[Paper Review] Probing new physics in class-I $B$-meson decays into heavy-light final states

Fang-Min Cai, Weijun Deng+2 more|arXiv (Cornell University)|Mar 6, 2021

Particle physics theoretical and experimental studies129 references36 citations

TL;DR

This paper investigates anomalies in class-I B-meson decays, specifically $¯x B^0 \to D^+ K^-$ and $¯x B_s^0 \to D_s^{+} \pi^-$, where experimental branching ratios deviate from Standard Model predictions by 4–5σ. Using QCD factorization, it identifies that new physics via four-quark operators with $̳\mu(1 - \gamma^5) \otimes \u0333\mu(1 - \gamma^5)$ structure can explain the deviations at the 1σ level, while other Dirac structures fail even at 2σ.

ABSTRACT

With updated experimental data and improved theoretical calculations, several significant deviations are being observed between the Standard Model predictions and the experimental measurements of the branching ratios of $\bar{B}_{(s)}^0 o D_{(s)}^{(*)+} L^-$ decays, where $L$ is a light meson from the set $\{\pi, ho,K^{(\ast)}\}$. Especially for the two channels $\bar{B}^0 o D^{+}K^-$ and $\bar{B}_{s}^0 o D_{s}^{+}\pi^-$, both of which are free of the weak annihilation contribution, the deviations observed can even reach 4-5$\sigma$. Here we exploit possible new-physics effects in these class-I non-leptonic $B$-meson decays within the framework of QCD factorization. Firstly, we perform a model-independent analysis of the effects from twenty linearly independent four-quark operators that can contribute, either directly or through operator mixing, to the quark-level $b o c\bar{u} d(s)$ transitions. It is found that, under the combined constraints from the current experimental data, the deviations observed could be well explained at the $1\sigma$ level by the new-physics four-quark operators with $\gamma^{\mu}(1-\gamma_5)\otimes\gamma_{\mu} (1-\gamma_5)$ structure, and also at the $2\sigma$ level by the operators with $(1+\gamma_5)\otimes(1-\gamma_5)$ and $(1+\gamma_5)\otimes(1+\gamma_5)$ structures. However, the new-physics four-quark operators with other Dirac structures fail to provide a consistent interpretation, even at the $2\sigma$ level. Then, as two specific examples of model-dependent considerations, we discuss the case where the new-physics four-quark operators are generated by either a colorless charged gauge boson or a colorless charged scalar, with their masses fixed both at the $1$~TeV. Constraints on the effective coefficients describing the couplings of these mediators to the relevant quarks are obtained by fitting to the current experimental data.

Motivation & Objective

• . The paper aims to explain significant deviations between Standard Model predictions and experimental measurements of branching ratios in class-I non-leptonic B-meson decays.
• It focuses on two clean channels, $\bar{B}^0 \to D^+K^-$ and $\bar{B}_s^0 \to D_s^+\pi^-$, which are free from weak annihilation contributions and show 4–5σ discrepancies.
• The objective is to determine whether these anomalies can be consistently explained by new physics via four-quark operators within the QCD factorization framework.
• It further explores model-dependent realizations of such new physics through a colorless charged gauge boson and a colorless charged scalar, both at 1 TeV mass.

Proposed method

• . The study employs QCD factorization (QCDF) to compute decay amplitudes, separating short-distance hard interactions from long-distance hadronic matrix elements.
• It performs a model-independent analysis of 20 linearly independent four-quark operators contributing to $b \to c\bar{u}d(s)$ transitions, including their mixing under renormalization.
• The hadronic matrix elements are evaluated using B(s) → D(∗)(s) transition form factors and light-cone distribution amplitudes of the final-state light mesons.
• Perturbative corrections up to next-to-leading order (NLO) in αs are included in the hard kernels Tij(u), ensuring high-precision amplitude calculations.
• For model-dependent analysis, the paper considers two specific mediators: a colorless charged gauge boson and a colorless charged scalar, each with mass fixed at 1 TeV.
• Effective couplings of these mediators to quarks are constrained by fitting to current experimental data on branching ratios and ratios R(∗)L.

Experimental results

Research questions

• RQ1 . Can the observed 4–5σ deviations in $\bar{B}^0 \to D^+K^-$ and $\bar{B}_s^0 \to D_s^+\pi^-$ branching ratios be explained by new physics in the four-quark operators?
• RQ2 . Which Dirac structures of four-quark operators are consistent with the current experimental data at the 1σ or 2σ level?
• RQ3 . Can the new physics contributions be realized through specific mediators such as a colorless charged gauge boson or scalar at 1 TeV mass?
• RQ4 . What are the allowed ranges for the effective Wilson coefficients of these new physics operators under combined experimental constraints?
• RQ5 . How do the predictions for ratios like Rπ, Rρ, RK, etc., constrain the new physics parameter space?

Key findings

• . The new physics four-quark operators with $\gamma^\mu(1 - \gamma^5) \otimes \gamma^\mu(1 - \gamma^5)$ structure can explain the observed deviations at the 1σ confidence level.
• . Operators with $(1 + \gamma^5) \otimes (1 - \gamma^5)$ and $(1 + \gamma^5) \otimes (1 + \gamma^5)$ structures are consistent at the 2σ level.
• . All other Dirac structures fail to provide a consistent explanation even at the 2σ level.
• . For a colorless charged gauge boson at 1 TeV, the allowed range for the effective coupling coefficient $C_{LL}^{(1)}(m_b)$ is $[-2.65, -0.849]$ at 1σ, and $[-4.06, -0.209]$ at 2σ.
• . For a colorless charged scalar at 1 TeV, the allowed range for $C_{LL}^{(1)}(m_b)$ is $[-2.54, -0.759]$ at 1σ, and $[-3.69, -0.191]$ at 2σ.
• . The combined constraints from all ten ratios $R^{(*)}_{(s)L}$ yield the tightest bounds, with $C_{LL}^{(1)}(m_b)$ constrained to $[-2.65, -0.849]$ at 1σ and $[-4.06, -0.209]$ at 2σ.