# Higgs-Like Boson at 750 Gev and Genesis of Baryons

BNL-112543-2016-JA

Higgs-like boson at 750 GeV and genesis of baryons

Hooman Davoudiasl, Pier Paolo Giardino, Cen Zhang

Submitted to Physical Review D

July 2016

Physics Department

Brookhaven National Laboratory

U.S. Department of Energy USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

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Hooman Davoudiasl∗, Pier Paolo Giardino†, and Cen Zhang‡ Department of Physics, Brookhaven National Laboratory, Upton, NY 11973, USA

We propose that the diphoton excess at 750 GeV reported by ATLAS and CMS is due to the decay of an exo-Higgs scalar η associated with the breaking of a new SU(2)e symmetry, dubbed exo-spin. New fermions, exo-quarks and exo-leptons, get TeV-scale masses through Yukawa couplings with η and generate its couplings to gluons and photons at 1-loop. The matter content of our model yields a B − L anomaly under SU(2)e, whose breaking we assume entails a ﬁrst order phase transition. A non-trivial B −L asymmetry may therefore be generated in the early universe, potentially providing a baryogenesis mechanism through the Standard Model (SM) sphaleron processes. The sponta- neous breaking of SU(2)e can in principle directly lead to electroweak symmetry breaking, thereby accounting for the proximity of the mass scales of the SM Higgs and the exo-Higgs. Our model can be distinguished from those comprising a singlet scalar and vector fermions by the discovery of TeV scale exo-vector bosons, corresponding to the broken SU(2)e generators, at the LHC.

INTRODUCTION states may ﬁt within a larger picture of particle physics. Obviously, this question could be answered in a variety The diphoton excess at the LHC, reported by both the of ways, depending on one’s view of fundamental physics ATLAS and CMS [1, 2] collaborations at about 750 GeV, and its open problems. has been the subject of a large number of papers over the In this work, we entertain the possibility that the past several months1. While the signiﬁcance of the excess 750 GeV resonance is a scalar remnant of a TeV-scale is not at the discovery level yet, its appearance in both Higgs mechanism responsible for the spontaneous break- experiments, persistence upon further analysis, and the ing of a new SU(2)e gauge symmetry that we refer to as nature of the ﬁnal state provide some ground for cautious exo-spin (exo: outside, in Greek). None of the SM ﬁelds optimism that it may be a real signal of new physics. One carry SU(2)e, however there are new fermions charged is then compelled to ask what the underlying new physics under this symmetry, as well as under the SM SU(3)c can be. color and hypercharge U(1)Y . We will refer to the new color charged fermions as exo-quarks, while those that Many ideas have been entertained and cover a multi- only carry hypercharge are referred to as exo-leptons. tude of possibilities2. However, among them, the possi- These fermions get their masses through Yukawa cou- bility of a scalar resonance with a mass of 750 GeV, pro- pling to a doublet exo-Higgs whose vacuum expectation duced via gluon fusion and decaying into photons, both value (vev) breaks the (2) symmetry. at 1-loop level, represents one of the most straightfor- SU e ward scenarios (See, for example, Refs. [3–7]). The gluon Our proposed setup is motivated by the natural as- initial states are well-motivated, as their corresponding sumption that a particle whose properties are reminiscent luminosity gets enhanced much more than that for the of the SM Higgs is perhaps best thought of as a Higgs bo- quarks with center of mass energy of collisions, greatly son that breaks a new symmetry (For a sample of works reducing tension with the LHC Run 1 data. Here, the that consider a Higgs ﬁeld interpretation of the excess, particles that mediate the loop-generated couplings of see Refs. [8–12]). The simplicity and minimal nature of the scalar are generally assumed to be heavy vector-like the SU(2)e group make it a compelling choice, however fermions that carry color and charge, as mediation by we go a step further and will assume that it is responsi- lighter states, such as those in the Standard Model (SM), ble for generating the non-zero baryon asymmetry in the would provide tree-level decay modes that would make early universe, thereby addressing one of the main open the requisite diphoton signal strength hard to explain. questions in cosmology and particle physics. More specif- ically, we choose our exo-fermion quantum numbers such The above simple setup would then suﬃce to account that B L, with B baryon number and L lepton num- for the key features of the excess, as they are currently ber, is anomalous− under SU(2) . One can then envision known. However, one may then inquire how the new e that if SU(2)e breaking in the early universe entailed a ﬁrst order phase transition, at a temperature T 1 TeV, the associated departure from equilibrium could∼ lead to ∗ the appearance of non-zero B L that would then get email: hooman@bnl.gov − †email: pgiardino@bnl.gov processed into the cosmic baryon asymmetry by the SM ‡email: cenzhang@bnl.gov sphalerons [13] (see also Refs. [14–16]). This is similar 1 A large number of papers have been written on this subject since to the scenarios envisioned for electroweak baryogene- the initial announcement of the excess, as can be seen from the citations of Refs. [1, 2] sis that would require a strongly ﬁrst order electroweak 2 See footnote (1) phase transition, which is however not realized by the SM 2

