 1/2 0 0 L0b 1/2 −1 X−b X X Xg0g5 0+ 1/2 0 0 L0b 1/2 −1 X−b X X X1 0− 1/2 0 0 − 1/2 −1 − X X Xg0 0− 1/2 1 0 − 1/2 −1 − 0 −2 −gj 1+ 1/2, 3/2 1 0 Sb, S∗b 1/2 −1 − 0 −2 W−bg0gj 1+ 1/2, 3/2 1 0 Sb, S∗b 1/2 −1 − 0 −2 W−bgjg5 1− 1/2, 3/2 0 0 − 1/2 −1 − X X Xg0gjg5 1− 1/2, 3/2 1 0 − 1/2 −1 − 0 −2 −Table 2: static-light baryon creation operators and their quantum numbers (jP: angular momentum andparity of the light degrees of freedom; J: total angular momentum; I: isospin; S: strangeness); operatorsmarked with “X” are identically zero, i.e. do not exist.4. Numerical resultsWe compute correlation matricesCGj,Gk(t) =  W|OtwistedGj (t)￿OtwistedGk (0)￿†|W . (4.1)3PoS(Lattice 2010)130The spectrum of static-light baryons in twisted mass lattice QCD Christian WieseWe use several techniques to improve the signal quality, including operator optimization by meansof APE and Gaussian smearing, the HYP2 static action and stochastic propagators combined withtimeslice dilution. These techniques are very similar to those used in a recent study of the static-light meson spectrum [9, 19] and will be explained in detail in [18].From the correlation matrices (4.1) we extract effective masses by solving a generalized eigen-value problem (cf. e.g. [20] and references therein). Mass values are obtained by ﬁtting constantsto effective mass plateaus at sufﬁciently large temporal separations. To exemplify the quality ofour results, we show effective masses and corresponding mass ﬁts for the L0b and the W−b baryon inFigure 1.00.10.20.30.40.50.60.70.80.90 2 4 6 8 10 12effectivemasstemporal separationm(L0b) = 0.5847±0.009900.10.20.30.40.50.60.70.80.90 2 4 6 8 10 12effectivemasstemporal separationm(W−b ) = 0.7478±0.0032Figure 1: effective masses and corresponding mass ﬁts; left: L0b at mq = 0.0040 from a 3×3 correlationmatrix; right: W−b at mq = 0.0040 from a 3×3 correlation matrix.Static-light baryon masses diverge in the continuum limit, because of the inﬁnite self energy ofthe static quark. Therefore, we consider mass differences to another static-light system, the lighteststatic-light meson (quantum numbers jP = (1/2)−, corresponding to the B and the B∗ meson,which are degenerate in the static limit). In such mass differences the self energies of the staticquarks exactly cancel.We use our results at three different light quark masses (cf. Table 1) by extrapolating massdifferences linearly in (mPS)2 to the physical u/d quark mass (mPS = 135MeV). Figure 2 (left)shows this extrapolation for the L0b, the Sb/S∗b and the W−b .Our results for the static-light baryon spectrum are collected in Table 3. In Wilson twistedmass lattice QCD isospin is explicitely broken by O(a). Therefore, states with I  = 0 and differentIz will have slightly different masses differing by O(a2). Because of this, in Table 3 two values arelisted for such states. Note, however, that within statistical errors there is no difference betweenany two such values, which is in agreement with the expectation that isospin breaking effects areO(a2) and, hence, should be rather small.5. Interpolation in the heavy quark mass and comparison to experimental dataTomake predictions regarding the spectrum of b baryons and to perform a meaningful compar-4PoS(Lattice 2010)130The spectrum of static-light baryons in twisted mass lattice QCD Christian Wiese020040060080010001352 3402 4232 5252m(baryon)−m(B)inMeV(mPS)2 in MeV2W−bSb / S∗bL0b 020040060080010000 0.35 1m(baryon)−m(B)inMeVmc/mQW−bSb / S∗bL0bexperimental resultsFigure 2: left: linear extrapolationof static-light mass differences in (mPS)2 to the physical u/d quark masscorresponding to mPS = 135MeV; right: linear interpolation between lattice static-light