Global fit to $b\to c\tau \nu$ anomalies as of Spring 2024

Abstract

Recently, several new experimental results of the test of lepton flavor universality (LFU) in $B\to D^{(\ast )}$ semi-leptonic decays were announced: the first result of $R_D$ from the LHCb Run 1 data, the first results of $R_D$ and $R_{D^{\ast }}$ from the LHCb Run 2 data, and the first result of $R_{D^{\ast }}$ from the Belle II collaboration. Including these new data, a global analysis still prefers the violation of the LFU between the tau and light leptons. A new world average of the data from the BaBar, LHCb, Belle, and Belle II collaborations is $R_D=0.342\pm 0.026$ and $R_{D^{\ast }}=0.287\pm 0.012$. Including this new data, we update a circumstance of the $b\to c\tau \overline{\nu }$ measurements and their implications for new physics (NP). Incorporating recent developments for the $B\to D^{(\ast )}$ form factors in the Standard Model (SM), we observe a $4.4\sigma$ deviation from the SM prediction. Our updates also include; model-independent NP formulae for the related observables; and the global fittings of parameters for leptoquark scenarios as well as single NP operator scenarios. Furthermore, we show future potential to indirectly distinguish different NP scenarios with the use of the precise measurements of the polarization observables in $B\to D^{(\ast )}\tau \overline{\nu }$ at the Belle II and the high-$p_{\mathrm{T}}$ flavored-tail searches at the LHC. We also discuss an impact on the LFU violation in ${\rm Y}\to l^{+}{l}^{-}$.

48 pages, 5 figures, 6 tables, this paper builds upon an unpublished manuscript arXiv:2210.10751; v2: references added; v3: version published in Physical Review D

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