Shining Light Through the Higgs Portal with $\Gamma\Gamma $ Colliders

$Shining Light Through the Higgs Portal with $\Gamma\Gamma $ Colliders$

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 Teórica, IFT-UAM/CSIC, Cantoblanco, 28049, Madrid, Spain 3Departamento de F´ısica Teórica, Universidad Autónomade 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.

+ − √ I. Introduction. The existence of dark sectors in Na- Future high-energy e e colliders like the √s = 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 H†H 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 |H| 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- √ 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 ω0 = 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 √ 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 (|λe| ≤ 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 longitudinal 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 √ 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. i.e. Lγγ (y) ∝ δ(y − y ). (ii) An analytic high-energy The scalar potential for the theory is γγ collider luminosity spectrum for κmax = 4.8 and 2 2λePγ = −1 without multiple Compton scattering and 2 2 4 µS 2 λS 4 V (H,S) = − µ |H| + λH |H| + S + S beamstrahlung effects obtained from [26] and labelled H 2 4 nc √ 2 2 here Lγγ (y). (iii):A s = 3 TeV luminosity spectrum + λHS |H| S , (4) 3 √ with H = (0, (v + h)/ 2) and v = 246 GeV the EW include for comparison√ the respective production cross scale. After EW symmetry breaking, the Z2 symmetry sections for s = 14 TeV LHC and a future FCC-hh at 2 2 2 √ is preserved for mS = µS + λHS v > 0. In this case, s = 100 TeV via the process pp → jj SS. All cross the singlet scalar does not mix with the SM Higgs boson sections are obtained at leading order (LO). For a 3 TeV after EW symmetry breaking and only interacts with the CLIC-based γγ collider in particular, the cross section SM through its portal coupling λHS to the Higgs boson. becomes much larger than that of LHC as mS increases, In particular, if mS > mh/2 ' 63 GeV, the h → SS and is ∼ 50 times smaller than that of FCC-hh, yet the Higgs boson decay into two singlet scalars is forbidden signal cross section ratio to the SM background is much and the only way to access the hidden sector directly (to more favorable than in the latter, due to the cleaner en- produce S) is via an off-shell Higgs [8, 14], which makes vironment of a lepton/γ collider as compared to a hadron this scenario very challenging to probe at colliders. collider. As outlined in the introduction, extending the SM by 100 LHC (pp jj SS) → the singlet scalar field S may impact the breaking of 1 FCC-hh (pp jj SS) 10− → γγ WW SS (√s = 2.49 TeV) EW symmetry in the early Universe: in the SM the EW → e+γ W +ν¯ SS (√s = 2.75 TeV) 2 → phase transition is found to be a smooth-cross over pro- 10− γγ WW SS (√s = 0.83 TeV) → e+γ W +ν¯ SS (√s = 0.92 TeV) cess using non-perturbative methods [32, 33]; it would 3 → 10− then not induce the needed departure from thermal equi- (pb) 4 librium to generate the matter-antimatter asymmetry at σ 10− 2 / the EW scale. The presence of the singlet field S to- 5 h

