The Higgs mass from a string-theoretic perspective

Abstract

The Higgs quartic coupling λ 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 β = 1 (i.e. λ = 0) is consistent with present data and has an independent theoretical appeal. We analyze the possible string-theoretic motivations for tan β = 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 λ 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 λ. Finally we show that, in contrast to naive expectations, λ < 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 λ < 0. This classically unstable theory then becomes metastable through running towards the IR. arXiv:1304.2767v4 [hep-th] 8 Oct 2013the Higgs sector appeared several years ago in [23] as well as very recently in [24]. A shift-symmetric Higgs has also been discussed in the context of inflation in [25]. An alternative origin of λ(m S ) = 0 was suggested in [26]. 4 Note that there is an unconventional alternative if one is willing to accept λ < 0 at the matching scale and possible metastability of the SM vacuum. This possibility is discussed in section 4.2.

Investigating the near-criticality of the Higgs boson

“…It is not difficult to imagine theories able to drive λ(M Pl ) to zero: high-scale supersymmetry with tan β = 1 [123][124][125][126][127][128]; partial N = 2 supersymmetry insuring D-flatness [129,130]; an approximate Goldstone or shift symmetry [131,132]; an infrared fixed-point of some transplanckian physics [121]; a powerlaw running in a quasi-conformal theory. Present data suggest that an exact zero of λ is reached at scales of about 10 10 -10 12 GeV, see eq.…”

Multi-natural inflation in supergravity

“…For m soft ∼ m 3/2 / log(M Pl /m 3/2 ) ∼ 10 12 GeV in the viable region for inflation, the Higgs mass becomes ∼ 126 GeV for tan β ∼ 1 [82]. The small value of tan β can be realized in the presence of a shift symmetry or an exchange symmetry in the Higgs sector [83][84][85].…”

Dark Radiation predictions from general Large Volume Scenarios

“…4 To give an example for the difficulties, note that the particular value z = 1 can be derived from a shift symmetry in the Higgs sector. In type IIB/F-theory such a symmetry can arise if the Higgs is contained in brane deformation moduli [15][16][17][18]. However, in this case the Kähler metric is independent of Kähler moduli and the lightest modulus τ b cannot decay to Higgs fields at all.…”