Abstract
This article analyses the available inputs in B → πℓνℓ and B → ρℓνℓ decays which include the measured values of differential rate in different q2-bins (lepton invariant mass spectrum), lattice, and the newly available inputs on the relevant form-factors from the light-cone sum rules (LCSR) approach. We define different fit scenarios, and in each of these scenarios, we predict a few observables in the standard model (SM). For example, R(M)=frac{mathcal{B}left(Bto M{ell}_i{nu}_{ell_i}right)}{mathcal{B}left(Bto M{ell}_j{nu}_{ell_j}right)},{R}_{ell_j}^{ell_i}(M)=frac{mathcal{B}left(Bto {ell}_i{nu}_{ell_i}right)}{mathcal{B}left(Bto M{ell}_j{nu}_{ell_j}right)} with M = π or ρ and ℓi,j = e, μ or τ. We also discuss the new physics (NP) sensitivities of all these observables and obtain bounds on a few NP Wilson coefficients in b → uτντ decays using the available data. We have noted that the data at present allows sizeable NP contributions in this mode. Also, we have predicted a few angular observables relevant to these decay modes.
Highlights
This article analyses the available inputs in B → π ν and B → ρ ν decays which include the measured values of differential rate in different q2-bins, lattice, and the newly available inputs on the relevant form-factors from the light-cone sum rules (LCSR) approach
There are two form-factors associated with B → π ν decays, namely f+(q2) and f0(q2),1 for which precise predictions from lattice at zero and non-zero recoils are available [14, 15], while the updates from LCSR is available in [2, 16]
We have inputs on the differential branching fractions in different q2-bins [18,19,20] which play an essential role in constraining the form-factors
Summary
Assuming neutrinos to be left-handed,the most general effective Hamiltonian that contains all possible four-fermion operators of the lowest dimension for the b → uτ ν transition is written as, Heff. Note that the decay rates for B → πτ ν and B → ρτ ν are sensitive to both the (V + A) and (V − A) type of quark currents and tensor type interaction OT. It is insensitive to scalar and tensor interactions With all this information at hand, we define the following sets of observables: R(π). The contributions from a new SM type interaction will cancel in the ratios Rττ (π) and Rττ (ρ). The ratios Rττ (π) and Rττ (ρ) are sensitive to OV2, the dependences could be very different which we will discuss in the result section. Amongst all these observables, R(π), R(ρ), Rττ (π), and Rττ (ρ) are sensitive to tensor currents while Rμτ (π) and Rμτ (ρ) are not.
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