Abstract
Recently, several $B$-physics experiments report interesting anomalies in the semi-leptonic decays of $B$-mesons, such as the excess in the $R_{D^{(\ast)}}$ measurements. These anomalies seem to suggest intriguing hints of lepton flavor non-universality, and the R-parity violating (RPV) interactions are candidates for explaining this non-universality. In this paper, we discuss the RPV interactions for resolving the $R_{D^{(\ast)}}$ anomaly with the Grand Unified Theory (GUT) assumption. To solve the $R_{D^{(\ast)}}$ anomaly, it is known that large RPV couplings and around $1~{\rm TeV}$ sfermion masses are required. At the same time, large RPV couplings are conducive to realize the bottom-tau Yukawa unification which appears in the GUT models. On the other hand, there are problems for realizing favorable sfermion masses in the constrained minimal supersymetric standard model. To resolve these problems, we show that two non-universalities, the non-universal sfermion masses and the non-universal gaugino masses, are favorable.
Highlights
Several interesting anomalies in semi-leptonic B-meson decays are reported by the B-physics experiments
We have shown that Oð1Þ R-parity violating (RPV) couplings are helpful for resolving the RDðÃÞ anomaly when the thirdgeneration sfermion masses are around 1 TeV, and Oð1Þ RPV couplings are favorable for realizing the SUð5Þ Yukawa relation, the bottom-tau Yukawa unification at the grand unified theory (GUT) scale
In the subsections III A and III B, we have shown that the nonuniversal sfermion and gaugino masses are helpful for resolving the two problems encountered in the constrained MSSM (CMSSM) scenario, to realize the RDðÃÞ measurements
Summary
Several interesting anomalies in semi-leptonic B-meson decays are reported by the B-physics experiments. As we will show later, models with the CMSSM assumption do not satisfy the RDðÃÞ measurements, because a large RPV coupling makes these models already excluded, and the right-handed sbottom mass becomes too heavy to explain the RDðÃÞ anomaly. To solve this problem, two nonuniversalities, the nonuniversal sfermion masses and the nonuniversal gaugino masses, which are compatible with the GUT framework, play an important role. As the lepton doublet superfields Li and the Higgs doublet superfield Hd have the same gauge and Lorentz quantum numbers in MSSM, the μi term in Eq (2.1) can be sent to zero via a rotation in the ðLi; HdÞ space [18,27], which will be assumed throughout this paper
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