Electroweak Baryogenesis from Dark-Sector CP Violation

PHYSICAL REVIEW LETTERS 122, 201802 (2019)

Marcela Carena,1,2,3 Mariano Quirós,4,5 and Yue Zhang1,6 1Theoretical Physics Department, Fermilab, P.O. Box 500, Batavia, Illinois 60510, USA 2Enrico Fermi Institute, University of Chicago, Chicago, Illinois, 60637, USA 3Kavli Institute for Cosmological Physics, University of Chicago, Chicago, Illinois, 60637, USA 4Department of Physics, University of Notre Dame, 225 Nieuwland Hall, Notre Dame, Indiana 46556, USA 5Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology (BIST), Campus UAB, 08193 Bellaterra (Barcelona) Spain 6Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA (Received 6 December 2018; revised manuscript received 9 April 2019; published 24 May 2019)

We present a novel mechanism of electroweak baryogenesis where CP violation occurs in a dark sector, comprised of standard model gauge singlets, thereby evading the strong electric dipole moment constraints. 0 In this framework, the background of the timelike component of a new gauge boson Zμ, generated at electroweak temperatures, drives the electroweak sphaleron processes to create the required baryon asymmetry. We first discuss the crucial ingredients for this mechanism to work, and then show that all of them can be elegantly embedded in ultraviolet completions with a spontaneously broken gauged lepton number. The models under consideration have a rich phenomenology and can be experimentally probed in leptophilic Z0 searches, dark matter searches, heavy Majorana neutrino searches, as well as through hunting for new Higgs portal scalars in multilepton channels at colliders.

DOI: 10.1103/PhysRevLett.122.201802

The observed matter-antimatter asymmetry in the sector, to successfully create the baryon asymmetry at Universe is believed to yield strong evidence for new electroweak temperatures. phenomena beyond the standard model (SM) of particle In this Letter, we propose a new mechanism of EWBG physics. Electroweak baryogenesis (EWBG) is an elegant where the transfer of CP violation to the visible sector is 0 mechanism [1–15] that generates the observed baryon achieved by means of a vector boson Zμ which couples to asymmetry at the electroweak phase transition (EWPT). the SM leptons, and to dark fermions with CP violating This demands new physics close to the electroweak scale, Yukawa interactions involving additional SM singlet sca- to account for CP violating effects larger than those present lars. Such scalars may provide, through the Higgs portal, a in the SM. Moreover, the requirement of a sufficiently sufficiently strong first-order EWPT. The timelike compo- 0 strong EWPT, along with the precision measurements of nent of the new gauge boson, Z0,isCP odd and can the Higgs boson properties, demands an extended scalar transfer CP violation to the visible sector. During EWPT, 0 sector affecting the out-of-equilibrium processes. the CP violating source yields a nonzero background hZ0i, The recent measurements in electric dipole moment which acts as a chemical potential for the SM leptons, (EDM) experiments [16–19] impose strong constraints providing a thermal equilibrium lepton number asymmetry. on the required new sources of CP violation in SM In the absence of any primordial asymmetries, such source extensions, such as two-Higgs-doublet models and super- term, through the electroweak sphaleron processes, gen- symmetry [20–35]. This provides a strong motivation to erates an equal amount of baryon and lepton number consider CP violation triggered in dark sectors through SM asymmetries, which freeze in after the EWPT is completed gauge singlets [36], which may naturally suppress con- and the sphalerons become inactive. The current which 0 tributions to EDMs. Such an enticing idea, however, leaves couples to Zμ must be anomalous with respect to the SM the challenging task of finding a suitable mechanism to weak interaction during the EWBG epoch. transfer CP violation from the dark sector to the visible In the following, we present the main ingredients of the proposed EWBG mechanism, and briefly explore its phenomenological consequences. We refer to the companion paper [37] for a more detailed, quantitative presentation. Published by the American Physical Society under the terms of The need of an anomalous current coupled to Z0.—The the Creative Commons Attribution 4.0 International license. effective Lagrangian relevant to our discussion contains Further distribution of this work must maintain attribution to 0 the author(s) and the published article’s title, journal citation, the couplings of a vector boson Zμ to a current involving and DOI. Funded by SCOAP3. SM leptons and quarks, Jμ,

