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Scalar flavour-changing neutral currents in the large-tan(beta) limit

Gino Isidori, Alessandra Retico

TL;DR

This work analyzes scalar flavor-changing neutral currents in two-Higgs-doublet frameworks with large tanβ, contrasting non-supersymmetric 2HDMs and the MSSM. It identifies the origin of tanβ enhancements in both ΔF=1 and ΔF=2 processes as arising from loop-induced couplings between H_u and down-type quarks, governed by parameters ε_0 and ε_Y, and shows how these enhancements differ between SUSY and non-SUSY realizations. The study derives initial conditions for Wilson coefficients in the effective Hamiltonians, evaluates the impact of box and double-penguin diagrams, and provides numerical bounds on the parameter space from ΔM_{d,s} and rare decays. It highlights B_{s,d} → ℓ^+ℓ^- decays, especially B_s → μ^+μ^-, as the most sensitive probes of large-tanβ scalar FCNCs, with potential order-of-magnitude enhancements in the MSSM under certain parameter choices, while B_{s,d} → τ^+τ^- offer complementary constraints and opportunities for discovery at future facilities.

Abstract

We analyse scalar flavour-changing neutral currents of down-type quarks in models with two Higgs doublets, coupled separately to up- and down-type quarks, in the limit where the ratio of the two expectation values ($\tan β= v_u/v_d$) is large. We clarify the origin of this phenomenon, both in $ΔF=1$ and $ΔF=2$ processes, analysing differences and analogies between supersymmetric and non-supersymmetric models. We confirm previous findings of a sizeable enhancement at large $\tanβ$ of specific $ΔF=1$ and $ΔF=2$ amplitudes in the MSSM and, in these cases, we discuss how large-$\tanβ$ corrections can be controlled beyond lowest order. Finally, we emphasize the unique role of the rare processes $B_{s,d} \to τ^+ τ^-$ and $B_{s,d} \to μ^+ μ^-$ in probing this scenario.

Scalar flavour-changing neutral currents in the large-tan(beta) limit

TL;DR

This work analyzes scalar flavor-changing neutral currents in two-Higgs-doublet frameworks with large tanβ, contrasting non-supersymmetric 2HDMs and the MSSM. It identifies the origin of tanβ enhancements in both ΔF=1 and ΔF=2 processes as arising from loop-induced couplings between H_u and down-type quarks, governed by parameters ε_0 and ε_Y, and shows how these enhancements differ between SUSY and non-SUSY realizations. The study derives initial conditions for Wilson coefficients in the effective Hamiltonians, evaluates the impact of box and double-penguin diagrams, and provides numerical bounds on the parameter space from ΔM_{d,s} and rare decays. It highlights B_{s,d} → ℓ^+ℓ^- decays, especially B_s → μ^+μ^-, as the most sensitive probes of large-tanβ scalar FCNCs, with potential order-of-magnitude enhancements in the MSSM under certain parameter choices, while B_{s,d} → τ^+τ^- offer complementary constraints and opportunities for discovery at future facilities.

Abstract

We analyse scalar flavour-changing neutral currents of down-type quarks in models with two Higgs doublets, coupled separately to up- and down-type quarks, in the limit where the ratio of the two expectation values () is large. We clarify the origin of this phenomenon, both in and processes, analysing differences and analogies between supersymmetric and non-supersymmetric models. We confirm previous findings of a sizeable enhancement at large of specific and amplitudes in the MSSM and, in these cases, we discuss how large- corrections can be controlled beyond lowest order. Finally, we emphasize the unique role of the rare processes and in probing this scenario.

Paper Structure

This paper contains 15 sections, 56 equations, 6 figures.

Table of Contents

  1. Introduction
  2. $\Delta F=1$ scalar currents
  3. The effective down-type Yukawa interaction
  4. Explicit estimates of $\epsilon_Y$
  5. $d_i \to d_j \ell^+\ell^-$ transitions
  6. $B_{d,s}$--${\bar{B}}_{d,s}$ mixing
  7. Generalities
  8. $\Delta B=2$ box diagrams
  9. Double-penguin diagrams
  10. Numerical bounds from $\Delta M_{d,s}$ in the MSSM
  11. Phenomenology of $B_{s,d} \to \ell^+ \ell^-$ decays
  12. Effective Hamiltonian
  13. Branching ratios
  14. Conclusions
  15. Loop functions

Figures (6)

  • Figure 1: Penguin diagrams generating a non-vanishing $\epsilon_Y$: a) non-supersymmetric $H_u$--$H_d$ mixing; b) chargino mixing.
  • Figure 2: Feynman diagrams relevant to the $d^i_R \to d_L^j \ell_L \ell_R$ amplitude: a) leading contribution computed by means of the effective Yukawa interaction; b) one-loop contribution to the mass mixing in the 2HDM.
  • Figure 3: Double-penguin diagram contributing to $C^{SLR}$; the black boxes denote the effective FCNC Yukawa interaction of Eq. (\ref{['eq:L_FCNC2']}).
  • Figure 4: Leading box-diagram contribution to $C^{SLL}$ in the non-supersymmetric 2HDM.
  • Figure 5: $h(x_{\mu L},x_{R L})$ as a function of $x_{L\mu}$$(=1/x_{\mu L})$ for different values of $x_{R L}$.
  • ...and 1 more figures