Novel kinematics from a custodially protected diphoton resonance
Jack H. Collins, Csaba Csaki, Jeff Asaf Dror, Salvator Lombardo
NNovel kinematics from a custodially protected diphoton resonance
Jack H. Collins, ∗ Csaba Csáki, † Jeff A. Dror, ‡ and Salvator Lombardo § Department of Physics, LEPP, Cornell University, Ithaca, NY 14853, USA
We study a simple, well-motivated model based on a custodial symmetry which describes thetree-level production of a 750 GeV diphoton resonance from a decay of a singly produced vector-like quark. The model has several novel features. The identification of the resonance as an SU(2) R triplet provides a symmetry explanation for suppression of its decays to hh , W W , and gg . Moreover,the ratio of the 13 TeV to 8 TeV cross sections can be larger than single production of a 750GeV resonance, reaching ratios of up to 7 for TeV scale vector-like quark masses. This eliminatesany tension between the results from Run I and Run II diphoton searches. Lastly, we study thekinematics of our signal and conclude that the new production mechanism is consistent with availableexperimental distributions in large regions of parameter space but, depending on the mass of thenew vector-like quarks, can be differentiated from the background with more statistics. I. INTRODUCTION
The recent observation of an excess in the diphoton chan-nel around 750 GeV invariant mass by ATLAS and CMSat √ s = 13 TeV [1, 2] has generated much interest inmodels with a heavy scalar resonance, φ , that decays totwo photons. Most explanations proposed so far are con-sidering loop induced resonance production, typically viaheavy vector-like quarks (VLQ) charged under the Stan-dard Model (SM). Otherwise, tree-level decays to SMparticles would naturally dominate the branching ratioof φ , either leading to a diphoton rate too small to ex-plain the excess or a production rate of two SM particleswith large invariant mass that is excluded by existingmeasurements.In this paper, we propose a novel tree-level productionmechanism where φ arises from the decay of a VLQ. TheVLQs can be singly produced due to their mixing withthe SM quarks, while the resonance is protected by theSU(2) L × SU(2) R custodial symmetry. In order to havesignificant mixing between the VLQs and the light quarkswithout modifying the Zq ¯ q couplings predicted by theSM, we introduce VLQs in a bidoublet representation ofthe custodial symmetry, while the resonance φ is part of atriplet under SU(2) R . The model has several advantagesand new features: • It is one of the few viable examples of tree-level pro-duction consistent with the excess signal rate, ex-isting experimental constraints, and the kinematicdistributions of the diphoton background events. • The ratio of production rates between 13 and 8 TeVis different than gluon or quark fusion. Dependingon the model the ratio can be as large as about 7(vs. 4.7 for gluon fusion), eliminating the tensionwith the 8 TeV diphoton searches. ∗ [email protected] † [email protected] ‡ [email protected] § [email protected] • The custodial symmetry protects the resonancefrom the leading one-loop decays to hh , W W , and gg , while allowing decays to γγ . The suppressionof the hh decay is particularly significant since inmost models this coupling will arise at tree-level,making it difficult to reconcile with the expectantlylarge diphoton branching ratio and unobserved hh decays. The γγ (as well as ZZ and Zγ ) decay widthis nonvanishing due to the explicit breaking of thecustodial symmetry from gauging the U(1) Y sub-group of SU(2) R . • The custodial symmetry also forbids one-loop gluonfusion production, explaining the dominance of thetree-level production via a decay of a VLQ.The scenario where φ is produced primarily from the de-cay of singly-produced VLQs has not been consideredin the diphoton excess literature, although some authorshave considered production of φ through a cascade decayof a heavier parent particle (e.g., [3–10]). Furthermore,several authors have pointed out the potential to mea-sure VLQ top or bottom partners decaying to φ [11–13].However, to explain the bulk of the excess signal througha decay of pair-produced top or bottom partners wouldrequire couplings at their perturbative limits to achievelarge enough γγ rate and to explain why the VLQ de-cay process dominates over gluon fusion [5]. Moreover,pair production of two VLQs per event would give sev-eral hard jets in the event in addition to the diphoton,which is inconsistent with the kinematic distributions ofevents in the excess region. The tree-level productionmechanism presented in this paper avoids these prob-lems. Interestingly, it has been pointed out in [14] thata top partner need not be a mass eigenstate but rathercould be a mixture of top and charm-like mass eigenstatesraising the possibility that the vector-like quarks whichmix with light quarks could also play a role in solving thelittle hierarchy problem.This paper is organized as follows. In Sec. II, we intro-duce a motivated model consistent with low energy fla-vor constraints in which a bidoublet of vector-like quarkswith m V (cid:38) m φ mix with the light-SM quarks. In Sec. III a r X i v : . [ h e p - ph ] J u l u Zq U φ uq γγ FIG. 1: The dominant production of the diphotonexcess from a decaying VLQ ( U ). In addition to theresonance, there are two additional jets. The p T of thejets (and hence the visibility of the signal) is stronglydependent on the mass of the VLQ.we discuss the production and decays of the new parti-cles and find that the model can easily accommodate thecurrent excess in the diphoton data without tension fromexisting searches, both from the TeV searches sensitiveto the 750 GeV resonance as well as searches sensitive toVLQs. Furthermore, we compare the kinematic distribu-tions of our signal and the diphoton background, findingthat, depending on the splitting between the VLQ andthe scalar, the distributions can be challenging to distin-guish without additional data.
II. CUSTODIAL SYMMETRY AND LIGHTQUARK MIXING
In this section, we present a model in which the resonanceis a decay product of an electroweak produced VLQ fromthe dominant t -channel process shown in figure 1. Singleproduction of VLQs requires a large mixing angle be-tween the light quarks and VLQs. One would naivelyexpect such mixing to yield large corrections to the Zq ¯ q couplings, which are strongly constrained by electroweakprecision observables. However, we can protect the Z couplings via the custodial symmetry by using a bidou-blet representation V for the VLQs [15]. In addition, weintroduce the SU(2) R triplet, Φ , whose neutral compo-nent (which we denote by φ ) will play the role of the 750GeV resonance. This model is an example of a custodi-ally symmetric model commonly considered in compositeHiggs and extra dimensional models [14, 16–23]. A. Field content and mixing
We organize the fields into irreducible representationsof SU(3) C × SU(2) L × SU(2) R × U(1) X in Table I, wherethe SU(2) R is a global symmetry and the fermions areleft-handed Weyl spinors. Hypercharge is embedded inSU(2) R × U(1) X as Y = T R + X . The SM quarks aretaken to be singlets under SU(2) R and we represent theHiggs doublet as a bifundamental, H = ( (cid:15)H ∗ , H ) . Field SU (3) C SU (2) L SU (2) R U (1) X Φ V +2 / V ¯ − / H Q +1 / u ¯ − / TABLE I: The representations of relevant fields. Thenew vector-like quarks are in a single bidoublet V , andthe 750 GeV resonance is the neutral component of Φ .The Higgs and the light quarks have the usual SMassignments. All fermionic fields are left-handed Weylspinors.Four VLQs form the bidoublet, V ≡ (cid:18) U XD U (cid:19) , V ≡ (cid:18) U DX U (cid:19) . (1)The charges of the new quarks are Q U = Q U = 2 / , Q D = − / , and Q X = 5 / .The Lagrangian for the VLQs (not including the termscoupling to the scalar Φ ) is L V LQ = m V Tr (cid:2) V V (cid:3) − λ V Tr (cid:2) H † V (cid:3) u (0) + h.c. , (2)where the (0) superscript denotes the quark fields in theSM mass basis of the up-type sector (the basis of di-agonal SM Yukawa couplings). We assume the VLQsonly mix with a single generation of right-handed up-type quark, however in appendix A 4 we also consider adifferent U(1) X charge for V and the case of mixing withone generation of right-handed down-type quark. Notethat we have made an important assumption regardingalignment: the bidoublet V couples to the up-type quarkin the mass basis of the SM. This assumption is to avoidlow energy flavor constraints from flavor changing neu-tral currents but is not a crucial ingredient for the colliderphenomenology that follows.The down-type quark masses are unaffected by the newVLQs. One flavor of the up-type quarks can mix signifi-cantly with the new VLQs through the off-diagonal massmatrix: (cid:16) u (0) U U (cid:17) λ u v/ √ − λ V v/ √ m V − λ V v/ √ m V u (0) U U + h.c. (3)where λ u is the Yukawa of the up-type quark. From hereon, we assume the mixing is with the up or charm quarkand neglect the up-type quark mass. The mass eigen-states ( u , U , and ˜ U ) are related to the gauge eigenstatesby: u (0) U U = / √ − / √
