We study semileptonic B decays, using MILC dynamical configurations with
$N_f=2+1$. NRQCD heavy and AsqTad light quark actions are used. We obtain the
semileptonic form factors $f_+(q^2)$ and $f_0(q^2)$ in the chiral limit.Comment: 6 pages, 3 figures, talk presented at Lattice 2005 (Heavy quark
  physics

Davies, Christine

Gray, Alan

Gulez, Emel

Lepage, Peter

Shigemitsu, Junko

Wingate, Matthew

English

arXiv

We study semileptonic B decays, using MILC dynamical configurations with $N_f=2+1$. NRQCD heavy and AsqTad light quark actions are used. We obtain the semileptonic form factors $f_+(q^2)$ and $f_0(q^2)$ in the chiral limit

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     Edinburgh Research Explorer                                      B semileptonic decays with 2+1 dynamical quark flavorsCitation for published version:Gulez, E, Davies, C, Gray, A, Lepage, P, Shigemitsu, J & Wingate, M 2005, B semileptonic decays with 2+1dynamical quark flavors. in XXIIIrd International Symposium on Lattice Field Theory. PoS - Proceedings ofScience, XXIIIrd International Symposium on Lattice Field Theory, Dublin, Ireland, 25-30 July.Link:Link to publication record in Edinburgh Research ExplorerDocument Version:Publisher's PDF, also known as Version of recordPublished In:XXIIIrd International Symposium on Lattice Field TheoryGeneral 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: 28. Apr. 2017arXiv:hep-lat/0510002v1  30 Sep 2005 PoS(LAT2005)220B semileptonic decays with 2+1 dynamical quarkflavorsEmel Gulez∗a, Christine Daviesb, Alan Graya, Peter Lepagec, Junko Shigemitsua,Matthew Wingateda Physics Department, The Ohio State University, Columbus, OH 43210, USA.b Department of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UKc LEPP, Cornell University, Ithaca, NY 14853, USA.d Institute for Nuclear Theory, University of Washington, Seattle, WA 98195, USA.We study semileptonic B decays, using MILC dynamical configurations with N f = 2+1. NRQCDheavy and AsqTad light quark actions are used. We obtain the semileptonic form factors f+(q2)and f0(q2) in the chiral limit.XXIIIrd International Symposium on Lattice Field Theory25-30 July 2005Trinity College, Dublin, Ireland∗Speaker.c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(LAT2005)220Emel Gulez1. IntroductionThis work is a continuation of the study of semileptonic B decays by the HPQCD collaboration[1], which was announced last year. Since then, we have included all 1/M corrections for thetemporal and spatial parts of the heavy-light electroweak currents |V0| and |Vk|. Previously, onlythe corrections that are lowest order in 1/M were included. Also, last year our data was on oneensemble, now we have more ensembles, listed in [2] and hence more full QCD data points inaddition to partially quenched results. Moreover, we have started implementing and examining theeffects of staggered chiral perturbation theory fits using formulas by Aubin and Bernard [3].2. Current MatchingWe constructed the heavy-light currents in terms of lattice operators so that they accuratelyrepresent the continuum heavy-light currents up to the desired order. We picked a process where theoperator to be matched is relevant. The corresponding scattering amplitude was matched betweenlattice and continuum through one loop in perturbation theory. The result is independent of theprocess picked to do the matching. Our process is a heavy quark scattering into a light quarkthrough the electroweak current. The corresponding Feynman diagram is calculated through oneloop in continuum perturbation theory; then the result is expanded in powers of 1/M. The termsin the expansion are identified as the continuum analogs of the necessary lattice operators. Theselattice currents are:Temporal Currents:J(0)0 (x) = q¯(x)Γ0 Q(x),J(1)0 (x) =−12(aM0)q¯(x)Γ0 γ ·∇Q(x),J(2)0 (x) =−12(aM0)q¯(x)γ ·←−∇ γ0 Γ0 Q(x).Spatial Currents:J(0)k (x) = q¯(x)Γk Q(x),J(1)k (x) =−12(aM0)q¯(x)Γk γ ·∇Q(x),J(2)k (x) =−12(aM0)q¯(x)γ ·←−∇ γ0 Γk Q(x),J(3)k (x) =−12(aM0)q¯(x)Γt ∇k Q(x),J(4)k (x) =12(aM0)q¯(x)←−∇ k γt Γk Q(x),where Γµ = γµ or γ5γµ , and Γt = 1 or γ5.Because of the symmetries of our action, axial vector and vector currents give the same results.We used this as a further check in our matching calculations.The continuum currents are a linear combination of the lattice currents through O(αs/M):220 / 2PoS(LAT2005)220Emel Gulez〈V0〉cont = (1+ αSρ0)〈J(0)0 〉+(1+ αSρ1)〈J(1),sub0 〉+ αSρ2〈J(2),sub0 〉,〈Vk〉cont = (1+ αSρ0)〈J(0)k 〉+(1+ αSρ1)〈J(1),subk 〉+ αSρ2〈J(2),subk 〉+ αSρ3〈J(3)k 〉+ αSρ4〈J(4)k 〉,where J(i),sub0 = J(i)0 −αSξi0J(0)0 . The subtracted currents J(i),subµ are more physical, as they havepower law contributions subtracted out through O(αS/aM).Last year, our calculation was correct through O(αs): it only included the first term, (1 +αSρ0)〈J(0)0 〉. We now take into account all the 1/M terms in the above expression. To this end, wecalculated both the nonperturbative matrix elements 〈J〉 and the perturbative coefficients ρi. Theperturbative calculations are described in [4].The difference between matching at O(αs/M) and at O(αs) is found to be very small. Thisdifference is plotted for one of the currents, J(1)0 in Fig.1.