Correlated Signals at the Energy and Intensity Frontiers from Nonabelian Kinetic Mixing

Transcription

1 Correlated Signals at the Energy and Intensity Frontiers fro Nonabelian Kinetic Mixing G. Barello, Spencer Chang and Christopher A. Newby Departent of Physics and Institute of Theoretical Science, University of Oregon, Eugene, Oregon We show that when a dark abelian gauge sector and SU() L kinetically ix it necessarily generates a relation between the kinetic ixing strength and the ass of the ediating particle. Rearkably, this correspondence aps the weak scale directly to the kinetic ixing strengths being probed by odern fixed-target experients and next generation flavor factories. This illuinates the exciting possibility of correlated discoveries of a new particle at the LHC and a dark photon at intensity frontier experients. To otivate the scenario, we construct a siple odel and explore its phenoenology and constraints. Thus, in theories with only nonabelian kinetic ixing, there is a strong correlation between signals of dark phoarxiv: v3 [hep-ph] 30 Aug 016 PACS nubers: Kinetic ixing (KM) is a phenoenon that produces an interaction between gauge bosons of two different gauge groups, and generically occurs when there are two U(1) gauge syetries in a theory. KM will be generated by loop processes whenever there are particles charged under both syetries [1, ]. This akes KM a coon ingredient of odels beyond the standard odel (SM) of particle physics. In Z [1] and any dark atter odels [3, 4], the SM is suppleented by an additional U(1) gauge syetry which can ix with U(1) Y. Such odels have otivated a large and diverse experiental effort with current and upcoing searches at intensity frontier experients (fixed-target and flavor factories) and the LHC (see [5] for overview and references). The ain focus of these searches and odels has been on the dynaics of the dark photon or signals of particles charged only under the dark sector, while little attention has been paid to the aforeentioned particle charged under both syetries, which ediates KM. The reason this ediating particle is ignored is that it s ass can usually be ade large while leaving the KM strength fixed. In the ost studied case of KM between two abelian sectors, where the ixing operator is diension four, the ediator ass only logarithically affects the strength of KM. Moreover, KM between abelian sectors is described by a renoralizable operator, so it can be included without reference to a ediator. Thus, in the abelian case, it is not guaranteed that the ediator will be light enough to be discovered. On the other hand, when KM goes through a nonabelian gauge sector, the operator is nonrenoralizable and inextricably linked to a ass scale. This fact gives nonabelian kinetic ixing odels unique predictive power which has not yet been studied in the literature. This study fills that gap. Furtherore, as we will show, nonabelian KM strengths relevant for current intensity frontier experients is unabiguously linked to a weak scale ediator, predicting a correlated signal at the energy frontier. Although such nonabelian ixing is already well known in the literature (see, for exaple, [4]) this study represents the first stateent of this connection, and the first presentation of a odel where a nonabelian operator is the sole origin of KM. In this paper we discuss a case of particular odern interest: an abelian dark sector ixing with SU() L of the SM. The lowest diensional operator involving only SM fields and the dark photon which kinetically ixes SU() L and the dark photon is c 16π ( H τ a H ) W a µνf µν D (1) where Wµν(F a µν D ) is the field strength of the SM SU() L gauge boson (dark gauge boson), H is the SM higgs field, and τ a are the Pauli atrices divided by two. Anticipating the origin of this operator, we include the ass of the ediator, a loop factor, and absorb O(1) nubers and couplings into the coefficient c. Once electroweak syetry is broken, Eq. (1) contains the canonical ixing between the photon and the dark photon ɛ F µνf µν D ; ɛ = c v s W 3π () where s W is the sine of the electroweak ixing angle, and v is the SM higgs vacuu expectation value (vev). Already this expression shows a connection between intensity and energy frontier experients: planned searches for the dark photon include i) fixed target experients, probing the region ɛ for a dark photon of ass M AD MeV and ɛ for M AD MeV (e.g. APEX [6] and HPS [7]), ii) next generation flavor factories, sensitive to ɛ for dark photon asses up to 10 GeV [5] (going beyond existing BABAR, BESIII liits [8, 9]), and iii) a proposed LHCb search sensitive to the range ɛ and M AD 100 MeV [10]. In our odels of interest, Eq. (3) shows that this paraeter space requires c v s W c = 3π ɛ 1 TeV. (3) ɛ/10 4

