The Higgs mass from a String-Theoretic Perspective

TL;DR

The paper investigates string-theoretic UV completions of the Standard Model that yield a vanishing Higgs quartic coupling at the SUSY-breaking scale, motivated by the observed 126 GeV Higgs. It analyzes shift and exchange symmetries in Higgs sectors realized on 6- and 7-branes within Type II/F-theory, comparing bulk-Higgs and intersection-curve realizations, and studies how these symmetries constrain $\tan\beta$ to unity and set $\lambda=0$ at high scales. It then computes radiative corrections to $\lambda$, including both symmetry-violating loop effects and threshold effects from integrating out heavy MSSM states, showing these corrections are generally modest but can shift the Higgs mass by a few GeV and, in certain NMSSM-like setups, permit $\lambda<0$ at the soft scale with a metastable electroweak vacuum. Overall, the work identifies concrete geometric settings where $\lambda\approx 0$ arises naturally, clarifies the role of extended SUSY in the Higgs sector, and broadens the landscape of viable high-scale UV completions compatible with current Higgs data.

Abstract

The Higgs quartic coupling has now been indirectly measured at the electroweak scale. Assuming no new low-scale physics, its running is known and, together with gauge and Yukawa couplings, it is a crucial new piece of information constraining UV completions of the Standard Model. In particular, supersymmetry broken at an intermediate or high energy scale with tan(beta)=1 (i.e. lambda=0) is consistent with present data and has an independent theoretical appeal. We analyze the possible string-theoretic motivations for tan(beta)=1 (including both the shift-symmetry and the more economical variant of a Z_2 symmetry) in a Higgs sector realized on either 6- or 7-branes. We identify specific geometries where lambda ~ 0 may arise naturally and specify the geometrical problems which need to be solved to determine its precise value in the generic case. We then analyze the radiative corrections to lambda. Finally we show that, in contrast to naive expectations, lambda<0 at the SUSY breaking scale is also possible. Specifically, string theory may produce an MSSM plus chiral singlet at a very high scale, which immediately breaks to a non-SUSY Standard Model with lambda<0. This classically unstable theory then becomes metastable through running towards the IR.

Figures (5)

• Figure 1: Due to destructive interference between these diagrams, the quartic $F$-term potential decouples at tree-level when the scalar $s$ is integrated out. This decoupling is not exact if the scalar mass receives additional soft breaking contributions.
• Figure 2: Sketch of the local intersection structure of the three relevant brane stacks in the D6-brane-realization of an exchange-symmetric Higgs mass matrix.
• Figure 3: The impact of squark decoupling corrections to the quartic Higgs coupling (left) and shift/exchange symmetry violation (right) on the physical Higgs mass. The narrow dark(broad light) bands are for $X_t^2=m_S^2\,(6 m_S^2)$ for the decoupling contributions from top partners, and $m_C=10^2\, m_S (\sqrt{m_S m_{Pl}})$ for the shift symmetry violation. The top quark masses are $m_t=175.5,173.5,171.5$ from upper (red) to lower (green) band. The scale $m_S$ should be understood as the effective SUSY scale as defined in (\ref{['eq:effectivesusyscale']}).
• Figure 4: A sketch of the effective potential with negative quartic coupling before running (solid) and after running to low energies (dashed). An uplift term to ensure vanishing cosmological constant in the electroweak (EW) vacuum has been added.
• Figure 5: An illustration of the scales involved in the localization of string states in the bifundamental representation.