Asymmetric Dark Matter Models and the LHC Diphoton Excess
CCP3-Origins-2016-14 DNRF90 and DIAS-2016-14
Asymmetric Dark Matter Models and the LHC Diphoton Excess
Mads T. Frandsen and Ian M. Shoemaker CP -Origins & Danish Institute for Advanced Study DIAS,University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark Department of Physics; Department of Astronomy &Astrophysics; Center for Particle and Gravitational Astrophysics,The Pennsylvania State University, University Park, PA 16802, USA (Dated: November 6, 2018)
Abstract
The existence of dark matter (DM) and the origin of the baryon asymmetry are persistent indicationsthat the SM is incomplete. More recently, the ATLAS and CMS experiments have observed an excessof diphoton events with invariant mass of about 750 GeV. One interpretation of this excess is decays ofa new spin-0 particle with a sizable diphoton partial width, e.g. induced by new heavy weakly chargedparticles. These are also key ingredients in models cogenerating asymmetric DM and baryons via sphaleroninteractions and an initial particle asymmetry. We explore what consequences the new scalar may havefor models of asymmetric DM that attempt to account for the similarity of the dark and visible matterabundances. a r X i v : . [ h e p - ph ] M a r . INTRODUCTION In [1, 2] the ATLAS and CMS experiments both report excesses in diphoton final states withinvariant masses around 750 GeV. If these excesses are interpreted as a narrow resonance the localsignificances correspond to 3.6 and 2.6 σ respectively leading to modest global significances of 2 σ in ATLAS and 1.2 σ in CMS — The significance is slightly higher in the ATLAS data if interpretedas a resonance with a width of about 50 GeV while the CMS significance is decreased slightly.Preliminary updates presented at Moriond 2016 show a slight increase in the significance of theCMS results with more data, while the ATLAS reanalysis of the 8 TeV data, results in a 2 sigmaexcess in the same mass region and thus in less tension between the 13 and 8 TeV data.Although the significances of the results are modest it is tantalizing to interpret this as the firstglimpse of new physics beyond the SM. It is then particularly motivated to investigate how thisputative resonance may fit into a bigger picture of the origin of mass, i.e. electroweak symmetrybreaking or the origin of dark matter (DM). Here we focus on a possible connection with the origin ofDM, motivated by the observation that the same basic ingredients, a new scalar resonance and newweak charged states, can account for the diphoton excess and are required in models of asymmetricDM.One interpretation of the diphoton excess is the s -channel production, via gluon (and photon)fusion, of a new (pseudo) scalar resonance φ with a mass m φ ∼
750 GeV gg ( γγ ) → φ → γ, (1)and a cross-section into diphotons of about σ γγ ∼ −
10 fb. The required cross-section, and theabsence of signals in other decay channels, indicates the presence of new (weak) charged states toenhance the diphoton decay width Γ φ → γγ . Alternatively new colored states could enhance both theproduction cross-section and the partial width into diphotons, but we do not consider new coloredstates in this study. Importantly, gluon induced production grows by a factor of ∼ q ¯ q induced production as has been discussed in several studies, e.g. [3]. Thediphoton induced production and its scaling between 8 TeV and 13 TeV is more uncertain but hasbeen argued to grow significantly from 8 TeV to 13 TeV, see e.g. [4–9].Meanwhile the cosmological dark matter abundance is curiously close to the abundance ofbaryons, suggesting a common origin. Since the baryonic density is known to originate from a pri-2 B /X /B /X SU (2) L sphalerons Model 1 Model 2
FIG. 1: The two classes of ADM models considered that φ may participate in. If φ is an SU (2) singlet,then X and B or L violating operators involving φ can establish a relation between the dark and baryonicasymmetries. If φ and X are doublets, DM can participate directly in the EW sphalerons and φ servesto deposit the X asymmetry into a SM singlet fermion X , via X → φ ( ∗ ) + X . In this latter case, theadditional fermion X is needed since SU (2) doublet DM is ruled out by direct detection for a wide rangeof masses. mordial particle-antiparticle asymmetry, it is natural to consider the possibility that DM emergedfrom a related mechanism. Asymmetric DM provides one compelling framework of this. Modelsfor the cogeneration of a DM and baryon asymmetry, able to explain the observed relic density ofDM today, require the same new states as may explain the diphoton excess — i.e. new electroweakcharged states, coupled to the EW sphalerons and new scalar states mediating the decay of theseEW charged states into neutral DM particles, as in e.g [10–12]. Already there has been considerablework on the possible connections of the diphoton resonance to DM [3, 13–31].In this paper we explore the possible connection between the asymmetric origin of DM and theexcess of diphotons at LHC, interpreted as a new scalar resonance. The paper is organized as follows:In Section II we provide a brief summary of the diphoton excess interpreted in terms of a spin-0state produced via gluon or photon fusion. In Section III we summarize two scenarios for generatingdark matter from an initial baryon asymmetry as well as possible implications of the resonance forthe annihilation of DM in the early universe. In Section IV we discuss singlet models of asymmetrytransfer, while in Section V we discuss doublet models that use SU (2) sphalerons to connect thedark and visible asymmetries and show that the diphoton resonance can be accommodated in suchmodels. Finally we summarize our results in Section V.3 I. INTERPRETATION OF THE DIPHOTON EXCESS