20 1 / √ / √ c θ − s θ s θ c θ
00 0 1 u ˜ UU (4) u (0) U U = / √ − / √
20 1 / √ / √ u ˜ UU where s θ ≡ sin θ and c θ ≡ cos θ with s θ = λ V vm U + , (5)where v (cid:39) GeV is the vacuum expectation value ofthe Higgs, and the masses of the VLQs are m U − = m D = m χ = m V and m U + = (cid:112) m V + λ V v . The down-sectordoes not experience any mixing, i.e. X and D are masseigenstates.The mixing, parameterized by s θ , leads to couplings be-tween a generation of SM quarks, SM gauge bosons, andthe VLQs (derived in more detail in appendix A): L EW = − es θ c w s w Z µ u † ¯ σ µ U − gs θ W − µ ( u † ¯ σ µ D + X † ¯ σ µ u )+ h.c. , (6)where s w ( c w ) is the sine (cosine) of the Weinberg an-gle and g ( e ) is the SU(2) L (QED) coupling constant. Ifthe mixing angle is sufficiently large, these couplings canresult in electroweak production of single VLQs ( U , D ,or X ) which can dominate over the VLQ pair productioncross section. Notice that only U , which will be responsi-ble for the production of the diphoton resonance, couplesto an up-type quark and the Z . ˜ U is not produced byelectroweak interactions in this model. This is becauseonly the linear combination U + U mixes with the up-type quark, which is a necessary feature for the protectionof the Zq ¯ q coupling in this model. B. Consequences of a custodial triplet
The 750 GeV diphoton resonance φ is embedded in anSU(2) R triplet scalar Φ as follows. Φ = (cid:32) φ/ √ φ + φ − − φ/ √ (cid:33) (7)This allows for a coupling of Φ to the VLQs of the form L Φ = √ y φ Tr (cid:2) V Φ V (cid:3) + h.c. (8) = y φ φ (cid:0) U U − U U + XX − DD (cid:1) + h.c. + ... (9) = y φ φ (cid:16) − s θ U ¯ u − ˜ U U − c θ U ˜ U + XX − DD (cid:17) + h.c. + ... (10) where the ellipses refer to terms involving the chargedcomponents of Φ . The relative minus sign between the U U and U U terms gives rise to the coupling of φ to U and the SM up quark (as opposed to a coupling to ˜ U )which is responsible for the production of the resonance.These interactions will generate couplings of φ to SM di-bosons, such as gg , W W , hh etc. via triangle diagramswith the VLQs. However, in the limit of exact custodialsymmetry, these amplitudes are forbidden. For exam-ple, the operator Φ G µν,A G Aµν has no custodially invari-ant contraction because the gluon field strength tensor G is a custodial singlet. Furthermore, the Higgs couplingto the scalar vanishes since (using HH † ∝ ),Tr (cid:2) H † Φ H (cid:3) ∝ Tr Φ = 0 . (11)In practice, the vanishing of the amplitudes is a conse-quence of cancellations of the contributions due to differ-ent VLQs running in the loop, which contain importantrelative minus signs as a consequence of the custodialsymmetry.The loop amplitudes for φ therefore require the inser-tion of SU(2) R violating interactions. The largest suchcouplings in the SM are the third generation Yukawas,however in the flavor alignment limit these couplings willnot directly affect the diphoton resonance sector sincewe assume mixing is not occurring with the third gener-ation up-type quark. The dominant source of custodialsymmetry breaking in this sector will therefore be theembedding of the hypercharge gauge group within the T R generator of SU(2) R , and so it is to be expected thatthe leading loop amplitude will be that coupling φ tohypercharge gauge bosons, φ B µν B µν . Indeed, the one-loop contributions to this operator do not cancel amongthe VLQs due to their differing hypercharges. The otherloop amplitudes will be generated at higher order and aresuppressed by an additional factor ∼ α/ πc w comparedto their naive sizes. These two-loop contributions caninduce a mixing angle between φ and the Higgs of order ∼ ( v/ π m φ ) ( α/ πc w ) (where m φ denotes the mass ofthe resonance), however this is much too small to inducesizable decays to t ¯ t . Direct couplings of φ to the up-typequarks can also arise at two-loops but is suppressed bya Yukawa coupling, making