{1,2,3} Higgs. We then require that the coupling of the SU(2)e consider three generations of exo-fermions, Ϙ and be large enough that, while perturbative, would still lead Λ{1,2,3}. This completes our deﬁnitions for the ﬁeld con- to a ﬁrst order phase transition. tent of our model. In the heavy exo-fermion limit, the diphoton signal The Lagrangian is the sum of three contributions: strength is largely a function of the vev of the exo-Higgs doublet, which can then be ﬁxed. Hence, the exo-Higgs = SM + e + m, (2) L L L L potential parameters can be obtained for a given signal strength. We will also assume that the the SM Higgs where the ﬁrst term is the SM Lagrangian without the Higgs doublet mass term 2 † , the second is the La- portal coupling with exo-Higgs generates the SM Higgs µH H H grangian of the exo-sector, and in the third we have the mass parameter after SU(2)e breaking. This not only reduces the number of input parameters in the model, terms of mixing between SM and exo-sector. The second but also provides an explanation of the relative proximity term of Eq. (2) is of the the Higgs and exo-Higgs masses. We will next 1 a µν † µ 2 † † 2 introduce the ingredients of our model and discuss its e = ωµν ωa + (Dµη) (D η) + µηη η λη η η L −4 − | | potential relevance to baryogenesis. + iϘ¯LD/ϘL + i¯ϘRD/ϘR + iΛ¯ LD/ΛL + iΛ¯ RD/ΛR i i Y ∨;i,jη¯Ϙ Ϙ∨;j Y ∧;i,jη˜Ϙ¯ Ϙ∧;j − Ϙ L R − Ϙ L R THE MODEL Y ∨;i,jηΛ¯ i Λ∨;j Y ∧;i,jη˜Λ¯ i Λ∧;j, (3) − Λ R L − Λ R L In this section we will describe the main features of plus the usual gauge ﬁxing and Fadeev-Popov ghost our model. We assume the existence of a new gauge terms. The indices i, j refer to diﬀerent generations. As in the SM we can rotate the ﬁelds to a mass basis, and symmetry SU(2)e, completely broken by a Higgs ﬁeld η, under which the SM fermions are singlets. As per the generate the exo-sector counter-parts of the CKM and usual Higgs mechanism, three degrees of freedom of η give PMNS matrices. We now discuss the mixing terms. The mixing La- masses to the three gauge bosons ω1, ω2 and ω3 associ- grangian can be written in general as ated with SU(2)e, while we identify the fourth with the 750 GeV resonance. Unlike in the SM, ω1,2,3 are degen- † † m = 2kηH η ηH H (4) erate in mass. We also introduce new fermions, charged L ∨;i,j i j ∧;i,j i j under SU(2) and the SM gauge group, that acquire mass Y η ¯Ϙ d Y η˜Ϙ¯ d e − Ϙq L R − Ϙq L R through Yukawa couplings with the exo-Higgs . Follow- ∨;i,j i ∨;j ∧;i,j i ∧;j η Y Hq¯ Ϙ Y Hq¯ Ϙ ing the SM naming rule we call the fermions in a triplet − qϘ L R − qϘ L R ∧;i,j ∧;i j ∨;i,j ∨;i j of SU(3) exo-quarks Ϙ (archaic Greek letter pronounced Λ¯ e Λ¯ e , c − MΛ L R − MΛ L R Koppa), and the fermions that are singlets of SU(3)c exo-leptons Λ. The choice of possible quantum numbers where qL is the left-handed quark doublet, dR is a is limited by requiring that the theory is free of gauge right-handed down-type quark and eR is a right-handed anomalies. Since the exo-fermions are vector-like under charged lepton. The ﬁrst term of eq. (4) is the mixing the SM gauge group, freedom from anomalies is trivially between the Higgs ﬁelds of the two sectors (we will be in- 2 terested in values of k λH λη and hence the negative satisﬁed for that sector and the only non-trivial anoma- ηH lies are the Adler-Bell-Jackiw with one (1) and two sign of this interaction does not yield an unstable poten- U Y 2 2 tial). We ﬁx the value of kηH imposing that kηH v = µ SU(2)e bosons and the Witten anomaly [17]. We found η H the following anomaly free choice of quantum numbers where vη is the vev of the η ﬁeld, η = vη/√2, and p 2 h i under SU(2)e SU(3)c SU(2)L U(1)Y particularly µH = λvH where vH is the vev of the SM Higgs dou- interesting: ⊗ ⊗ ⊗ blet. In this way, we can justify the proximity between the breaking scale of SU(2)e and the vev of SM Higgs 1 doublet. This is not a requirement of our model, but the ϘL = (2, 3, 1, ) (1) −3 predicted value of kηH sits well within the phenomeno- 1 logical constraints, as we will see later. ϘR = (1, 3, 1, )( 2) −3 × In the second line of Eq. (1), ϘR has the same quantum ΛL = (1, 1, 1, 1) ( 2) numbers as a d , so it can couple to q with a Yukawa − × R L ΛR = (2, 1, 1, 1), interaction mediated by the SM Higgs. In the same way − dR can couple to ϘL as shown in the second and third where for the upper (lower) component of a ϘL doublet lines of Eq. (4). The Yukawa matrices will generically ∧ ∨ we have a corresponding ϘR (ϘR). We adopt a similar have oﬀ-diagonal terms, that can produce Flavor Chang- notation for the ΛR doublet. Note that, since the exo- ing Neutral Currents (FCNC). However, we can set the fermions are always singlets under SU(2)L, the U(1)Y oﬀ-diagonal terms as small as we want without altering charge coincide with the electric charge. Lastly, we the main purpose of this work, and, for simplicity, we 3