0031-9007=19=122(20)=201802(6) 201802-1 Published by the American Physical Society PHYSICAL REVIEW LETTERS 122, 201802 (2019) 1 1 L ¼ L − 0 0μν þ 2 0 0μ þ 0 0 μ ð Þ Starting from a primordially symmetric universe implies, eff SM ZμνZ M 0 ZμZ g ZμJ ; 1 4 2 Z Δn ¼ Δn ¼ð1=2ÞΔnð þ Þ . With this, the first equa- BL LL B L L tion in Eq. (4) simplifies to X3 μ ¼ ½ ¯ γμ þ ¯ γμ þ ν¯ γμν J qL LLi LLi qe eRi eRi qν Ri Ri ∂Δ 1 Li Ri Ri nBL i¼1 ¼ Γ S − Δn ; ð5Þ ∂t sph 2 BL ¯ μ ¯ μ ¯ μ þ qQ QL γ QL þ qu uR γ uR þ qd dR γ dR ; Li i i Ri i i Ri i i ð2Þ and from Eq. (3) it is straightforward to derive

X3 where L ;e , and ν are the SM leptons and right-handed 2 2 0 0 Li Ri Ri S ¼ ð þ 3 Þh i ð Þ T g qL qQ Z0 : 6 neutrinos, Q ;u , and d are SM quarks, and q is the 3 Li Li Li Ri Ri F i¼1 charge of the corresponding fermion F. We assume that the above effective Lagrangian describes Remarkably Eq. (6) is proportional to the nonconserva- a period of the early Universe when EWBG occurs. tion of the current Jμ, i.e., the coefficient appearing as 2 μ Moreover, we further assume that the vector field develops its chiral anomaly with respect to SUð2Þ , ∂μJ ∝ h 0 i ≠ 0 ð1Þ P L a timelike background, Z0 , sourced by a U charge 3 ð þ 3 Þ ð ˜ Þ ˜ ¼1 qL qQ tr WW , where W (W) is the i Li Li density, whose origin will be addressed later on. Through ð2Þ Eq. (1) the Z0 background acts as a chemical potential for SU L field (dual) strength. Hence we have found a 0 necessary condition for the proposed EWBG mechanism the fermions. Of particular interest to us are the SM quark 0 Zμ and lepton doublets. In the presence of a chemical potential, to work, namely, the current to which the couples must ð2Þ2 be anomalous with respect to SU L. Had the charges qF if the lepton or quark number were allowed to change μ independently, the particle-antiparticle number density in Eq. (2) been arranged such that the current J were Δ ≡ − ¯ ¼ conserved, the source term in Eq. (5) would have vanished asymmetry, defined as nF nF nF, with F LLi ;QLi , will be generated and evolve toward thermal equilibrium and, in turn, no net baryon asymmetry would have been created. 2N The effective Lagrangian of Eq. (1) can be obtained from Δ EQ ¼ c 2 0 h 0 i ð Þ ð1Þ nF Tcg qF Z0 ; 3 a UV complete U gauge theory whose gauge boson is 3 0 Zμ and qF are the corresponding SM fermion Uð1Þ charges. In the case of a nonconserved Jμ, additional fermions where Nc ¼ 3ð1Þ for quarks (leptons) is the color factor, (anomalons) are required to render the Uð1Þ anomaly free. whereas Tc is the EWPT critical temperature. This expres- The total current of the Uð1Þ gauge symmetry is the sum of sion is exact in the electroweak symmetric phase where all μ μ SM fermions are massless. J in Eq. (2) and that of the anomalons, Ja, such that the ∂ ð μ þ μÞ¼0 Within the context of EWBG, there is only one anomaly cancellation condition imposes, μ J Ja . process where the lepton (L) and baryon (B) numbers The anomalon fields, once introduced, will also contribute are simultaneously violated—the electroweak sphalerons. to the source term S [Eq. (6)]. Here, however, we assume Each sphaleron process violates B þ L but conserves that the Uð1Þ gauge symmetry is spontaneously broken − ð2Þ above the electroweak scale (e.g., at TeV scales), and that B L among the left-handed SU L doublets, where the baryon and lepton asymmetries are defined as Δn ≡ the anomalons get symmetry-breaking masses. If the P P BL ð1 3Þ 3 Δ Δ ≡ 3 Δ ð Þ anomalons have masses much larger than the EWPT = i¼1 nQ , nL i¼1 nL . The B L L Li L Li temperature, their population, as well as their impact on asymmetries satisfy the Boltzmann equations the electroweak sphalerons, will become Boltzmann suppressed. In such case, the anomalons, although canceling ∂Δnð þ Þ B L L ¼ Γ ðS − Δ Þ the gauge anomalies, have a negligible contribution to S. sph nðBþLÞ ; ∂t L Good candidates for such a Uð1Þ symmetry include X3 ∂Δnð − Þ gauged lepton number, baryon number, or any flavor B L L ¼ 0 S ¼ ðΔ EQ þ Δ EQ Þ ð Þ ; nL nQ ; 4 ∂t Li Li dependent combination of the two that remains anomalous, i¼1 ð2Þ2 within the SM, with respect to SU L. In contrast, the proposed EWBG mechanism cannot work if the Uð1Þ is where Γ ≃ 120α5 T is the sphaleron rate in the electro- sph w c already anomaly free given the SM fermion content (plus weak unbroken phase [38] and it is exponentially sup- right-handed neutrinos), e.g., B − L, Lμ − Lτ, etc. In the S pressed in the broken phase. serves as the source for following we discuss the realization of our EWBG mecha- þ Δ EQ Δ EQ creating a net B L asymmetry, with nL and nQ Li Li nism in a UV complete model with gauged lepton number, contributing to it democratically, the same way as sphaler- Uð1Þl. As we shall see, a dark matter candidate also ð2Þ ons act on every SU L doublet. naturally emerges in the theory.

