[Paper Review] $b o s\ell^+\ell^-$ Transitions in Two-Higgs-Doublet Models

Andreas Crivellin, Dario Müller+1 more|arXiv (Cornell University)|Mar 25, 2019

Particle physics theoretical and experimental studies77 references4 citations

TL;DR

This paper investigates $b \to s\ell^+\ell^-$ transitions in two-Higgs-doublet models (2HDMs) with generic Yukawa couplings and right-handed neutrinos, performing one-loop matching to the effective Hamiltonian. It finds that including right-handed neutrinos enables a consistent explanation of both the $b \to s\mu^+\mu^-$ anomalies and the muon anomalous magnetic moment, though stringent constraints from $h \to \tau\mu$ decay limit the viable parameter space due to small Higgs mixing.

ABSTRACT

In this article we study $b o sμ^+μ^-$ transitions and possible correlations with the anomalous magnetic moment of the muon ($a_μ$) within two-Higgs-doublet models with generic Yukawa couplings, including the possibility of right-handed neutrinos. We perform the matching on the relevant effective Hamiltonian and calculate the leading one-loop effects for $b o s\ell\ell^{(\prime)}$, $b o sγ$, $ΔB=ΔS=2$, $b o sν\barν$ and $\ell o\ell^\primeγ$ transitions in a general $R_ξ$ gauge. Concerning the phenomenology, we find that an explanation of the hints for new physics in $b o sμ^+μ^-$ data is possible once right-handed neutrinos are included. If lepton flavour violating couplings are allowed, one can account for the discrepancy in $a_μ$ as well. However, only a small portion of parameter space gives a good fit to $b o sμ^+μ^-$ data and the current bound on $h oτμ$ requires the mixing between the neutral Higgses to be very small if one aims at an explanation of $a_μ$.

Motivation & Objective

• To explore whether two-Higgs-doublet models with generic Yukawa couplings and right-handed neutrinos can simultaneously explain the $b \to s\mu^+\mu^-$ anomalies observed in LHCb data and the long-standing discrepancy in the muon anomalous magnetic moment $a_\mu$.
• To perform a complete one-loop matching onto the effective Hamiltonian for $b\to s\ell^+\ell^-$, $b\to s\gamma$, $\Delta B=\Delta S=2$, $b\to s\nu\bar{\nu}$, and $\ell\to\ell'\gamma$ transitions in a general $R_\xi$ gauge.
• To assess the viability of such models under constraints from $h \to \tau\mu$ decay, which imposes strong limits on neutral Higgs mixing if $a_\mu$ is to be explained.
• To determine whether vector operators—necessary for explaining $b\to s\ell^+\ell^-$ anomalies—can be generated via loop effects in 2HDMs without violating other low-energy precision observables.

Proposed method

• Perform one-loop matching of the 2HDM with generic Yukawa couplings and right-handed neutrinos onto the effective Hamiltonian for $b\to s\ell^+\ell^-$, $b\to s\gamma$, $\Delta B=\Delta S=2$, $b\to s\nu\bar{\nu}$, and $\ell\to\ell'\gamma$ transitions in a general $R_\xi$ gauge.
• Use a general $R_\xi$ gauge to ensure gauge invariance and consistency in loop calculations, particularly for Higgs and gauge boson self-energies.
• Compute leading one-loop contributions involving charged Higgs, neutral Higgs, and right-handed neutrinos, including scalar and vector operators in the effective Hamiltonian.
• Include loop functions $f_i(b)$, $I_j(a,b)$, and $I_{11}(a,b,c)$ to systematically evaluate the amplitude for $b\to s\ell^+\ell^-$ transitions with complex Yukawa couplings.
• Apply constraints from $h \to \tau\mu$ decay, which requires small mixing between the neutral Higgs states to remain consistent with current LHC bounds.
• Perform a global fit to $b\to s\mu^+\mu^-$ data and $a_\mu$, assessing the allowed parameter space under all relevant experimental and theoretical constraints.

Experimental results

Research questions

• RQ1 Can a 2HDM with generic Yukawa couplings and right-handed neutrinos simultaneously explain the $b\to s\mu^+\mu^-$ anomalies observed in LHCb data and the discrepancy in the muon anomalous magnetic moment $a_\mu$?
• RQ2 What is the role of right-handed neutrinos in generating the necessary vector operators (e.g., $O_9$) required to explain $b\to s\ell^+\ell^-$ data, given that scalar operators alone are insufficient?
• RQ3 How do constraints from $h \to \tau\mu$ decay limit the viable parameter space when attempting to explain $a_\mu$ in such models?
• RQ4 Can loop-induced processes like $b\to s\gamma$, $b\to s\nu\bar{\nu}$, and $B_s$-$\bar{B}_s$ mixing be kept consistent with SM predictions in this setup?
• RQ5 What is the impact of Higgs mixing angles on the viability of explaining both $b\to s\mu^+\mu^-$ and $a_\mu$ within the same 2HDM framework?

Key findings

• An explanation of the $b\to s\mu^+\mu^-$ anomalies is possible in 2HDMs with generic Yukawa couplings only when right-handed neutrinos are included, as they enable the necessary vector operators via loop effects.
• The inclusion of lepton-flavor-violating couplings in the right-handed neutrino sector allows for a simultaneous explanation of the $a_\mu$ discrepancy, which is not possible in models without such couplings.
• A small portion of the parameter space—specifically with very small mixing between the neutral Higgs states—can simultaneously satisfy the $b\to s\mu^+\mu^-$ data and the $h \to \tau\mu$ decay constraint.
• The $h \to \tau\mu$ decay branching fraction imposes a strong upper bound on the mixing angle between the CP-even and CP-odd Higgs states, severely restricting the parameter space if $a_\mu$ is to be explained.
• The model remains consistent with $b\to s\gamma$ and $B_s$-$\bar{B}_s$ mixing when the relevant Wilson coefficients are tuned appropriately, though these processes constrain the parameter space.
• The effective Hamiltonian approach, including loop functions $I_j(a,b)$ and $f_i(b)$, successfully captures the full one-loop dynamics of $b\to s\ell^+\ell^-$ transitions in the presence of multiple Higgs states and right-handed neutrinos.