Standard Model stability bounds for new physics within LHC reach

Abstract

We analyse the stability lower bounds on the Standard Model Higgs mass by carefully controlling the scale independence of the effective potential. We include resummed leading and next-to-leading-log corrections, and physical pole masses for the Higgs boson, M_H, and the top-quark, M_t. Particular attention is devoted to the cases where the scale of new physics Λis within LHC reach, i.e. Λ\leq 10 TeV, which have been the object of recent controversial results. We clarify the origin of discrepancies and confirm our earlier results within the error of our previous estimate. In particular for Λ=1 TeV we find that M_H[GeV]>52+0.64(M_t[GeV]-175)-0.50\frac{α_s(M_Z)-0.118}{0.006}. For fixed values of M_t and α_s(M_Z), the error from higher effects, as the lack of exact scale invariance of the effective potential and higher-order radiative corrections, is conservatively estimated to be \simlt 5 GeV.

Figures (4)

• Figure 1: Plots of the lower bound on the Higgs mass based on condition (15) [thick solid line], and on the condition $\lambda(\alpha\Lambda)=0$ [thin solid line], as functions of the parameter $\alpha$, defined by $\mu(t)=\alpha\phi(t)$, for $\Lambda=1$ TeV, $\alpha_s(M_Z)=0.118$ and $M_t=175$ GeV.
• Figure 2: Plot of the effective potential [thick solid line] for $\Lambda$, $\alpha_s(M_Z)$ and $M_t$ as in Fig. 1, and $M_H=52$ GeV. Dashed lines are plots of $\lambda_{\rm eff}(\mu=\alpha^*\phi)$ [thick one] and $\lambda(\mu=\phi)$ [thin one].
• Figure 3: Plots of the lower bound on $M_H$ as a function of $M_t$ from condition $\lambda_{\rm eff}=0$ [solid lines] as in Fig. 1, for $\alpha_s(M_Z)=0.118$ [central line], $\alpha_s(M_Z)=0.124$ [lower line] and $\alpha_s(M_Z)=0.112$ [upper line]. The bound based on the condition $\lambda(\Lambda)=0$ and $\alpha_s(M_Z)=0.118$ is also plotted for the sake of comparison [dashed line].
• Figure 4: Plots of the lower bound on $M_H$ as a function of $\Lambda$ for different values of $M_t$ and $\alpha_s(M_Z)=0.118$.