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b-physics signals of the lightest CP-odd Higgs in the NMSSM at large tan beta

Gudrun Hiller

TL;DR

This work analyzes the low-energy signatures of a light CP-odd Higgs $A_1^0$ in the NMSSM at large $\tan\beta$ by computing the $b \to s A_1^0$ amplitude at leading order in $\tan\beta$ and exploring the ensuing constraints from rare $K$/ $B$ decays, $B-\bar B$ mixing, and $B_s \to \mu^+ \mu^-$. It shows that $m_{A_1^0}$ can be as small as ${\cal O}(10)$ MeV and that neutral-Higgs effects can induce sizeable renormalization of the photon and gluon dipole operators, breaking the MSSM correlation between $B_s \to \mu^+ \mu^-$ and $\Delta m_s$. The NMSSM-specific features, such as large loop-induced effects and a potential breakdown of MSSM-like relations, yield distinctive predictions for $b$-physics, including possible signals in $b \to s \ell^+ \ell^-$, $b \to s \gamma$, and $b \to s \tau^+ \tau^-$ processes, as well as in radiative $\Upsilon$ decays. Overall, the paper maps viable NMSSM parameter space and highlights concrete experimental channels to probe a light $A_1^0$.

Abstract

We investigate the low energy phenomenology of the lighter pseudoscalar $A_1^0$ in the NMSSM. The $A_1^0$ mass can naturally be small due to a global $U(1)_R$ symmetry of the Higgs potential, which is only broken by trilinear soft terms. The $A_1^0$ mass is further protected from renormalization group effects in the large $\tan β$ limit. We calculate the $b \to s A_1^0$ amplitude at leading order in $\tan β$ and work out the contributions to rare $K$, $B$ and radiative $Υ$-decays and $B -\bar B$ mixing. We obtain constraints on the $A_1^0$ mass and couplings and show that masses down to ${\cal{O}}(10)$ MeV are allowed. The $b$-physics phenomenology of the NMSSM differs from the MSSM in the appearance of sizeable renormalization effects from neutral Higgses to the photon and gluon dipole operators and the breakdown of the MSSM correlation between the $B_s \to μ^+ μ^-$ branching ratio and $B_s - \bar B_s$ mixing. For $A_1^0$ masses above the tau threshold the $A_1^0$ can be searched for in $b \to s τ^+ τ^-$ processes with branching ratios $\lsim 10^{-3}$.

b-physics signals of the lightest CP-odd Higgs in the NMSSM at large tan beta

TL;DR

This work analyzes the low-energy signatures of a light CP-odd Higgs in the NMSSM at large by computing the amplitude at leading order in and exploring the ensuing constraints from rare / decays, mixing, and . It shows that can be as small as MeV and that neutral-Higgs effects can induce sizeable renormalization of the photon and gluon dipole operators, breaking the MSSM correlation between and . The NMSSM-specific features, such as large loop-induced effects and a potential breakdown of MSSM-like relations, yield distinctive predictions for -physics, including possible signals in , , and processes, as well as in radiative decays. Overall, the paper maps viable NMSSM parameter space and highlights concrete experimental channels to probe a light .

Abstract

We investigate the low energy phenomenology of the lighter pseudoscalar in the NMSSM. The mass can naturally be small due to a global symmetry of the Higgs potential, which is only broken by trilinear soft terms. The mass is further protected from renormalization group effects in the large limit. We calculate the amplitude at leading order in and work out the contributions to rare , and radiative -decays and mixing. We obtain constraints on the mass and couplings and show that masses down to MeV are allowed. The -physics phenomenology of the NMSSM differs from the MSSM in the appearance of sizeable renormalization effects from neutral Higgses to the photon and gluon dipole operators and the breakdown of the MSSM correlation between the branching ratio and mixing. For masses above the tau threshold the can be searched for in processes with branching ratios .

Paper Structure

This paper contains 18 sections, 55 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The $b \to s A_1^0$ amplitude at large $\tan \beta$
  3. Viable points in the NMSSM parameter space
  4. Phenomenology of the light ${A_1^0}$
  5. Rare $K$ and $B$-decays
  6. $2 m_e < m_{A_1^0} <2 m_\mu$
  7. $2 m_\mu <m_{A_1^0} < 2 m_\tau$
  8. $2 m_\tau < m_{A_1^0} \stackrel{<}{_\sim} m_B$
  9. NMSSM neutral Higgs contributions to $B -\bar{B}$ mixing
  10. $B_s \to \mu^+ \mu^-$ decays
  11. Non-FCNC bounds
  12. Implications for $b \to s \ell^+ \ell^-$ and $b \to s \gamma, g$
  13. Estimates of $C_S+C_P$ and $C_R^b$
  14. Conclusions
  15. Higgs spectrum and couplings
  16. ...and 3 more sections

Figures (3)

  • Figure 1: The leading $b \to s A_1^0$ diagrams at large $\tan \beta$ in the NMSSM.
  • Figure 2: Constraints on the $A_1^0$ mass as a function of $|\delta_- v/x|$ at $\tan \beta=30$ in the NMSSM. Shaded regions are excluded. The left bottom corner is excluded by rare $K$-decay, see Eq. (\ref{['eq:Ktopi']}). The triangular region to the lower right is obtained from radiative $\Upsilon(1s)$ decays, see Eq. (\ref{['eq:yps']}). The region to the left of the vertical dashed blue lines can only be reached if $m_A$ is bigger than the value indicated, see Section \ref{['sec:space']}. Constraints from $\Delta m_d$ are given for $m_A \geq 500$ GeV and $m_A\geq 1000$ GeV. We also show the missing energy condition for $B \to K$ decays given in Eq. (\ref{['eq:nunubound']}) (dashed green line). The vertical dashed lines indicate $m_{A_1^0}= 2 m_\mu$ and $3 m_\pi$.
  • Figure 3: The correlation between $C_S+C_P$ and $\sqrt{|C_S|^2+|C_P+\delta_{10}^{SM}|^2 }$ in the NMSSM for $\tan \beta=30$, $m_{A}=500$ GeV and $m_{A_1^0}=0.1 , 1$ and $10$ GeV. Also shown is the experimental upper bound given in Eq. (\ref{['eq:CSPbound']}) (dashed line).