2 tons at the intensity frontier and the corresponding ediator particles at the LHC. This conclusion is independent of the specific realization of nonabelian KM. In the rest of this paper we present a siple odel where the only KM that occurs is nonabelian. In such scenarios, the ediator particle s signals at the LHC are correlated with the dark photon searches of the intensity frontier. We will analyze the odel s dynaics and then discuss the ediator particle s phenoenology and relevant constraints. Model: In this odel, there is a dark gauge syetry U(1) D with a dark photon, A D. The field ediating KM is a scalar SU() L triplet with unit dark charge that we call. In order to give the dark photon ass we introduce a dark higgs, H D, with unit dark charge that gets a vev H D = v D /. The ost general, renoralizable theory with these fields has any ters in its scalar potential. Only a subset of the will be relevant for our discussion, and the ters we study are V (H, H d, ) = λ H 4 µ H + λ D H D 4 µ D H D + + λ ix ( T a )(H τ a H) ] +κ [ a (H τ a H)H D + h.c. (4) where κ can be taken to be real after a field redefinition and T a is the triplet representation s generators for SU() L. Of particular iportance is the ter with coefficient λ ix as it is responsible for KM. After integrating out, KM is generated with strength ɛ = gg Dλ ix v ( ) 400 GeV 96π s W 10 4 g D λ ix (5) where g is the gauge coupling for SU() L, and g D is the dark gauge coupling. As the final expression shows, if the new couplings are order one, ixings relevant to intensity frontier experients are spanned by in the range 100 GeV 1 TeV. This odel does not contain a particle charged under both U(1) D and hypercharge so there is no abelian kinetic ixing generated at low energies. Although an ultraviolet contribution to abelian kinetic ixing can exist, it can be suppressed if the Standard Model is ebedded into a grand unified theory (GUT). That way there is no abelian kinetic ixing in the ultraviolet, since hypercharge becoes part of a nonabelian group. In such scenarios, particles with GUT-scale asses can generate abelian kinetic ixing fro two-loop diagras with ixing strengths on the order ɛ as discussed in [11]. In this and siilar odels, nonabelian kinetic ixing can be doinant over abelian ixing. This eans that we can use Eq. (5) to predict the ediator ass fro the kinetic ixing strength. Mass Spectru: The ter responsible for KM also generates a ass splitting in the states. Two states, labeled χ ± and η ±, are charged under electroagnetis and have asses χ = + λ ixv, η = λ ixv. (6) 4 4 This splitting can cause the lightest charged state s ass to becoe tachyonic, spontaneously breaking U(1) EM and giving the photon ass. This places a constraint that > λ ixv /4. The two reaining, neutral degrees of freedo are the real and iaginary parts of the third coponent of, denoted 0 R and 0 I, respectively. These states will be nearly degenerate with ass a very sall splitting is generated which vanishes as κ 0. Throughout we will use to refer to all of these states collectively and their individual naes when specificity is required. Potential Miniization: The κ ter in the potential was introduced in order for the particles to decay, but also has other iportant effects that can constrain the odel. Once the electroweak and dark syetries are broken, this ter induces a vev for the real, neutral coponent of. The size of this vev is = κv v D 4. (7) Since this is only in the neutral coponent, U(1) EM reains unbroken, but it does shift the W boson ass, with a contribution to the T paraeter T 10 3 κ ( v D 1 GeV ) ( ) 4 00 GeV, (8) which is very sall as long as the dark photon scale is sub-gev. In addition, there is a one loop contribution to T fro the particles due to their ass splitting [1] which in the liit of sall splitting goes as λ ( ) ix T loop v4 00 GeV 0.1 λ ix. (9) 19πs W c W Z Contributions to S are negligible, so to be consistent with electroweak precision constraints requires T < 0. (95% C.L.) [13], putting a lower bound on (fro Eq. (9)) and an upper bound on κ (fro Eq. (8)). The κ ter also causes ixing between 0 R, h D, and the SM higgs. This leads to a correction to the µ D ter of size κ v 4 /(16 ). Thus, a large hierarchy between the dark and electroweak scales requires a tuning in the value of µ D. The severity of this tuning depends on κ, and for certain regions of paraeter space this tuning can be sall. It is however interesting that the tuning in this odel is indirectly observable. This is in contrast to the SM where the details of tuning depend on soe unknown, as-of-yet-unobservable higher scale. If KM with SU() L is observed, this odel will provide insight into the validity of tuning as a theoretical constraint.

