We describe the form factors for semileptonic B to rho l nu and radiative B
to K* gamma decays with just two parameters and the two form factors for
semileptonic B to pi l nu decays with three parameters. The parametrizations
are constrained by lattice results and are consistent with heavy quark
symmetry, kinematic constraints and light cone sum rule scaling relations.Comment: 3 pages, latex, 2 eps files, uses epsf.sty and espcrc2.sty, poster
  presented at Lattice 97, Edinburgh, 22-26 July 199

Ball

Belyaev

Burford

Flynn

J. Nieves

J.M. Flynn

Khodjamirian

L. Del Debbio

L. Lellouch

Lellouch

Stech

English

arXiv

We describe all the form factors for semileptonic and radiative B decays to the same light vector meson with just two parameters and the two form factors for semileptonic B decays to a light pseudoscalar meson with a further two or three parameters. This provides simple parametrizations of the form factors for the physical  --> ,  -->  and (B) over bar --> K*gamma decays. The parametrizations are consistent with heavy quark symmetry, kinematic constraints and lattice results, which we use to determine the parameters. In addition, we test versions of the parametrizations consistent (or not) with light-cone sum rule scaling relations at q(2) = 0

Del Debbio, Luigi

Flynn, Jonathan M.

Lellouch, Laurent

Nieves Pamplona, Juan Miguel

Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura

Lattice-constrained parametrizations of form factors for semileptonic and rare radiative B decays

Crossref

Nuclear Physics B - Proceedings Supplements

We describe the form factors for semileptonic B to rho l nu and radiative B to K* gamma decays with just two parameters and the two form factors for semileptonic B to pi l nu decays with three parameters. The parametrizations are constrained by lattice results and are consistent with heavy quark symmetry, kinematic constraints and light cone sum rule scaling relations