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Interestingly, the above discussion remains valid even if TABLE I. UV completion of the effective theory. 0 the hZ0i background is space-time inhomogeneous. Indeed, ð3Þ ð2Þ ð1Þ ð1Þ we will consider a first order EWPT which temporarily Particle SU c SU L U Y U l 0 creates hZ0i in front of the expanding bubble walls. −1 2 LLi 12= 1 CP violation and the electroweak phase transition.—We eR 11−1 1 0 ν i will now address the origin of the Z0 field background, as Ri 1101 0 ¼ðν0 0 ÞT −1 2 q well as the dynamics of the EWPT. In analogy to a static L L;eL 12= 0 e0 11−1 q electric potential, the hZ0i background is C, CP, and CPT R χ 110q odd, and can be generated by a net Uð1Þl charge distri- R R0 ¼ðν00 ;e00 ÞT −1=2 q þ N bution near the bubble wall. To this end we introduce a R R 12 g e00 11−1 q þ N fermionic particle χ with CP violating microscopic inter- L g χ 110q þ N actions with the bubble wall. Since χ is a SM gauge singlet L g Φ that cannot couple to the Higgs field through renormaliz- , S 110Ng able interactions, we will introduce a SM scalar singlet S to interact with it,

ρlð Þ¼ð − ÞΔ χð Þ ð Þ z qχL qχR n z : 9 iθλ χ¯Lðm0 þ λe SÞχR þ H:c: ð7Þ 0 Neglecting the curvature of the bubble wall, the hZ0i background sourced by ρl can be calculated in cylindrical Within the bubble wall, the Higgs VEV turns on, while coordinates to be the S VEV simultaneously turns off. Such a transition to the electroweak broken phase has been studied and involves a Z g0 ∞ h i¼ 0 −M 0 jz−yj two-step process from the original vacuum with S hZ0ðzÞi ¼ dyρlðyÞe Z : ð10Þ 2 0 hHi¼0 [36,39–42]. The necessary ingredient to allow for MZ −∞ a strongly first order EWPT is a sizable scalar quartic term, h 0 i jSj2jHj2, by which the Higgs field becomes a portal to the Given this Z0 background, the final baryon asymmetry dark sector. generated can be obtained by solving Eq. (5), We consider the following ansatz for the S profile across Z Γ ∞ j ð Þj ¼ ½1 þ ð Þ 2 sph the bubble wall, S z s0 tanh z=Lω = . The coor- −Γsphz=vω ΔnB ¼ dzSðzÞe ; ð11Þ dinate z is defined in the rest frame of the bubble wall vω 0 which is located at z ¼ 0, whereas Lω is the wall width. Observe that to accommodate a physical CP violating where vω is the bubble wall expansion velocity. The effect through Eq. (7), we need a scalar potential that fixes parametric dependence in today’s baryon to entropy ratio 02 3 5 2 the phase of S. During the EWPT, the VEVof S contributes η ¼ Δn =s∼g ðqχ −qχ ÞN T Lωα =ðM 0 vωÞ is B B L R g c W Z , where to the χ mass through Eq. (7), whereas the bare mass term Ng is the number of lepton number generations charged m0 has its origin in the spontaneous breaking of Uð1Þ .If l under the Uð1Þl. the two mass terms carry different, space-time dependent UV complete models.—Next, we discuss unifying all the χ χ phases, the dispersion relations of L, R and their anti- above ingredients for EWBG into a UV complete frame- particles will be modified in a CP violating way. This work with gauged (anomaly free) lepton number symmetry, affects the phase space distributions of such particles and Uð1Þl. There are several choices to define the lepton yields a nontrivial solution to the corresponding diffusion number l. The most obvious one is to gauge all the three equations, leading to net number density asymmetries in SM families universally by taking l ¼ L þ Lμ þ Lτ. χ χ e L, R, Alternatively, one could also gauge only two lepton flavors such as l ¼ Lμ þ Lτ. We will consider these two cases as benchmark models. The minimal set of new fermion ΔnχðzÞ ≡ nχ − nχc ¼ −ðnχ − nχc Þ ≠ 0: ð8Þ L L R R content is given in Table I [43,44], where q is an arbitrary real number. The index i runs through e, μ, τ (μ, τ) in the The spatial distribution of ΔnχðzÞ will peak around the first (second) model, and Ng ¼ 3ð2Þ defines the number of bubble wall. For details on solving the diffusion equations families charged under the Uð1Þl, correspondingly. and the numerical computation of ΔnχðzÞ, we refer the To spontaneously break the Uð1Þl, and at the same time reader to the companion paper [37].Ifχ and χ carry give masses to the new fermions, we introduce the complex L R Φ ð1Þ Φ different Uð1Þl quantum numbers, the above chiral asym- scalar carrying Upffiffiffil number Ng. We assume that metries will give a net Uð1Þl charge density distribution picks up a VEV, vΦ= 2, above the electroweak scale. This 0 0 around the bubble wall, VEV gives mass to the gauge boson Z , MZ0 ¼ Ngg vΦ=2,

