PHYSICAL REVIEW D 99, 015018 (2019) Decay and detection of a light scalar boson mixing with the Higgs boson Martin Wolfgang Winkler* Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10 691 Stockholm, Sweden (Received 10 September 2018; published 9 January 2019) The simplest extension of the standard model consists in adding one singlet scalar field which mixes with the Higgs boson. OðGeVÞ 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. DOI: 10.1103/PhysRevD.99.015018 I. INTRODUCTION sensitivities to a light scalar thus crucially depend on its decay rate and decay pattern. Many prominent extensions of the standard model Since the chiral expansion breaks down shortly above the (SM) feature a gauge singlet scalar ϕ with a mass below two-pion threshold, while a perturbative QCD calculation or at the weak scale. Within the relaxion mechanism [1] becomes reliable for masses of a few GeV, the scalar decay the new scalar is introduced to cure the (little) hierarchy rate in the window mϕ ≃ 0.5–2 GeV suffers from notorious problem. In well-motivated dark matter models, a light uncertainties (see e.g., [8]). The problem already man- scalar emerges as the mediator which links the dark and ifested itself when a light SM Higgs was still considered the visible sector [2]. A light scalar appears in super- viable [9]. In the late 1980s, it was realized that the form symmetric theories such as the next-to-minimal super- factors determining the Higgs (or general scalar) decay rate symmetric standard model [3]. It has been identified with to meson final states are accessible through dispersion the field driving cosmic inflation [4,5] and it is present relations [10]. Unfortunately, the two most comprehensive in models which address the cosmological constant calculations based on this technique by Truong and Willey problem through radiative breaking of classical scale [11] and Donoghue et al. [12] disagree by orders of invariance [6]. magnitude at mϕ ∼ GeV. It was argued in [12] that Through mixing with the Higgs, the light scalar inherits Truong and Willey had obtained the wrong interference the Higgs couplings to SM matter reduced by a universal pattern between elastic and inelastic contributions to the suppression factor. While for scalar masses around the form factors due to a sign error. In this work, we will electroweak scale, LEP and LHC constraints on extended reinvestigate the discrepancy and recalculate the decay rate Higgs sectors apply, rare meson decays offer a particular of a light scalar to pions and kaons. Our evaluation profits powerful search channel for scalars below the bottom mass from progress in the description of pion/kaon phase shift threshold [7]. If the mixing is suppressed, the scalar may, data entering the dispersive integral. however, travel a macroscopic distance before decay. In After identifying the favored parameter regions for this case, searches including missing energy or displaced some of the most promising SM extensions with light vertices become relevant. Present and future experimental scalars, we will update the existing limits and future experimental sensitivities. These were previously based *[email protected] on varying sets of assumptions on the scalar decay. In several cases, we find the sensitivities to be substantially Published by the American Physical Society under the terms of alteredbyournew-founddecayrates.Thisholdsin the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to particular in the context of beam dump experiments which the author(s) and the published article’s title, journal citation, are very sensitive to the scalar decay length through the and DOI. Funded by SCOAP3. location of the detector. 2470-0010=2019=99(1)=015018(15) 015018-1 Published by the American Physical Society MARTIN WOLFGANG WINKLER PHYS. REV. D 99, 015018 (2019) II. STANDARD MODEL EXTENSIONS WITH by the mixing angle sθ. The annihilation cross section σ ¼ σ 2 LIGHT SCALARS times relative velocity vrel is of the size vrel 1vrel A new scalar can connect to the SM at the renormalizable with [13,15] level via the Higgs portal κ4 9 4 − 8 2 2 þ 2 4 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mχ mχ mχmϕ mϕ 2 2 σ1 ≃ mχ − m ; ð4Þ 2 † 24π ð2 2 − 2 Þ4 ϕ L ⊃ ðg1ϕ þ g2ϕ ÞðH HÞ: ð1Þ mχ mϕ 1 2 where we assumed a vanishing trilinear scalar self-coupling Once electroweak symmetry is broken, the couplings g ; 1 induce mixing between the scalar and the Higgs. We