it negligible. We verify theeffects of custodial symmetry breaking explicitly in A 3.This custodial protection mechanism generates a naturalhierarchy between the decays of the resonance to dipho-tons and its decays to gg , W W , hh , and also suppressesthe gluon fusion production of φ .We now briefly compare this to a scenario in which thediphoton resonance is assumed to be a custodial singlet S with couplings L S = y S S Tr (cid:2) V V (cid:3) + h.c. (12) = y S S (cid:0) U U + U U + DD + XX (cid:1) + h.c. (13) = y S S (cid:16) s θ ˜ U u + U U + c θ ˜ U ˜ U + DD + XX (cid:17) + h.c. (14)In this case, the only S -quark-VLQ coupling involves ˜ U ,which does not couple to SM gauge bosons and there-fore cannot be produced via VLQ single production. ˜ U is pair-produced and can decay ˜ U → Su , however therate for pair production is subdominant to electroweakproduction of U and insufficient to explain the excess.Furthermore, this singlet does not exhibit custodial pro-tection, which is a consequence of the couplings in eq. 13adding constructively rather than destructively. III. DIPHOTON CROSS SECTION
Above we presented a model in which φ can be producedas a decay product of a singly produced VLQ (we will as-sume m V > m φ throughout). The dominant productionmechanism for the diphoton resonance is depicted in fig-ure 1. In this section, we demonstrate that the γγ rateis sufficient to explain the diphoton excess while avoidingconstraints from existing VLQ searches and electroweakprecision tests. We consider two variations of the model,one where the VLQs mix with the up quark and anotherwith the VLQs mixing with the charm quark.Since the γγ final state arises from a decay chain, the in-clusive cross section into γγ is given in the narrow widthapproximation by σ γγ = σ ( pp → U ¯ u, ¯ U u ) × Br ( U → φu ) × Br ( φ → γγ ) . (15)Each of these contributions has different dependence onthe relevant parameters of the model, y φ and s θ . Theproduction cross section of the VLQs, σ ( pp → U ¯ u, ¯ U u ) ,is proportional to s θ but is independent of y φ . A. Branching ratios
The complete formulae for the branching ratios of φ and U are given in appendix A 2. We summarize the resultshere. U has two decay channels, U → Zj and U → φj with the dominant decay being Zj . This results in thebranching ratio of U → uφ ranging between 1-10%, pro-portional to y φ and independent of the mixing angle. φ has competing decays between a -body tree-level decayand loop-induced 2-body decays. The only tree-level de-cay of φ is to Zu ¯ u through an off-shell U with a rate isproportional to s θ y φ , making it highly sensitive to the Secondary production modes from UZ production, pair produc-tion of VLQs, and direct φZ production mediated by a VLQmake up 10-30% of inclusive diphoton cross section. We explorethe size of different contributions in Sec. IV B, but since the sizeof the subdominant modes is highly dependent on the detailedparameters of the model, we only include the dominant produc-tion when studying the inclusive diphoton rate and kinematics. y φ s θ u R benchmark 0.7 0.1 c R benchmark 2 0.3 TABLE II: Benchmark points for the up quark andcharm quark mixing models. For the u R model, thereare more stringent constraints on the mixing anglethough a larger production cross section.mixing angle. φ has additional loop-induced decays into γγ , Zγ , and ZZ . These decays arise from gauging hy-percharge resulting in the relative ratios, Γ γγ : Γ γZ : Γ ZZ = 1 : 2 tan θ w : tan θ w . (16)The loop-induced rates are largely independent of themixing, proportional to y φ . The leading branching ratios of φ are shown in figure 2 fora benchmark point relevant in the case of up-mixing with s θ = 0 . (left) and charm-mixing with s θ = 0 . (right).A couple comments on the choice of benchmark points(displayed in Table II) are in order. First, regarding thesize of the mixing angle, we have provided constraints onthe allowed mixing angle for electroweak produced VLQsin appendix B, obtained by reinterpreting the constraintsfrom direct LHC searches on light quark composite part-ner models [14]. For the up-quark mixing, the mixing an-gle is experimentally constrained to be s θ (cid:46) . , whilefor charm mixing, the constraints are much weaker with s θ (cid:46) . . Larger mixing angles are allowed for the caseof charm mixing since the electroweak production crosssection of the VLQs are suppressed by the charm partondistribution function. B. The inclusive cross section
