Electric Dipole Moments as Probes of $B$ Anomaly

Abstract

The measurements of the lepton flavor universality (LFU) in $\mathcal{B}(\bar{B}\to D^{(\ast )}l\bar{\nu })$ indicate a significant deviation from the standard model prediction at a 3-4$\sigma$ level, revealing a violation of the LFU ($R_{D^{(\ast )}}$ anomaly). It is known that the $R_{D^{(\ast )}}$ anomaly can be easily accommodated by an $SU(2{)}_L$-singlet vector leptoquark (LQ) coupled primarily to third-generation fermions, whose existence is further motivated by a partial gauge unification. In general, such a LQ naturally leads to additional $CP$-violating phases in the LQ interactions. In this paper, we point out that the current $R_{D^{(\ast )}}$ anomaly prefers the $CP$-violating interaction although $\mathcal{B}(\bar{B}\to D^{(\ast )}l\bar{\nu })$ are $CP$-conserving observables. The $CP$-violating LQ predicts a substantial size of the bottom-quark electric dipole moment (EDM), the chromo-EDM, and also the tau-lepton EDM. Eventually at low energy, the nucleon and electron EDMs are radiatively induced. Therefore, we conclude that the $R_{D^{(\ast )}}$ anomaly with the $SU(2{)}_L$-singlet vector LQ provides unique predictions: neutron and proton EDMs with opposite signs and a magnitude of $\mathcal{O}(10^{-27})e$cm, and suppressed electron EDM. Furthermore, we show that a similar EDM pattern is predicted in an $SU(2{)}_L$-doublet scalar LQ scenario that can accommodate the $R_{D^{(\ast )}}$ anomaly as well. These EDM signals could serve as crucial indicators in future experiments.

12 pages, 8 figures, 1 table; v2: typos in the code fixed, discussion of scalar LQ added, references added; v3: version accepted for publication in Physical Review D

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