Calculations of B leptonic decays and B- bar B mixing using NRQCD heavy and
Asqtad light valence quarks on the MILC dynamical configurations are described.
Smearing has been implemented to substantially reduce the statistical errors of
the matrix elements needed for the determination of f_B. The four-fermion
matrix elements needed for the determination of f_{B_s}^2B_{B_s} have been
calculated and a preliminary result is given.Comment: 3 pages, 3 figures, talk given at Lattice2004(heavy), Batavia,
  Illinois, 21-26 Jun 200

A. Gray

Bernard

C. Davies

Davies

E. Gulez

G.P. Lepage

Gulez

J. Shigemitsu

M. Wingate

Wingate

English

arXiv

Gray, A

Davies, C

Gulez, E

Lepage, GP

Shigemitsu, J

Wingate, M

Enlighten

B leptonic decays and B-(B)over-bar mixing with 2+1 flavors of dynamical quarks

Calculations of B leptonic decays and B- bar B mixing using NRQCD heavy and Asqtad light valence quarks on the MILC dynamical configurations are described. Smearing has been implemented to substantially reduce the statistical errors of the matrix elements needed for the determination of f_B. The four-fermion matrix elements needed for the determination of f_{B_s}^2B_{B_s} have been calculated and a preliminary result is given

Gray, A.

Davies, C.

Gulez, E.

P. Lepage, G.

Shigemitsu, J.

Wingate, M.