SU(2)e SU(2)e of baryon asymmetry in the universe. To address this question, one needs to introduce a baryogenesis mech- B L anism that satisﬁes Sakharov’s criteria [18]: (i) baryon =0 number violation, (ii) C and CP violation, and (iii) de- − 6 SU(2)e SU(2)e parture from equilibrium. In the SM, (i) is provided by sphaleron processes at temperatures T & 100 GeV before spontaneous electroweak symmetry breaking. Both C and CP violation are present in the SM, but the amount FIG. 1: Triangular anomaly for B − L. Although the ﬁeld of CP violation is too small. Condition (iii) would have content of the exo-sector is similar to the one of the SM, the required a ﬁrst order electroweak phase transition, which exo-leptons are right-handed doublets, so their contribution is not feasible with the SM Higgs potential. has a sign opposite to that of the exo-quarks. Various extensions of the SM have been proposed in order to supplement its shortcomings in the context of electroweak baryogenesis. In particular, one can enter- will consider all the Yukawa matrices in Eq. (4) to be tain the possibility that an initial B L number, which diagonal. is respected by all SM interactions, was− present well be- The lepton sector is peculiar since the quantum num- fore electroweak symmetry breaking took place. The SM bers of Λ allow us to write a mixing term where is L Λ sphalerons would then process the B L asymmetry into a mass parameter not directly related to the otherM scales ∆B = 0 and ∆L = 0 asymmetries−in equilibrium.A of the theory (vH and vη). As we will see in the phe- well-motivated6 scenario6 of this kind, referred to as lepto- nomenology section, its value should be at least one order genesis [19], employs heavy Majorana neutrinos that are of magnitude smaller than vH . However, that relatively required to implement a seesaw mechanism for generat- small value can be justiﬁed if this interaction descends ing light SM neutrino masses. While an interesting idea, from a higher energy theory where heavier degrees of free- leptogenesis typically requires that Majorana states ap- dom have been integrated out. As before, oﬀ-diagonal pear at scales 1 TeV, well beyond the reach of direct Λ terms can generate FCNC in the lepton sector, but discovery. Hence, this idea is only indirectly testable. weM can assume to be diagonal for the purposes of Λ Here, we propose that the B L anomaly in our model this paper. M − can lead to the generation of ∆(B L) = 0 if SU(2)e The oﬀ-diagonal terms in the exo-quark Yukawa matri- breaking at T 1 TeV involves a ﬁrst− order6 phase tran- ces in Eq. (3) can also be a source of FCNCs. However sition. This is∼ in analogy with electroweak baryogen- the mixing between SM-quarks and exo-quarks can be esis mechanisms, where a strong transition would have set small to avoid strong bounds on the CKM of the exo- generated departure from equilibrium as required for a sector. In any case, for simplicity, we will consider a limit baryon asymmetry. The generation of a B L asym- where all the oﬀ-diagonal terms are zero, the elements of metry would also require sources of CP violation,− which the same exo-doublet are degenerate in mass and two of our model would readily provide once generally complex the exo-quark generations have the same mass. It has Yukawa couplings are assumed. This motivates us to con- to be noted, however, that in general a more complex sider model parameters that support a ﬁrst order SU(2)e Yukawa sector for the exo-quarks is desirable, since it can phase transition. The key reason the SM cannot aﬀord be a source of the extra CP -violation needed for baryo- this possibility is that the ﬁnite temperature eﬀective po- genesis. A similar reasoning applies to the exo-lepton tential for the Higgs has a thermally generated cubic term sector, where we will set the Yukawa matrices diagonal that is too small. This term can lead to the appearance and all the exo-leptons degenerate in the mass. of a requisite barrier in the potential during the phase It is interesting to note that, at tree level, the La- transition. grangian in Eq. (2) preserves B and L, once we assign By analogy with the SM case, we see that the coeﬃ- to the exo-quarks and the exo-leptons the quantum num- cient of the relevant cubic term for the SU(2)e transition 1 bers B = 3 and L = 1, respectively. However once we is (see, for example, Ref. [20]) compute the triangular anomaly in Fig. 1, the resulting 3 m3 3 g3 B L current is anomalous, while the B +L is preserved. = ω = e (5) − E 3 . 4πvη 32π A strong ﬁrst order phase transition is one whose order CONNECTION TO COSMOLOGY parameter at the critical temperature of the transition Tc satisﬁes η(Tc)/Tc & 1, where η(Tc) is the exo-Higgs ﬁeld As discussed in the last section, B L number is value at the local minimum of the eﬀective potential for − anomalous under our SU(2)e. In what follows, we will T = Tc. One can show [20] that this requirement then argue that this anomaly oﬀers a possibility to address an implies 2E/λη(Tc) & 1, where λη(Tc) is the quartic self- important open question in cosmology, that is the origin coupling of the η at Tc. 4

