Abstract
As a consequence of the Ward identity for hadronic matrix elements, we find relations between the differential decay rates of semileptonic decay modes with the underlying quark-level transition b → cτν, which are valid in scalar models. The decay-mode dependent scalar form factor is the only necessary theoretical ingredient for the relations. Otherwise, they combine measurable decay rates as a function of the invariant mass-squared of the lepton pair q2 in such a way that a universal decay-mode independent function is found for decays to vector and pseudoscalar mesons, respectively. This can be applied to the decays Bto {D}^{ast}tau v,{B}_sto {D}_s^{ast}tau v,{B}_cto J/psi tau v and B → Dτv, Bs → Dsτv, Bc → ηcτv, with implications for R(D(*)), Rleft({D}_s^{left(ast right)}right) , R(J/ψ), R(ηc), and ℬ(Bc → τv). The slope and curvature of the characteristic q2-dependence is proportional to scalar new physics parameters, facilitating their straight forward extraction, complementary to global fits.
Highlights
An updated Standard Model (SM) prediction using additional data on decays to light leptons [15] is provided in ref. [16]
As a consequence of the Ward identity for hadronic matrix elements, we find relations between the differential decay rates of semileptonic decay modes with the underlying quark-level transition b → cτ ν, which are valid in scalar models
In contrast to non-leptonic sum rules, which are based on the approximate flavor symmetry of QCD, the relations that we consider here are based on ones between hadronic form factors which follow from the Ward identity, and are exact
Summary
For the Standard Model (SM) expressions of Bq → {V, P }τ ν decays like B → D∗τ ν, Bs → Ds∗τ ν, Bc → J/ψτ ν and B → Dτ ν, Bs → Dsτ ν, Bc → ηcτ ν we employ the notation of refs. [11, 13, 58]. DΓ{τ,V2,,PT}H depends on the form factors P1 and f0, respectively, which can be provided by Lattice QCD or Heavy Quark Effective Theory (HQET). They are related as follows to the convention of ref. Note that dΓ{τ,V1,,PE}XP/dw contains only information from decays to light leptons dΓ{EVX,PP}/dw, see eq (2.2). The latter is given in terms of helicity amplitudes as [58, 90, 91, 200, 201]. The corresponding decay rates to τ -leptons are related to those for light leptons as dΓVτ,,ETX±P dq.
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