Edinburgh Research Explorer

     Edinburgh Research Explorer                                      B Leptonic Decays and B- bar B Mixing with 2+1 Flavors ofDynamical QuarksCitation for published version:Gray, A, Davies, C, Gulez, E, P. Lepage, G, Shigemitsu, J & Wingate, M 2004, 'B Leptonic Decays and B-bar B Mixing with 2+1 Flavors of Dynamical Quarks', Nuclear Physics B - Proceedings Supplements, vol.140, pp. 446–448. https://doi.org/10.1016/j.nuclphysbps.2004.11.317Digital Object Identifier (DOI):10.1016/j.nuclphysbps.2004.11.317Link:Link to publication record in Edinburgh Research ExplorerDocument Version:Early version, also known as pre-printPublished In:Nuclear Physics B - Proceedings SupplementsGeneral rightsCopyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s)and / or other copyright owners and it is a condition of accessing these publications that users recognise andabide by the legal requirements associated with these rights.Take down policyThe University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorercontent complies with UK legislation. If you believe that the public display of this file breaches copyright pleasecontact openaccess@ed.ac.uk providing details, and we will remove access to the work immediately andinvestigate your claim.Download date: 04. Jan. 2021arXiv:hep-lat/0409040v1  10 Sep 2004B Leptonic Decays and B − B̄ Mixing with 2+1 Flavors of DynamicalQuarksA. Graya, C. Daviesb, E. Guleza, G. P. Lepagec, J. Shigemitsua, M. WingatedaPhysics Department, The Ohio State University, Columbus, OH 43210, USA.bDepartment of Physics & Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK.cLaboratory of Elementary Particle Physics, Cornell University, Ithaca, NY 14853, USA.dInstitute for Nuclear Theory, University of Washington, Seattle, WA 98115, USA.Calculations of B leptonic decays and B − B̄ mixing using NRQCD heavy and Asqtad light valence quarks onthe MILC dynamical configurations are described. Smearing has been implemented to substantially reduce thestatistical errors of the matrix elements needed for the determination of fB . The four-fermion matrix elementsneeded for the determination of f2BsBBs have been calculated and a preliminary result is given.1. IntroductionB − B̄ mixing is a key process in standardCKM analysis. Calculations of the B(Bs) lep-tonic decay constant fB(fBs) and bag parame-ter BB(BBs) are needed to constrain Vtd(Vts).In particular, we aim to calculate the ratiofBs√BBs/fB√BB accurate to the few percentlevel allowing a determination of Vts/Vtd in whichtheoretical errors do not dominate those from ex-periment.The Asqtad improved staggered formulationhas allowed precise determinations of a varietyof quantities [1], and recent progress has allowedthe use of improved staggered valence quarks inheavy-light simulations [2]. Here we report onthe progress of B leptonic decay and mixing cal-culations using NRQCD heavy quarks and im-proved staggered (Asqtad) light quarks. We usethe MILC nf = 2 + 1 dynamical configurations[3].2. B leptonic decaysIn previous work [4] the chiral behavior offBs√mBs/fB√mB was masked by large statis-tical errors. Here these errors have been sub-stantially reduced with the introduction of smear-ing. Two dynamical ensembles were used; one in-corporating a light dynamical quark mass mf ≡mu,d = ms/4 while the other has mf = ms/2wherems is the physical strange quark mass. Thevalence light quark mass mq was varied from msto ms/8, i.e. some runs were in the partiallyquenched approximation. For b quarks, the stan-dard tadpole improved Lattice NRQCD actioncorrect through O(1/(amb)2) was used along withzeroth and first order in 1/amb currents. a−1 andmb were fixed by Υ while mu,d and ms were fixedby π and K respectively.A ground state hydrogenic style wavefuctionwas used to smear the heavy quark at both sourceand sink and the optimal radius was found as thatwhich minimized the fit errors while maintain-ing a reasonable χ2/dof. For each combination ofsource and sink smearing, the functional form ofthe kth order in 1/amb correlator is given by theoscillating functionG(t) =nexp−1∑j=0C(kj)(−1)jte−mjt. (1)Bayesian multi-exponential fits were done to thek = 0, 1 correlators, and Φ(k)B were determined asΦ(k)B =√2C(k0). (2)12fB correct through 1-loop is given throughΦB ≡ fB√mB = (1 + αsρ0)Φ(0)B+ (1 + αs(ρ1 + ρ2))Φ(1)B,sub (3)whereΦ(1)B,sub = Φ(1)B − αsζΦ(0)B (4)and the factors ρ0, ρ1, ρ2, ζ have been perturba-tively calculated [5].Figure 1 compares Φ(0)B values from singlecorrelator fits to simultaneous multi-correlationmatrix (smeared source and sink) and vector(smeared source only) fits. It can be seen thatthe errors are significantly reduced in the matrixcase.Figure 2 shows the effects of smearing onξΦ = ΦBs/ΦB. Note that the most chiral par-tially quenched non-smeared result incorporatesonly half the statistics of its smeared counter-part, while the statistics match in the other cases.Fully unquenched and partially quenched chi-ral extrapolations which incorporate staggeredtaste breaking effects [6] are underway to thenew smeared data, in addition to more fully un-quenched simulations at mq/ms = 1/8.3. B − B̄ Mixing3-point correlators were generated with the cre-ation of a B̄ at t = −tB̄, conversion to a B withthe use of a four-fermion operator O at t = 0and destruction of the B at t = tB. The samesimulation parameters as in the B leptonic decaycase were used but only so far with mf = 0.01,mq = 0.04 (i.e the Bs). No smearing has yet beenperformed, and so far only zeroth order in 1/ambcurrents have been considered.The continuum four fermion operator 〈OL〉MSis given in terms of lattice operators at 1-loop bya6〈OL〉MS = [1 + ρLL αs] 〈OL〉lat+ ρLS αs 〈OS〉lat (5)whereOL = [ ψ̄Q γµ(1 − γ5)ψq ] [ ψ̄Q̄ γµ(1 − γ5)ψq ]OS = [ ψ̄Q (1 − γ5)ψq ] [ ψ̄Q̄ (1 − γ5)ψq ] (6) 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3a3/2ΦB(0)no smearing matrix vectorsrc sm     sk smamq=amf=0.01Figure 1. Determinations of a3/2Φ(0)B using singlecorrelator (no smearing), matrix (source and sinksmearing) and vector (source or sink smearing)fits.and ρLL and ρLS have been calculated perturba-tively [5].The lattice correlators have the functional formC(tB , tB̄) =nexp−1∑j,k=0Ajk(−1)jtBe−mjtB∗ (−1)ktB̄e−mktB̄ . (7)A preliminary Bayesian fit has been successful fornexp = 4, as can be seen in Figure 3 which com-pares the data and fit function of the effectiveamplitude (correlator with ground energy contri-butions removed). The oscillations in both tB andtB̄ can clearly be seen to be nicely represented bythe fit function, and the fit has a good χ2/dof.Work is underway to obtain fits at other nexp inorder to solidify these results.〈OL,S〉lat are determined through12MBa3〈OL,S〉lat =A(OL,S)00ξBB(8)where ξBB = C(00); the 2-point ground stateleading order in 1/amb amplitude from the previ-ous section. Note that the fit is done directly tothe 3-point correlators without first taking the ra-tio over the 2-point. This means that fits at low t,3 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 0  0.2  0.4  0.6  0.8  1ξ Φmq/msFigure 2. ξΦ vs. ratio of light and strange va-lence quark masses. Closed symbols indicate thatsmearing has been used while open symbols indi-cate smearing has not been used. Squares repre-sent fully unquenched results and triangles repre-sent results in the partially quenched approxima-tion.where the correlator has good statistical noise, arepossible using multiple exponentials without theinefficiency and ambiguity of needing a plateau.BB is defined through〈OL〉MS =83f2BM2BBB (9)and our results preliminarily givefBs√BBs(mb) = 0.197(16)(28)GeV. (10)The first error arises from the fact that the fitsare still preliminary and the second error is fromsystematics, the main contributions being fromthe neglection of O(ΛQCD/mb) and O(α2s) con-tributions.4. ConclusionsWe report here on the status of B leptonic de-cays and B− B̄ mixing simulations with NRQCDheavy and Asqtad light quarks. The use of smear-ing has significantly reduced the statistical errorsfunctiondata 0  2  4  6  8  10  12  14  16tB  0  2 4  6 8  10 12 14 16tBbar 0 0.005 0.01C(tB,tBbar)eE0(tB+tBbar)Figure 3. Fit result to four-fermion correlatorwith ground state energy contributions removed.Squares show data points while lines show fitfunction.for the leptonic decay case. Chiral extrapola-tions and more fully unquenched simulations arein progress. A successful fit to the BB̄ correlatorhas allowed a preliminary result for fBs√BBs .5. AcknowledgmentsThis work was supported by the DOE, PPARCand NSF. Simulations were carried out atNERSC.REFERENCES1. MILC/HPQCD, C. T. H. Davies et al.,Phys. Rev. Lett. 92, 022001 (2004),[hep-lat/0304004].2. M. Wingate, J. Shigemitsu, C. T. H. Davies,G. P. Lepage and H. D. Trottier, Phys. Rev.D67, 054505 (2003), [hep-lat/0211014].3. C. W. Bernard et al., Phys. Rev. D64,054506 (2001), [hep-lat/0104002].4. M. Wingate et al., Nucl. Phys. Proc. Suppl.129, 325 (2004), [hep-lat/0309092].5. E. Gulez et al., these proceedings; E. Gulez,J. Shigemitsu, M. Wingate Phys. Rev. D69,074501 (2004), [hep-lat/0312017].6. C. Aubin and C. Bernard, these proceedingsand private communication.

B Leptonic Decays and B- bar B Mixing with 2+1 Flavors of Dynamical Quarks

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