The diphoton excess reported by the ATLAS and CMS collaborations can be interpreted in avariety of ways [3–5, 13, 14, 16, 18, 20, 32–149].Here we assume the diphoton excess is due to a new (pseudo) scalar state φ produced via gluon(and photon) fusion. The diphoton coupling is enhanced via the presence of new weakly chargedstates near the weak scale while we do not assume the presence of new colored states at the weakscale.Below electroweak symmetry breaking the Yukawa interactions of φ with fermions can be sum-marized as L φ = (cid:88) f y φf φ ¯ f Γ f (2)where f denotes any SM or new fermions, and Γ ≡ { iγ , } in the case of a (pseudo) - scalarresonance. The SM Higgs corresponds to Γ = 1 , y φf = m f /v EW (cid:39) / √ φ → ¯ ff (cid:39) N c ( f )8 π y φf m φ (3)Γ φγγ = α G F √ π m φ (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:88) f N c ( f ) e f c φf A φf ( τ f ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (4)where N c ( f ) denotes the fermions and c φf are reduced Yukawa couplings normalized to m f v EW followingthe notation in [150]. The loop function for a CP odd φ is A φf ( τ f ) = 2 τ − f ( τ ) , τ f = m φ m f , f ( τ ) = arcsin ( √ τ ) , τ ≤ − (cid:104) log (cid:16) √ − τ − −√ − τ − (cid:17) − iπ (cid:105) , τ > . (5)The LHC production cross section of φ via top-induced gluon fusion and/or photon fusion maybe approximated by σ γγ (cid:39) ( σ gg → φ, y φt + σ γγ → φ, Γ φ → γγ Γ γγ, ) Br φ → γγ . (6)From [151] we have that the gluon-fusion reference cross-section is σ gg → φ, = 1 . y φt = 1 (cid:39) √ y h SM t where h SM is the the SM Higgs. The photon-fusion referencecross-section is σ γγ → φ, (cid:39) γγ, = 0 .
34 GeV [151] but the error on thisestimate is large and we refer the reader to recent studies [4–9]. .4o address the observed signal cross-section σ γγ ∼ −
10 fb via the gluon fusion contribution weneed y φt (cid:38) × − . At this minimum possible value for the gluon fusion production cross-sectionwe require Br φ → γγ (cid:39) φ → γγ > Γ φ → tt (cid:39) . × − m φ ∼ . y φt (cid:39) × − ).However, it follows Eq. (6) that at this minimum value of the y φt coupling, the photon fusion cancontribute comparably, see e.g. [151] for details.From the diphoton decay rate in Eq. (4) we have that Γ φγγ ∼ − m φ (cid:12)(cid:12)(cid:12)(cid:80) f N c ( f ) e f c φf A φf ( τ f ) (cid:12)(cid:12)(cid:12) for m φ (cid:39)
750 GeV and thus we need (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:88) f N c ( f ) e f c φf A φf ( τ f ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:38)
30 (7)which is possible to achieve given the upper limit of | A φf ( τ ) | (cid:46) y φf (cid:46) π fromperturbativity. We display sufficiently large diphoton partial widths in an explicit model in Fig. 5and give the production cross-section in Eq (69). III. IMPLICATIONS OF THE RESONANCE FOR ANNIHILATION AND ASYMME-TRIES
The observation that the cosmological abundance of DM and baryons are similarΩ DM (cid:39) B , (8)may imply that they shared a common origin. Since we know that the baryon abundance is relatedto an asymmetry, a natural possibility is to consider models which relate the baryon asymmetry to aDM asymmetry (for reviews see [152, 153]). This requires that DM is a complex particle carrying aparticle number, X -number, e.g. a (pseudo-) Dirac particle charged under a global U (1) X symmetry.The key ingredient in such models are transfer operators of the form O tr = O B − L O X , (9)where O B − L is a ( B − L ) carrying operator and O X carries nonzero DM number. Thus O tr re-lates an asymmetry amongst baryons η B to a DM asymmetry η X by establishing chemical equi-librium between the two sectors. These operators can be the electroweak sphalerons or otherhigher-dimensional operators that freeze-out at relatively high scales. Often the scales are so highthat DM is still relativistic, and consequently the baryon and DM number densities are similar, n X ∼ n B . In this case the cosmological observation that Ω DM / Ω B ∼ m X ∼ O (5 GeV) in5he absence of a symmetric component of DM or multiple components. We give an explicit model ofthe diphoton excess leading to this relation in section V. However, importantly, larger DM massescan also be consistent with the desire to achieve Ω DM / Ω B ∼