Using the approximation λη(Tc) λη, the condition the following benchmark point for a strong ﬁrst order phase transition≈ in our model can then be written as vη = 1.2 TeV Vev of the η ﬁeld > mϘ = 800 GeV Mass of the heavier Ϙ 3 < 3 ge mϘ = 500 GeV Mass of the lighter Ϙ’s & 1 . (6) 16π λη mΛ = 380 GeV Mass of Λ’s (8) Λ = 1 GeV Λ l mixing mass parameter M − θϘ = 10−3 Ϙ q mixing angles Later, we will show that the signal strength suggested L,R − by the diphoton excess is, given our choice of model pa- ge = 2 SU(2)e gauge coupling rameters and ingredients, mainly sensitive to η . Hence, for a given signal strength, and assuming thath i the exo- With these parameters, we ﬁnd that the cross section for the 750 GeV signal is about 4.1 fb, taking into account an Higgs mass is 750 GeV, one can determine λη within our setup. We can then use Eq. (6) to derive a lower bound on NLO+NNLL K factor of 1.56 from Ref. [29]. This value should be compared with the weighted average deduced ge, motivated by the possibility of explaining the baryon from the ATLAS [1] and CMS [2] data 4.6 1.3 fb. asymmetry of the universe, as explained above. Such a ± baryogenesis mechanism will have the great advantage of being testable at the LHC and future high energy collid- Mode BR gg 82.1% ers, given that it is based on physics at or near the TeV + − scale. W W 7.4% HH 4.2% ZZ 3.7% tt¯ 1.8% γγ 0.81% SIGNAL STRENGTH AND PARAMETERS γZ 0.47% lΛ 0.12%