3 3 Fixed Target Benchark: Now lets consider a benchark set of paraeters, chosen in order to reain within the region of iediate interest to fixed-target experients: AD = 0.1 GeV and g D = 0.5. This choice iplies that v D = 0. GeV, and we set hd = 0.4 GeV so that the dark higgs can decay into two dark photons. Note that the dark higgs and photon asses are negligibly sall relative to electroweak scale asses, so we can safely neglect the in later forulas. We also set λ ix = 1 which puts a lower liit on of 155 GeV due to the electroweak precision constraint. In our analysis we specifically explore the range 150 GeV < < 500 GeV in order to be relevant for collider searches while reaining in the 10 5 < ɛ < 10 3 window, though it should be kept in ind that precision electroweak constraints exclude the sall part of this region < 155 GeV. Additionally, in this low ass region, the lightest charged state will have ass η < 100 GeV which is in tension with results fro LEP searches for charged particles, e.g. [14]. Decays: A particle can decay directly into gauge and higgs bosons through the κ ter, or undergo cascade decays through its ass states by radiating W ( ) bosons. The cascade decay rate, in the large and assless ferion liit, is Γ(χ ± W ± 0 R,I) = Γ( 0 R,I W η ± ) = f f N c G f 5 15π 3 (10) where G f is the Feri constant, is the ass splitting between states, and f f includes all ferion pairs except the top-botto pair for which the splitting is too sall to produce. The κ ediated decay rates, in the liit that hd, AD 0, are Γ( 0 R hh D ) = Γ( 0 I ha D ) = κ v ( 64π 3 ) h, (11) Γ(χ ± W ± h D ) = Γ(χ ± W ± A D ) κ v ( = χ ) 3 W, (1) 18π 4 3 χ Γ(η ± W ± h D ) = Γ(η ± W ± A D ) (13) κ v ( = η ) 3 W. 18π 4 3 η The decay phenoenology depends sensitively on κ. If κ is sufficiently sall the cascade decays will doinate, and heavier will tend to decay down to the lightest state, η ±, eitting two ferions via an off-shell W per step, followed by the η ± decaying half the tie to W ± h D and half the tie to W ± A D. On the other hand, if κ is large, κ ediated decays doinate with the neutral coponents of decaying as 0 R hh D, 0 I ha D and η ±, χ ± decaying to W ± h D, W ± A D equally. Note that the siplicity of the decays are a consequence of our benchark choice. As the value of v D is increased fro our benchark, additional decay odes due to κ becoe ore iportant, e.g. 0 R hh, ZZ, W W and η ± W ± h, W ± Z. However, since these decay rates are proportional to vd, only when v D 100 GeV do these start to becoe iportant and thus in the intensity frontier paraeter space we do not expect these decays to have appreciable rates. κ ϵ = - ϵ = - ϵ = - ϕ ( ) FIG. 1: This figure shows regions of interest in the (,κ) plane. Starting fro the top, the regions are where the new higgs decays are greater than 10% of its SM expected total width (green region), where µ D is tuned to > 10% (above the thick orange curve) and where the electroweak cascade decays are faster than the κ decays (below the green curve). Vertical dashed lines ark values of ɛ, labeled at the top. In Fig. 1, we highlight soe of the iportant regions of our benchark paraeter space. Soe characteristic values of ɛ are given at three values in dashed lines, though these can be scaled up or down by changes in g D, λ ix. The green line denotes the value of κ where the cascade decays are coparable to the κ induced decays below which the off-shell cascade decays doinate. The iddle region of Fig. 1 shows where the tuning in µ D is worse than 10%, and the last region at the top shows when the SM higgs has new decays with a branching ratio greater than 10%, which will be discussed below. Production Rates: In order to observe these decays, particles will need to be produced, which at a hadron collider proceeds predoinantly through Drell-Yan production. The production cross sections at the 13 TeV LHC