5, in models where the asymmetrytransfer decouples when DM has already started to become non-relativistic (see e.g. [154]). In whatfollows we will keep the DM mass free in order to be as general as possible.Having now established a relation between η B and η X , the final ingredient is to relate the particleasymmetries to the mass density ratio of DM and baryons [155] m X m p η X η B = (cid:18) − r ∞ r ∞ (cid:19) Ω DM Ω B (10)where r ∞ ≡ n − /n + with n ± being the number density of (anti-)DM. Notice that the fractionalasymmetry, r ∞ is not uniquely determined by the DM asymmetry η X but instead also depends onthe annihilation cross section [155–157] r ∞ (cid:39) exp (cid:32) − . η X M Pl m X σ √ g ∗ x n +1 f ( n + 1) (cid:33) , (11)where g ∗ is the relativistic degrees of freedom, M Pl is the Planck mass, and (cid:104) σv (cid:105) = σ ( T /m X ) n where n = 0 and n = 1 are for s - and p -wave annihilation respectively. Lastly, x f = m X /T f isa dimensionless measure of the DM freeze-out temperature when DM annihilation processes ceasebeing more rapid than the Hubble rate. This number is only logarithmically dependent on the DMmass and cross section, being typically x f (cid:39) r ∞ limit [158] by combining Eq.(10) and (11) (cid:104) σv rel (cid:105) ADM (cid:39) × − cm s − log (cid:18) r ∞ (cid:19) , (12)such that larger annihilation cross section result in much smaller fractional asymmetries. This is inline with the generic expectation that ADM models require larger than WIMP-sized annihilationcross sections since the “symmetric component” needs to be annihilated away for the asymmetricexcess to account for the DM abundance.The preceding discussion applies to a wide class of ADM models. Now let us investigate theimplications of the new resonance state for ADM.6 � = � π � � = � � � = ���
200 400 600 80010000.0010.0050.0100.0500.1000.5001 �� ����� � � [ ��� ] �� �� �� �� � � � � � �� � � � � � � ∞ ��� ������������ 〈σ � ��� 〉 � _ � ⟶ �� Ω � > Ω �� �� � �� � - �� � ( ���� ) ��� � ( ���� ) �� � �� � - ��� � ( � � � � � ) - �� ����� � � [ ��� ] � � �� �� ��� �� �� � � � FIG. 2:
Left panel:
Annihilation to gluons in the CMB, taking the gluon- φ coupling φG µν ˜ G µν to beΛ = 5 TeV [26]. Right panel:
Current and future direct detection limits on a gauged U (1) X model ofthe DM relic abundance. In addition to current LUX [159] and CRESST-II [160] limits we also display aCRESST-III phase 2 projection based on 100 eV threshold with 1000 kg-day exposure [161]. Here we havefixed the kinetic mixing parameter ε = 10 − and the vector mass m A (cid:48) = 10 MeV. A. Generic Implications
As discussed above, ADM models must feature a sizeable DM annihilation cross section inorder to remove the symmetric component [155, 157]. Since this condition applies generically weinvestigate it first. A simple connection of DM to the diphoton excess might be a direct couplingof DM to the new resonance. This immediately implies new annihilation channels for DM such as¯ XX → φ → gg (13)¯ XX → φ → γγ (14)In addition, if DM is sufficiently heavy ( m X > m φ ) then we also have t -channel annihilation,¯ XX → φφ. (15)However, because of the gluon couplings these annihilation channels also imply DM signals atboth hadron colliders (jet(s) plus missing energy) and elastic scattering signals at direct detectionexperiments. For the O (10 GeV) DM range, natural for ADM, these constraints rule out the7bove annihilation modes as the ones setting the relic density or annihilating away the symmetriccomponent of DM [26].It has been argued that late time CMB annihilation can constrain both symmetric [162–164] andasymmetric DM annihilation [158, 165]. This constraint comes from the injection of energy intothe electromagnetic plasma during recombination and therefore relies on the efficiency of energydeposition f eff which depends on the DM annihilation channel. For the γγ and gg final states ofinterest to us the efficiency is roughly independent of the DM mass and is of the size, f gg (cid:39) . f γγ (cid:39) . r ∞ , f eff (cid:104) σv (cid:105) m X r ∞ (cid:18)
21 + r ∞ (cid:19) < . × − cm s − (16)where the right-hand side applies the current (WMAP9+Planck+ACT+SPT+BAO+HST+SN)CMB limit at 95 % CL [167]. We find that gluon annihilation dominates over the photon channelin setting the most stringent CMB limit, which we display in Fig. 2 for a pseudo-scalar mediatorwhich provides s -wave annihilation, (cid:104) σv rel (cid:105) gg (cid:39) y X m X π Λ (cid:0) m X − m φ (cid:1) + Γ φ m φ (17)Note that of the annihilation modes considered here those mediated by the s -channel pseudo-scalar are the only ones that yield strong limits from CMB data since all the others are strongly p -wave suppressed.We note that all models need additional DM interactions beyond a coupling to the resonance inorder to provide a viable thermal relic. This is a result of the complementarity of collider, directand indirect astrophysical searches of DM (see e.g. [26]). In particular for scalar resonances thespin-independent direct detection limits from LUX [159] are strong enough to rule out DM massesless than m φ /
