[Paper Review] Diquark Explanation of $b o s\ell^+\ell^-$

Andreas Crivellin, M. Kirk|Zurich Open Repository and Archive (University of Zurich)|Sep 13, 2023

Particle physics theoretical and experimental studiesPhysics and Astronomy151 references3 citations

TL;DR

This paper proposes a diquark-mediated mechanism in which a colored scalar (diquark) induces a Wilson coefficient for the $(\bar{s}\gamma^\mu P_L b)(\bar{c}\gamma_\mu P_L c)$ operator at tree level, which then mixes into the $C_9$ coefficient via an off-shell photon penguin. The model successfully explains the $b\to s\ell^+\ell^-$ anomalies with a lepton-flavor-universal $C_9 \approx -0.5$, consistent with $R(K^{(*)})$ and $B_s\to\mu^+\mu^-$ data, while evading constraints from $\Delta M_s$, $\Delta\Gamma$, $B\to X_s\gamma$, and $D^0$-$\bar{D}^0$ mixing, predicting a light diquark mass around 500 GeV.

ABSTRACT

The discrepancies between $b o s\ell^+\ell^-$ data and the corresponding Standard Model predictions point to the existence of new physics with a significance at the $5σ$ level. While previously a lepton flavour universality violating effect was preferred, the new $R(K^{(*)})$ and $B_s oμ^+μ^-$ measurements are now compatible with the Standard Model, favouring a lepton flavour universal beyond the Standard Model contribution to $C_9$. Since heavy new physics is generally chiral, and because of the stringent constraints from charged lepton flavour violation, this poses a challenge for model building. In this article, we point out a novel possibility: a diquark, i.e. a coloured scalar, induces the Wilson coefficient of the $(\bar s γ^μP_L b) (\bar c γ_μP_L c)$ operator at tree-level, which then mixes into $O_9$ via an off-shell photon penguin. This setup allows for a lepton flavour universal effect of $C_9\approx-0.5$, without violating bounds from $ΔM_s$, $ΔΓ$, $B o X_sγ$ and $D^0-\bar D^0$ mixing. This scenario predicts a small and negative $C_9^{\prime}$ and a light diquark, preferably with a mass around $500\,$GeV, as compatible with the CMS di-di-jet analysis, and a deficit in the inclusive $b o c\bar c s$ rate.

Motivation & Objective

• To resolve the persistent $b\to s\ell^+\ell^-$ anomalies in $B$ decays, particularly the $P_5'$ and branching ratio tensions, which remain at $4.7\sigma$ in the $B\to K\mu^+\mu^-$ mode.
• To address the challenge of constructing a lepton-flavor-universal new physics model that avoids stringent constraints from charged lepton flavor violation (cLFV), especially $\mu\to e\gamma$.
• To explore a novel mechanism where a colored scalar (diquark) mediates the $b\to s\ell^+\ell^-$ transition via tree-level coupling to $\bar{c}c$ current, followed by penguin-induced mixing into $C_9$.
• To identify a viable, minimal model that explains the $C_9$ anomaly with $C_9 \approx -0.5$ while remaining compatible with $B_s\to\mu^+\mu^-$, $\Delta M_s$, $\Delta\Gamma$, and $B\to X_s\gamma$ constraints.

Proposed method

• A colored scalar (diquark) couples to the $(\bar{s}\gamma^\mu P_L b)(\bar{c}\gamma_\mu P_L c)$ operator at tree level, generating a non-universal $C_9$-like contribution.
• The diquark-induced operator mixes into the $C_9$ Wilson coefficient via an off-shell photon penguin diagram, enabling a lepton-flavor-universal $C_9$ contribution.
• The model is analyzed using effective field theory techniques, with loop functions and matching conditions derived from the full UV theory involving the diquark and quark couplings.
• Constraints from $\Delta M_s$, $\Delta\Gamma$, $B\to X_s\gamma$, $D^0$-$\bar{D}^0$ mixing, and $\mu\to e\gamma$ are evaluated using existing experimental bounds and lattice QCD inputs.
• The model predicts a small, negative $C_9'$ and a light diquark mass around 500 GeV, consistent with the CMS di-jet resonance search.
• The $B_s$ lifetime ratio and semi-leptonic asymmetry $a_{\text{sl}}^s$ are evaluated to test consistency, though current precision limits their sensitivity.

Experimental results

Research questions

• RQ1 Can a diquark-mediated mechanism generate a lepton-flavor-universal $C_9$ contribution to $b\to s\ell^+\ell^-$ decays that explains the observed anomalies without violating cLFV bounds?
• RQ2 How can a tree-level coupling to $\bar{c}c$ currents generate a $C_9$-like effect via penguin mixing, and what are the resulting constraints on the diquark mass and couplings?
• RQ3 Is the model consistent with the latest $R(K^{(*)})$ and $B_s\to\mu^+\mu^-$ measurements, which now favor lepton-flavor universality?
• RQ4 What are the implications of the model for $\Delta M_s$, $\Delta\Gamma$, $B\to X_s\gamma$, and $D^0$-$\bar{D}^0$ mixing, and can it evade these stringent constraints?
• RQ5 Does the model predict a measurable signal in di-jet resonance searches, and is the diquark mass compatible with the CMS di-jet analysis?

Key findings

• The model successfully generates a lepton-flavor-universal $C_9 \approx -0.5$, which is the dominant explanation for the $b\to s\ell^+\ell^-$ anomalies in the current global fit.
• The diquark-induced operator mixes into $C_9$ via an off-shell photon penguin, enabling a tree-level $\bar{c}c$ coupling while preserving lepton universality.
• The model predicts a small and negative $C_9' \approx -0.1$, which is consistent with current experimental bounds and does not introduce new tensions.
• A light diquark with mass around 500 GeV is favored, and this is compatible with the CMS di-jet resonance search, which shows no significant signal but allows for such a state.
• The model evades constraints from $\Delta M_s$, $\Delta\Gamma$, $B\to X_s\gamma$, and $D^0$-$\bar{D}^0$ mixing due to the specific structure of the diquark couplings and the absence of large GIM cancellations.
• The $B_s$ lifetime ratio and semi-leptonic asymmetry $a_{\text{sl}}^s$ are predicted to deviate from the SM, but the current experimental precision is too low to distinguish the model from the SM.