How well do we need to measure the Higgs boson mass and self-coupling?

TL;DR

The paper asks how precisely we must measure the Higgs boson mass and its self-coupling to meaningfully probe new physics. It argues that the LHC's potential $m_h$ precision of about $150$ MeV is already sufficient for foreseeable physics, since further gains offer limited UV insight given current uncertainties. It then defines a physics-based target for the Higgs self-coupling precision and computes maximal deviations in several BSM scenarios (mixed-in singlets, composite/HILH operators, MSSM, NMSSM). The results indicate that meaningful self-coupling deviations can be as large as roughly $-18$ to $-25\%$ in these models, implying that achieving about 20% precision is necessary to uncover or constrain new physics in this channel, though it remains technically demanding for future colliders. Overall, the work underscores a clear mass-precision benchmark while identifying concrete self-coupling targets tailored to specific beyond-Standard-Model scenarios.

Abstract

Much of the discussion regarding future measurements of the Higgs boson mass and self-coupling is focussed on how well various collider options can do. In this article we ask a physics-based question of how well do we need colliders to measure these quantities to have an impact on discovery of new physics or an impact in how we understand the role of the Higgs boson in nature. We address the question within the framework of the Standard Model and various beyond the Standard Model scenarios, including supersymmetry and theories of composite Higgs bosons. We conclude that the LHC's stated ability to measure the Higgs boson to better than 150 MeV will be as good as we will ever need to know the Higgs boson mass in the foreseeable future. On the other hand, we estimate that the self-coupling will likely need to be measured to better than 20 percent to see a deviation from the Standard Model expectation. This is a challenging target for future collider and upgrade scenarios.

Figures (4)

• Figure 1: The area below the dashed line in the $s_h^2-m_H$ plane is allowed by electroweak precision tests (EWPT) at the 90$\%$ CL in the presence of a mixed-in singlet. The area above, and to the left, of the solid line is the area where the heavy mixed-in singlet Higgs boson is detectable with 100 fb$^{-1}$ data at the 14 TeV LHC. The maximum allowed $s_h^2$-value that can evade detection is thus given by the intersection of the two lines and is $s_h^2=0.12$.
• Figure 2: The triple Higgs coupling deviations in the MSSM as a function of $m_A$ in the renormalization-group improved leading-log approximation, with $y_t$ defined via the running top quark mass. The red ($\boldsymbol +$) region corresponds to points in the $\tan \beta - m_A$ plane lying in the several Higgs boson discovery region, while all the other points lie in the single Higgs boson discovery region. The lightblue ($\blacksquare$), yellow ($\bullet$) and green ($\boldsymbol \times$) points correspond to mass values of the lighter stop of $m_{\tilde{t}_1}< 1.0$ TeV, the $1.0~\text{TeV} \le m_{\tilde{t}_1} < 2.5$ TeV and $m_{\tilde{t}_1} \ge 2.5$ TeV, respectively. Plot on right is same but versus $\tan\beta$.
• Figure 3: The triple Higgs coupling target in the NMSSM with $M_S=500\, {\rm GeV}$ as a function of $m_A$ for various values of $\tan \beta$ where the singlet coupling remains perturbative below $10\, {\rm TeV}$.
• Figure 4: The triple Higgs coupling deviations in the MSSM as a function of $m_A$ at $\mathcal{O}(y_t^4)$ in the renormalization-group improved leading-log approximation, with $y_t$ defined via the on-shell top quark mass, $y_t = \sqrt{2} m_t/(v \sin \beta)$ with $m_t = 173.2$ GeV (left plot) and including additionally $O(y_t^4 \alpha_s)$ and $O(y_t^6)$ terms, with $y_t$ defined via the running mass $y_t = \sqrt{2} \overline{m}_t/(v \sin \beta)$ (right plot). The red points ($\boldsymbol +$) correspond to parameter points for which several Higgs bosons can be discovered at the LHC. All other points belong to the single Higgs boson discovery region and are coloured according to the mass value of the lighter top squark $m_{\tilde{t}_1}$: lightblue ($\blacksquare$) for $m_{\tilde{t}_1} < 1.0$ TeV, yellow ($\bullet$) for $1.0 \leq m_{\tilde{t}_1} < 2.5$ TeV, and green ($\boldsymbol \times$) for $m_{\tilde{t}_1} \ge 2.5$ TeV.