2, while the upcoming LZ collaboration will probe the remaining window at high massthermal DM [26]. And in the case of a scalar resonance, the indirect searches are very weak sinceall of the minimal annihilation channels are p -wave suppressed.In contrast for pseudo-scalar resonances, indirect limits on DM annihilation can be strong whiledirect detection is extremely weak. The weakness of direct detection in this case is due to themomentum-suppression in the cross section as well as the fact that pseudo-scalar interactions me-diate spin-dependent scattering, for which the present limits are much weaker due to the lack of8oherent enhancement. As a result of the combination of LHC monojet [168] and the recent Fermi γ -ray line limits [169], thermal DM with masses below m φ / U (1) X gauge symmetrywith a massive gauge boson, A (cid:48) µ lighter than the DM mass. Interestingly this possibility endowsDM with rather large velocity-dependent self-interactions, which may be suggested by the small-scale structure problems of collisions cold DM [170–172]. The presence of light scale vectors withsizeable kinetic mixing with the photon can be unveiled in a DM halo-independent manner withthe combination of multiple detector types [173].For illustrative purposes we show in the right panel of Fig. 2 the current and projected directdetection limits on this U (1) X gauge interaction model for DM annihilation. Elastic scatteringproceeds via kinetic mixing with the SM photon, εF µν F (cid:48) µν where F (cid:48) µν is the U (1) X field strength.In Fig. 2 we fix ε = 10 − and m A (cid:48) = 10 MeV. We note that experiments sensitive to electron-DMscattering may offer additional constraints in the sub-GeV regime [174–176]. B. Model-dependent Implications for the Asymmetry
One can establish a relation between the baryonic and DM asymmetries in one of two ways: (1)Generate η X (cid:54) = 0 primordially and then transfer it to baryons via Eq.(9) (or vice versa); or (2) Gen-erate both η X (cid:54) = 0 and η B (cid:54) = 0 simultaneously and circumvent the need to transfer the asymmetry.Here we will not explore this latter possibility in much detail, but comment on the possibilities of re-lating the resonance with “cogenesis” mechanisms. For example, in supersymmetric (SUSY) modelsit may be associated with a flat direction (in the SUSY preserving and renormalizable limit) of thescalar potential that allows for the generation of a large primordial asymmetry via the Affleck-Dinemechanism [177, 178]. Models of this type have been generalized beyond traditional baryogenesisto allow for the simultaneous production of dark and baryonic asymmetries [179–182].Here we shall consider two model classes that realize a connection between the diphoton excessand ADM via the transfer of the asymmetries, summarized schematically in Fig. 1 and discussedbriefly below: • Model 1: New Asymmetry Transfer Operators : If the diphoton resonance and DMare both EW singlets, then EW sphalerons cannot transfer a particle asymmetry between thedark and visible sectors, but φ can play this role. For example, two operators involving φ that9ccomplish this task for singlet φ and X are O SM = 1Λ tr φ ( LH ) , (18) O X = y X φXX, (19)which act to establish chemical equilibrium between dark and leptonic asymmetries. As longas these interactions are in equilibrium above the EW scale, sphalerons will establish a relationbetween the X and baryon numbers. Note that in the limit where φ is sufficiently heavy thatit can be integrated out we recover the transfer operator studied in [183].We study this model in Sec. IV. • Model 2: EW Sphalerons and new SU (2) Charged States : If the diphoton resonanceis part of an SU (2) doublet it may signal additional EW structure. If DM carries weakquantum numbers and a particle number X that is classically conserved, but violated by theweak anomaly, then DM can be produced asymmetrically in the EW sphaleron transitions. O Sphaleron = (
QQQL ) X (20)However, as is well-known, the simplest incarnation of this setup where DM itself is part ofan elementary SU (2) doublet is in tension with direct detection constraints since the DMfermion participating in sphalerons also scatters on nuclei via the Z boson.A simple way to avoid this problem is to consider models in which a heavy doublet X carrying X number decays into the resonance scalar φ and a light singlet DM state X in the earlyuniverse. In this case X can acquire an asymmetry via sphalerons while the decay X → φX via O decay = X X φ (21)transfers the asymmetry into the SU (2) neutral state X . The X , , φ states may be funda-mental [10, 12] or composite [11]. The φ state may be identified with the SM Higgs as in [12]but that is now constrained by e.g. the Higgs diphoton decay rate and it is therefore relevantto identify φ with a new spin-0 doublet in addition to the SM one, as in the 2HDM. We studysuch a model in Sec. V. 10 �� - ������������ � ���������� �� ����� � � � [ ��� ] � � � � � � � � � �� � � � Λ [ � � � ] FIG. 3: Here we show what values of the transfer operator scale are needed in order to obtain non-relativistic decoupling for a range of DM masses. For values of the transfer scale above this critical valueonly rather light DM can be accommodated (see Eq.(31)).
