[Paper Review] Does Supersymmetry Require Two Higgs Doublets?

Masahiro Ibe, Arvind Rajaraman+1 more|arXiv (Cornell University)|Dec 22, 2010

Particle physics theoretical and experimental studies6 citations

TL;DR

This paper proposes a class of low-energy supersymmetric models with a chiral Higgs sector containing only one Higgs doublet ($H_u$), not $H_d$, by introducing new electroweak-charged chiral states to cancel gauge anomalies. The model generates down-type fermion masses via higher-dimensional operators involving $H_u$, avoiding the $μ$-problem and enabling novel dark matter phenomenology, with viable UV completions and distinct LHC signatures due to new colored or highly charged particles.

ABSTRACT

We discuss a new class of low energy supersymmetric models in which the Higgs sector includes a single doublet, for example H_u, but not H_d. Chiral gauge anomalies are canceled against new electroweak-charged states. We discuss the main challenges in building such models, and present several models where these issues are addressed. The resulting phenomenology can be distinguished from that of the MSSM in a number of ways, most notably in physics related to down-type quarks and charged leptons. As a first step toward a chiral Higgs sector, we discuss the scenario of an inert H_d doublet. We show that a UV completion of such model naturally includes dark matter with novel, flavorful couplings to SM quarks.

Motivation & Objective

• To construct anomaly-free, phenomenologically viable supersymmetric models that require only one Higgs doublet ($H_u$) instead of the standard pair ($H_u$, $H_d$) in the MSSM.
• To address the challenge of generating down-type quark and charged lepton masses without $H_d$, using higher-dimensional operators from supersymmetry breaking.
• To explore the viability of a chiral Higgs sector by constructing effective field theories and UV-complete models with new chiral matter.
• To identify distinctive phenomenological signatures, such as enhanced Higgs production and novel LHC signals, from new colored or highly charged particles.
• To investigate the potential for flavorful dark matter with novel couplings to SM quarks via an inert $H_d$ doublet in a UV-complete framework.

Proposed method

• Introduce a chiral Higgs sector with only $H_u$, where $H_d$ is either inert (no couplings to SM fermions) or absent, to avoid the $μ$-problem.
• Cancel chiral gauge anomalies using new electroweak-charged chiral superfields that are given large masses to ensure phenomenological viability.
• Generate down-type fermion masses via higher-dimensional operators involving $H_u$, $F_X$ (supersymmetry breaking), and a cutoff scale $M$, via terms like $\int d^4\theta \frac{X^\dagger}{M^2} H_u^\dagger Q \bar{d}$.
• Construct UV-complete models using additional chiral superfields such as $T$, $D$, $\rho$, $\phi$, and $N$ to realize anomaly cancellation and mass generation through Yukawa and non-holomorphic terms.
• Use the superpotential and Kähler potential to derive mass terms for new particles and the Higgsino, ensuring consistency with supersymmetry and gauge invariance.
• Analyze the resulting spectrum and phenomenology, including the $S$ and $T$ parameters, Higgs production cross sections, and collider signatures from new colored or highly charged states.

Experimental results

Research questions

• RQ1 Can a supersymmetric model with only one Higgs doublet ($H_u$) be anomaly-free and phenomenologically viable?
• RQ2 How can down-type quark and charged lepton masses be generated without a $H_d$ doublet, while preserving gauge and supersymmetry consistency?
• RQ3 What are the implications of an inert $H_d$ doublet that couples only to the Higgsino and not to SM fermions?
• RQ4 Can a fully chiral Higgs sector be constructed with a single $H_u$ doublet, and what are the necessary new chiral fields for anomaly cancellation?
• RQ5 What distinctive collider signals, such as enhanced Higgs production or exotic decays, arise from such chiral Higgs models?

Key findings

• Anomalies are canceled by introducing new chiral superfields that are given large masses, ensuring the model remains viable despite the absence of $H_d$.
• Down-type fermion masses are generated via higher-dimensional operators involving $H_u$, $F_X$, and a cutoff scale $M$, with the mass matrix $m_d = y'_{d} v_u \frac{F_X}{M^2} + Y_d v_d$, allowing for large $\tan\beta$ without perturbativity issues.
• In the inert $H_d$ scenario, the $b\bar{b}$ decay rate of the Higgs is suppressed by $1/\tan^2\beta$ compared to MSSM, and $H_u$ behaves like the SM Higgs.
• UV-complete models with a mirror fourth generation or multiple Higgs doublets (e.g., three or four) are constructed, featuring doubly, triply, or quadruply charged particles.
• The Higgs production cross section is significantly enhanced in models with a mirror fourth generation, making them testable at the LHC, with $m_h < 600~{\rm GeV}$ already excluded by CMS at 95% C.L.
• The models predict novel LHC signatures due to new colored or highly charged chiral states, offering a way to distinguish them from the MSSM and other extensions.