and correspondingexperimentalcharm-lightmassdifferencesinmc/mQ tothephysicalbquarkmasscorrespondingtomc/mb =0.35.jP I S name m(baryon)−m(B) in MeV0+ 0 0 L0b 434(46)1+ 1 0 Sb/S∗b 671(46)/632(39)0− 0 0 − 1389(113)1− 1 0 − 1008(92)/1014(79)0+ 1/2 −1 X−b 630(41)/677(36)1+ 1/2 −1 − 789(45)/798(49)0− 1/2 −1 − 1200(90)/1262(77)1− 1/2 −1 − 1233(58)/1285(69)1+ 0 −2 W−b 903(42)1− 0 −2 − 1315(79)Table 3: mass differences of static-light baryons and the lightest static-light meson extrapolated to thephysical u/d quark mass.ison with experimental data, we interpolate linearly mc/mQ, where mQ is the heavy quark mass, tothe physical point mc/mb ≈ m(D)/m(B) = 0.35. We do this by using our static-light lattice results(cf. Table 3) corresponding to mc/mQ = 0 and rather precise experimental data for correspondingcharm-light systems corresponding to mc/mQ = 1. In Figure 2 (right) we show the interpolationfor L0b, Sb/S∗b and W−b .In Table 4 we compare results of these interpolations with experimentally available data for bbaryons. Our lattice results are around 15% larger than the corresponding experimental results, atendency, which has already been observed in our recent study of the static-light meson spectrum5PoS(Lattice 2010)130The spectrum of static-light baryons in twisted mass lattice QCD Christian Wiese[9, 19]. In view of this discrepancy it is interesting to compare with results obtained by other latticegroups. When comparing mass differences in units of r0, i.e. dimensionless quantities, e.g. with [4],we ﬁnd agreement within statistical errors. Note, however, that the scale setting is rather different:r0 = 0.49fm in [4], while the corresponding ETMC value is r0 = 0.42fm.name m(baryon)−m(B) in MeV (lattice) m(baryon)−m(B) in MeV (experiment)L0b 429(30) 341(2) (from [21])Sb 629(28) 528(3) (from [21])S∗b 651(28) 550(3) (from [21])X−b 635(25) 513(3) (from [21])W−b 877(27) 775(7) (from [22])Table 4: lattice predictions versus experimental results for mass differences between various b baryons andthe B meson.For the negative parity states listed in Table 3 experimental results for b baryons do not exist.There are also no lattice predictions for these states we are aware of. However, one can comparewith phenomenological models, e.g. with [23], for which one ﬁnds qualitative agreement.6. ConclusionsWe have studied the static-light baryon spectrum by means of Nf = 2 Wilson twisted masslattice QCD. We have considered three different values of the dynamical quark mass correspondingto 340MeV<∼mPS <∼525MeV. We have performed an extrapolation in the light quark mass to thephysical u/d mass as well as an interpolation in the heavy quark mass to the physical b mass. Ourresults agree within around 15% with currently available experimental results for b baryons.Future plans regarding this project include increasing the statistical accuracy of our correlationmatrices to a level, where also excited states can reliably be extracted. Moreover, we intend toinvestigate the continuum limit, which amounts to considering other ﬁner values of the latticespacing. Finally we plan to perform similar computations on Nf = 2+1+1 ﬂavor gauge ﬁeldconﬁgurations currently produced by ETMC [24].AcknowledgmentsWeacknowledge useful discussions withJaume Carbonell, William Detmold, VladimirGalkin,Karl Jansen, Andreas Kronfeld, Chris Michael and Michael Müller-Preussker. This work hasbeen supported in part by the DFG Sonderforschungsbereich TR9 Computergestützte TheoretischeTeilchenphysik.References[1] A. K. 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The spectrum of static-light baryons in twisted mass lattice QCD

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