10− m gether with a sizable portal coupling λHS may dramati- = S

6 m cally change this conclusion, triggering a first-order EW 10− phase transition strong enough to allow for baryogene- 7 10− sis [6–8, 10] or produce a stochastic background of gravi- 50 100 150 200 250 300 350 400 450 500 tational waves observable by LISA (see [34, 35] and refer- mS (GeV) ences therein). The combined Higgs-singlet field dynam- FIG. 3. LO cross section for singlet pair production (for ics in the early Universe may yield a first-order EW phase + λHS = 1) as a function of mS via γγ → W W − SS (solid) transition already through the interplay of tree-level and and e+γ → W +νSS¯ (dashed) for a 3 TeV CLIC-based col- thermal effects, via a two-step symmetry breaking pro- lider (green) and a 1 TeV ILC-based collider (orange). The max cess [7, 36]: the Z2 symmetry would be broken first along Eγ /Ee = 0.83 factor is explicitly taken into account. Also the S field direction and restored later, when EW sym- shown are the LO cross sections for 14 TeV LHC (blue) and metry breaking occurred. The evolution of the potential 100 TeV FCC-hh (red) via the process pp → jjSS. minimum (hSi , hHi) from high to low temperature would Considering hadronic decays for the W -bosons, the be (0, 0) → (0, wT ) → (vT , 0), with vT and wT respec- dominant SM background to the γγ → W +W −SS sig- tively the Higgs and singlet vevs at finite temperature T . nal comes from triboson production γγ → W +W −Z with The potential barrier between (0, wT ) and (vT , 0) minima Z → νν¯. Both for the 1 TeV ILC and 3 TeV CLIC anal- would induce a strongly first-order phase transition. The yses, we generate our signal and SM background samples lowest value of λHS as a function of mS for which such a at LO with MadGraph 5 [29], requiring parton-level two-step first-order EW phase transition occurs has been j jets to satisfy pT > 20 GeV and |ηj| < 4.5. Generation is obtained in [37] including 1-loop corrections and higher- done for the three γγ luminosity spectra from Fig.2. For order thermal effects (which qualitatively preserve the the non-idealized spectra, we perform a fine√ discretiza- above picture). Such λHS value provides a specific sen- tion of Lγγ (y), generate event samples for s = y and sitivity target for future colliders [38]. appropriately re-weight and combine the various samples IV. Collider Analysis. We now investigate the sen- to include the effect of the photon energy distributions sitivity that a γγ collider based on ILC or CLIC could f(x) in the γγ collisions (for each event, we fix the lon- achieve in probing the Higgs portal scenario to a dark sec- gitudinal boost in the laboratory frame via a random tor discussed in the previous section above the kinematic generation according to f(x) and the corresponding y). For the extraction of the signal, we introduce the decay threshold for h → SS (that is, for mS > 63 GeV), via the process γγ → W +W −SS. First, we show in Fig.3 “missing invariant mass” mmiss: the (pair) production cross section of the singlet scalar S √ √ q 2 at a s = 1 TeV ILC and a s = 3 TeV CLIC (including 2 2 / 2 2 mmiss = sˆ + (pzWW + p/ ) − EWW −ET −p/ , (5) √ √ max z z the s|γγ / s|ee = Eγ /Ee = 0.83 reduction factor for γγ collisions) for the idealized luminosity spectrum from √ with sˆ the c.o.m. energy of the partonic collision, Fig.2, as a function of the singlet scalar mass mS and q q 2 2 2 2 for λHS = 1. We also show the corresponding γe produc- EWW = mW + |~pW + | + mW + |~pW − | the energy tion cross sections via the process e+γ → W +νSS¯ , and of the W +W − system, p = p + p the sum of zWW zW + zW − 4 longitudinal momenta of the W -bosons and p the lon- still useful, but needs to be preceded by an event selection /z gitudinal component of the missing momentum. Both to increase the signal significance, since the mmiss recon- E and p can be accurately reconstructed from struction is degraded in this case. Focusing on Lnc (y) WW zWW √ γγ the hadronic W decay products. For the idealized lumi- and s|ee = 3 TeV for concreteness we show in Fig.4 max nosity spectrum Lγγ (y) ∝ δ(y − y ), knowledge of the (top) the angular separation of the two hadronic W s in γγ collision c.o.m. energy together with the condition the transverse plane ∆φWW , for the SM background and p = −p (absence of longitudinal boost for the col- m = 200 GeV signal. The clear difference between sig- /z zWW s lisions in the laboratory frame) allow to very efficiently nal and background is due to the different spin nature of disentangle the signal from the SM background: the re- the intermediate particle (h vs Z) and we select events constructed events peak around mmiss = mZ for the SM with ∆φWW < 1. After this selection, we show in Fig.4 background while having a lower bound mmiss ≥ 2 mS (middle) the momentum of the hardest W -boson |~pW1 | vs for the signal. A cut mmiss > 160 GeV suppresses the the rapidity difference between W s, ∆ηWW . For the sig- SM background below the O(1)% level, while retaining a nal (right) the two variables are heavily correlated, and 2 2 2 2 large signal fraction for mS > 63√ GeV. The correspond- we require (cθX + sθY ) /r1 + (sθX − cθY ) /r2 < 1, with ing 2σ exclusion sensitivity S/ B = 2 (with S and B θ = 0.3, r1 = 3.1, r2 = 1, X = |~pW | /(100 GeV)−c1(mS), the respective number of signal and background events) Y = ∆ηWW − c2(mS). The functions c1,2(mS) are fit- for λHS as function of mS is shown in Fig.5. ted to the signal data, yielding: c1 = 9.8 − 0.41 mS − 2 2 0.12 0.097 mS, c2 = 5.3 − 0.175 mS − 0.042 mS (mS in units Signal (mS = 200 GeV) 0.10 SM background of 100 GeV).