IV. MODELS OF ASYMMETRY TRANSFER WITH SPIN-0 SINGLETS
We follow [184] for the notation and setup of chemical equilibrium in the early universe. Thisparticular transfer operator evolution is similar to a model considered in [155], whose approach wealso follow. We solve for the ratio of baryon number to DM number by breaking the problem intotwo steps. In the first step, we find the value of the baryon density and L (cid:48) density ( L (cid:48) = X − L ) atthe sphaleron temperature since these two quantum numbers are conserved.The chemical equilibrium conditions are Q ∝ µ u − µ d − µ e = 0 (22) µ u − µ d = µ ν − µ e (23) µ u + 2 µ d + µ ν = 0 (24)2 µ X + 2 µ ν = 0 (25)(26)following from EM charge conservation, W ± exchange, and the transfer operator (Eqs.(18 and1119))). At the sphaleron decoupling scale T sph these yield B = − µ e , (27) L (cid:48) = (cid:18) f ( m X /T sph ) f (0) + 32 (cid:19) B, (28)where the function f ( x ) encodes the Boltzmann suppression in the DM density as it becomes non-relativistic at the epoch of decoupling, f ( x ) = 14 π (cid:90) ∞ dy y cosh (cid:16) (cid:112) x + y (cid:17) . (29)Note that in case the of scalar DM the above function is the same modulo the replacement cosh( x ) → sinh( x ).Next, we impose these value of B and L (cid:48) as initial conditions for the evolution from T sph throughthe transfer operator decoupling at T D . Solving finally for the ratio of dark and baryon numberswe find η X η B =
54 + 11 f ( m X /T sph ) f (0)
360 + 36 f ( m X /T D ) f (0) f ( m X /T D ) f (0) (30)Thus for example when DM is very light compared to both the sphaleron and the transfer temper-atures, the DM to baryon asymmetry ratio is η X /η B (cid:39) .
16 implying from Eq. (10) that the DMmass can range from m X = . , r ∞ = 01 . , r ∞ = 0 . n X σ tr (cid:39) H ( T D ) where the transfer operator cross section induced from Eqs. (18) and(19) is σ tr (cid:39) (cid:18) v Λ tr (cid:19) y X πm φ m X (32)This results in the transfer operator decoupling temperature T D = m X log (cid:20)(cid:16) v Λ tr (cid:17) y X M Pl πm φ m X (cid:21) . (33)12e thus see that DM masses in the 1 GeV - 1 TeV range are well accommodated for even veryhigh scales of the transfer operator Λ tr . This makes the transfer component of the model quite safefrom experimental scrutiny, though we note that future direct detection constraints can limit theYukawa y X involved directly in the operator O X , in Eq. (19). Moreover, here we have assumed that φ does not obtain a vacuum expectation value. If that assumption is broken however then Eq. (19)induces a Majorana mass for the DM allowing for X − ¯ X oscillations [183, 185–187]. The final relicabundance can be impacted in this case depending on the precise scale of the Majorana term, andof course present-day annihilation can proceed at sizeable rates.Finally of course the available annihilation channels in the minimal setup for the transfer operatorand diphoton signal and not sufficient for the DM relic abundance. As mentioned earlier however,this is achieved in models where DM is charged under a new gauge symmetry that has low-scalegauge boson, m A (cid:48) (cid:28) m X . Data from direct detection experiments with disparate target media maybe able to constrain the mass of this gauge boson via the momentum dependence in the elasticscattering cross section [173]. V. MODELS OF ASYMMETRY TRANSFER WITH SPIN-0 DOUBLETS