are shown in Fig.. We used FeynRules [15] to generate our Lagrangian and CalcHEP [16] to generate the events using the cteq6l parton distribution function for the proton. Pair production of the neutral particles does not occur due to the lack of photon, Z couplings. Also, production rates for 0 I are identical to 0 R and so are not included on the plot. The strategy for searches should start with adaptations to the existing searches for dark photons and lepton jets [11, 17 19]. All events contain either h D or A D particles produced at significant boosts, which coupled with the decay h D A D A D, will lead to any events

4 4 Σ fb Η Η Η ± 0 Φ R Χ ± 0 Φ R Χ Χ photon. The widths of these decays are κ 4 v 6 Γ(h h D h D ) = Γ(h A D A D ) = 51π h 4 (14) ( Γ(h A D γ) = v ɛ h ) 3 (15) 8π v ( ) Γ(h A D Z) cw = Γ(h A D γ). (16) s W FIG. : This figure shows the pair production cross section for various ass states of at the s = 13 TeV LHC. The different curves are: two η states (red), an η and a 0 R or 0 I (orange) a χ and a 0 R or 0 I (green) and two χ states (blue). The legend is arranged in order of decreasing cross section. Curves were generated using the cteq6l parton distribution function of CalcHEP [16]. with boosted lepton pairs. For sall enough ɛ, any of these A D decays will be displaced. If the value of κ is sall, where cascade decays doinate, there will also be soft leptons or jet activity fro the off-shell W s. An interesting signal in this regie is the possibility of sae sign η production due to the cascade decays of 0 R, 0 I going equally into η ± (see Eq. (10)). Their subsequent decay produces a like-sign pair of W s leading to sae sign lepton events in addition to the lepton jets of the event. On the other hand, if the value of κ is large, there can be other associated objects like the SM higgs bosons produced in 0 R, 0 I decays (see Eq. (13)), which could be of interest in ters of tagging or reconstructing the events. To suarize, this scenario s predoinant collider signal is lepton jets in association with W, h with ass resonances between a lepton jet and the W or h. Since the benchark s dark photon ass restricts it to electron decays, the lepton jets could be challenging to pick out. Boosted electron pairs are uch ore difficult to distinguish fro jets and in fact, ost existing lepton jet searches rely on uons (with significant constraints only for M AD > µ 0. GeV). To overcoe these challenges, soe proising strategies could be to look for displaced jets and/or jets with significant electroagnetic energy deposit. We leave studies of such issues as well as existing LHC constraints and discovery reach for such particles to future work. SM Higgs Phenoenology: This odel also predicts new decays for the SM higgs. The doinant new decays are into dark higgs bosons and dark gauge bosons. The kinetic ixing operator itself, Eq. (1), generates new decays of the higgs to a dark photon and either a Z or a again we take the liit where A D and h D are assless. These new decay widths are indirectly constrained by the relatively good fits of the SM higgs decay signal strengths [0]. As an approxiation of this constraint, the top green region of Fig. 1 shows where higgs decays into the dark sector exceed 10% of the SM higgs total width. In particular, decays of the higgs involving the dark photon are a direct consequence of the kinetic ixing ter, and provide a odel independent signal of nonabelian kinetic ixing. For ɛ 10 3 the branching ratio of the higgs to a dark photon will be Br(h A D + Z/γ) There is potential for the LHC to detect these higgs decays, if the dark photon is heavier than our benchark. For exaple, if AD GeV, the LHC can be sensitive to the dark photon through higgs decays into A D [1] and a recent LHC analysis constrains Br(h A D ) for AD = GeV []. While the fixed target paraeter space otivates searches at uch