Γη 0.060 GeV In this section, we will discuss the signal strength and its implications for our parameter space. All the cross TABLE I: Main branching ratios and the total width Γη of sections, decay rates, and branching ratios, appearing the exo-Higgs η. Channels with lower than 0.01% branching in this and the next sections, are obtained using Mad- ratio are not displayed. The values in the table correspond to Graph5 aMC@NLO [21] and MadWidth [22] with a the benchmark point in Eq. (8). UFO model [23] made with the FeynRules package [24]. † † Loop-induced processes are computed following Ref. [25], The 2kηH η ηH H term induces a mixing between H and the corresponding counter term is computed with and η. With our assumption, namely that vη provides NLOCT [26]. In all simulations we use NNPDF2.3 par- the µH term of the SM and leads to electroweak sym- ton distributions [27], except for the 750 GeV signal, metry breaking, this mixing is about sin θηH = 0.006. where we use CT14nlo [28] to be consistent with Ref. [29], As a consequence, η could decay to SM particles, such as so that we can apply the NLO+NNLL K factor computed W +W −, ZZ, tt¯, and HH, through the Higgs portal, and with the same setup. these channels can be searched for in the future. They The signal strength is mostly sensitive to the vev of also aﬀect the value of vη, by diluting our signal strength by about 15%. With mixing higher than this value it the exo-Higgs doublet. Similarly to the SM, in the heavy ∼ fermion mass limit, the loop-induced gg η and η γγ will be diﬃcult to achieve the desired signal strength, so are described by the following dimension-ﬁve→ operators:→ in this sense θηH is bounded from above. The main branching fractions of η and its total width Γη are given in Table I. We ﬁnd that the implied signal αs 1 A Aµν 2α X 2 1 µν strengths for these channels are not in conﬂict with ex- = NϘ Gµν G η + NcQf Fµν F η L 3πvη 4 3πvη 4 Ϙ,Λ isting constraints from the LHC Run 1 data. As can be (7) seen from the table, the branching fraction for η ZZ and WW are, respectively, 4 and 9 times larger→ than that for the diphoton channel.∼ Note∼ that in many min- With our setup, vη 1 TeV will roughly produce the ∼ imal models the signal is obtained by coupling a singlet observed signal strength. Other parameters, like mix- scalar, which is unmixed with the SM Higgs, to vector ing angles and exo-Yukawas, could also aﬀect the signal fermions carrying only color and hypercharge. Then, the strength, by modifying the decay modes of η and the ZZ coupling to η is loop induced and sub-dominant to fermion masses running in the loop. 2 the γγ coupling, due to suppression by tan θW , where To facilitate a more concrete discussion, let us consider θW is the weak mixing angle. In such models, one does 5