We now discuss models of ADM such as those in [10–12] featuring new spin-0 and spin-1/2 weakdoublets allowing to interpret the diphoton excess as a pseudo-scalar resonance. As mentionedearlier, in this case an X -charged EW doublet (fermion) state can participate in the sphalerontransitions and generate a nonzero DM number in tandem with a nonzero baryon number. Toevade direct detection constraints though, this state cannot be the DM today. Instead the heavier X -carrying state decays to EW singlet DM. We assume the production of a baryon asymmetry atsome high scale and only require the model be able to transfer this asymmetry.As a concrete example consider introducing the following left handed fermions,Ψ L = ψ L ψ − L ∼ (2 , − , ,η + L ∼ (1 , , − ,η L ∼ (1 , , − , (cid:101) χ L ∼ (1 , , − , and (cid:101) Ψ L = (cid:101) ψ + L (cid:101) ψ L ∼ (¯2 , , , (cid:101) η − L ∼ (1 , − , − , (cid:101) η L ∼ (1 , , − ,χ L ∼ (1 , , , (34)13harged under the weak gauge symmetries and a global U (1) X symmetry, SU (2) L ⊗ U (1) Y ⊗ [ U (1) X ] . The second doublet (cid:101) Ψ L is here needed for anomaly cancellation, and we introduced the right handedfields η, (cid:101) η to allow Dirac masses for both the charged and neutral components.We also introduce two scalar doublets Φ i , i = 1 , S Φ i ∼ (2 , − ,
0) = φ i φ − i , S ∼ (1 , , . (35)The doublet Φ is coupled to the SM fermions, and yields the (mostly) SM higgs doublet, while Φ is coupled only to the new weak doublets. The scalar sector is thus an extension of a Type-I twoHiggs doublet model. We also introduce Yukawa interactions of Φ with the new fermions − L ⊃ y ( (cid:101) Φ † Ψ L η + L + Φ † (cid:101) Ψ L (cid:101) η − L ) + h . c . (36)+ y (Φ † Ψ L η L + (cid:101) Φ † (cid:101) Ψ L (cid:101) η L ) + h . c . (37)+ y (Φ † Ψ L (cid:101) χ L + (cid:101) Φ † (cid:101) Ψ L (cid:101) χ L ) + h . c . (38)+ λ S S (cid:101) χ L χ L + h . c . (39)Below the EW scale we then identify two electrically charged Dirac fermions, carrying also X -charge,as X − = ψ − L η + † L , (cid:101) X − = (cid:101) ψ + L (cid:101) η −† L (40)These will contribute to the diphoton decay of the (dominantly) Φ physical scalars.Taking for simplicity y = y = y and y , λ s to be parametrically smaller than y the heavycharged and neutral (approximate) mass eigenstates have the common mass m X = m (cid:101) X = yv √ y /y, λ s /y are X (cid:39) ψ L η † L , (cid:101) X (cid:39) (cid:101) ψ L (cid:101) η † L , (42)while the light neutral mass eigenstate is X (cid:39) χ L (cid:101) χ † L , m X (cid:39) λ s v s (43)14lectroweak sphalerons and the associated ‘t Hooft operator( u L d L d L ν L ) Ψ R Ψ L = ( u L d L d L ν L ) (cid:101) Ψ L Ψ L . (44)violate X -number by two units. The origin of the DM particle (cid:101) χ L is therefore as follows.i) In the early universe we assume an initial baryon asymmetry is produced. ii) Below thisscale B − L is conserved, but sphalerons transfer the initial asymmetry into Ψ L , (cid:101) Ψ L . iii) Below thesphaleron freeze out the Ψ L , (cid:101) Ψ L states decay into the mass eigenstate X † R (cid:39) (cid:101) χ L via Eq. (38).We note that the specific Yukawa structure we assume above, notably the distinction betweenthe neutral η and χ states can be ensured by endowing the new fermions, except for χ, (cid:102) chi withlepton number as done in [10], at the expense of having to introduce another lepton charged scalardoublet mediating the interaction in Eq. (38). Another relevant variation of the model is given in[12] where baryon number instead of X number is assigned to the states.The ratio of DM number X and baryon number B in the model above is XB (cid:39) (1 + 4 f ( m X /T ∗ ) /f (0)) (45)such that using Eq. (10) we arrive at m X (cid:39) r ∞ = 00 . , r ∞ = 0 . . (46)Thus in contrast with the singlet model of Sec. IV, we achieve much lighter DM in the case ofrelativistic transfer decoupling and the initial ( B − L ) charge vanishes. The variations in [10, 12]produce a similar mass for the DM candidate while [11] provides a composite realization. A. Scalar sector
