# Importance of Loop Effects in Explaining the Accumulated Evidence for New Physics in $B$ Decays with a Vector Leptoquark

Crivellin, Andreas (Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland) ; Greub, Christoph (Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, CH-3012 Bern, Switzerland) ; Saturnino, Francesco (Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, CH-3012 Bern, Switzerland) ; Müller, Dario (Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland and Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland)

11 January 2019

Abstract: In recent years experiments revealed intriguing hints for new physics (NP) in $B$ decays involving $b\to c\tau \nu$ and $b\to s{\ell }^{+}{\ell }^{-}$ transitions at the $4\sigma$ and $5\sigma$ level, respectively. In addition, there are slight disagreements in $b\to u\tau \nu$ and $b\to d{\mu }^{+}{\mu }^{-}$ observables. While not significant on their own, they point in the same direction. Furthermore, ${V}_{us}$ extracted from $\tau$ decays shows a slight tension ($\approx 2.5\sigma$) with its value determined from Cabibbo-Kobayashi-Maskawa unitarity, and an analysis of BELLE data found an excess in ${B}_{d}\to {\tau }^{+}{\tau }^{-}$. Concerning NP explanations, the vector leptoquark SU(2) singlet is of special interest since it is the only single particle extension of the standard model which can (in principle) address all the anomalies described above. For this purpose, large couplings to $\tau$ leptons are necessary and loop effects, which we calculate herein, become important. Including them in our phenomenological analysis, we find that neither the tension in ${V}_{us}$ nor the excess in ${B}_{d}\to {\tau }^{+}{\tau }^{-}$ can be fully explained without violating bounds from $K\to \pi \nu \overline{\nu }$. However, one can account for $b\to c\tau \nu$ and $b\to u\tau \nu$ data finding intriguing correlations with ${B}_{q}\to {\tau }^{+}{\tau }^{-}$ and $K\to \pi \nu \overline{\nu }$. Furthermore, the explanation of $b\to c\tau \nu$ predicts a positive shift in ${C}_{7}$ and a negative one in ${C}_{9}$, being nicely in agreement with the global fit to $b\to s{\ell }^{+}{\ell }^{-}$ data. Finally, we point out that one can fully account for $b\to c\tau \nu$ and $b\to s{\ell }^{+}{\ell }^{-}$ without violating bounds from $\tau \to \varphi \mu$, $\Upsilon \to \tau \mu$, or $b\to s\tau \mu$ processes.

Published in: Physical Review Letters 122 (2019)
DOI: 10.1103/PhysRevLett.122.011805
arXiv: 1807.02068

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