Abstract
We consider the form factors for the radiative semileptonic decays overline{B} (v) → D(*)(v′)ℓ overline{nu} ℓγ in the kinematic region where the photon momentum, k, is small enough that heavy quark symmetry (HQS) can be applied without the radiated photon changing the heavy quark velocity (i.e., v(′) ∙ k < m(b,c)). We find that HQS is remarkably powerful, leaving only four new undetermined form factors at leading order in 1/m(b,c). In addition, one of them is fixed in terms of the leading order Isgur-Wise function in the kinematic region, v(′) ∙ k < ΛQCD.
Highlights
Matrix elementSince B → D(∗) νγ is a radiative process all matrix elements will have a photon polarization vector, εμ appended
Radiative semileptonic Bdecays are an irreducible background to the measurement of non-radiative semileptonic measurements, in the kinematic regions where the photon is not reconstructed
We have studied the implications of heavy quark symmetry (HQS) for radiative semileptonic Bdecays
Summary
Since B → D(∗) νγ is a radiative process all matrix elements will have a photon polarization vector, εμ appended We factor this out immediately, defining M ≡ ε∗μMμ where M is the total matrix element. Where q e is the electromagnetic charge of the lepton, p is the lepton momentum, and k is the photon momentum We write this matrix element in terms of hadronic matrix elements, FΓν, where Γ = V implies Γν = γν and Γ = A implies Γν = γνγ5.1 This is a textbook example of how HQS severely restricts the number of independent form factors. We turn to radiation off the light degrees of freedom, Mμlight, e.g., the Feynman diagram in the bottom left panel of figure 1. The last class of Feynman diagrams is from radiation off the heavy quarks, shown in the right column of figure 1.
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