We now investigate the scalar sector of the model with the aim of explaining the LHC diphotonexcess. The scalar sector is a 2 Higgs doublet model (2HDM)— augmented by a singlet scalar S and new weak charged fermions. We first disregard effects of the scalar S assuming it is only weaklycoupled to the 2HDM and consider the CP -conserving potential, e.g. [188]. V = m Φ † Φ + m Φ † Φ − [ m Φ † Φ + h . c . ]+ 12 λ (Φ † Φ ) + 12 λ (Φ † Φ ) + λ (Φ † Φ )(Φ † Φ ) + λ (Φ † Φ )(Φ † Φ )+ (cid:26) λ (Φ † Φ ) + (cid:2) λ (Φ † Φ ) + λ (Φ † Φ ) (cid:3) Φ † Φ + h . c . (cid:27) . (47)15e define two angles β , the ratio of the scalar vevs t β ≡ tan β ≡ v v , (48)with 0 ≤ β ≤ π/
2. And α determining the ‘Higgs mixtures’ upon diagonalization. The physicalstates — the CP -even higgs scalar h and heavy scalar H , the CP -odd A and the charged scalars H ± — as well as the absorbed Goldstone bosons G are then given byΦ ± = c β G ± − s β H ± , Φ ± = s β G ± + c β H ± , Φ = √ [ v + c α H − s α h + ic β G − is β A ] , Φ = √ [ v + s α H + c α h + is β G + ic β A ] . (49)For α → , β → π/ is a pure SM Higgs. We may approach this decouplinglimit via the small parameter δ ≡ β − α − π/
2, with c β − α (cid:39) − δ (cid:28) , s β − α (cid:39)
1. Spectrum
In the decoupling limit δ (cid:28) m A (cid:39) v (cid:34) (cid:98) λc β − α + λ A − (cid:98) λ c β − α (cid:35) (cid:39) v (cid:34) − (cid:98) λδ + λ A + (cid:98) λ δ (cid:35) , (50) m h (cid:39) v ( λ − (cid:98) λ c β − α ) (cid:39) v ( λ + (cid:98) λ δ ) , (51) m H (cid:39) v (cid:34) (cid:98) λc β − α + λ − (cid:98) λ c β − α (cid:35) (cid:39) m A + ( λ − λ A − (cid:98) λ δ ) v , (52) m H ± (cid:39) v (cid:34) (cid:98) λc β − α + λ A + 12 λ F − (cid:98) λ c β − α (cid:35) = m A + 12 λ F v . (53)where λ ≡ λ c β + λ s β + 12 λ s β + 2 s β ( λ c β + λ s β ) , (54) (cid:98) λ ≡ s β (cid:2) λ c β − λ s β − λ c β (cid:3) − λ c β c β − λ s β s β , (55) λ A ≡ c β ( λ c β − λ s β ) + λ s β − λ + 2 λ c β s β − λ s β c β , (56) λ F ≡ λ − λ , (57)16nd λ ≡ λ + λ + λ .Thus from the observation of the 125 GeV scalar and the putative 750 GeV state that we willidentify with the CP -odd scalar A we require( λ + (cid:98) λ δ ) (cid:39) / , − (cid:98) λδ ∼
10 (58)Further we require that the decay mode from the A → ZH coupling is negligible, thus m H ≥ m A and for H to contribute to the signal also M H − M A < M V , thus( λ − λ A + (cid:98) λ c β − α ) v ( M H + M A ) M Z = m h + (2 (cid:98) λ c β − α − λ A ) v ( M H + M A ) M Z (cid:46) δ (cid:39) − . , ˆ λ (cid:39) , λ = λ A (cid:39) / B. Couplings and diphoton rates
The 2HDM we consider is Type-I like with only Φ coupled to the SM fields. The reducedcouplings, normalized to the SM higgs couplings, of the 125 GeV scalar h are then to first order in δ , see e.g. [189, 190], c hf = c α /s β = 1 − cot β δ (60) c hV = c α s β − s α c β = s β − α = 1 , (61)which for cot β < δ ∼ O (10 − ) are very close to the SM higgs values. Similarly the couplingsof the heavy neutral scalar H and pseudoscalar A to the SM fields are c Hf = s α /s β (cid:39) − δ − cot β (62) c HV = c β − α (cid:39) − δ (63) c Af = ic β /s β = i cot β . (64)Therefore to produce A at the level of ∼ β (cid:38) . × − from Eq. (6).Finally the couplings to the new fermions are c AX = − i tan β (65) c HX = c α /c β (cid:39) tan β − δ (66) c hX = − s α /c β (cid:39) δ tan β (67)17 � = � λ � = ��� λ � = � λ � = ��� ��� ( β ) β λ � λ λ � = � λ � = ��� λ � = ��� Γ ( � ⟶γγ ) < ���� Γ �� ( � ⟶γγ ) β � � - � � �� � � ��� �� �� � � � � ( � ) FIG. 4: Left: The values of λ , (cid:98) λ and tan β as a function of the angle β . For β ∼ .
45 we find valuesof ˆ λ, λ corresponding to m h (cid:39)
125 GeV, m A (cid:39)
750 GeV and tan β ∼ O (10). Right: The value of theYukawa coupling of the heavy fermions to the 125 GeV Higgs as a function of the angle β . In both plotsthe additional parameters of the scalar potential are λ = 0 . , λ = 0 . , λ = 6 , λ = 2. To avoid large contributions of the new states to the higgs diphoton rate, we require δ tan β ∼ − δ ∼ − . , ˆ λ (cid:39) , λ = λ A (cid:39) / β ∼ O (10). In Fig. 4on the left panel, we show the value of ˆ λ, λ and tan β as a function of β . On the right panel weshow c hX = 1 + δ tan β for the same parameters. For β ∼ .