0.08 Finally, we carry out the mmiss reconstruction for the√ surviving events. We first remark that approximating√ sˆ 0.06 purely via global event kinematic variables, e.g. sˆ ∼ √ √ 0.04 2 2 1/2 s [39, 40] or sˆ ∼ ES ≡ EWW + (E/ + p ) min √ T zWW 0.02 (note that ES > smin), does not yield an acceptable Normalized Distribution m reconstruction for both signal and SM background: 0.00 miss √ 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 the average difference sˆ − ES is significantly larger for ∆φWW 8 8 the signal than for the SM background, and this effect SM Background Signal (mS = 200 GeV) 7 7 increases√ as mS grows. We use an averaged approxima- 2 2 1/2 6 6 tion sˆ ∼ (E + |~p | + |~p | + (E/ + p ) )/2, L W1 W2 T zWW 5 5 with EL = 2370 GeV corresponding to the maximum WW WW

η 4 η 4 nc ∆ ∆ of the Lγγ (y) spectrum (see Fig2-top). Assuming also 3 3 p/ ' −pzWW , we show in Fig.4 (bottom) the resulting 2 2 z distribution of mmiss vs ES. Fig.4 (bottom) highlights 1 1 the degrading in the reconstruction of mmiss for non- 0 0 0 200 400 600 800 1000 1200 1400 0 200 400 600 800 1000 1200 1400 ~p (GeV) ~p (GeV) idealized luminosity spectra, from the impossibility of ac- W1 W1 √ 2500 2500 curately accessing sˆ and p for each γγ collision. Still, /z

2000 2000 deﬁning the signal region as mmiss > ES −E0 (see Fig.4), 2 with ﬁtted E0(mS)/TeV = 2.24 − 0.117 mS − 0.028 mS 1500 1500 (mS in units of 100 GeV), improves the signal discrimi- (GeV) (GeV) S S

E 1000 E 1000 nation, particularly for large mS.