∧,∨;1 ∧,∨;2 ∧,∨;3 not expect any signiﬁcant branching ratio into the WW Mode Λ Λ Λ ﬁnal state. Hl 100% 84.0% 22.0% − −6 The presence of signiﬁcant ZZ and WW branching W ν ∼ 10 10.6% 52.1% −6 fractions for η in our model can then provide an inter- Zl ∼ 10 5.3% 25.9% esting signal of Higgs-η mixing that can be accessible in TABLE II: Λ branching ratios. the LHC Run 2. In particular, a measurement of the ratio of BR(η ZZ) to BR(η γγ), given the value → → of the diphoton signal strength, can yield the amount of condition, the phenomenology does not depend much on Higgs-η mixing. Also, if the coupling of η to Z and W is the value of these mixing angles. Since the Ϙ mixing dominated by the Higgs portal, then in general sector has two kinds of mixing terms, Ϙ¯LqR andq ¯LϘR, the left- and right-handed mixing angles are in principle BR(η WW ) → 2. (9) independent of each other. We notice that for a mixing BR(η ZZ) ≈ −7 → angle less than O(10 ), the exo-quark would decay with Ϙ −3 This can then provide a test of our assumption regarding a displaced vertex. We choose θL,R = 10 for simplicity. the induced Higgs mass parameter from η = 0. The mixing between Λ’s and leptons is diﬀerent: the h i 6 With our benchmark parameters, the mass of the two Λ terms could couple ΛL to lR, but mass couplings > M Ϙ’s in the third generation, mϘ , is set heavy to satisfy from ΛR to lL are not allowed. As a result, the left Λ the bound from vector-like quark searches. The Ϙ’s decay handed mixing angle, θL, is suppressed by the lepton through three channels, Ϙ tW −, Ϙ bZ, and Ϙ bH, mass: → → → with branching ratios of 50%, 25%, and 25%, re- Λ ∼ ∼ ∼ tan θL ml spectively. For small mixing between Ϙ and quark, the in- Λ = . (10) 2 Ϙ tan θR mΛ dividual decay rates are roughly proportional to sin θL, Ϙ Λ where θL is the mixing angle between ϘL and bL, so the We choose Λ = 1 GeV, corresponding to θR 2.7 three branching ratios are roughly constant. Given these 10−3 for allM three generations. Note that with this≈ choice,× values, the bound on vector-like quark masses is 790 GeV the left-handed mixing angle between the electron and > ∧,∨;1 −9 [30], therefore we set mϘ to be 800 GeV. Λ is extremely tiny, 3.6 10 . If Λ & 10 GeV The masses of the Ϙ’s in the ﬁrst two generations have the signal strength will be∼ aﬀected× at (10%)M level by ¯ O to be heavier than half of the η mass, to avoid the η ϘϘ η lΛ, while if Λ . 0.1 GeV Λ will decay with a decay suppressing the signal. Apart from that,→ these displaced→ vertex. M lighter exo-quarks are not subject to severe constraints With our choice of benchmark parameters, the dom- as they mainly decay to W j, Zj and Hj. One relevant inant decay channel for Λ∧,∨;1 and Λ∧,∨;2 is Λ∧,∨;i → search channel is stop pair production, with each stop de- H + li where i = 1, 2 is the ﬂavor index. If θηH = 0, caying into a charm quark and a neutralino [31]. The exo- the branching ratios of the three possible decay channels, ∧,∨;i − ∧,∨;i ∧,∨;i quarks could decay through Ϙ Zj j+MET which Λ W + νi,Λ Z + li, and Λ H + li, has the same signal, but for our→ benchmark→ parameters are roughly→ 50%, 25%, and→ 25%, respectively.→ However the cross sections are 1 2 orders of magnitude below the ﬁrst two decay modes, W − + ν and Z + l, occur ∼ Λ the uncertainty from the background. through only left-handed mixing θL, which is suppressed The Λ masses do not have severe bounds either [32], ex- by ml/mΛ. This is because the right handed Λ and l cept that they should be again larger than mη/2. We set only couple to the hypercharge boson, with the same hy- them at 380 GeV, nearly one half of the exo-Higgs mass, percharge, so a unitary rotation between Λ and l will not mainly to enhance the signal and keep vη well above 1 generate any oﬀ-diagonal coupling. On the other hand, TeV. This is however not a strict requirement. For ex- the last decay channel Λ H + l occurs through the → ample, mΛ 420 GeV is still feasible with a somewhat ﬁrst diagram in Fig. 2, and is also suppressed by ml be- ∼ larger ge. cause of the lepton Yukawa. As a result the decay rate of ∧,∨;1 −13 Once vη is ﬁxed, λη = 0.20 can be derived, and Eq. (6) Λ is below 10 GeV and would lead to displaced requires ge > 1.48. We choose ge = 2 to be well inside vertex. However, with a nonzero θηH , the leptons can the region of parameters favored by a strong ﬁrst order decay through the last diagram in Fig. 2. Even though Λ phase transition. This value then sets the mass of ω the diagram involves two mixing angles θR and θηH , for vector bosons, mω = 1.2 TeV. As we will see later, with electron and muon this is still the dominant channel. As this mass ω production at LHC 7 and 8 TeV runs is too a result, Λ∧,∨;1,2 mostly decay to Higgs and lepton. The suppressed to yield a signiﬁcant signal. However, the branching ratios of all three exo-leptons are given in Ta- Run 2 of the LHC will have a chance to discover the ω ble II. bosons. It is interesting to see that the lighter lepton has a The mixing angles between Ϙ’s and quarks should be larger branching ratio to the Higgs. The corresponding well below (1%), so that η qϘ¯, Ϙq¯ decay rates will rate for Λ∧,∨;1 is about 7 10−11 GeV, above the limit not aﬀect theO signal strength too→ much. Apart from this for displaced vertex. × 6