Depending on the size of mixing, the inclusive cross sec-tion for diphoton production scales differently with themixing angle. There are two distinct regimes, large andsmall mixing angles. If the mixing angle is large, thenthe dominant decay of φ is through the -body decay.In this case the branching ratio into diphotons is ∝ /s θ giving an inclusive cross section σ γγ ∝ y φ s θ ( large mixing ) . (17) We have checked that non-zero mixing has at most a 10% effecton the loop-induced rates in the region of parameter space weare interested in. Furthermore, these effects will not have anybearing on the size of the γγ rate and thus we ignore these effectsin our analysis.
800 1000 1200 1400 1600 1800 20000.0050.0100.0500.1000.5001 800 1000 1200 1400 1600 1800 20000.0050.0100.0500.1000.5001
FIG. 2: The different branching ratios for φ . The loop-induced decays to γγ , γZ , and ZZ always compete with the -body decay. At large mixing, the -body decay is the preferred decay mode, however for small-mixing, theloop-induced decays (which are roughly independent of the mixing) dominate. Left:
The branching ratios for the u R benchmark point (small-mixing). Right:
The branching ratios for the c R benchmark (large-mixing).For small mixing, the -body φ decay is heavily sup-pressed making the diphoton rate the dominant mode,i.e. Br ( φ → γγ ) ≈ , independent of y φ or s θ . In thiscase, the inclusive cross section scales as σ γγ ∝ y φ s θ ( small mixing ) . (18)The transition between the two regimes occurs around s θ ∼ . , and this is the point where the cross section ismaximized. Due to the constraints, the up mixing caseis always in the small mixing scenario while the charmcan be either the large or small mixing regimes. For ourchosen benchmark point, the charm scenario correspondsto large mixing.To reproduce the excess, we simulate the production of φ at leading order using a custom FeynRules model [25]with
MadGraph5 [26]. To roughly estimate the size ofnext-to-leading order (NLO) effects, we compute the pro-duction cross section with an additional jet, finding thatit makes up about 50% of the leading order cross section.This suggests an NLO K -factor of about 1.5, and we usethis correction throughout. We compute the diphotonrate using equation 15 and the branching ratios given inappendix A 2. Figure 3 shows the inclusive diphoton pro-duction cross section for different VLQ masses and valuesof y φ for the two benchmark points.We see in the left of figure 3 that we need y φ ∼ . to getenough cross section to explain the excess in the up quarkvariation of the model. Larger Yukawa couplings are re-quired in the charm-mixing benchmark point, requiring y φ ∼ to achieve the minimum cross section needed toexplain the excess.As with many models explaining the diphoton excess,such Yukawa couplings can lead to non-perturbativity ofthe model before the GUT scale. The up-mixing bench-mark becomes non-perturbative at around 100 TeV, al-though there is some parameter space where the coupling remains perturbative beyond the GUT scale. The charm-mixing model is more problematic given the Yukawa cou-pling runs to its perturbative limit at a few TeV, puttinginto question the validity of our analysis. However, thisproblem can be easily overcome by adding additional fla-vors of bidoublets (these may or may not mix with theSM quarks) which feed into the running, but also boostthe diphoton decay rate as the square of the number offlavors allowing for much smaller couplings, and a muchhigher scale of strong coupling. C. Eliminating tension with TeV data
One of the puzzling features of the 13 TeV diphoton ex-cess is its seemingly large cross section compared to crosssection limits from 8 TeV searches. A 750 GeV resonanceis not ruled out by Run I searches but, depending on theproduction mechanism and width, may be in tension withRun I limits [24, 27]. Thus to reproduce the excess, itis important to have sufficiently large scaling, r , definedas the ratio of the cross section at 13 TeV to that at 8TeV. We compute the scaling for our model as a functionof the VLQ mass (the scaling is independent of the cou-plings) and assuming the K -factor is constant from to TeV. The results are shown in figure 4 alongside thescaling of other proposed models, including gluon fusion, q ¯ q production [28], and photon fusion [29–31]. The up-mixing model inherits the scaling from the u ¯ u productionat m V ∼ GeV but grows with the mass of the VLQdue to the higher center-of-mass energy. For heavy VLQmasses near 1500 GeV, the scaling is comparable to gluonfusion. The charm variation of the model, however, scalesmuch better due to the parton distribution function of thecharm in the initial state. For VLQ masses nearly degen-erate with m φ ( GeV (cid:46) m V (cid:46) GeV) for which