500 500 The above analysis is repeated for the non-idealized luminosity spectrum Lc (y). In each case, we compute SM Background Signal (mS = 200 GeV) γγ 0 0 √ 0 200 400 600 800 1000 0 200 400 600 800 1000 mmiss (GeV) mmiss (GeV) the 2σ exclusion sensitivity S/ B = 2 for λHS as a nc √ FIG. 4. Lγγ (y), s|ee = 3 TeV events. Top: Normal- function of mS. These sensitivities are then shown in ized ∆φWW distribution for the SM background (orange) and Fig.5. The integrated luminosity we quote in each non- mS = 200 GeV signal (red). The selection cut ∆φWW < 1 idealized scenario corresponds to that of the high-energy is also shown (dashed-black line). Middle: |~p | vs ∆η W1 WW part of the γγ spectrum, L (y > 0.8 ymax) (recall the distribution for the SM background (left) and m = 200 GeV γγ S discussion around Eq. (2)). We also show the 2σ exclu- signal (right) after ∆φ selection. Signal selection is shown WW sion sensitivities achievable at HL-LHC and FCC-hh via as a dashed-black ellipse (see text for details). Bottom: mmiss vs ES distribution for the SM background (left) and mS = 200 pp → jj + E/ T obtained respectively from [14] and [8], as GeV signal (right) prior to the ﬁnal signal region selection a comparison. In addition we depict in Fig.5 the low- mmiss > ES − E0 (depicted as a dashed-black line).√ est value of λHS compatible with a (two-step) ﬁrst order For the non-idealized luminosity spectra, sˆ is not EW phase transition [37] in this scenario. Fig.5 high- known, and neither is the longitudinal boost of each col- lights that for comparable integrated luminosities, multi- lision in the laboratory frame. Yet, the above strategy is TeV γγ collisions would directly probe dark sectors via 5

5.0

4.5

4.0 [1] B. Patt and F. Wilczek, (2006), arXiv:hep-ph/0605188 3.5 [hep-ph].

3.0 [2] G. Bertone, D. Hooper, and J. Silk, Phys. Rept. 405, 279 (2005), arXiv:hep-ph/0404175 [hep-ph].