lower dark photon asses, a siple odification of our benchark can give these heavier asses. In these odified bencharks, if one iproves the higgs branching ratio constraint to BR new < BR liit, this would constrain the range κ > 0.5( /00 GeV)Br 1/4 liit. As our forulas and discussion show, increasing AD to these larger values, either through increasing g D or v D, changes very little in the phenoenology, however, in this heavier paraeter space correlated signals at the intensity frontier could only be seen at future flavor factories for AD < 10 GeV. Conclusions: In this letter, we have argued for a direct connection between current intensity frontier searches for dark photons and the signals of new particles at the LHC. The connection occurs if KM involves a nonabelian gauge syetry, since the ixing operator requires higgs fields to be gauge invariant and thus closely ties the ediator particle ass to the vev of the higgs and the strength of KM. To illustrate this, we wrote down a siple odel where the only KM which occurs is between a new dark U(1) gauge syetry and SU() L. This requires a scalar triplet of SU() L which is charged under the dark U(1). Analyzing the odel, we looked at the constraints and briefly considered the phenoenology of the particles at the LHC which could be searched through siple odifications of existing dark photon searches. Aside fro our siple odel, there are obvious extensions to explore. Ferionic ediators, ixing with a nonabelian dark gauge syetry and incorporating dark

5 5 atter are all intriguing odifications, which will all produce the sae, odel-independent correlation of signals. Interestingly, these directions all tend to lead to larger ultiplicity in the dark sector, suggesting that the odel in this paper is unique in its siplicity. Investigation of these directions, as well as a detailed collider study of this odel is forthcoing. To conclude, KM of the SU() L of the SM and an abelian dark sector is tiely and well otivated given the current run of the LHC, ongoing fixed target experients, and potential next generation flavor factories. The connection it draws between intensity and energy frontier experients is unabiguous and leads to correlated signals at these experients, proising unprecedented insight into the physics of the dark sector. Acknowledgeents: The authors would like to thank J. Mardon for helpful discussions regarding the new decays of the SM higgs. This work was supported in part by the Departent of Energy under grants DE-SC (G.B. and S.C.) and DE-SC (C.A.N.). [1] P. Galison and A. Manohar, Phys. Lett. B136, 79 (1984). [] B. Holdo, Phys.Lett. B166, 196 (1986). [3] M. Pospelov, A. Ritz, and M. B. Voloshin, Phys. Lett. B66, 53 (008), [4] N. Arkani-Haed, D. P. Finkbeiner, T. R. Slatyer, and N. Weiner, Phys.Rev. D79, (009), [5] R. Essig et al., in CSS 013: Snowass (013), [6] R. Essig, P. Schuster, N. Toro, and B. Wojtsekhowski, JHEP 0, 009 (011), [7] A. Celentano (HPS), J. Phys. Conf. Ser. 556, (014), [8] J. Lees et al. (BaBar), Phys.Rev.Lett. 113, (014), [9] V. Prasad, H. Li, and X. Lou (BESIII) (015), [10] P. Ilten, J. Thaler, M. Willias, and W. Xue (015), [11] N. Arkani-Haed and N. Weiner, JHEP 1, 104 (008), [1] L. Lavoura and L.-F. Li, Phys. Rev. D49, 1409 (1994), hep-ph/ [13] K. Olive et al. (Particle Data Group), Chin.Phys. C38, (014). [14] K. Ackerstaff et al. (OPAL), Phys. Lett. B433, 195 (1998), hep-ex/ [15] A. Alloul, N. D. Christensen, C. Degrande, C. Duhr, and B. Fuks, Coput. Phys. Coun. 185, 50 (014), [16] A. Belyaev, N. D. Christensen, and A. Pukhov, Coput. Phys. Coun. 184, 179 (013), [17] G. Aad et al. (ATLAS), Phys. Lett. B719, 99 (013), [18] V. Khachatryan et al. (CMS) (015), [19] G. Aad et al. (ATLAS) (015), [0] Tech. Rep. ATLAS-CONF , CERN, Geneva (015), URL [1] D. Curtin, R. Essig, S. Gori, and J. Shelton, JHEP 0, 157 (015), [] G. Aad et al. (ATLAS) (015),