Collaboration, UKQCD

Del Debbio, L

flynn, J

Lellouch, L

Nieves, J

Edinburgh Research Explorer

     Edinburgh Research Explorer                                      Lattice-Constrained Parametrizations of Form Factors forSemileptonic and Rare Radiative B DecaysCitation for published version:Collaboration, UKQCD, Del Debbio, L, flynn, J, Lellouch, L & Nieves, J 1997, 'Lattice-ConstrainedParametrizations of Form Factors for Semileptonic and Rare Radiative B Decays', Physics Letters B, vol.416, no. 3-4, pp. 392–401. https://doi.org/10.1016/S0370-2693(97)01350-6Digital Object Identifier (DOI):10.1016/S0370-2693(97)01350-6Link:Link to publication record in Edinburgh Research ExplorerDocument Version:Early version, also known as pre-printPublished In:Physics Letters BGeneral 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/9708025v1  28 Aug 19971Lattice-Constrained Parametrizations of Form Factors for Semileptonicand Rare Radiative B DecaysUKQCD Collaboration: L Del Debbioa, J M Flynnb (presenter), L Lelloucha and J NievescaCentre de Physique The´orique, CNRS Luminy, Case 907, F-13288 Marseille Cedex 9, France (Unite´Propre de Recherche 7061)bDepartment of Physics & Astronomy, University of Southampton, Southampton SO17 1BJ, UKcDepartamento de Fisica Moderna, Avenida Fuentenueva, 18071 Granada, SpainWe describe the form factors for B¯0 → ρ+l−ν¯l and B → K∗γ decays with just two parameters and the twoform factors for B¯0 → pi+l−ν¯l with three parameters. The parametrizations are constrained by lattice results andare consistent with heavy quark symmetry, kinematic constraints and light cone sum rule scaling relations.We obtain a simple yet phenomenologicallyuseful description of the form factors for semilep-tonic and rare radiative heavy-to-light meson de-cays for all q2, the squared momentum transferto the leptons or photon. Lattice calculations de-termine the form factors over a limited region athigh q2. We use model input to extend the resultsto q2=0, seeking consistency with:• kinematic constraints: F1(0) = F0(0) andT1(0) = iT2(0)• heavy quark symmetry (HQS)• light cone sum rule (LCSR) scaling relations:all form factors scale like M−3/2 as M→∞ atq2=0, where M is the heavy meson mass• dispersive constraintsThe normalisation is fixed using lattice results.The outcome is a two parameter fit for B¯0 →ρ+l−ν¯l or B → K∗γ and a three parameter fit forB¯0 → π+l−ν¯l. More details can be found in [1].The leading order HQS analysis shows thatheavy-to-light P→P decay form factors are deter-mined by two universal (“Isgur-Wise”) functions,while P→V decays are governed by four moresuch functions (P and V denote pseudoscalar andvector mesons respectively). We adopt a model ofStech [2] which keeps just one universal functionfor P→P and one more for P→V .Lattice simulation details can be found in [3,4]with details of the chiral extrapolation for B¯0 →π+l−ν¯l in [5]. All form factors are calculated forfour values of the heavy quark mass around thecharm mass and for a variety of q2. In our previ-ous work [3,4], the form factors were extrapolatedat fixed four-velocity recoil, ω = v·(pP,V /mP,V ),near the zero recoil point ω = 1, using the heavy-quark scaling relations:fΘMnf/2 = γf(1 +δfM+ǫfM2+ · · ·)where nf = −1, 1,−1,−1, 1,−1,−1, 1 for f =F1, F0, A0, V, A1, A2, T1, T2 and γf , δf and ǫf arefit parameters. Θ comes from leading logarith-mic matching and is chosen to be 1 at the Bmass. This procedure neglects the fact that forM→∞, HQS predicts A1 = 2iT2 and V = 2T1at fixed ω not too far from q2max. We enforce thiscondition by performing a combined fit, at fixedω, of the pairs (A1, T2) and (V, T1) imposing theconstraints: γA1 = 2iγT2 and γV = 2γT1 . Thisguarantees that the extrapolated form factors areconsistent with HQS in the infinite mass limit andreduces statistical errors by decreasing the num-ber of parameters.1. B¯0 → ρ+l−ν¯l AND B → K∗γ DECAYSWe use the freedom to adjust quark masses inlattice calculations and consider two situations forthe light quark q into which the b decays:2Table 1Form factor results for B¯0 → ρ+l−ν¯l and B → K∗γ. For B¯0 → ρ+l−ν¯l the fit parameters are: A1(0) =0.27(54), M1 = 7.0(126)GeV, χ2/dof = 24/20. For B → K∗γ: A1(0) = 0.29(43), M1 = 6.8(74)GeV,χ2/dof = 27/20.q2 A1 A2 A0 V T1 T20 0.27(54) 0.26(53) 0.30(64) 0.35(65) 0.16(21)q2max 0.46(21) 0.88(53) 1.80(95) 2.07(116) 0.90(54) 0.25(11)A q=u: matrix elements of u¯ σµν(1+γ5)b are un-physical but constrain B¯0 → ρ+l−ν¯l.B q=s: s¯γ µ(1−γ 5)b is unphysical but constrainsB → K∗γ.We complete the parametrization by specifyingone of the form factors. To meet all our require-ments, including the LCSR scaling condition atq2 = 0, we chooseA1(q2) =A1(0)1− q2/M21(1)with free parameters A1(0) and M1. This allowsA1, A2 and T2, which receive contributions from1+ resonances, to diverge at larger q2 