will for simplicity. Since the annihilation cross section is p-wave focus on the case where the scalar mass is considerably suppressed, strong indirect dark matter detection constraints below the electroweak scale. In the low energy effective are avoided. The fermion relic density is approximated theory, the Higgs can then be integrated out and it arises the as [16] coupling of the new scalar to SM fermions 2 2 −11 −2 mχ Ωχh ¼ 2.8 × 10 GeV pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; ð5Þ sθmf ¯ ð Þσ 2 L ⊃− ϕff; ð2Þ gà TF 1TF v where gà denotes the number of relativistic degrees where sθ denotes the sine of the Higgs-scalar mixing angle of freedom and TF the freeze-out temperature which and v the Higgs vacuum expectation value (vev). With we take from [17]. For a given set of masses, the coupling 2 regard to experimental searches, the light scalar behaves as κ is fixed by requiring that Ωχh matches the observed dark a light version of the Higgs boson with universally sup- pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi matter relic density. We find κ ¼ð0.03–0.05Þ × mχ=GeV pressed couplings. In concrete models, a more complicated 2 for mχ ¼ 10 MeV–10 TeV. coupling pattern may emerge if they feature e.g., more than one Higgs doublet. While we focus on the simplest case We have implicitly assumed a standard thermal freeze- given above, many of our results can be applied to more out of the singlet fermion. This is justified if the dark sector general couplings after simple rescaling. In order to identify was in thermal equilibrium with the SM bath prior to freeze-out. We, therefore, require that the thermalization the most promising parameter space for the mixing angle, Γ we shall briefly discuss some well-motivated SM exten- rate therm of the dark sector exceeds the Hubble rate of expansion H at freeze-out, i.e., sions with light scalars. rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4π3 ð Þ 2 Γ ð Þ ð Þ¼ gà TF pffiffiffiffiffiffiTF ð Þ A. Connection to dark matter therm TF >H TF 45 : 6 8πMP New particles with a weak scale annihilation cross Γ 2 section have been considered among the leading dark Since therm scales with sθ, (6) puts a lower limit on the matter candidates since—within the thermal production mixing angle. Notice that thermal decoupling of the dark mechanism—their relic density naturally matches the sector is not a strict exclusion criterion. It would, however, observed dark matter density. The absence of a signal in invalidate the simple connection between mχ, κ and Ωχh, direct detection experiments, however, suggests even fee- making the relic density a UV sensitive quantity. bler interactions between dark matter and nuclei. An At the same time, large mixing angles are excluded due appealing possibility is that dark matter resides within a to direct dark matter detection. The dark matter-nucleon dark sector of particles which do not directly feel the strong cross section reads3 [14] or electroweak forces [2]. In this scenario, a scalar boson 2 2 could be the mediator which communicates between dark 4μχ sθκ σ ≃ n ð Þ n 2 mnf 7 and visible matter. In the simplest realization, dark matter π 2vmϕ is identified with a gauge singlet Majorana fermion χ which is stable due to a (discrete) symmetry and couples to the with scalar via the Yukawa term [13,14] 6 κ fn ¼ fn þ fn þ fn þ f : ð8Þ L ⊃ ϕχχ¯ ð Þ u d s 27 G 2 : 3 1 We will assume mχ >mϕ, such that a hierarchy between The general expression for the annihilation cross section for nonvanishing trilinear coupling can be found in [15]. the annihilation cross section and the dark matter nucleus 2 This holds unless for very degenerate cases mχ − mϕ < cross section can naturally be realized: the fermions 0.01mχ. annihilate into scalars via the (unsuppressed) coupling κ, 3The formula is valid for scalar masses substantially larger than while dark matter nucleus interactions are suppressed the momentum transfer, i.e., mϕ ≳ 100 MeV. 015018-2 DECAY AND DETECTION OF A LIGHT SCALAR BOSON … PHYS. REV. D 99, 015018 (2019) Here, mn denotes the nucleon mass and μχ the reduced loop, is sufficiently suppressed and does not trap the mass of the dark matter-nucleon system. The scalar relaxion before electroweak symmetry breaking [25,26]. n ϕ ∼ coefficients fu;d;s and fG define the quark and gluon The relaxion slowly rolls down its potential and, at ¼ 1 − n − n − n M=g triggers electroweak symmetry breaking.