Bayesian fit analysis to full distribution data of $$ \overline{\mathrm{B}}\to {\mathrm{D}}^{\left(\ast \right)}\mathrm{\ell}\overline{\nu }:\left|{\mathrm{V}}_{\mathrm{cb}}\right| $$ determination and new physics constraints

Abstract

A bstract We investigate the semi-leptonic decays of $$ B\to {D}^{\left(\ast \right)}\mathrm{\ell}\overline{\nu } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>B</mml:mi> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>D</mml:mi> <mml:mfenced> <mml:mo>∗</mml:mo> </mml:mfenced> </mml:msup> <mml:mi>ℓ</mml:mi> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> in terms of the Heavy-Quark-Effective-Theory (HQET) parameterization for the form factors, which is described with the heavy quark expansion up to $$ \mathcal{O}\left(1/{m}_c^2\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mi>c</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:mfenced> </mml:math> beyond the simple approximation considered in the original CLN parameterization. An analysis with this setup was first given in the literature, and then we extend it to the comprehensive analyses including (i) simultaneous fit of | V cb | and the HQET parameters to available experimental full distribution data and theory constraints, and (ii) New Physics (NP) contributions of the V 2 and T types, such as $$ \left(\overline{c}{\upgamma}^{\mu }{P}_Rb\right)\left(\overline{\mathrm{\ell}}{\gamma}_{\mu }{P}_L\nu \mathrm{\ell}\right)\kern0.5em \mathrm{and}\kern0.5em \left(\overline{c}{\sigma}^{\mu \nu}{P}_Lb\right)\left(\overline{\mathrm{\ell}}{\sigma}_{\mu \nu}{P}_L{\nu}_{\mathrm{\ell}}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mrow> <mml:mover> <mml:mi>c</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:msup> <mml:mi>γ</mml:mi> <mml:mi>μ</mml:mi> </mml:msup> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>R</mml:mi> </mml:msub> <mml:mi>b</mml:mi> </mml:mrow> </mml:mfenced> <mml:mfenced> <mml:mrow> <mml:mover> <mml:mi>ℓ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>L</mml:mi> </mml:msub> <mml:mi>ν</mml:mi> <mml:mi>ℓ</mml:mi> </mml:mrow> </mml:mfenced> <mml:mspace/> <mml:mtext>and</mml:mtext> <mml:mspace/> <mml:mfenced> <mml:mrow> <mml:mover> <mml:mi>c</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:msup> <mml:mi>σ</mml:mi> <mml:mi>μν</mml:mi> </mml:msup> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>L</mml:mi> </mml:msub> <mml:mi>b</mml:mi> </mml:mrow> </mml:mfenced> <mml:mfenced> <mml:mrow> <mml:mover> <mml:mi>ℓ</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>μν</mml:mi> </mml:msub> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>L</mml:mi> </mml:msub> <mml:msub> <mml:mi>ν</mml:mi> <mml:mi>ℓ</mml:mi> </mml:msub> </mml:mrow> </mml:mfenced> </mml:math> , to the decay distributions and rates. For this purpose, we perform Bayesian fit analyses by using Stan program, a state-of-the-art public platform for statistical computation. Then, we show that our | V cb | fit results for the SM scenarios are close to the PDG combined average from the exclusive mode, and indicate significance of the angular distribution data. In turn, for the SM + NP scenarios, our fit analyses find that non-zero NP contribution is favored at the best fit point for both SM + V 2 and SM + T depending on the HQET parameterization model. A key feature is then realized in the $$ \overline{B}\to {D}^{\left(\ast \right)}\tau \overline{\nu} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>D</mml:mi> <mml:mfenced> <mml:mo>∗</mml:mo> </mml:mfenced> </mml:msup> <mml:mi>τ</mml:mi> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> observables. Our fit result of the HQET parameters in the SM(+ T ) produces a consistent value for R D while smaller for $$ {R}_{D^{\ast }} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:msub> </mml:math> , compared with the previous SM prediction in the HFLAV report. On the other hand, SM + V 2 points to smaller and larger values for R D and $$ {R}_{D^{\ast }} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:msub> </mml:math> than the SM predictions. In particular, the $$ {R}_{D^{\ast }} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:msub> </mml:math> deviation from the experimental measurement becomes smaller, which could be interesting for future improvement on measurements at the Belle II experiment.

Topics & Concepts