[Paper Review] Muon g-2 and a type-X two Higgs doublet scenario: some studies in high-scale validity

Atri Dey, Jayita Lahiri+1 more|arXiv (Cornell University)|Jun 2, 2021

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper investigates the high-scale validity of a Type-X two Higgs doublet model (2HDM) that explains the observed muon anomalous magnetic moment ($g-2$) through a light pseudoscalar boson. Using two-loop renormalization group equations, it identifies parameter regions—particularly with large $ aneta$ and degenerate non-Standard Model scalar masses—where perturbative unitarity and vacuum stability hold up to the Planck scale, suggesting UV-completable UV completions for this $g-2$-compatible scenario.

ABSTRACT

We study the high-scale validity of a Type-X two Higgs doublet scenario which provides an explanation of the observed value of muon $(g-2)$. This region admits of a pseudoscalar physical state, which is well below the observed 125-GeV scalar in mass. A second neutral scalar particle can be both above and below 125 GeV in such a scenario. Admissible regions in the parameter space are obtained by using the most recent data on muon $(g-2)$, theoretical constraints such as low-scale perturbativity and vacuum stability, and also all experimental constraints, including the available LHC results. Among other things, both the aforesaid orders of CP-even neutral scalar masses are included in our benchmark studies. Two-loop renormalisation group equations are used to predict the values of various couplings at high scales, and the regions in the space spanned by low-scale parameters, which retain perturbative unitarity as well as vacuum stability upto various scales are identified. We thus conclude that such a scenario, while successfully explaining the observed muon $(g-2)$, can be valid upto energy scales ranging from $10^{4}$ GeV to the Planck scale, thus opening up directions of thought on its ultraviolet completion.

Motivation & Objective

• To assess the high-scale validity of a Type-X 2HDM that explains the observed muon anomalous magnetic moment ($g-2$) via a light pseudoscalar.
• To identify viable parameter regions satisfying low-scale perturbativity, vacuum stability, and all experimental constraints, including LHC limits on $h_{SM} \to AA$.
• To determine whether such a $g-2$-compatible model can remain perturbative and stable up to high energy scales, including the Planck scale.
• To explore the implications for UV completion, particularly in relation to gauge coupling unification and the role of $ an\beta$, Yukawa sign, and scalar mass degeneracy.
• To compare one- and two-loop renormalization group evolution effects, confirming qualitative robustness of results.

Proposed method

• Employing two-loop renormalization group equations (RGEs) to evolve quartic couplings from the electroweak scale to high energy scales.
• Applying theoretical constraints: low-scale perturbative unitarity, vacuum stability, and tree-level positivity of the scalar potential.
• Incorporating experimental constraints: the latest $g-2$ measurement at 3$σ$ deviation, LHC bounds on $h_{SM} \to AA$ branching ratios, and $m_A < 100$ GeV for the pseudoscalar.
• Scanning parameter space across four cases: varying the 125-GeV Higgs as lighter or heavier CP-even scalar, and considering both right- and wrong-sign Yukawa couplings.
• Using benchmark points to study the behavior of quartic couplings ($\lambda_1, \lambda_2, \lambda_3, \lambda_4, \lambda_5$) under RGE flow, identifying regions of high-scale validity.
• Comparing one- and two-loop RGE results to confirm qualitative robustness, especially for identifying key controlling parameters like $\lambda_1$ and $\lambda_5$.

Experimental results

Research questions

• RQ1 Can a Type-X 2HDM with a light pseudoscalar ($m_A \lesssim 100$ GeV) successfully explain the observed muon $g-2$ discrepancy while remaining consistent with all LHC and electroweak constraints?
• RQ2 What are the regions of the parameter space in the Type-X 2HDM where perturbative unitarity and vacuum stability are preserved up to high energy scales, including the Planck scale?
• RQ3 How do the values of $τ\beta$ and the masses of non-Standard Model scalars influence the high-scale validity of the model?
• RQ4 What is the role of the quartic couplings $\lambda_1$, $\lambda_5$, and $\lambda_2$ in determining the UV behavior of the model, and how are they affected by $g-2$ and $BR(h_{SM} \to AA)$ constraints?
• RQ5 Does the high-scale validity of the model depend on the 125-GeV Higgs being the lighter or heavier CP-even scalar, and how does this affect UV completion prospects?

Key findings

• The model can explain the observed muon $g-2$ discrepancy with large $τ\beta > 20$, which is favored by the $g-2$ data but creates tension with high-scale validity.
• Regions with small quartic couplings at the electroweak scale exhibit higher scale validity, extending up to the Planck scale, particularly when non-Standard Model scalar masses are degenerate and near 125 GeV.
• The quartic couplings $\lambda_1$ and $\lambda_5$ are the primary drivers of high-scale behavior and remain largely unaffected by $g-2$ or $BR(h_{SM} \to AA)$ constraints.
• The coupling $\lambda_2$ is strongly constrained by $g-2$ and $BR(h_{SM} \to AA)$ but plays a minor role in determining high-scale validity.
• High-scale validity is most favorable when the non-Standard Model scalars are nearly degenerate and close in mass to the 125-GeV Higgs, especially in scenarios where the 125-GeV state is the heavier CP-even scalar.
• The case where the 125-GeV Higgs is the lighter CP-even scalar (Case 1) is least favorable for high-scale validity, while Cases 3 and 4 (with lighter non-Standard Model scalars) show extended validity up to the Planck scale.