Abstract
The V-A structure of the weak interactions leads to definite amplitude hierarchies in exclusive heavy-to-light decays mediated by b → (d, s)γ and bto left(d, sright)ell overline{ell} . However, the extraction of right-handed currents beyond the Standard Model is contaminated by V-A long-distance contributions leaking into right-handed amplitudes. We propose that these quantum-number changing long-distance contributions can be controlled by considering the almost parity-degenerate vector meson final states by exploiting the opposite relative sign of left- versus right-handed amplitudes. For example, measuring the time-dependent rates of a pair of vector V (JP = 1−) and axial A(1+) mesons in B → (V, A)γ, up to an order of magnitude is gained on the theory uncertainty prediction, controlled by long-distance ratios to the right-handed amplitude. This renders these decays clean probes to null tests, from the theory side.
Highlights
Non-perturbative matrix elements, connecting Heff to amplitudes, can dilute the cleanliness of the signal
Sizeable tree-level four-quark operators with charm and up quarks, Heff ∼ dLγμU ULγμb (U = u, c), induce genuine longdistance (LD) effects, which are more difficult to control. It was argued, based on studying the inclusive B → Xsγ decay, that such contaminations could be rather significant [12], whereas actual computations show smaller effects in exclusive channels [13,14,15,16,17]. We show that these LD effects can be controlled by a symmetry that in turn explains the smallness found in the concrete computation [13] quoted just above
This argument establishes the main point of this work, and we turn to the discussion of how this can be applied beyond the symmetry limit
Summary
After briefly discussing the structure of B → V γ amplitudes in section 2.1, we demonstrate in section 2.2 how the left- and right-handed amplitudes of opposite parity states come with a relative minus sign. Each chirality amplitude can be decomposed into contributions from O and O operators (1.1): ABχ→V γ = Aχ + Aχ , χ = L, R ,. V |sL(R)σ·F b|B , and i V,χ includes the ratio of Wilson coefficients and the QCD matrix element but not the CKM contribution λi ≡ λi/λt (with (D) superscript suppressed). The breakdown (2.6) reveals that, in a vector-meson final state of definite parity, i V,R cannot be distinguished from the RHC. It is the aim of this work to show, that ∆Reiφ∆R can be unambiguously identified when two parity-doubler vector meson final states, to be listed, are taken into account.
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