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A Shift Symmetry in the Higgs Sector: Experimental Hints and Stringy Realizations

Arthur Hebecker, Alexander K. Knochel, Timo Weigand

TL;DR

This work proposes that the hint of a 125 GeV Higgs can be understood within a framework of high-scale supersymmetry breaking, provided the Higgs sector enjoys a shift-symmetric Kähler potential that drives the quartic coupling to zero at a high UV scale. It links this mechanism to string-theoretic UV completions, showing how shift symmetry can naturally arise from Higgs fields as Wilson line moduli in heterotic orbifolds and various D-brane constructions, including open-string Wilson lines and bulk adjoint matter. The authors analyze the phenomenology, showing how $ an\beta\approx1$ and $\,\lambda(m_S)=0$ lead to specific RG-driven Higgs mass predictions and quantify the sensitivity to $m_t$ and $\alpha_s$ through loop corrections. Collectively, the paper provides a concrete bridge between LHC Higgs hints and a class of string compactifications that realize the required shift symmetry, suggesting a route to-testable UV completions.

Abstract

We interpret reported hints of a Standard Model Higgs boson at ~ 125 GeV in terms of high-scale supersymmetry breaking with a shift symmetry in the Higgs sector. More specifically, the Higgs mass range suggested by recent LHC data extrapolates, within the (non-supersymmetric) Standard Model, to a vanishing quartic Higgs coupling at a UV scale between 10^6 and 10^18 GeV. Such a small value of lambda can be understood in terms of models with high-scale SUSY breaking if the Kahler potential possesses a shift symmetry, i.e., if it depends on H_u and H_d only in the combination (H_u+\bar{H}_d). This symmetry is known to arise rather naturally in certain heterotic compactifications. We suggest that such a structure of the Higgs Kahler potential is common in a wider class of string constructions, including intersecting D7- and D6-brane models and their extensions to F-theory or M-theory. The latest LHC data may thus be interpreted as hinting to a particular class of compactifications which possess this shift symmetry.

A Shift Symmetry in the Higgs Sector: Experimental Hints and Stringy Realizations

TL;DR

This work proposes that the hint of a 125 GeV Higgs can be understood within a framework of high-scale supersymmetry breaking, provided the Higgs sector enjoys a shift-symmetric Kähler potential that drives the quartic coupling to zero at a high UV scale. It links this mechanism to string-theoretic UV completions, showing how shift symmetry can naturally arise from Higgs fields as Wilson line moduli in heterotic orbifolds and various D-brane constructions, including open-string Wilson lines and bulk adjoint matter. The authors analyze the phenomenology, showing how and lead to specific RG-driven Higgs mass predictions and quantify the sensitivity to and through loop corrections. Collectively, the paper provides a concrete bridge between LHC Higgs hints and a class of string compactifications that realize the required shift symmetry, suggesting a route to-testable UV completions.

Abstract

We interpret reported hints of a Standard Model Higgs boson at ~ 125 GeV in terms of high-scale supersymmetry breaking with a shift symmetry in the Higgs sector. More specifically, the Higgs mass range suggested by recent LHC data extrapolates, within the (non-supersymmetric) Standard Model, to a vanishing quartic Higgs coupling at a UV scale between 10^6 and 10^18 GeV. Such a small value of lambda can be understood in terms of models with high-scale SUSY breaking if the Kahler potential possesses a shift symmetry, i.e., if it depends on H_u and H_d only in the combination (H_u+\bar{H}_d). This symmetry is known to arise rather naturally in certain heterotic compactifications. We suggest that such a structure of the Higgs Kahler potential is common in a wider class of string constructions, including intersecting D7- and D6-brane models and their extensions to F-theory or M-theory. The latest LHC data may thus be interpreted as hinting to a particular class of compactifications which possess this shift symmetry.

Paper Structure

This paper contains 6 sections, 28 equations, 3 figures.

Table of Contents

  1. Introduction and Summary
  2. Phenomenology of Higgs sector shift symmetry
  3. Towards a stringy model
  4. Shift symmetry in heterotic orbifold models
  5. Shift symmetry for open string Wilson lines
  6. Shift symmetry for bulk matter

Figures (3)

  • Figure 1: The two-loop RG running of the Higgs quartic coupling in the SM. Left: $m_H=125$ GeV, $m_t=170.7, 172.9, 175$ GeV from top to bottom. Right: $m_t=172.9$ GeV, $m_H=126,125,124$ GeV from top to bottom.
  • Figure 2: The Higgs mass as a function of the top mass and the soft breaking scale for $\cos^2 2\beta\in[0\dots 2\epsilon_y^2]$. Shown here are the case of a variable compactification scale $m_S=m_C^2/M_{Pl}$ (left) and $m_S=10^{-2} m_C$ (right). The lower (green), middle (orange) and upper (red) bands correspond to top masses of $m_t=170.7, 172.9$ and $175$ GeV respectively. The strong coupling is fixed at $\alpha_s(m_Z)=0.1184$. A shaded band $m_h=124\dots 126$ GeV is included for orientation.
  • Figure 3: An illustration of the group theoretic origin of Higgs doublets from Wilson lines in the $SU(6)$ orbifold case. The components of $su(6)$ are displayed as a 6$\times$6 matrix. The generators of the gauge groups on the fixed points, $SU(5)\times U(1)$ and $SU(4)\times SU(2)\times U(1)$, are marked by a dashed blue and solid green border respectively. The components corresponding to unbroken generators are shaded. The coset which corresponds to generators broken on both fixed points (and thus the massless components of $\Phi$) is marked with $H$.