800 1000 1200 1400 1600 1800 20000.050.100.50151050 800 1000 1200 1400 1600 1800 20000.050.100.50151050
FIG. 3: The inclusive cross section into γγ as a function of VLQ mass and varying the values of y φ . In gray we showthe rough cross section necessary to explain the excess with a narrow width ( . − fb) [24]. Left:
The cross sectionfor the u R benchmark point. Right:
The cross section for the c R benchmark point.
800 1000 1200 1400 1600 1800 200012345678
FIG. 4: The ratio of √ s = 13 to TeV cross section ofthe up-mixing signal (blue) and charm-mixing signal(red). We have included the scaling properties of thedown-type version of this model where the down(green), strange (pink), or bottom (light blue) quarkmix with VLQs. The scaling of other proposedproduction processes are shown as dashed lines andwere taken from [3].the extra jet from the U decay is relatively soft, the scal-ing is as large as for b ¯ b production. For larger masses,the charm-mixing scenario has r (cid:38) , but in this regionof parameter space, the φ would be accompanied by ahigh- p T jet in the final state (we explore the plausibilityof this scenario in Sec. IV). We conclude that, dependingon the mass of the VLQ, our signal can achieve largercross section scaling from 8 to 13 TeV than any proposedmodel of single resonance production. For simplicity, we have only considered mixing with up-type quarks. It is possible to construct a similar modelin which new VLQs mix with the down-type quarks. Theterms in the Lagrangian responsible for production of adown-type variation of this model are presented in ap-pendix A 4. We include the scaling properties of pro-duction from down, strange, and bottom quark mixingin figure 4. The bottom quark mixing scenario has thelargest ratio of 13 to 8 TeV cross section, while the downand strange quark scenarios interpolate between the scal-ing of the up and charm scenarios. IV. KINEMATICSA. Comparing with ATLAS
In addition to the diphoton resonance signature at m γγ ∼ GeV, our signal has two additional jets, with oneof the jets typically in the forward direction. ATLASand CMS have remarked that events in the excess regionare consistent with the background kinematics. Further-more, ATLAS has recently provided kinematic distribu-tions of the excess events [32] for the number of jets, N jets (ATLAS defined a jet using p jT > GeV for η < . and p jT < GeV for η < . ), and the transverse mo-mentum of the γγ resonance, p γγT . Furthermore, ATLASprovided estimates for the expected SM diphoton back-ground from simulations. The distributions are providedfor the region GeV < m γγ < GeV and with therequirements on the leading and subleading photon en-ergies E γ T > . m γγ and E γ T > . m γγ . In this bin,ATLAS found a total of events, about 10 of which arediphoton excess candidates.To compare the compatibility of the kinematics of the ex-cess with our signal we simulate our signal using a combi-nation of MadGraph5 , Pythia 8.2 [33], and
Delphes
FIG. 5: The kinematic distributions of the sum of the signal and background for vector-like quark mass of (blue) and
GeV (red) compared to the distributions observed by ATLAS (black) with 3.2 fb − of data. We alsoprovide gluon fusion kinematics (green) for comparison. The N jets and p γγT distributions for the background andobserved events are obtained from the slides presented by ATLAS [32]. FIG. 6: The leading-jet p T and forward jet pseudorapidity distributions of the signal for vector-like quark mass of (blue) and GeV (red) along with a gluon fusion signal (green) for comparison. For VLQs almost degeneratewith the resonance, the signal is difficult to differentiate from the QCD background or a resonance produced viagluon fusion since these events also contain soft, forward jets from initial state radiation. [34] making