IFT-UAM-CSIC-20-154 FTUAM-20-24 Shining light through the Higgs portal with γγ colliders A. Garcia-Abenza1 and J. M. No2, 3 1Instituto de F´ısica Fundamental, CSIC, Serrano 121, 28006, Madrid, Spain 2Instituto de F´ısica Te´orica, IFT-UAM/CSIC, Cantoblanco, 28049, Madrid, Spain 3Departamento de F´ısica Te´orica, Universidad Aut´onomade Madrid, Cantoblanco, 28049, Madrid, Spain (Dated: November 10, 2020) High-energy γγ colliders constitute a potential running mode of future e+e− colliders such as the ILC and CLIC. We study the sensitivity of a high-energy γγ collider to the Higgs portal scenario to a hidden sector above the invisible Higgs decay threshold. We show that such γγ collisions could allow to probe the existence of dark sectors through the Higgs portal comparatively more precisely than any other planned collider facility, from the unique combination of sizable cross-section with clean final state and collider environment. In addition, this search could cover the singlet Higgs portal parameter space yielding a first-order electroweak phase transition in the early Universe. + − p I. Introduction. The existence of dark sectors in Na- Future high-energy e e colliders like the ps = 1 TeV ture, uncharged under the gauge symmetries of the Stan- International Lineal Collider (ILC) or the s = 1:5=3 dard Model (SM), and interacting with the SM through TeV Compact Linear Collider (CLIC) could provide the the Higgs boson h is a well-motivated possibility: both ideal setup to probe the Higgs portal above the mh=2 theoretically, since the operator HyH is the only super- threshold due to a combination of reach in energy and renormalizable SM Lorentz invariant operator singlet un- clean collision environment. However, for e+e− collisions der the SM gauge symmetries [1], and in connection to the dominant VBF process to produce a pair of singlet open problems in particle physics and cosmology, like the scalars is e+e− ! ννSS, thus completely invisible and nature of dark matter (DM) [2{5]. In addition, a singlet impossible to trigger on at colliders. scalar field S coupled to the SM via the Higgs portal La- In this letter, we show that a γγ (or e±γ) operating 2 grangian interaction jHj S2 (with H the SM Higgs dou- mode of a high-energy e+e− collider like ILC or CLIC blet) is arguably the simplest possible extension of the would overcome the above problems, providing an opti- SM, further motivated by the fact that it could yield a mal setup to probe the Higgs portal to a dark sector, via + − strongly first-order electroweak (EW) phase transition in the process γγ ! W W + E= T , see Fig.1-right. After the early Universe [6{9], possibly allowing for EW baryo- discussing the key aspects of γγ colliders in section II, genesis as the origin of the observed matter-antimatter we introduce the singlet scalar extension of the SM in asymmetry of the Universe [10, 11] (see [12] for a review). section III as the benchmark scenario for our study, and Despite its simplicity and appeal, such a singlet Higgs briefly discuss its impact on the EW phase transition. We portal scenario is very challenging to probe experimen- then analyze the sensitivity of an ILC and CLIC-based tally1 at high-energy colliders when the Higgs boson de- γγ collider to the Higgs portal above threshold scenario cay h ! SS is not kinematically open (i.e. for singlet in section IV. scalar masses m above the decay threshold). At the s q0 Large Hadron Collider (LHC) it is possible to directly W ∓ q γ probe the hidden sector in final states with hadronic S S = ± jets and missing transverse energy ET , via the vector- W W ± arXiv:2011.03551v1 [hep-ph] 6 Nov 2020 boson-fusion (VBF) process pp ! jj + SS [8, 14] (see h h Fig.1-left), with the pair of singlet scalars giving rise W ∓ ∓ to E= T . The High-Luminosity LHC would however only W be sensitive to very large values of the Higgs portal cou- q S γ S pling [8, 14]. A future FCC-hh [15] hadron collider oper- p q0 W ± ating at a center-of-mass (c.o.m.) energy s = 100 TeV would improve on the LHC sensitivity [14, 16], profiting FIG. 1. Feynman diagrams for singlet scalar S pair produc- from the large enhancement of the VBF off-shell Higgs tion through the Higgs portal. Left: hadron colliders (for process at high energy. Yet, the messy hadronic environ- e+e− colliders, initial state fermions would be