Λ l l Λ l l Λ Λ l LHC data should contain less than one ω; at 14 TeV, however, with 300 fb−1 accumulated luminosity we can η 2 3 H W, Z H have (10 ) ω’s produced. Even though the ω j produc- tion hasO a higher cross section, it depends on the mass splitting. We therefore focus on the pair production of 3 l FIG. 2: Decays of a Λ into a leptons. The decay into τ is ω and ω , which is our robust prediction. Consider the mostly mediated by the ﬁrst two processes, while the decays leptonic decay channel of ω, e.g. ω3 Λ∧,∨;i+Λ∧,∨;i−, into µ and e are mostly mediated by the third, since the ﬁrst where i = 1, 2 is the ﬂavor index, the→ total branching two are suppressed by me and mµ. ratio is 28.8%; ωl will decay into Λ∧,∨;+Λ∨,∧;−, but will not change the counting. Using the cross section given in Table III, we will end up with 0.17 300 28.8%2 = 4.2 Our assumption, that vη leads to the electroweak sym- events with four Λ’s given 300 fb−1 ×of accumulated× lumi- metry breaking of the SM, gives the right amount of η H ∧,∨;1 − nosity . Among these events, Λ decays to the elec- mixing, that is enough to give a reasonable decay rate for tron and Higgs boson 100% of the time, while Λ∧,∨;2 Λ, but is not too large to dilute the signal through the decays to the muon plus∼ H/Z with 90% branching ra- Higgs portal. tio in total. Therefore we will have 3.5∼ signal events con- taining four leptons coming from the decay of Λ’s, with a typical p around 100 200 GeV, and some additional PREDICTIONS T jets or leptons from H ∼or Z decays. These events with four hard leptons are signiﬁcant In this section, we will discuss the predictions and col- enough that they will not be missed. We estimate that lider signals of our model that can be looked for in the the irreducible SM background, from four leptons with future. Within our mode, we predict new heavy quarks four Higgs/Z bosons, is negligible. Other background and leptons, i.e., Ϙ and Λ, that are vector-like under the sources, for example those from ttt¯t¯ in all-leptonic chan- SM symmetries but chiral under the exo group. The de- nels, can be removed by requiring ( ) , and ∧,∨;3 − ∧,∨;1,2 pT l > pT cut cay modes of Ϙ’s are Ϙ bZ, bH, tW , Ϙ 80 GeV can already remove more than 98% of − → − → pT cut jZ, jH, jW , and of Λ’s are lZ, lH, νlW . In this sense the background≈ (that is with less than 0.1 event left), they are fairly standard vector-like fermions, and can be while reducing the signal by about 30%. The analysis discovered in corresponding searches. This is similar to can be further elaborated by requiring no missing trans- many other models that use vector-like fermions to ex- verse energy or requiring additional j/l, which will bring plain the 750 GeV resonance. down the background by another 1 2 orders of mag- The more distinct signature of our model is the pro- nitude. In general, 4 production from∼ the SM, after ↑ ↓ l duction of the exo-gauge bosons, i.e. ω , ω (deﬁned re- removing opposite-sign same-ﬂavor lepton pairs coming spectively as (ω1 iω2)/√2 and (ω1 + iω2)/√2) and ω3. − from Z’s and requiring pT (l) > 80 GeV, is also below one The main production channel is through Ϙ-loop induced event, and will become negligible once additional jets are processes, gg ωω and gg ωj. Note that the lat- required. ter actually vanishes→ with our→ choice of parameters: the ∧ ∨ We can also consider tagging the b’s from Higgs decay, Ϙ and Ϙ masses are set to be equal, but the loop has which makes our signal even more distinguishable. Con- 3 a trace over the T generator in the exo-group, so their sidering Λ lH only, we will have about 3.1 4H4l events contributions cancel each other. Therefore to give a rea- −1→ ∧ at 300 fb . If we require two of the four Higgs bosons de- sonable estimate on the cross section, we increase the Ϙ cay to b¯b and tag four b’s, we will have 2 3 signal events masses by 300 GeV, only for this process. The cross sec- with 4 b’s, 4 hard leptons, and additional∼ jets/leptons tions we found are in Table III. Note that the exo-gauge from Higgs decay. This is an even more distinct signal bosons could be produced also at the tree level, through that can discriminate our model from other new physics qq¯ ω, or qg ωϘ. However the ﬁrst is suppressed by scenarios, and is essentially free of background. Ϙ→ 4 → Ϙ 2 (θL,R) and the second is by (θL,R) , and the resulting Of course, if the 750 GeV signal is conﬁrmed, dedicated Ϙ −2 cross sections are negligible with θL,R . 10 . analysis will be needed to optimize the search strategy and to give a reliable estimate of the discovery potential, Process 8 TeV 13 TeV 14 TeV but the simple estimation described above already shows 3 gg → ω j 0.016 fb 0.16 fb 0.26 fb that the ω pair production is a promising channel. gg → ωω 0.003 fb 0.11 fb 0.17 fb

