Decay and detection of a light scalar boson mixing with the Higgs boson

The simplest extension of the standard model consists in adding one singlet scalar field which mixes with the Higgs boson. $\mathcal{O}(\mathrm{GeV})$ masses of the new scalar carry strong motivation from relaxion, dark matter and inflation models. The decay of a GeV scalar is, however, notoriously difficult to address since, at this mass scale, the chiral expansion breaks down and perturbative QCD does not apply. Existing estimates of the GeV scalar decay rate disagree by several orders of magnitude. In this work, we perform a new dispersive analysis in order to strongly reduce these uncertainties and to address discrepancies in earlier results. We will update existing limits on light scalars and future experimental sensitivities which are in some cases strongly affected by the new-found decay rates. The meson form factors provided in this work, can be used to generalize our findings to non-universally coupled light scalars.

Figure 1

Evaluations of the light scalar decay rate to pions by Voloshin [27], Raby and West [10], the Higgs Hunter’s Guide [9], Truong and Willey [11], Donoghue et al. [12] and Monin et al. [28]. In this figure $s_{\theta }$ has been set to unity.

Figure 2

Modulus (upper panel) and phase (lower panel) of the pion and kaon form factors.

Figure 3

Light scalar decay rate into pions from this work, from Truong & Willey [11] and from Donoghue et al. [12]. We also show Truong and Willey’s decay rate after correcting a sign error in their $T$-matrix parametrization (see text).

Figure 4

Hadronic and leptonic decay rates of a light scalar mixing with the Higgs. These were obtained from our dispersive analysis ($m_{\varphi }<2\mathrm{GeV}$) and from the perturbative spectator model ($m_{\varphi }>2\mathrm{GeV}$). The possible impact of the charmonium resonances on the hadronic decay rate is illustrated by the gray line. All decay rates scale with $s_{\theta }^2$ which was set to unity in this plot.

Figure 5

Radiative $\mathrm{\Upsilon }$ decays and flavor changing $B$ decays mediated by a light scalar.

Figure 6

LHCb constraints on light scalars derived from rare $B$ decays. Masses around the charmonium resonances have been masked by the collaboration or by us (see Sec. 3d).

Figure 7

SHiP sensitivity to light scalars found in this work compared to [76]. The blue shaded region is obtained for the scalar decay rates derived in Sec. 3 and represents our preferred estimate. The yellow region is obtained if we treat the scalar decay in the perturbative spectator model.

Figure 8

Constraints on light scalars mixing with the Higgs. The filled regions with solid boundaries correspond to model-independent constraints. Sensitivity projections are indicated by the dashed boundary. The hatched regions refer to model-dependent exclusions which apply to the relaxion model (cyan) and the dark matter model (red, ocher) discussed in Sec. 2. Masses around the charmonium resonances have been masked in some probes.