The Higgs mass from a String-Theoretic Perspective

TL;DR

This paper explores string-theoretic origins of the Higgs quartic coupling, examining geometries and symmetries that could naturally produce a near-zero lambda, and discusses implications for high-scale supersymmetry and vacuum stability.

Contribution

It identifies specific string geometries and symmetries that can naturally lead to lambda ~ 0 and analyzes the possibility of lambda<0 at high scales within string theory frameworks.

Findings

Lambda ~ 0 can arise naturally in certain string geometries.

Lambda < 0 at the SUSY breaking scale is possible and leads to metastable vacua.

String theory can produce high-scale MSSM scenarios with novel vacuum properties.

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.