45 we find values of ˆ λ, λ correspondingto m h (cid:39)
125 GeV, m A (cid:39)
750 GeV and tan β ∼ O (10).With the above couplings we identify our diphoton resonance with the CP -odd resonance φ ≡ A and the diphoton decay rate of A is given asΓ Aγγ (cid:39) α G F √ π tan β m A (cid:12)(cid:12) A AX ( τ X ) (cid:12)(cid:12) (68)In figure 5 we show the diphoton rate as a function of the fermion masses m X = m (cid:101) X nearthreshold for tan β = 5 ,
10. As is clear from the figure we can get sufficient diphoton rate nearthreshold for tan β ∼ O (10).In particular, using Eq. 6 to express the scaling of the diphoton cross-section we find σ γγ (cid:39) (cid:18) (5 −
8) tan β + (1 −
2) tan β (cid:19) ×
11 + 5 × − tan β fb . (69)where the range refers to m X = 380 − A (cid:39) Γ A → tt + Γ A → γγ . Itfollows that for tan β ∼ O (10) and near threshold we can also accommodate the diphoton excess.18 �� ( β )= ����� ( β )= ������ �����
350 400 450 5000.00000.00010.00020.00030.00040.00050.00060.0007 � � � [ ��� ] Γ γγ / � � FIG. 5: The diphoton width of the CP -odd resonance φ ≡ A as a function of the new weak doublet fermionmasses m X for two different values of tan β . C. Constraints
We conclude the model discussion by briefly summarizing relevant constraints on the model fromvacuum stability, Higgs decay into diphotons and searches for weakly charged particles.Necessary conditions for the stability of the scalar potential in Eq. (47) are [191, 192], λ , > , λ > − (cid:112) λ λ , λ + λ − | λ | > − (cid:112) λ λ , | λ + λ | < λ + λ λ . (70)These conditions are satisfied for our representative parameter choices λ = 0 . , λ = 0 . , λ =6 , λ = 2 , λ = 0 − . σ h → γγ is however affected by the presence of the new doublets. Wedefine the ratio R gg ( γγ ) = σ h → γγ /σ h SM → γγ and expand the reduced couplings c h as c h = 1 + δc h andfinally δc γγ M SM γγ parameterizes new contribution to the diphoton amplitude — here from the newfermions - in units of the SM ones. We can then write [189] R gg ( γγ ) (cid:39) δc hγγ − . δc ht + 2 . δc hV (cid:39) . c hX (71)From the right panel of Fig. (4) and the current limit on the diphoton decay width from ATLASof µ = 1 . +0 . − . [193] and CMS [194], we see that in the relevant part of parameter space we are ingood agreement with the limit. 19he estimate in Eq. (69) assumes that the the top and diphoton partial widths dominate thewidth of φ . This requires the partial decay widths A → X X → X γ and A → X X ∗ → X → γ to be negligible. The former requires y < cot β where cot β ∼ (1 − × − above. This alsoimmediately suppresses (beyond the off-shell suppression) the second process since A → X ∗ X ∗ → X → γ ∼ y .There is still sufficient freedom in the scalar potential to ensure that e.g. λ A , λ F such that m H (cid:38) m A and m H + (cid:38) m A . The H state can contribute to the diphoton signal, but the gluonfusion production of a scalar is smaller. Also there is two small canceling contributions in c f ( H ) aswell as between the W-loop (even if suppressed) and the new fermions in Eq. (62) so we expect asubleading contribution to the diphoton signal.Finally there are no flavor changing neutral currents in the model since only one doublet iscoupled to the SM fermions and flavor constraints on the charged H ± are very weak for large tan β as considered here [190]. Limits on the new weak charged fermions have been recently summarizedin [195] and require only that they have masses (cid:38)
130 GeV. While recent ATLAS searches of thecharged Higgs states in the H ± t b channel constrain the charged Higgs mass to be m H ± (cid:38) − of data at √ s = 8 TeV. VI. SUMMARY
The recently observed excess of diphotons by the ATLAS and CMS experiments may be inter-preted as a new spin-0 resonance with a sizable diphoton partial width induced by loops of newEW charged fermions. If these excesses are confirmed with future data it is of great interest todetermine how this resonance fits into a broader framework able to address the origin of EWSBand dark matter.Models of asymmetric DM cogenesis, in which SM sphalerons transfer an initial baryon asym-metry into DM, also require new spin-0 weak doublets coupled to new fermionic weak doublets. Inan explicit model example the scalar sector is an extended Type-I 2HDM and we showed that ina part of the parameter space we can accommodate the observed diphoton excess while being inagreement with current constraints, including the diphoton width of the 125 GeV scalar. Maintain-ing perturbative Yukawa couplings require the new fermions to be near threshold, around 400 GeV,and we also commented on a composite realization.Lastly, we emphasize that low-threshold direct detection offers one of the best avenues to detect20he class of dark matter models here (see e.g. the right panel of Fig. 2), which prefer DM at the O (GeV) scale. [1] T. A. collaboration, Search for resonances decaying to photon pairs in 3.2 fb − of pp collisions at √ s = 13 TeV with the ATLAS detector , .[2] CMS
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