<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:math>, lepton flavor universality and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3</mml:mn><mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mi>F</mml:mi></mml:msub></mml:math> symmetry breaking in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>B</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mi>s</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mo>*</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><mml:mo>ℓ</mml:mo><mml:msub><mml:mi>ν</mml:mi><mml:mo>ℓ</mml:mo></mml:msub></mml:math> decays through unitarity and lattice QCD
G. Martinelli, Manuel Naviglio, Silvano Simula, Ludovico Vittorio
Abstract
In addition to the well-known $B\ensuremath{\rightarrow}{D}^{(*)}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ decays, semileptonic ${B}_{s}\ensuremath{\rightarrow}{D}_{s}^{(*)}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ processes offer the possibility to determine the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{cb}|$. We implement the dispersive matrix approach to describe the hadronic form factors (FFs) for the ${B}_{s}\ensuremath{\rightarrow}{D}_{s}^{(*)}$ transition in the whole kinematical range, starting from recent lattice QCD computations at large values of the four-momentum transfer. We extract $|{V}_{cb}|$ from the experimental data, obtaining $|{V}_{cb}|\ifmmode\times\else\texttimes\fi{}{10}^{3}=(41.7\ifmmode\pm\else\textpm\fi{}1.9)$ from ${B}_{s}\ensuremath{\rightarrow}{D}_{s}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ and $|{V}_{cb}|\ifmmode\times\else\texttimes\fi{}{10}^{3}=(40.7\ifmmode\pm\else\textpm\fi{}2.4)$ from ${B}_{s}\ensuremath{\rightarrow}{D}_{s}^{*}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ decays. After averaging with the values of $|{V}_{cb}|$ obtained from the $B\ensuremath{\rightarrow}{D}^{(*)}$ channels [G. Martinelli et al., Phys. Rev. D 105, 034503 (2022); G. Martinelli et al., arXiv:2109.15248.], we get $|{V}_{cb}|\ifmmode\times\else\texttimes\fi{}{10}^{3}=(41.2\ifmmode\pm\else\textpm\fi{}0.8)$, which is compatible with the most recent inclusive estimate $|{V}_{cb}{|}_{\mathrm{incl}}\ifmmode\times\else\texttimes\fi{}{10}^{3}=42.16\ifmmode\pm\else\textpm\fi{}0.50$ [M. Bordone et al., Phys. Lett. B 822, 136679 (2021).] at the $1\ensuremath{\sigma}$ level. In addition we test the lepton flavor universality by computing the $\ensuremath{\tau}/\ensuremath{\ell}$ ratios of the total decay rates (where $\ensuremath{\ell}$ is a light lepton), obtaining $R({D}_{s})=0.298(5)$ and $R({D}_{s}^{*})=0.250(6)$. We also address the issue of the $SU(3{)}_{F}$ symmetry breaking by comparing the hadronic FFs entering the semileptonic $B\ensuremath{\rightarrow}{D}^{(*)}$ and ${B}_{s}\ensuremath{\rightarrow}{D}_{s}^{(*)}$ channels.