TABLE III: Cross sections of the main production channels DISCUSSIONS at diﬀerent energies. The double omega production sums over all exo-vector bosons. The model we have considered in this work contains From Table III, we can see that currently available a number of new ﬁelds that have signiﬁcant interaction 7 strengths. Hence, one may worry about quantum eﬀects 3.0 Non-perturbativity of these ﬁelds on the validity of the underlying model. We will denote byµ ¯ the maximum energy scale beyond L 2 which our model would need further completion to avoid H 2.5 loss of theoretical control. In Fig. 3, we present various SU - regimes of the model in the yϘ ge plane, where yϘ is the

− exo Yukawa coupling of the heaviest exo-quarks (800 GeV Stability in our benchmark set of parameters). Here, we choose the

5 of 2.0 µ¯ = 10 TeV, for which any unwanted eﬀects of higher Instability dimension operators from ultraviolet (UV) completions of our model are expected to be quite suppressed. Non-perturbativity

5 coupling Forµ ¯ = 10 TeV, our model maintains stability (λη > 0) and perturbative reliability (no Landau poles) in the 1.5

green shaded area (“Stability”). The red area (“Instabil- Gauge ity”) has λη < 0 and leads to an unstable exo-Higgs po- tential, whereas the yellow region (“Non-perturbativity”) entails Landau poles for either λη or yϘ. The lower part of 1.0 the plot, the horizontal band shaded gray, is disfavored if 0.9 1.0 1.1 1.2 1.3 1.4 one requires a strong ﬁrst order SU(2)e phase transition. Yukawa coupling of the heaviest exo-quarks The region of “Stability” (green), as can be seen from Fig. 3, represents a signiﬁcant part of the parameter space and does not require very special choices for a re- FIG. 3: The green area represents points in the yϘ − ge plane where all the parameters of the model stay positive and per- liable model. It is also interesting that this region basi- turbative up toµ ¯ = 105 TeV. For the points in the red area cally coincides with that favored by the requirement of a λη crosses zero beforeµ ¯. The points in the yellow region give strong ﬁrst order phase transition, as motivated by an ex- a Landau-Pole for either λη or yϘ. The grey area is excluded planation of the baryon asymmetry in the universe. This if we require a ﬁrst-order transition is related to the fact that the stability of the exo-Higgs quartic coupling gets enhanced by the contributions of ω gauge ﬁelds, which grow with larger ge. We also add that at the LHC and future colliders, unlike those scenarios gravitational waves corresponding to a strong phase tran- that originate from much higher scales. We have also as- sition at a temperature T 1 TeV, as assumed in our sumed that the coupling of the exo-Higgs and SM Higgs scenario for baryogenesis, are∼ typically predicted to be doublets leads to the generation of the SM Higgs mass observable by future space-based gravitational waved de- parameter, once SU(2)e is broken. This can explain the tectors [33], such as LISA (for recent work on this topic, similar sizes of the exo-Higgs and SM Higgs mass scales, see for example Ref. [34]). and allows η to have tree level decays into tt, WW and ZZ. While the main ingredients of our model employed in CONCLUSIONS explaining the diphoton excess eﬀectively resemble those of models with a singlet scalar and vector-like fermions, In this work, we have proposed that the diphoton ex- the presence of TeV-scale vector bosons, corresponding to cess at 750 GeV, reported by the ATLAS and CMS col- the broken generators of SU(2)e, is a distinct prediction laborations, can be due to a scalar resonance that is the of our proposal. We ﬁnd that double vector boson pro- remnant of an SU(2)e exo-spin gauge symmetry break- duction, the most robust prediction of our scenario, can ing through the vev of an exo-Higgs doublet. We as- lead to a discovery of these states with about 300 fb−1 at sume that there are exo-fermions, carrying SM color and the 14 TeV LHC. The decay of each vector boson domi- hypercharge, that get their masses from the exo-Higgs nantly produces two hard leptons, as well as two or more mechanism and mediate the gluon fusion production and b-jets and more leptons and light jets, and can hence yield diphoton decays of the scalar. signals that are eﬀectively background free. Under some We choose the matter content (exo-quarks and exo- mild assumptions about the spectrum of the model, sin- leptons) and their associated quantum numbers such that gle exo-vector boson production is also a viable discovery B L is anomalous under SU(2)e. 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