Radiative decays of heavy-light mesons and the $$ {f}_{H,{H}^{\ast },{H}_1}^{(T)} $$ decay constants
Ben Pullin, Roman Zwicky
Abstract
A bstract The on-shell matrix elements, or couplings $$ {g}_{H{H}^{\ast}\left({H}_1\right)\upgamma} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>g</mml:mi> <mml:mrow> <mml:mi>H</mml:mi> <mml:msup> <mml:mi>H</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mfenced> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mfenced> <mml:mi>γ</mml:mi> </mml:mrow> </mml:msub> </mml:math> , describing the $$ B{(D)}_q^{\ast } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> <mml:msubsup> <mml:mfenced> <mml:mi>D</mml:mi> </mml:mfenced> <mml:mi>q</mml:mi> <mml:mo>∗</mml:mo> </mml:msubsup> </mml:math> → B ( D ) q γ and B 1 q → B q γ ( q = u, d, s ) radiative decays, are determined from light-cone sum rules at next-to-leading order for the first time. Two different interpolating operators are used for the vector meson, providing additional robustness to our results. For the D * -meson, where some rates are experimentally known, agreement is found. The couplings are of additional interest as they govern the lowest pole residue in the B ( D ) → γ form factors which in turn are connected to QED-corrections in leptonic decays B ( D ) → ℓ $$ \overline{\nu} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> . Since the couplings and residues are related by the decay constants $$ {f}_{H^{\ast}\left({H}_1\right)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mfenced> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mfenced> </mml:mrow> </mml:msub> </mml:math> and $$ {f}_{H^{\ast}\left({H}_1\right)}^T $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>f</mml:mi> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mfenced> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mfenced> </mml:mrow> <mml:mi>T</mml:mi> </mml:msubsup> </mml:math> , we determine them at next-leading order as a by-product. The quantities $$ \left\{{f}_{H^{\ast}}^T,{f}_{H_1}^T\right\} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:msubsup> <mml:mi>f</mml:mi> <mml:msup> <mml:mi>H</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mi>T</mml:mi> </mml:msubsup> <mml:msubsup> <mml:mi>f</mml:mi> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mi>T</mml:mi> </mml:msubsup> </mml:mfenced> </mml:math> have not previously been subjected to a QCD sum rule determination. All results are compared with the existing experimental and theoretical literature.