[Paper Review] Higgs boson, renormalization group, and cosmology

A. O. Barvinsky, Alexander Yu. Kamenshchik+3 more|arXiv (Cornell University)|Oct 6, 2009

Particle physics theoretical and experimental studies2 references14 citations

TL;DR

This paper investigates the Standard Model Higgs boson as an inflaton with strong non-minimal coupling to gravity, using renormalization group improvement to show that the Higgs mass is constrained to 135.6 GeV < MH < 184.5 GeV by the WMAP lower bound on the CMB spectral index. It reveals asymptotic freedom induced by curvature coupling, which stabilizes the theory in the weak-coupling regime, making SM phenomenology sensitive to cosmological data and suggesting future CMB precision as a complementary test to the LHC.

ABSTRACT

We consider the renormalization group improvement in the theory of the Standard Model (SM) Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. It suggests the range of the Higgs mass 135.6 GeV . MH . 184.5 GeV entirely determined by the lower WMAP bound on the CMB spectral index. We find the phenomenon of asymptotic freedom induced by this non-minimal curvature coupling, which brings the theory to the weak coupling domain. Asymptotic freedom fails at the boundaries of this domain, which makes the SM phenomenology sensitive to the current cosmological data and thus suggests future more precise CMB measurements as a SM test complementary to the LHC program.

Motivation & Objective

• To explore the Higgs boson as a candidate inflaton in the Standard Model with strong non-minimal coupling to gravity.
• To apply renormalization group methods to assess the stability and behavior of the Higgs sector under such coupling.
• To determine how cosmological data, particularly the CMB spectral index, constrain the Higgs mass in this framework.
• To investigate whether the non-minimal coupling induces asymptotic freedom and alters the renormalization group flow of the Higgs sector.
• To propose future CMB measurements as a complementary test of the Standard Model beyond the LHC program.

Proposed method

• Employ renormalization group improvement in the context of the Standard Model Higgs with non-minimal coupling to gravity.
• Use the curvature coupling to modify the running of the Higgs self-coupling and gauge couplings via beta functions.
• Apply the WMAP lower bound on the CMB spectral index as a constraint on the Higgs mass range.
• Analyze the fixed-point structure of the renormalization group equations to identify asymptotic freedom behavior.
• Identify the boundaries of the mass domain where asymptotic freedom holds and where it breaks down.

Experimental results

Research questions

• RQ1 What is the range of Higgs masses consistent with the WMAP bound on the CMB spectral index when the Higgs is an inflaton with non-minimal coupling to gravity?
• RQ2 Does the non-minimal curvature coupling induce asymptotic freedom in the Higgs sector of the Standard Model?
• RQ3 How does the renormalization group flow of the Higgs self-coupling change under strong non-minimal coupling to gravity?
• RQ4 What is the sensitivity of the Standard Model phenomenology to current cosmological data in this setup?
• RQ5 Can future, more precise CMB measurements serve as a complementary test of the Standard Model to the LHC program?

Key findings

• The Higgs mass is constrained to the range 135.6 GeV < MH < 184.5 GeV by the lower bound on the CMB spectral index from WMAP.
• The non-minimal coupling to gravity induces asymptotic freedom in the Higgs sector, driving the theory into a weak-coupling domain.
• Asymptotic freedom breaks down at the boundaries of the allowed Higgs mass range, signaling a sensitivity to cosmological data.
• The stability and behavior of the Standard Model in this framework are thus directly tied to current cosmological observations.
• Future, more precise CMB measurements could serve as a complementary test of the Standard Model, independent of the LHC program.