[Paper Review] Challenges for New Physics in the Flavour Sector

Andreas Crivellin|arXiv (Cornell University)|Sep 2, 2014

Particle physics theoretical and experimental studies191 references3 citations

TL;DR

This paper examines the challenges of embedding new physics (NP) in the flavour sector, focusing on models that reconcile deviations in $B \to K^{*}\mu^{+}\mu^{-}$ and tauonic $B$ decays with stringent constraints from rare decays and $\Delta F=2$ processes. It analyzes the 2HDM in the decoupling limit and identifies that generic flavour structures often lead to tensions, while models with specific couplings—such as those involving $Z'$ or scalar interactions—can explain anomalies without violating flavour bounds.

ABSTRACT

In these proceedings I present a personal perspective of the challenges for new physics (NP) searches in the flavour sector. Since the CKM mechanism of flavour violation has been established to a very high precision, we know that physics beyond the Standard Model can only contribute sub-dominantly. Therefore, any realistic model of physics beyond the Standard Model (SM) must respect the stringent constrains from flavour observables like $b o s γ$, $B_s oμ^+μ^-$, $ΔF=2$ processes etc., in a first step. In a second step, it is interesting to ask the question if some deviations from the SM predictions (like the anomalous magnetic moment of the muon or recently observed discrepancies in tauonic $B$ decays or $B o K^*μ^+μ^-$) can be explained by a model of NP without violating bounds from other observables.

Motivation & Objective

• To assess the viability of new physics models in the flavour sector that explain observed deviations from the Standard Model (SM) predictions.
• To analyze how stringent constraints from $\Delta F=2$ processes, radiative decays ($b \to s\gamma$), and $B_{s} \to \mu^{+}\mu^{-}$ decays limit viable NP models.
• To investigate whether models explaining anomalies in $B \to K^{*}\mu^{+}\mu^{-}$ and tauonic $B$ decays can simultaneously satisfy all existing flavour observables.
• To evaluate the role of flavour structures—such as non-holomorphic couplings and $Z'$-mediated interactions—in balancing anomalies and constraints.
• To determine whether the observed tensions in $B \to K^{*}\mu^{+}\mu^{-}$ and $R_K$ measurements can be explained by minimal flavour violation or require more complex NP structures.

Proposed method

• Uses the 2HDM in the decoupling limit as a benchmark model, with generic Yukawa couplings that allow for non-holomorphic flavour-changing neutral currents (FCNCs).
• Applies effective field theory techniques to derive the low-energy Lagrangian, including terms with $H_u^1$, $H_d^2$, and $\epsilon^{q}_{ij}$ parameters for flavour-violating couplings.
• Performs a global fit to flavour observables, including $B_{s,d} \to \mu^{+}\mu^{-}$, $b \to s\gamma$, $K^0$-$\overline{K}^0$ mixing, and $\mu \to e\gamma$, to constrain NP parameters.
• Analyzes $B \to K^{*}\mu^{+}\mu^{-}$ decay angular distributions and $R_K$ ratios to identify deviations from SM predictions.
• Compares model predictions with experimental data from LHCb, BaBar, and CDF, focusing on $q^2$-dependent observables and form-factor-independent measurements.
• Evaluates the viability of $Z'$-boson and scalar-mediated NP models in explaining anomalies while remaining consistent with $\Delta F=2$ and lepton flavour violation bounds.

Experimental results

Research questions

• RQ1 Can a 2HDM with generic Yukawa couplings explain the $B \to K^{*}\mu^{+}\mu^{-}$ anomalies without violating constraints from $B_{s} \to \mu^{+}\mu^{-}$ or $b \to s\gamma$?
• RQ2 To what extent do $\mu \to e\gamma$ and $K_L \to \mu^+\mu^-$ bounds constrain the parameter space of 2HDM models with non-holomorphic couplings?
• RQ3 Can $Z'$-boson or scalar-mediated NP explain the $R_K$ anomaly and $B \to K^{*}\mu^{+}\mu^{-}$ data while satisfying $\Delta F=2$ and $\ell_i \to \ell_f \gamma$ bounds?
• RQ4 How do $\epsilon^{q}_{ij}$ parameters in the 2HDM Lagrangian affect the compatibility of NP models with global flavour fits?
• RQ5 What is the impact of non-minimal flavour structures on the tension between $B \to K^{*}\mu^{+}\mu^{-}$ data and SM predictions?

Key findings

• The 2HDM with generic Yukawa couplings leads to strong constraints from $\Delta F=2$ processes and $B_{s} \to \mu^{+}\mu^{-}$, limiting the size of NP contributions to less than 10% in most cases.
• Models with $Z'$-boson exchange can explain the $B \to K^{*}\mu^{+}\mu^{-}$ anomaly and $R_K$ deviation while remaining consistent with $B_{s} \to \mu^{+}\mu^{-}$ and $\mu \to e\gamma$ bounds, provided the $Z'$ couples preferentially to third-generation fermions.
• Scalar-mediated NP models, particularly those with $Z'$-like couplings to $b \to s\mu\mu$, can explain the $B \to K^{*}\mu^{+}\mu^{-}$ angular distribution anomalies without violating $\Delta F=2$ constraints.
• The $R_K$ anomaly—measured as $R_K = \text{Br}(B \to K \mu^+\mu^-)/\text{Br}(B \to K e^+e^-)$—shows a 2.5–3σ deviation from the SM, suggesting possible lepton flavour non-universality.
• The $B \to K^{*}\mu^{+}\mu^{-}$ angular distribution exhibits a significant deviation from SM predictions in the low-$q^2$ region, particularly in the $P_5'$ observable, which is not explained by SM QCD corrections.
• Non-minimal flavour structures, such as non-holomorphic couplings in the 2HDM, often lead to tensions with $\mu \to e\gamma$ and $K_L \to \mu^+\mu^-$, requiring fine-tuning or additional symmetries to remain viable.