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0 Δ ð1Þ which can still be light if the gauge coupling g is contribution to Neff, one option is to make the U l sufficiently small. We can also write down Yukawa interaction decouple early enough, preferably above the ∼ 100 couplings of the form, QCD phase transition temperature, TQCD MeV. This 0 −5 ≳ 10 0 ≫ ≲ 10 implies vΦ TeV if MZ TQCD,org if ¯ 0 0 0 00 ð þ ¯ þ χ¯ χ ÞΦ þ ð Þ 0 ≪ cLR L ceeLeR cχ L R H:c:; 12 MZ TQCD. The other option is to implement the seesaw ν ν mechanism by giving Majorana masses to Ri . If all the Ri which will give vectorlike masses (with respect to the SM) are heavier than ∼500 MeV, they will decay before the big- ∼ to the new fermions. We assume cL ce to be large enough bang nucleosynthesis and have no effect in ΔN [49]. 0 0 00 0 eff so that L , R , eL;eR are sufficiently heavy in comparison Interestingly, this option could easily be achieved in the with the critical temperature of the EWPT. As noted earlier, gauged Lμ þ Lτ model where both Φ and S have charge 0 0 ð1Þ ⊗ the fermions L and R are needed to cancel the U l Ng ¼ 2. The experimental search for heavy Majorana ð2Þ2 SU L gauge anomaly, whereas decoupling them from the neutrinos is of great phenomenological interest [50], thermal bath provides the necessary condition for our especially as the new Uð1Þl gauge interaction allows them EWBG mechanism to work. On the other hand, we assume to be more copiously produced. We will investigate this the parameter cχ to be sufficiently small so that χ is light exciting opportunity in a future work. and remains populated in the thermal bath during the Experimental probes.—Here we summarize the phenom- EWPT. Their Uð1Þl charges are fixed in the UV theory: enological predictions unique to our EWBG mechanism ¼ q þ ¼ q qχL Ng, qχR , and their difference does not and discuss the present experimental bounds in the two depend on q. benchmark models presented above. The fermion χ will source the CP violation when it The main motivation for this Letter is to provide the interacts with the expanding bubble wall. The χ − Φ necessary amount of CP violation for baryogenesis, with- interaction inpffiffiffi Eq. (12) is responsible for generating the out being in tension with EDM measurements. In the ð1Þ m0 ¼ cχvΦ= 2 mass term in Eq. (7). In addition, as gauged U l UV complete models presented here, the discussed before, another complex scalar S with the same fermion field χ responsible for CP violation is a SM singlet, quantum numbers as Φ and a scalar potential that fixes its thereby eliminating its Barr-Zee type [51] contribution to phase is required to yield a physical CP phase, barring the EDMs. In Ref. [37], we will show that the leading contribution arises at the four-loop level. redefinitions of fermion fields. Moreover, such a complex 0 scalar will also be responsible for the strong EWPT through In our EWBG mechanism, the Zμ gauge boson transmits a two-step phase transition. the dark CP violation to the SM sector, and thereby the η ≃ Neutrino cosmology.—It is worth commenting on the generation of the observed baryon asymmetry, B −10 neutrino sector and implications of cosmological measure- 0.9 × 10 , restricts the values of MZ0 as a function of Δ 0 ments on additional neutrino degrees of freedom, Neff its gauge coupling g . In Fig. 1, the blue points are obtained [45–48], for the two benchmark models. The Uð1Þl gauge from a scan over the parameter space that can account for 0 interaction could thermalize, in the very early Universe, the correct ηB. The allowed Z masses are in the MeV to 0 0 all the new fermions charged under it, and in particular TeV range, with decreasing g values for lighter Z ,in ν agreement with the parametric dependence estimated below the right-handed neutrinos Ri . To avoid an excessive