use of the NNPDF2.3LO parton distri-bution functions [35]. To compare with the distributionsobserved by ATLAS, we perform a weighted sum of oursignal and the background estimates provided by ATLAS N = rN sig + (1 − r ) N bkg . (19)This is done for each bin and we take r ≈ / . Wealso simulate gluon fusion at leading order and performthis procedure in order to compare our signal with thekinematics of single production. By comparing the distri-butions in figure 5, we conclude that although our signalhas two extra jets in the final state, the distributions for N jets and p γγT are consistent with the data provided byATLAS (as is also the case for the gluon fusion signal).Furthermore, the mass of the VLQ has only a mild effecton these distributions since the number of jets from thehard process is independent of m V . The signal does havedistinctive features in other distributions, however, andwe explore these features in the next section. B. Additional signatures
Our signal predicts observable jet signatures that can beused to discern this process from background events or from other resonance production mechanisms. In partic-ular, we expect a forward jet as well as one central jetwith higher p T , depending on m V . The distributions forthe p T of the leading jet ( p j T ) and the absolute value ofthe pseudorapidity of the most forward jet ( | η F J | ) forthe signals with m V = 800 and 1000 GeV are shown infigure 6 along with the gluon fusion signal for compar-ison. Note that ATLAS and CMS did not provide thebackground or observed kinematic distributions for theseobservables, so we did not combine the background andthe signal in these plots.The distributions have some distinctive characteristics.Firstly, we see that for small splitting p j T is peakedaround zero since, at these splittings, the central jet,which will typically be the leading jet, has low p T . How-ever, for larger splitting the distribution has a kinematicedge with the end-point at the splitting between the VLQand the resonance. This is prototypical of a jet arisingfrom a heavy particle decay to a second heavy particle.Interestingly, such a distribution can suggest the massof the VLQ. The forward jet in the event is most easilyprobed using its pseudorapidity. The distribution has adip at η ≈ . as a consequence of the cuts used by AT-LAS for the jet definition (see above). As expected, thesignal has a jet with large η , however this is also true ofthe dominant background, γγ . In this background, jetsare emitted from the initial state and hence tend to be inthe forward region. This can result in the feature beingwell hidden inside the SM background of the searches.In addition to the features of the dominant productionmode, there are secondary production modes of the ex-cess. In principle, one may expect that any of the VLQscould decay into the resonance, but this is not the case.Due to the custodial structure of the model, only U cou-ples to the resonance and a SM quark (see equation 10),and hence its the only single VLQ production mode.However, there are three subdominant modes which cancontribute significantly to the cross section, single VLQproduction through pp → U Z, U Z , QCD pair produc-tion of VLQs through pp → U U , and direct productionof the resonance through a t -channel VLQ, pp → φZ .The cross section composition depends strongly on thechoice of mixing angle and mass of the VLQ. The var-ious contributions to the total cross section as a func-tion of the mass for our benchmark points are shown atleading order in figure 7 (for simplicity we do not apply K -factors when comparing between these different chan-nels). We conclude that the additional production modesmake up 10-30% of the inclusive diphoton cross sectionfor reasonable choices of parameters. With more statis-tics, excesses in these subleading channels could be usedto differentiate our signal.Lastly we note that in principle the charged scalars,which are almost degenerate with φ , can also be observedas they are singly produced by a similar mechanism as φ .However, the loop-induced decays to W Z and
W γ bothvanish in the custodial limit, rendering their -body de-cays dominant in almost all of parameter space. These -body decays could be probed, but such studies are likelyless sensitive then other searches. V. CONCLUSIONS
