We report on exploratory studies of heavy-light meson semileptonic decays
using Asqtad light quarks, NRQCD heavy quarks and Symanzik improved glue on
coarse quenched lattices. Oscillatory contributions to three-point correlators
coming from the staggered light quarks are found to be handled well by Bayesian
fitting methods. B meson decays to both the Goldstone pion and to one of the
point-split non-Goldstone pions are investigated. One-loop perturbative
matching of NRQCD/Asqtad heavy-light currents is incorporated.Comment: 3 pages, 3 postscript figures, Lattice2003(heavy

Davies, C. T. H.

Gray, A.

Gulez, E.

Lepage, G. P.

Shigemitsu, J.

Wingate, M.

English

arXiv

We report on exploratory studies of heavy-light meson semileptonic decays using AsqTad light quarks, NRQCD heavy quarks and Symanzik improved glue on coarse quenched lattices. Oscillatory contributions to three-point correlators coming from the staggered light quarks are found to be handled well by Bayesian fitting methods. B meson decays to both the Goldstone pion and to one of the point-split non-Goldstone pions are investigated. One-loop perturbative matching of NRQCD/AsqTad heavy-light currents is incorporated

Davies, C.T.H.

Lepage, G.P.

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Heavy-light meson semileptonic decays with staggered light quarks

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We report on exploratory studies of heavy-light meson semileptonic decays using Asqtad light quarks, NRQCD heavy quarks and Symanzik improved glue on coarse quenched lattices. Oscillatory contributions to three-point correlators coming from the staggered light quarks are found to be handled well by Bayesian fitting methods. B meson decays to both the Goldstone pion and to one of the point-split non-Goldstone pions are investigated. One-loop perturbative matching of NRQCD/Asqtad heavy-light currents is incorporated

