What is the limit on the Higgs mass?

TL;DR

The paper investigates how electroweak precision tests constrain gauge-invariant, flavour-symmetric, CP-even dimension-6 operators that can arise from new physics at a scale $\Lambda$. Using an effective field theory with $L_{\rm eff}=L_{\rm SM}+\sum_i \frac{c_i}{\Lambda^p}{\cal O}_i^{(4+p)}$, they map operator coefficients to corrections in vacuum polarizations and vertex couplings, summarized by the $\epsilon_i$ parameters, and fit to precision data as a function of $m_h$, $m_t$, and couplings. The results show that, for $m_h\approx 100\,\text{GeV}$, the allowed $\Lambda$ lie roughly between $2$ and $10\ \text{TeV}$, with bounds often stronger than prior literature; certain operators can, in principle, ease the tension of a heavier Higgs, but only under contrived sign choices. Overall, the findings imply that new physics should lie above the multi-TeV scale unless specific operator dynamics cancel SM effects, and upcoming colliders will help test these possibilities.

Abstract

We obtain the bounds on all the gauge invariant, flavour symmetric, CP-even operators of dimension 6 that can affect the electroweak precision tests. For the preferred Higgs mass of about 100 GeV, their minimal scales range from 2 to 10 TeV. Depending on the individual operator, these limits are often significantly stronger than those quoted in the literature, when they exist at all. The impact, if any, of these bounds on the upper limit con the Higgs mass itself is discussed.

Figures (3)

• Figure 1: Level curves of $\Delta \chi^2=\{1,2.7,6.6,10.8\}$ for the first 3 operators in table 2 (${\cal O}_{WB}$, ${\cal O}_{H}$, and ${\cal O}_{LL}$ in the order) and $c_i=-1$.
• Figure 2: Distribution of the limits on $\Lambda/\,{\rm TeV}$ at $95\%\,\hbox{\rm C.L.}$ for the set of 1024 "theories" defined in the text.
• Figure 3: Contour plot of the 'average' $\chi^2_{\rm av}$, at $\Delta \chi^2=\{1,2.7,6.6,10.8\}$.