[Paper Review] Finite mass corrections in orbifold gauge theories

Gero von Gersdorff, Nikos Irges+1 more|ArXiv.org|Jun 4, 2002

Black Holes and Theoretical Physics11 references18 citations

TL;DR

This paper investigates finite mass corrections in orbifold gauge theories, demonstrating that brane-localized quadratic divergences in the Higgs mass are absent at one-loop order due to a remnant higher-dimensional gauge symmetry. The authors identify a custodial shift symmetry on the brane that protects the Higgs mass from radiative corrections, offering a non-supersymmetric solution to the hierarchy problem via the Hosotani mechanism in a 5D gauge theory compactified on $S^1/Z_2$. This symmetry forbids mass terms at all perturbative orders, ensuring no need for fine-tuning or mass counterterms.

ABSTRACT

The Standard Model Higgs boson can be identified with the extra dimensional component of a gauge boson in a higher dimensional theory where the gauge group is broken to the Standard Model group by the orbifold action. In that case the Standard Model symmetry can be radiatively broken by the Hosotani mechanism and the Higgs boson mass is protected from bulk quadratic divergences by the higher dimensional gauge theory without any need of supersymmetry. However the latter does not protect a priori the Higgs mass from brane quadratic divergences. We show by an explicit calculation in the orbifold $S^1/Z_2$ that such effects are absent at one-loop. Moreover we identify the symmetry that protects such brane mass terms to all orders in perturbation theory and thus guarantees the absence of a corresponding mass counterterm

Motivation & Objective

• To address the hierarchy problem in non-supersymmetric higher-dimensional gauge theories without fine-tuning.
• To investigate whether brane-localized quadratic divergences can generate mass terms for the Higgs boson in orbifold compactifications.
• To identify the underlying symmetry protecting the Higgs mass from radiative corrections on the brane.
• To establish that the absence of such divergences is not accidental but enforced by a remnant of higher-dimensional gauge invariance.

Proposed method

• Analyzing the $S^1/Z_2$ orbifold compactification of a 5D gauge theory with $\mathcal{G} = U(3)_c \times U(3)_w$.
• Performing one-loop calculations of the Higgs mass corrections in the bulk and on the brane.
• Identifying a local $\mathbb{R}^{d_{\mathcal{K}}}$ shift symmetry on the brane from the higher-dimensional gauge symmetry, parameterized by $\xi^\hat{a}(x_5)$.
• Deriving the transformation laws of bulk and brane fields under this symmetry, particularly $\delta_{\mathcal{K}} A_5^{\hat{a}} = \partial_5 \xi^{\hat{a}}$, which forbids mass terms.
• Using the invariance of the field strength $F_{\mu 5}^{\hat{a}}$ under this symmetry to constrain allowed brane-localized operators.
• Applying the symmetry to show that terms like $A_5^{\hat{a}} M_{\hat{a}\hat{c}} A_5^{\hat{c}} \delta(x_5)$ are not invariant, thus forbidden.

Experimental results

Research questions

• RQ1 Can finite mass corrections from brane-localized quadratic divergences generate a Higgs mass term in orbifold gauge theories at one-loop order?
• RQ2 What symmetry, if any, protects the Higgs mass from such divergences on the brane?
• RQ3 Is the absence of these divergences accidental or enforced by a deeper symmetry?
• RQ4 Can the Hosotani mechanism in a 5D gauge theory provide a non-supersymmetric solution to the hierarchy problem?
• RQ5 How does the remnant of higher-dimensional gauge invariance constrain the structure of brane-localized operators?

Key findings

• No one-loop quadratic divergences are generated for the Higgs mass on the brane in the $S^1/Z_2$ orbifold compactification.
• A remnant $\mathbb{R}^{d_{\mathcal{K}}}$ shift symmetry on the brane, arising from the 5D gauge symmetry, forbids brane-localized mass terms for the Higgs bosons.
• This symmetry is preserved at all orders in perturbation theory, implying that no mass counterterms are needed for the Higgs at any loop level.
• The symmetry acts as $\delta_{\mathcal{K}} A_5^{\hat{a}} = \partial_5 \xi^{\hat{a}}$, and its non-invariance under mass terms ensures their absence.
• The field strength $F_{\mu 5}^{\hat{a}}$ at the brane is invariant under this symmetry, confirming its role in constraining the effective theory.
• Higher-loop divergences may still exist but are absorbed into wave function renormalization and do not require explicit mass counterterms.