e±, and final ment hinders very strong sensitivity improvements. state fermions would be neutrinos). Right: γγ colliders. II. γγ colliders. The possibility of a high-energy γγ 1 If S is not itself the DM particle, since otherwise direct detection (or γe) collider based on a linear e+e− collider has been DM constraints on the singlet scalar scenario apply [13]. considered since the early 1980's [17{19]. The physi- 2 cal principle is the generation of high-energy photons 4 through Compton back-scattering of laser photons by the + − high-energy electrons or positrons of the e e collider 3 beams, a mechanism that has subsequently been exten- sively studied (see e.g. [20{28]). In the conversion region a photon with energy E0 is scattered on an electron with 2 energy Ee at a small collision angle α (almost head-on). ) (arbit. units) y The photons from Compton back-scattering have a spec- ( γγ 1 max L trum with maximum energy Eγ given by 2 max κ 4 Ee E0 cos (α=2) 0 Eγ = Ee ; κ = 2 (1) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1 + κ me y = Eγγ=(2Ee) 1.0 where me is the electron mass. According to Eq. (1), the largest possible laser frequency !0 = E0=~ should be 0.8 max used in order to increase Eγ . This also increases the fraction of hard photons in the spectrum [20]. However, 0.6 at large κ the resulting high-energy photons are then con- verted to e+e− pairs in collisions with laser photons, so max 0.4 the optimum value κ = κ is the threshold of this con- ) (arbit. units) x ( version process, given for a head-on collision by [20, 28] f EmaxE = m2. Combining this threshold condition with 0.2 γ 0 e p Eq. (1) yields κmax = 2 (1 + 2) ≈ 4:83, resulting in a max 0.0 highest energy Eγ ≈ 0:83Ee. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 The energy spectrum of the resulting photon beam is x max FIG. 2. TOP: Luminosity spectra Lγγ (y) used in this work: peaked at Eγ , and the number of high energy photons idealized spectrum / δ(y − ymax) (black); analytic spectrum dramatically increases for polarised beams with 2λePγ = nc max Lγγ (y) for κ = 4:8 and 2λePγ = −1 (red); spectrum −1, being λe (jλej ≤ 1=2) the mean helicity of the initial c Lγγ (y) including multiple Compton scattering effects and electron and Pγ that of the laser photon. In addition beamstrahlung (blue). All of then are normalized to the same max to this high-energy peak there is also a factor 5-8 larger value of Lγγ (y > 0:8 y ) (see text for details). BOTTOM: (in luminosity) low-energy spectrum which is produced Photon energy distribution f(x) for each of the above lumi- by multiple Compton scattering and beamstrahlung pho- nosity spectra Lγγ (y). tons. These low-energy collisions have a large longitudi- nal boost in the detector reference frame. The γγ lu- including the effect at low energies from multiple Comp- ton scatterings and beamstrahlung fitted from [25], la- minosity Lγγ in the high-energy part of the spectrum is c proportional to the geometric luminosity of the electron belled here Lγγ (y). The three spectra are shown jointly in Fig.2 (top). From these luminosity spectra we de- beams LG [22, 26]. Considering y = Eγγ =(2Ee), one ap- proximately has [21, 22] rive the respective photon energy distributions f(x) (see Fig.2 (bottom)), given by max max max Lγγ (y > 0:8 y ) ≈ 0:1 LG ; (2) Z x Z x p Lγγ (y) = dx1 dx2 f(x1) f(x2) δ(y − x1x2) (3) where the maximum possible value of y is given by 0 0 max max max max y = Eγ =Ee ' 0:83. As discussed in [21, 25, 27], with x = y . The luminosity spectra and photon max 34 −2 −1 luminosities Lγγ (y > 0:8 y ) ∼ 10 cm s (and energy distributions will then be used together with a perhaps up to 1035 cm−2 s−1 [21]) could be reached at Monte Carlo event generation from MadGraph 5 [29] a multi-TeV γγ collider, comparable to those of the HL- and Whizard [30, 31] to construct event samples for the LHC. SM background and our BSM signal in section IV. In the rest of this work we consider three differ- III. The singlet scalar extension of the SM. The ent Lγγ (y) spectra for a multi-TeV γγ collider: (i) simplest realization of the Higgs portal to a dark sector An idealized spectrum, with the energy of the back- max consists of an extension of the SM by a real scalar singlet scattered photons essentially localized at Eγ = 0:83Ee, max field S [3,4,6, 10] which is odd under a Z2 symmetry.