B d,s → $$ \gamma \mathrm{\ell}\overline{\mathrm{\ell}} $$ decay with an energetic photon

Abstract

A bstract We calculate the differential branching fraction, lepton forward-backward asymmetry and direct CP asymmetry for B d,s → $$ \gamma \mathrm{\ell}\overline{\mathrm{\ell}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>γ</mml:mi><mml:mi>ℓ</mml:mi><mml:mover><mml:mi>ℓ</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math> decays with an energetic photon. We employ factorization methods, which result in rigorous next-to-leading order predic- tions in the strong coupling at leading power in the large-energy/heavy-quark expansion, together with estimates of power corrections and a resonance parameterization of sub- leading power form factors in the region of small lepton invariant mass q 2 . The B d,s → $$ \gamma \mathrm{\ell}\overline{\mathrm{\ell}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>γ</mml:mi><mml:mi>ℓ</mml:mi><mml:mover><mml:mi>ℓ</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math> decay shares features of the charged-current decay B u → $$ \gamma \mathrm{\ell}{\overline{\nu}}_{\mathrm{\ell}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>γ</mml:mi><mml:mi>ℓ</mml:mi><mml:msub><mml:mover><mml:mi>ν</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>ℓ</mml:mi></mml:msub></mml:math> . , and the FCNC decays B → $$ {K}^{\left(\ast \right)}\mathrm{\ell}\overline{\mathrm{\ell}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>K</mml:mi><mml:mfenced><mml:mo>∗</mml:mo></mml:mfenced></mml:msup><mml:mi>ℓ</mml:mi><mml:mover><mml:mi>ℓ</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math> . As in the former, the leading-power decay rates can be expressed in terms of the B -meson light-cone distribution amplitude and short-distance factors. However, similar to B → $$ {K}^{\left(\ast \right)}\mathrm{\ell}\overline{\mathrm{\ell}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>K</mml:mi><mml:mfenced><mml:mo>∗</mml:mo></mml:mfenced></mml:msup><mml:mi>ℓ</mml:mi><mml:mover><mml:mi>ℓ</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math> , four-quark and dipole operators contribute to the B d,s → $$ \gamma \mathrm{\ell}\overline{\mathrm{\ell}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>γ</mml:mi><mml:mi>ℓ</mml:mi><mml:mover><mml:mi>ℓ</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math> decay in an essential way, limiting the calculation to q 2 ≲ 6 GeV 2 below the charmonium resonances in the lepton invariant mass spectrum. A detailed analysis of the main observables and theoretical uncertainties is presented.

Topics & Concepts