T. H. Davies, C.

P. Lepage, G.

Edinburgh Research Explorer

     Edinburgh Research Explorer                                      Heavy-Light Meson Semileptonic Decays with Staggered LightQuarksCitation for published version:Shigemitsu, J, T. H. Davies, C, Gray, A, Gulez, E, P. Lepage, G & Wingate, M 2003, 'Heavy-Light MesonSemileptonic Decays with Staggered Light Quarks', Nuclear Physics B - Proceedings Supplements, vol.129-130, pp. 331–333. https://doi.org/10.1016/S0920-5632(03)02572-6Digital Object Identifier (DOI):10.1016/S0920-5632(03)02572-6Link: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: 23. Oct. 2019arXiv:hep-lat/0309039v1  10 Sep 20031Heavy-Light Meson Semileptonic Decays with Staggered Light QuarksJ.Shigemitsua, C.T.H.Daviesb, A.Grayb, E.Guleza, G.P.Lepagec, M.WingateaaPhysics 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.We report on exploratory studies of heavy-light meson semileptonic decays using AsqTad light quarks, NRQCDheavy quarks and Symanzik improved glue on coarse quenched lattices. Oscillatory contributions to three-pointcorrelators coming from the staggered light quarks are found to be handled well by Bayesian fitting methods.B meson decays to both the Goldstone pion and to one of the point-split non-Goldstone pions are investigated.One-loop perturbative matching of NRQCD/AsqTad heavy-light currents is incorporated.1. IntroductionA major systematic error in many studies ofheavy-light meson decays has been the uncer-tainty due to chiral extrapolations in the lightvalence and light dynamical quark masses. Thesechiral extrapolation errors can be reduced sig-nificantly by working with light quark actionsthat have good chiral properties and this hasmotivated us to initiate a program to studyheavy-light physics using improved staggered (orequivalently improved naive) light quarks coupledwith NRQCD heavy quarks [1]. Our first re-sults on B and D meson decay constants on theMILC dynamical configurations were presentedby M.Wingate at this conference [2]. Here wediscuss initial semileptonic decay results.Our semileptonic studies are at a much morepreliminary stage compared to the decay con-stant calculations. We report on quenched sim-ulations with light quark mass around mstrangeand the heavy quark mass around the b-quarkmass. We employ the Asqtad light quark ac-tion, the O(1/M) and O(a2) improved NRQCDheavy quark action and the tree-level Symanzikimproved glue action. We work with 200 123×32quenched configurations with a−1 ≈ 1.0 GeV.2. Fitting Oscillatory Three-point Corre-latorsTwo- and three-point correlators involvingnaive or staggered propagators have contributionsthat oscillate with time and this makes it morechallenging to carry out fits and extract ground-state contributions. Experience gained recentlywith NRQCD/staggered heavy-light two-pointcorrelators have demonstrated the usefulness ofBayesian fitting methods [1,3]. Hence, much ofthe effort in this exploratory study of semilep-tonic decays has focused on testing Bayesian fitsto oscillatory three-point correlators. The basiccorrelator of interest is,C(3)(~pπ, ~pB, t, TB) =∑~z∑~y〈 Φπ(0)Jµ(~z, t)Φ†B(~y, TB) 〉× ei~pB·~y ei(~ppi−~pB)·~z (1)In the present simulations the B meson decaysat rest (~pB = 0) and calculations have been per-formed with TB = 12 and TB = 16. The locationof the current insertion t was varied between 1and TB. The three-point correlator is fit to theform,2C(3)(~pπ, ~pB, t, TB)→Npi−1∑k=0NB−1∑j=0(−1)k∗(t−1) (−1)j∗(TB−t)×Aj,k e−E(k)pi (t−1) e−E(j)B(TB−t) (2)In this ansatz every second exponential comeswith an oscillatory amplitude in both the pionand the B channels, We were able to get goodfits with Nπ = 1 or 2 and NB = 3 to 8. Fur-thermore we found it useful to do simultane-ous fits to C(3) and to the B meson two-pointcorrelator. Fits were done to all data betweent = 2 and t = TB − 1, i.e. to all but thefirst and the last timeslices, those timeslices onwhich the pion and the B meson respectively werecreated. Figs. 1 & 2 give examples of fits to ma-trix elements of the temporal (V0) component ofthe heavy-light vector current. The plots show,C(3)(~pπ, t, TB) eE(0)pi (t−1) eE(0)B(TB−t). By factor-ing out the groundstate contributions, the op-posite parity oscillatory terms and other excitedstate contributions show up more clearly. Despitethe presence of these excitations, the Bayesian fit-ting methods allow us to extract the groundstateamplitude of interest, A00 in eq.(2).The two figures are for the cases when thepion has momentum (0, 1, 1) in units of 2π/(aL).Good χ2/dof were found with Nπ = 1 andNB = 6. The difference between the TB = 12and TB = 16 results is typical for all matrix el-ements. With TB = 12, statistical errors are re-duced and more accurate fits can be made. Onthe other hand, with TB = 16 a hint of a plateaucan be observed (which will likely disappear withhigher statistics and a more expanded verticalscale). Since with multi-exponential Bayesian fitsthe presence of a plateau is not required, one isbetter off with the more accurate TB = 12 data.Nevertheless, working with two different TB val-ues provides a good consistency check, which weexploit in the next section.Figure 1. Fit results for the groundstate am-plitude A00 from the 〈V0〉 three-point correla-tor with TB = 12. The pion momentum is(0, 1, 1)2π/(aL). Nexp gives Nπ +NB.Figure 2. Same as Fig.1 but for TB = 16.33. Results for Form FactorsGiven the amplitudes A00 from fits to three-point correlators one can determine various formfactors. In these preliminary investigations wefind it most convenient to work with the formfactors f‖ and f⊥ defined as,f‖ =A00(V0)√ζ(0)π ζ(0)B√2Eπ ZV0 (3)f⊥ =A00(Vk)√ζ(0)π ζ(0)B pπ,k√2Eπ ZVk (4)ζ(0)π and ζ(0)B denote the groundstate amplitudesof the pion and B correlators respectively. TheZVµ are the matching coefficients for the heavy-light currents. We use one-loop perturbative re-sults for them.In Fig.3 we show results for f‖ and f⊥. Ourmain results are the octagons and diamonds,which correspond to TB = 12 and TB = 16 re-sults respectively, for decays into local Goldstonepions. One sees consistency between the two TBresults, with, as expected, smaller statistical (andfitting) errors when TB = 12.We have also considered B decays to one of thepoint-split non-Goldstone pions, namely the one-link pion. The masses of the one-link and localpions differ as Mπ(one− link)/Mπ(local) = 1.13.The “bursts” in Fig.3 show form factors for thedecay to the one-link pion. One sees that at lowmomentum agreement is reasonable with the lo-cal pion results. Things start to differ at higherpion momentum, however the data has started todeteriorate at those momenta and one also ex-pects lattice artifacts to be worse there. Thingsshould improve considerably as one goes to lat-tices finer than the a−1 ≈ 1GeV lattices of thepresent study. One can conclude from Fig.3 thattaste-breaking lattice artifact errors are smallerin form factors than in the corresponding pionmasses, particularly at low pion momenta.The above form factor results come from thelowest order (in 1/M) heavy-light currents. Wehave also analysed matrix elements of all the di-mension 4 current corrections that come in at thenext order (two additional currents for V0 andFigure 3. Semileptonic decay form factors f‖ andf⊥ versus the pion energy Eπ in the B rest frame.four more for Vk). We find that their contribu-tions are small for B mesons giving at most a∼ 2 − 3% correction.4. SummaryExploratory quenched studies of heavy-lightmeson semileptonic decays with Asqtad lightquarks look promising. Simulations are underwayto calculate form factors on the MILC dynamicalconfigurations.Acknowledgements : This work was supportedby the DOE, PPARC and NSF. Simulations werecarried out at the Ohio Supercomputer Center.REFERENCES1. M. Wingate et al.; Phys. Rev. D67, 054505(2003).2. M. Wingate et al.; these proceedings and inpreparation.3. G.P. Lepage et al.; Nucl. Phys. B(Proc.Suppl.)106, 12 (2002).

Heavy-Light Meson Semileptonic Decays with Staggered Light Quarks

Heavy-Light Meson Semileptonic Decays with Staggered Light Quarks

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