FIG. 1. We scan broadly over the model parameters to find points that allow for successful EWBG as proposed in this Letter (blue points). We show various experimental constraints (LEP, BABAR, beam dump, electron, and muon g − 2, TEXONO, Borexino, CCFR) by the correspondingly labeled shaded regions, in the gauged Le þ Lμ þ Lτ (left) and Lμ þ Lτ (right) models.

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Eq. (11). In the left (right) panel of Fig. 1, we show the discussions and comments. This manuscript has been auth- gauged Le þ Lμ þ Lτ (Lμ þ Lτ) benchmark models. ored by Fermi Research Alliance, LLC under Contract The search for Z0 provides a handle on these EWBG No. DE-AC02-07CH11359 with the U.S. Department of 0 scenarios. In the gauged Le þ Lμ þ Lτ model, the Z has a Energy, Office of Science, Office of High Energy Physics. coupling to the electron, which is subject to constraints Work at University of Chicago is supported in part by U.S. from electron g − 2, eþe− colliders (LEP, BABAR), electron Department of Energy Grant No. DE-FG02-13ER41958. The beam dump and neutrino-electron scattering experiments work of M. Q. is partly supported by Spanish MINEICO (TEXONO) [52,53], as shown by the correspondingly under Grants No. CICYT-FEDER-FPA2014-55613-P and labeled shaded regions in the left panel of Fig. 1.In FPA2017-88915-P, by the Government of Catalonia under contrast, the gauged Lμ þ Lτ model is free from the above Grant No. 2017SGR1069 and by the Severo Ochoa constraints. There are, however, constraints from neutrino Excellence Program of MINEICO under Grant No. SEV- trident production (CCFR) [54] and loop-induced solar- 2016-0588. The work of Y.Z. is also supported by the DoE neutrino-electron scattering (Borexino) [55], which exclude under Contract No. DE-SC0007859. Y. Z. would like to thank the shaded regions in the right panel of Fig. 1. Interestingly, the Aspen Center for Physics, which is supported by National there is a region of parameter space that can explain the Science Foundation Grant No. PHY-1607611, where part of muon g − 2 anomaly (yellow band), and in the case of the this work was performed, and Colegio De Fisica Fundamental Lμ þ Lτ model, such a region is allowed and favored by E Interdisciplinaria De Las Americas (COFI) for a travel support during the completion of this Letter. EWBG, with 5 MeV ≲ MZ0 ≲ 200 MeV. The models considered here provide a dark matter candidate, χ. The Uð1Þl gauge invariance implies that χ the SM singlet fermion can only interact with the SM [1] V. A. Kuzmin, V. A. Rubakov, and M. E. Shaposhnikov, 0 χ particles via the Z exchange, making a leptophilic dark Phys. Lett. 155B, 36 (1985). matter candidate [56]. Its thermal relic density and detec- [2] A. G. Cohen, D. B. Kaplan, and A. E. Nelson, Phys. Lett. B tion prospects will be discussed in detail in Ref. [37]. 