HS 2.5

λ 1 [3] V. Silveira and A. Zee, Phys. Lett. 161B, 136 (1985). γγ WW SS, ILC 500 fb− → 1 γγ WW SS, ILC 3 ab− [4] J. McDonald, Phys. Rev. D50, 3637 (1994), arXiv:hep- 2.0 → 1 γγ WW SS, CLIC 500 fb− (Ideal) → ph/0702143 [HEP-PH]. 1 γγ WW SS, CLIC 3 ab− (Ideal) 1.5 → 1 nc γγ WW SS, CLIC 3 ab− ( ) [5] C. P. Burgess, M. Pospelov, and T. ter Veldhuis, Nucl. → Lγγ 1 c γγ WW SS, CLIC 3 ab− ( ) 1.0 → Lγγ Phys. B619, 709 (2001), arXiv:hep-ph/0011335 [hep-ph]. 1 pp jj SS, HL-LHC 3 ab− → 1 [6] S. Profumo, M. J. Ramsey-Musolf, and G. Shaughnessy, 0.5 pp jj SS, FCC-hh 3 ab− → (Two-step) 1st order EWPT threshold JHEP 08, 010 (2007), arXiv:0705.2425 [hep-ph]. 0.0 60 100 140 180 220 260 300 340 380 420 460 500 [7] J. R. Espinosa, T. Konstandin, and F. Riva, Nucl. Phys. mS (GeV) B854, 592 (2012), arXiv:1107.5441 [hep-ph]. FIG. 5. 2σ sensitivity in the (λHS , mS ) plane of the sin- [8] D. Curtin, P. Meade, and C.-T. Yu, JHEP 11, 127 + − glet Higgs portal√ model, for a γγ collider based√ on an e e (2014), arXiv:1409.0005 [hep-ph]. c.o.m. energy s = 1 TeV (”ILC”) and s = 3 TeV [9] C.-Y. Chen, J. Kozaczuk, and I. M. Lewis, JHEP 08, (”CLIC”). Different curves correspond to: ILC 500 fb−1 with 096 (2017), arXiv:1704.05844 [hep-ph]. −1 ideal Lγγ (dashed-yellow), ILC 3 ab with ideal Lγγ (solid- [10] J. R. Espinosa, B. Gripaios, T. Konstandin, and F. Riva, −1 yellow), CLIC 500 fb with ideal Lγγ (dashed-light-blue), JCAP 1201, 012 (2012), arXiv:1110.2876 [hep-ph]. −1 −1 CLIC 3 ab with ideal Lγγ (solid-light-blue), CLIC 3 ab [11] J. M. Cline and K. Kainulainen, JCAP 1301, 012 (2013), nc −1 c with Lγγ (solid-black) and CLIC 3 ab with Lγγ (solid-dark- arXiv:1210.4196 [hep-ph]. blue). We also show the 2σ sensitivity of HL-LHC (solid-red) [12] D. E. Morrissey and M. J. Ramsey-Musolf, New J. Phys. and FCC-hh (dashed-red) via the process pp → jj SS. The 14, 125003 (2012), arXiv:1206.2942 [hep-ph]. dotted-black line shows the lower threshold for a two-step 1st [13] J. M. Cline, K. Kainulainen, P. Scott, and C. Weniger, order EW phase transition, as obtained from [37]. Phys. Rev. D88, 055025 (2013), [Erratum: Phys. Rev.D92,no.3,039906(2015)], arXiv:1306.4710 [hep-ph]. [14] N. Craig, H. K. Lou, M. McCullough, and A. Thalapillil, the Higgs portal with precision similar to, and√ poten- JHEP 02, 127 (2016), arXiv:1412.0258 [hep-ph]. tially higher than, future hadron colliders. A s = 3 [15] A. Abada et al. (FCC), Eur. Phys. J. ST 228, 755 (2019). TeV - based γγ collider could cover the whole parameter [16] T. Golling et al., CERN Yellow Rep. , 441 (2017), space region compatible with a two-step singlet-driven arXiv:1606.00947 [hep-ph]. strongly first-order EW phase transition that could al- [17] I. F. Ginzburg, G. L. Kotkin, V. G. Serbo, and V. I. low for baryogenesis. Telnov, JETP Lett. 34, 491 (1981), [Pisma Zh. Eksp. Teor. Fiz.34,514(1981)]. Before concluding, we stress the possibility of further [18] I. F. Ginzburg, G. L. Kotkin, V. G. Serbo, and V. I. enhancing the sensitivity to Higgs portal scenarios in γγ Telnov, Nucl. Instrum. Meth. 205, 47 (1983). collisions by analyzing W +W − semi-leptonic and/or lep- [19] I. F. Ginzburg, G. L. Kotkin, S. L. Panfil, V. G. Serbo, tonic final states. The contribution to the E/ of the and V. I. Telnov, Workshop on High-Energy Spin Physics T Protvino, USSR, September 14-17, 1983, Nucl. Instrum. events from the W decays in this case however demands Meth. A219, 5 (1984). a different strategy to suppress SM backgrounds (e.g. the [20] V. I. Telnov, Nucl. Instrum. Meth. A355, 3 (1995). use of transverse mass variables MT and MT 2 [41, 42]), [21] V. I. Telnov, Future high-energy colliders. Proceedings, and we leave such a study for the future. Symposium, Santa Barbara, USA, October 21-25, 1996, AIP Conf. Proc. 397, 259 (1997), arXiv:physics/9706003 [physics.acc-ph]. Acknowledgements [22] V. I. Telnov, in Proceedings, 17th International Con- ference on High-Energy Accelerators, HEACC 1998: Dubna, Russian Federation, September 07–12, 1998 Feynman diagrams were drawn using TikZ- (1998) pp. 88–93, arXiv:hep-ex/9810019 [hep-ex]. Feynman [43]. J. M. N. was supported by Ramón [23] V. I. Telnov, High energy photon colliders. Proceedings, y Cajal Fellowship contract RYC-2017-22986, and also International Workshop, GG 2000, Hamburg, Germany, acknowledges support from the Spanish MINECO’s June 14-17, 2000, Nucl. Instrum. Meth. A472, 280 “Centro de Excelencia Severo Ochoa” Programme (2001), arXiv:hep-ex/0012047 [hep-ex]. under grant SEV-2016-0597, from the European Union’s [24] V. I. Telnov, High energy photon colliders. Proceedings, International Workshop, GG 2000, Hamburg, Germany, Horizon 2020 research and innovation programme under June 14-17, 2000, Nucl. Instrum. Meth. A472, 43 (2001), the Marie Sklodowska-Curie grant agreement 860881 arXiv:hep-ex/0010033 [hep-ex]. (ITN HIDDeN) and from the Spanish Proyectos de I+D [25] H. Burkhardt and V. I. Telnov, CERN-SL-2002-013-AP, de Generación de Conocimiento via grant PGC2018- CLIC-NOTE-508, (2002). 096646-A-I00. A. G.-A. thanks the MICIU, for his grant [26] B. Badelek et al. (ECFA/DESY Photon Collider Working within the “Garant´ıaJuvenil” program. Group), Int. J. Mod. Phys. A19, 5097 (2004), arXiv:hep- 6