than themore singular V , A0 and T1. We also tried otherparametrizations but all results below will useA1(q2) in eq. (1). Figure 1 shows the fit for afinal state with the mass of the K∗, and Table 1gives results for the form factors.2. B¯0 → π+l−ν¯l DECAYSStech’s model makes F0(q2max) vanish in the chi-ral limit, contradicting our results and made un-likely by unitarity bounds [5]. Furthermore, theB∗ which contributes a pole very close to q2maxin F1, induces the same singularity in F0 in themodel. This provokes a much stronger q2 depen-dence for F0 than seen in the lattice results or in-duced by the nearest 0+ resonance. Therefore werestrict to polar-type q2-dependences, consistentwith the kinematical constraint, F1(0) = F0(0),HQS and unitarity bounds. Our preferred model,consistent with LCSR scaling relations at q2 = 0,isF1(q2) =F (0)(1−q2/m21)2, F0(q2) =F (0)(1−q2/m20).0 5 10 15 2000.511.52 Situation B (K∗)VA0A1T1T2q2(GeV2)Figure 1. Fit to the lattice predictions for A0, A1,V , T1 and T2 for a K∗ meson final state (Situa-tion B) assuming a pole form for A1. The dashedvertical line indicates q2max.The result of the fit is: F (0) = 0.27(11),m1 = 5.79(58)GeV and m0 = 6.1(15)GeV withχ2/dof = 0.1/3. All results below will be quotedusing this pole/dipole model.3. PHENOMENOLOGYUsing our fits we can calculate total rates anddifferential decay spectra in q2 and lepton en-ergy E for the decays B¯0 → ρ+l−ν¯l (Figure 2)and B¯0 → π+l−ν¯l. In Table 2 we give our re-sults, illustrating the good agreement of our formfactor values at q2=0 with LCSR calculations,and compare rates and ratios for semileptonicdecays. For B → K∗γ we evaluate the ratioRK∗ = Γ(B → K∗γ)/Γ(b → sγ) = 16(43)%, tobe compared with (18±7)% from experiment [6].3Table 2Form factor values at q2 = 0 with B → π, ρ semileptonic decay rates and ratios from this calculationand from light cone sum rules (LCSR). Decay rates are given in units of |Vub|2 ps−1. Γρ/pi ≡ Γ(B¯0 →ρ+l−ν¯l)/Γ(B¯0 → π+l−ν¯l) and ΓL/T denotes the ratio of rates to longitudinally and transversely polarisedrho mesons in B¯0 → ρ+l−ν¯l. l denotes a massless lepton.F1(0) A1(0) A2(0) V (0) T1(0) Γpilν¯ Γρlν¯ Γρ/pi ΓL/T Γpiτν¯τ Γρτν¯τ0.27(11) 0.27(54) 0.26(53) 0.35(65) 0.16(21) 8.5(3314) 16.5(3523) 1.9(97) 0.80(43) 5.8(184) 8.8(149)LCSR[7] 0.27(5) 0.28(5) 0.35(7) 13.5(40) 1.7(5) 0.52(8)[8] 0.24(4) 0.28(6) 0.16(3)[9] 0.24–0.29 8.7[10] 0.15(3)0 5 10 15 2000.20.40.60.80 0.5 1 1.5 2 2.50246810121416dΓ/dq2 (|Vub|210−12GeV−1)dΓ/dE (|Vub|210−12)q2(GeV2) E(GeV)Figure 2. Differential decay spectra for B¯0 → ρ+l−ν¯l for massless leptons: (a) dΓ/dq2 in units of10−12|Vub|2GeV−1, (b) dΓ/dE in units of 10−12|Vub|2. The dashed lines show the envelope of the 68%bootstrap errors computed separately for each value of q2 or E respectively.REFERENCES1. UKQCD collab, L Del Debbio et al, preprintCPT–97/P.3505, SHEP–97–13, UG–DFM–4/97 (1997), hep-lat/97080082. B Stech, Phys Lett B 354 (1995) 447, hep-ph/95023783. UKQCD collab, DR Burford et al, NuclPhys B 447 (1995) 425, hep-lat/95030024. UKQCD collab, JM Flynn et al, Nucl Phys B461 (1996) 327, hep-ph/95063985. L Lellouch, Nucl Phys B 479 (1996) 353, hep-ph/95093586. CLEO collab, R Ammar et al, preprint CLEOCONF 96–05 (1996)7. P Ball and VM Braun, Phys Rev D 55 (1997)5561, hep-ph/97012388. A Ali, VM Braun and H Simma, Z Phys C 63(1994) 437, hep-ph/94012779. VM Belyaev, A Khodjamirian and R Ru¨ckl,Z Phys C 60 (1993) 349, hep-ph/9305348;VM Belyaev et al, Phys Rev D 51 (1995)6177, hep-ph/9410280; A Khodjamirian andR Ru¨ckl, Proc ICHEP 96, 28th Int Conf onHigh Energy Physics, 1996, World Scientific,Singapore (1997) 902, hep-ph/961036710. D Becirevic, preprint LPTHE–Orsay 97/16(1997), hep-ph/9707271

Lattice-Constrained Parametrizations of Form Factors for Semileptonic and Rare Radiative B Decays

Luigi Del Debbio

Jonathan M Flynn

Laurent Lellouch

Juan Nieves

Physics Letters B

We describe the form factors for B to rho lepton neutrino and B to K* gamma decays with just two parameters and the two form factors for B to pi lepton neutrino with a further two or three parameters. The parametrizations are consistent with heavy quark symmetry, kinematic constraints and lattice results, which we use to determine the parameters. In addition, we test versions of the parametrizations consistent (or not) with light-cone sum rule scaling relations at q^2=0

flynn, Jonathan

Nieves, Juan

https://www.pure.ed.ac.uk/ws/files/1660940/9708025v1

Lattice-Constrained Parametrizations of Form Factors for Semileptonic
  and Rare Radiative B Decays

Lattice-Constrained Parametrizations of Form Factors for Semileptonic and Rare Radiative B Decays

Abstract

Similar works

Full text

Available Versions

Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura

Crossref

Edinburgh Research Explorer

Crossref

Edinburgh Research Explorer