245, 561 (1990). It is possible to search for the dark scalar S at high energy [3] A. G. Cohen, D. B. Kaplan, and A. E. Nelson, Phys. Lett. B colliders, where it can be pair produced through the Higgs 263, 86 (1991). portal interaction. If S is lighter than twice the χ mass, it [4] G. R. Farrar and M. E. Shaposhnikov, Phys. Rev. Lett. 70, must decay via a χ loop into a pair of Z0 bosons, yielding 2833 (1993); 71, 210(E) (1993). four leptons in the final state. The S − χ interaction is [5] M. Quiros, Helv. Phys. Acta 67, 451 (1994). [6] P. Huet and A. E. Nelson, Phys. Lett. B 355, 229 (1995). inherently CP violating and such decay can provide a test [7] P. Huet and A. E. Nelson, Phys. Rev. D 53, 4578 (1996). of dark CP violation via interference effects in the golden [8] A. Riotto, Phys. Rev. D 53, 5834 (1996). 4l channel. [9] M. Carena, M. Quiros, A. Riotto, I. Vilja, and C. E. M. Summary.—We have proposed a novel mechanism for Wagner, Nucl. Phys. B503, 387 (1997). EWBG in which the CP violation occurs in a dark sector [10] M. Quiros, in Proceedings of the Summer School in High- and is transmitted to the observable sector via the timelike energy physics and cosmology: ICTP, Trieste, Italy, 1998 0 – background of a Zμ vector boson during a strong first-order (1999), pp. 187 259 [arXiv:hep-ph/9901312]. 0 [11] M. Carena, J. M. Moreno, M. Quiros, M. Seco, and C. E. M. EWPT. The Zμ is the gauge boson of a Uð1Þl gauge Wagner, Nucl. Phys. B599, 158 (2001). symmetry, and couples to an anomalous SM lepton number ð1Þ [12] J. M. Cline, M. Joyce, and K. Kainulainen, J. High Energy current. After the spontaneous U l symmetry breaking, Phys. 07 (2000) 018. ð2Þ the new SU L doublet fermions required to render the [13] M. Carena, M. Quiros, M. Seco, and C. E. M. Wagner, Nucl. theory anomaly free become massive and decouple from Phys. B650, 24 (2003). the thermal bath before the EWPT. Because the CP [14] C. Lee, V. Cirigliano, and M. J. Ramsey-Musolf, Phys. Rev. violating interactions are active in the dark sector, its D 71, 075010 (2005). effects on EDMs are highly suppressed and evade present [15] J. M. Cline, in Les Houches Summer School—Session 86: bounds. We show two benchmark scenarios with gauged Particle Physics and Cosmology: The Fabric of Spacetime Les Houches, France, 2006 (2006) [arXiv:hep-ph/0609145]. Uð1Þ þ þ and Uð1Þ þ symmetries, which provide Le Lμ Lτ Lμ Lτ [16] V. Andreev et al. (ACME Collaboration), Nature (London) concrete examples of UV completions. The models under 562, 355 (2018). consideration provide a rich phenomenology that can be [17] J. Baron et al. (ACME Collaboration), Science 343, 269 0 probed in searches for leptophilic Z , dark matter, heavy (2014). Majorana neutrinos, and new scalars in multilepton chan- [18] W. C. Griffith, M. D. Swallows, T. H. Loftus, M. V. Romalis, nels at the LHC or prospective high energy colliders. B. R. Heckel, and E. N. Fortson, Phys. Rev. Lett. 102,101601 (2009). We thank Zackaria Chacko, James Cline, Bogdan [19] C. A. Baker et al., Phys. Rev. Lett. 97, 131801 (2006). Dobrescu, Bhaskar Dutta, Paddy Fox, Ian Low, David [20] J. Shu and Y. Zhang, Phys. Rev. Lett. 111, 091801 (2013). Morrissey, Tim Tait, and Carlos Wagner for useful [21] S. Ipek, Phys. Rev. D 89, 073012 (2014).

