[Paper Review] Review of Semileptonic $B$ Anomalies

Bernat Capdevila, Andreas Crivellin+1 more|arXiv (Cornell University)|Sep 4, 2023

Particle physics theoretical and experimental studiesPhysics and Astronomy176 references3 citations

TL;DR

This paper reviews anomalies in semi-leptonic B decays, identifying significant deviations from Standard Model predictions in b →sℓ+ℓ− and b →cτν transitions. It proposes a combined New Physics explanation via a left-handed vector current (e.g., U1 leptoquark or S1+S3 scalar leptoquarks) that simultaneously explains R(D∗), the P′5 anomaly, and RK, achieving a global significance of 6.3σ with a 20% NP contribution to CU9.

ABSTRACT

We review the current status and implications of the anomalies (i.e. deviations from the Standard Model predictions) in semi-leptonic $B$ meson decays, both in the charged and in the neutral current. In $b o s\ell^+\ell^-$ transitions significant tensions between measurements and the Standard Model predictions exist. They are most pronounced in the branching ratios ${\cal B}_{B o Kμ^+μ^-}$ and ${\cal B}_{B_s oϕμ^+μ^-}$ (albeit quite dependent on the form factors used) as well as in angular observables in $B o K^*μ^+μ^-$ (the $P_5^\prime$ anomaly). Because the measurements of ${\cal B}_{B_s o μ^+μ^-}$ and of the ratios $R_K$ and $R_{K^*}$ agree reasonably well with the SM predictions, this points towards (dominantly) lepton flavour universal New Physics coupling vectorially to leptons, i.e. contributions to $C_9^{ m U}$. In fact, global fits prefer this scenario over the SM hypothesis by $5.8σ$. Concerning $b o cτν$ transitions, $R(D)$ and $R(D^*)$ suggest constructive New Physics at the level of $10\%$ (w.r.t. the Standard Model amplitude) with a significance above $3σ$. We discuss New Physics explanations of both anomalies separately as well as possible combined explanations. In particular, a left-handed vector current solution to $R(D^{(*)})$, either via the $U_1$ leptoquark or the combination of the scalar leptoquarks $S_1$ and $S_3$, leads to an effect in $C_9^{ m U}$ via an off-shell penguin with the right sign and magnitude and a combined significance (including a tree-level effect resulting in $C_{9μ}^\mathrm{V}=-C_{10μ}^\mathrm{V}$ and $R(D^{(*)})$) of $6.3σ$. Such a scenario can be tested with $b o s τ^+τ^-$ decays. Finally, we point out an interesting possible correlation of $R(D^{(*)})$ with non-leptonic $B$ anomalies.

Motivation & Objective

• To assess the current experimental and theoretical status of semi-leptonic B decay anomalies.
• To evaluate global fits of New Physics explanations for both b→sℓ+ℓ− and b→cτν anomalies.
• To explore combined explanations that simultaneously address multiple anomalies with a single NP framework.
• To identify testable predictions, such as b→sτ+τ− decays, for the proposed NP scenarios.

Proposed method

• Performs global fits of semi-leptonic B decay observables using Weak Effective Theory (WET) and effective Hamiltonians.
• Analyzes branching ratios, angular observables (e.g., P′5), and LFU ratios (RK, RK∗) in B→K∗μ+μ−, Bs→ϕμ+μ−, and B→Kμ+μ−.
• Applies optimized observables P′1,2,3,4,5,6,8 to reduce hadronic uncertainties and enhance sensitivity to short-distance NP.
• Considers model-independent fits and specific NP models, including U1 leptoquarks, scalar leptoquarks S1 and S3, and Z′ bosons.
• Evaluates NP contributions to Wilson coefficients C9 and C10, particularly C9μ and C10μ, and their impact on R(D∗) and R(K∗).
• Uses data-driven charm loop determination in unbinned LHCb analysis to validate NP contributions to P′5.

Experimental results

Research questions

• RQ1 What is the global significance of the combined b→sℓ+ℓ− and b→cτν anomalies when interpreted as New Physics?
• RQ2 Can a single NP model explain both the R(D∗) anomaly and the P′5 anomaly in B→K∗μ+μ−?
• RQ3 What are the implications of the U1 leptoquark or S1+S3 scalar leptoquark models for both LFU-violating and LFU-conserving observables?
• RQ4 How do constraints from Bs−B¯s mixing and b→sτ+τ− decays affect viable NP scenarios?
• RQ5 What is the predictive power of the combined scenario for future measurements, such as R(B→Kτ+τ−)?

Key findings

• Global fits prefer a New Physics scenario with vectorial coupling to leptons (CU9) over the SM by 5.8σ, with a combined significance of 6.3σ when including R(D∗).
• The P′5 anomaly in B→K∗μ+μ− shows a ∼2σ deviation in two bins, supported by charged mode measurements.
• The U1 leptoquark model with U(2)q flavour symmetry naturally links R(D∗) and P′5 anomalies, predicting RK = 0.909 ± 0.060 and RK∗ = 0.914 ± 0.053.
• The scenario predicts measurable b→sτ+τ− branching ratios at the level of R(D∗), with rates potentially testable at LHCb.
• An explanation via S1 leptoquark may also correlate with emerging non-leptonic B decay anomalies.
• An unbinned LHCb analysis confirms that a NP contribution to C9 of the same size as in prior fits is required to explain P′5, even with data-driven charm loop determination.