ex/0108012 [hep-ex]. [33] F. Csikor, Z. Fodor, and J. Heitger, Phys. Rev. Lett. 82, [27] E. Accomando et al. (CLIC Physics Working Group), 21 (1999), arXiv:hep-ph/9809291. in Proceedings, 11th International Conference on Hadron [34] C. Caprini et al., JCAP 04, 001 (2016), arXiv:1512.06239 spectroscopy (Hadron 2005): Rio de Janeiro, Brazil, Au- [astro-ph.CO]. gust 21-26, 2005 (2004) arXiv:hep-ph/0412251 [hep-ph]. [35] C. Caprini et al., JCAP 03, 024 (2020), arXiv:1910.13125 [28] J. Q. Yu, H. Y. Lu, T. Takahashi, R. H. Hu, Z. Gong, [astro-ph.CO]. W. J. Ma, Y. S. Huang, C. E. Chen, and X. Q. Yan, [36] H. H. Patel and M. J. Ramsey-Musolf, Phys. Rev. D 88, Phys. Rev. Lett. 122, 014802 (2019), arXiv:1805.04707 035013 (2013), arXiv:1212.5652 [hep-ph]. [physics.plasm-ph]. [37] D. Curtin, P. Meade, and H. Ramani, Eur. Phys. J. C [29] J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, 78, 787 (2018), arXiv:1612.00466 [hep-ph]. O. Mattelaer, H. S. Shao, T. Stelzer, P. Torrielli, and [38] M. J. Ramsey-Musolf, JHEP 09, 179 (2020), M. Zaro, JHEP 07, 079 (2014), arXiv:1405.0301 [hep- arXiv:1912.07189 [hep-ph]. ph]. [39] P. Konar, K. Kong, and K. T. Matchev, JHEP 03, 085 [30] W. Kilian, T. Ohl, and J. Reuter, Eur. Phys. J. C71, (2009), arXiv:0812.1042 [hep-ph]. 1742 (2011), arXiv:0708.4233 [hep-ph]. [40] P. Konar, K. Kong, K. T. Matchev, and M. Park, JHEP [31] W. Kilian, S. Brass, T. Ohl, J. Reuter, V. Rothe, 06, 041 (2011), arXiv:1006.0653 [hep-ph]. P. Stienemeier, and M. Utsch, in International Work- [41] C. Lester and D. Summers, Phys. Lett. B 463, 99 (1999), shop on Future Linear Collider (LCWS2017) Strasbourg, arXiv:hep-ph/9906349. France, October 23-27, 2017 (2018) arXiv:1801.08034 [42] A. Barr, C. Lester, and P. Stephens, J. Phys. G 29, 2343 [hep-ph]. (2003), arXiv:hep-ph/0304226. [32] K. Kajantie, M. Laine, K. Rummukainen, and [43] J. Ellis, Comput. Phys. Commun. 210, 103 (2017), M. E. Shaposhnikov, Phys. Rev. Lett. 77, 2887 (1996), arXiv:1601.05437 [hep-ph]. arXiv:hep-ph/9605288.