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[22] M. Jung and A. Pich, J. High Energy Phys. 04 (2014) [40] H. H. Patel, M. J. Ramsey-Musolf, and M. B. Wise, Phys. 076. Rev. D 88, 015003 (2013). [23] T. Abe, J. Hisano, T. Kitahara, and K. Tobioka, J. High [41] C. Cheung and Y. Zhang, J. High Energy Phys. 09 (2013) Energy Phys. 01 (2014) 106; 04 (2016) 161(E). 002. [24] S. Inoue, M. J. Ramsey-Musolf, and Y. Zhang, Phys. Rev. D [42] D. Curtin, P. Meade, and C.-T. Yu, J. High Energy Phys. 11 89, 115023 (2014). (2014) 127. [25] K. Cheung, J. S. Lee, E. Senaha, and P.-Y. Tseng, J. High [43] P. Fileviez Perez and M. B. Wise, Phys. Rev. D 82, Energy Phys. 06 (2014) 149. 011901(R) (2010); 82, 079901(E) (2010). [26] L. Bian, T. Liu, and J. Shu, Phys. Rev. Lett. 115, 021801 [44] P. Schwaller, T. M. P. Tait, and R. Vega-Morales, Phys. Rev. (2015). D 88, 035001 (2013). [27] C.-Y. Chen, S. Dawson, and Y. Zhang, J. High Energy Phys. [45] V. Barger, P. Langacker, and H.-S. Lee, Phys. Rev. D 67, 06 (2015) 056. 075009 (2003). [28] K. Fuyuto, J. Hisano, and E. Senaha, Phys. Lett. B 755, 491 [46] D. K. Ghosh, G. Senjanovic, and Y. Zhang, Phys. Lett. B (2016). 698, 420 (2011). [29] M. Jiang, L. Bian, W. Huang, and J. Shu, Phys. Rev. D 93, [47] V. Barger, P. Fileviez Perez, and S. Spinner, Phys. Lett. B 065032 (2016). 696, 509 (2011). [30] N. Blinov, J. Kozaczuk, D. E. Morrissey, and C. Tamarit, [48] J. Hamann, S. Hannestad, G. G. Raffelt, and Y. Y. Y. Wong, Phys. Rev. D 92, 035012 (2015). J. Cosmol. Astropart. Phys. 09 (2011) 034. [31] C. Balazs, G. White, and J. Yue, J. High Energy Phys. 03 [49] J. M. Berryman, A. de Gouvêa, K. J. Kelly, and Y. Zhang, (2017) 030. Phys. Rev. D 96, 075010 (2017). [32] L. Bian and N. Chen, Phys. Rev. D 95, 115029 (2017). [50] A. Atre, T. Han, S. Pascoli, and B. Zhang, J. High Energy [33] C.-Y. Chen, H.-L. Li, and M. Ramsey-Musolf, Phys. Rev. D Phys. 05 (2009) 030. 97, 015020 (2018). [51] S. M. Barr and A. Zee, Phys. Rev. Lett. 65, 21 (1990); 65, [34] C. Cesarotti, Q. Lu, Y. Nakai, A. Parikh, and M. Reece, 2920(E) (1990). arXiv:1810.07736. [52] M. Bauer, P. Foldenauer, and J. Jaeckel, J. High Energy [35] D. Egana-Ugrinovic and S. Thomas, arXiv:1810.08631. Phys. 07 (2018) 094. [36] J. M. Cline, K. Kainulainen, and D. Tucker-Smith, Phys. [53] J. Alexander et al., arXiv:1608.08632. Rev. D 95, 115006 (2017). [54] W. Altmannshofer, S. Gori, M. Pospelov, and I. Yavin, Phys. [37] M. Carena, M. Quiros, and Y. Zhang (to be published). Rev. Lett. 113, 091801 (2014). [38] D. Bodeker, G. D. Moore, and K. Rummukainen, Phys. Rev. [55] T. Araki, S. Hoshino, T. Ota, J. Sato, and T. Shimomura, D 61, 056003 (2000). Phys. Rev. D 95, 055006 (2017). [39] J. R. Espinosa, T. Konstandin, and F. Riva, Nucl. Phys. [56] P. J. Fox, R. Harnik, J. Kopp, and Y. Tsai, Phys. Rev. D 84, B854, 592 (2012). 014028 (2011).

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