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1Epi in GeV-0.1-0.09-0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.0100.01j(1)/j(0)v020-m020 naivev020-m020 O(αs) subtractedv010-m010 naivev010-m010 O(αs) subtractedFigure 1: The size of 1/M current correction J(1)0 is shown. The more physical subtracted currents have aneven smaller effect than the naive ones, with the central value of the largest J(1)0 /J(0)0 around 1 percent.3. Form FactorsThe semileptonic form factors are defined by the following relation with the hadronic matrixelement of electroweak currents between a B meson and a pion:220 / 3PoS(LAT2005)220Emel Gulez〈pi(ppi)|V µ |B(pB)〉 = f+(q2)[pµB + pµpi −M2B−m2piq2qµ]+ f0(q2) M2B−m2piq2qµ=√2MB [vµ f‖ + pµ⊥ f⊥],where vµ = pµBMB , pµ⊥ = pµpi − (ppi · v)vµ , qµ = pµB − pµpi .0 0.005 0.01 0.015 0.02 0.025mq/ms00.511.522.5f ⊥ (GeV-1/2 )Epi=0.7Epi=0.8Epi=1.0Epi=1.2physicalFigure 2: Linear extrapolations of f⊥ to the physical chiral limit at several fixed values of Epi .The three-point correlatorC(3)(~ppi ,~pB, t,TB) = ∑~z∑~y〈Φpi(0)Jµ(~z, t)Φ†B(~y,TB)〉ei~pB·~y ei(~ppi−~pB)·~z,where Φ’s are interpolating operators for the mesons, is fit using Bayesian fitting algorithms to thefollowing form to obtain A00:C(3)(~ppi ,~pB, t,TB)→Npi−1∑k=0NB−1∑j=0(−1)k∗t(−1) j∗(TB−t)A jke−E(k)pi te−E( j)B (TB−t).A00 is directly related to form factors f‖ and f⊥ in the following way:f‖ = A00(V0)√ζ (0)pi ζ (0)B√2Epi ,220 / 4PoS(LAT2005)220Emel Gulezf⊥ = A00(Vk)√ζ (0)pi ζ (0)B pkpi√2Epi ,where A00 includes the effects of matching, and ζ (0)B,pi are the groundstate amplitudes from the Bmeson and the pion 2− pnt correlators respectively.4. Procedure for Approaching the Chiral Limit0 5 10 15 20 25q2 (GeV2)00.20.40.60.811.21.41.61.822.22.42.62.83previous f0previous f+new f0new f+Soft Pion fB/fpiFigure 3: The form factors f+(q2) and f0(q2), calculated using the same ensemble as the previous year,including the 1/M current corrections are shown and compared with the results from last year. The curveshown is a BK [5] fit to last year’s data. Results from other ensembles and more sophisticated chiral extrap-olations have not been included yet in this plot.One needs to extrapolate the form factors obtained as described in the previous section to thephysical chiral limit. We first interpolate f‖ and f⊥ to the same values of Epi . After interpolating,we do chiral extrapolation at several fixed Epi values to get the form factors at the physical point.A plot of f⊥ showing the interpolated points at fixed Epi , and linear extrapolation to the physicallimit can be seen in fig.2. So far, only simple linear fits were used in our results. We have startedlooking into doing more complicated chiral fits using [3].220 / 5PoS(LAT2005)220Emel GulezUsing the chirally extrapolated f‖ and f⊥, we obtain f+(q2) and f0(q2). The form factorsf+(q2) and f0(q2), calculated using the same ensemble as the previous year, including the 1/Mcurrent corrections are shown in Fig.3 and compared with the results from last year. The curveshown is a BK [5] fit to last year’s data. Our results are in the region of q2 larger than 15GeV .We perform fits of our results to model ansatze for the q2 dependence in order to obtain the formfactors at smaller q2. A new approach "Moving NRQCD" [6] shows promise to directly calculatethe form factors even at small q2.5. SummaryLast year, unquenched studies of semileptonic B decays using NRQCD heavy and improvedstaggered (AsqTad) light quark actions were reported. The main change since then is that we haveincluded all 1/M corrections to currents through O(αs,aαs,αs/aM,αsΛQCD/M), instead of onlyO(αs). We also have more ensembles, instead of just one ensemble with dynamical quark massam = 0.01. We have started coding and examining the effects of staggered chiral perturbationtheory. The results shown in this article, however, used only linear fits. We also have new data onfiner lattice spacing that needs to be fit and included. Once our analysis is complete, and we havethe corresponding f+(q2) and f0(q2), this will enable us to extract the CKM matrix element |Vub|using the new experimental B−> pilν branching fraction results, for instance due to Belle, BaBar,CLEO.References[1] J. Shigemitsu et al.; Nucl. Phys. B Proc. Suppl. 140,464 (2005), hep-lat/0408019.[2] J. Shigemitsu; these proceedings.[3] C. Aubin and C. Bernard; Staggered Chiral Perturbation Theory Notes; private communication.[4] E. Gulez et al.; Phys. Rev. D69,074501 (2004).[5] D. Becirevic and A. B. Kaidalov; Phys. Lett. B478,417 (2000),[6] K. Foley and G. P. Lepage; Nucl. Phys. Proc. Suppl. 119,635 (2003),K. Foley et al.;Nucl. Phys. B Proc. Suppl. 140,470 (2005)A. Dougall; these proceedings220 / 6

B semileptonic decays with 2+1 dynamical quark flavors

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