We have presented a model describing a 750 GeV dipho-ton resonance arising from a custodial triplet which isproduced as a decay product of a singly-produced VLQ.Our model has novel kinematics compared to other pro-posed production mechanisms and eliminates the tensionfrom the 8 TeV diphoton searches while maintaining con-sistency with the kinematic distributions in the excessregion. With additional statistics, our signal could beconfirmed by the presence of a forward jet in the dipho-ton events or as a kinematic edge in the leading-jet p T distributions if the VLQ mass is significantly heavier than800 GeV. The scalar resonance enjoys custodial protec-tion, explaining the dominance of the γγ decay rate over W W , hh , and dijet decays.Additional signatures of the model include a correspond-ing excess in the Zγ and ZZ channels with fixed rateswith respect to the γγ rate. Furthermore, searches forsingle production of VLQs in Run II will probe deep intothe viable parameter space of this model.We now note some interesting model building possibili-ties which we leave for future studies. First, in this workwe focus on the case where the new scalar arises from anSU (2) R triplet but is uncharged under SU (2) L . However,many of the benefits enjoyed by this model are present insimilar representation choices, in particular if φ is a ( , ) or ( , ) under ( SU (2) L , SU (2) R ) . These models also for-bid gluon fusion and the tree-level production mechanismcan dominate. Another interesting possibility is if theVLQs are related to the the top sector, as one mightexpect in a composite Higgs model, and the custodialsymmetry is broken explicitly by the top Yukawa. Sucha breaking can induce φ production through gluon fusion,perhaps in a controlled manner such that the decays to hh as well as decays to W + W − are still suppressed. Finally,we comment on some ways to further reduce the size ofthe Yukawas. In this work we focused on a single flavorof VLQ for simplicity. However, if there are additionalflavors (with or without mixing to the other SM quarks),this can greatly enhance the diphoton decay rate, reduc-ing the size of Yukawas necessary to reproduce the excess.An additional possibility is if SU(2) R is gauged. In thiscase, the additional gauge bosons will propagate in thediphoton loop giving a significant enhancement to thediphoton rate. ACKNOWLEDGMENTS
We thank Eric Kuflik for collaboration in the early stagesof this project. We are grateful to Kiel Howe and WeeHao Ng for useful discussions. This work was supportedin part by the NSF through grant PHY-1316222. JD issupported in part by the NSERC Grant PGSD3-438393-2013.
Appendix A: Model details1. Couplings
In this section, we derive the couplings relevant for themodel between the quarks and the vector-like quarks, be-ginning with the Z couplings. The Z boson interactionswith the up-type quarks in the interaction basis are givenby (we define /Z ≡ ¯ σ µ Z µ )
800 1000 1200 1400 1600 1800 20000.010.050.100.501510 800 1000 1200 1400 1600 1800 20000.050.100.501510
FIG. 7: The cross sections for the different production modes at our benchmark points. We see that productionthrough single VLQ dominates with the secondary production modes providing up to 10-30% corrections on theinclusive diphoton cross section. L Z = ec w s w (cid:26) s w u (0) † /Zu (0) + (cid:18)
12 + 23 s w (cid:19) U † /ZU + (cid:18) −
12 + 23 s w (cid:19) U † /ZU (cid:27) (A1) = es w c w U (0) † s w + s w
00 0 − + s w /Z U (0) , U (0) ≡ u (0) U U . (A2)Notice that we can split the coupling matrix into twopieces, s w + 12 − . (A3)The first matrix is diagonal and commutes with the ro-tation to the mass basis while the second matrix yieldsnew couplings between the VLQs and the quarks uponmoving to the mass basis. Performing the rotation (therotation matrices are given in eq. 4) gives, L Z = ec w s w (cid:26) U † − s θ − c θ − s θ − c θ /Z U + 23 s w U † /Z U (cid:27) , U ≡ u ˜ UU . (A4)Notice that the rotation to the mass basis has left the top-left entry of the coupling matrix unchanged. This is very Note that U is the upper component of an SU(2) L doublet,while U is the lower component of a second doublet. important as it means the mixing with the VLQs doesnot affect the Z ¯ u ¯ u coupling which is tightly constrainedexperimentally. We see that we have a new coupling be-tween the quark and the VLQ: L ZuU = − ec w s w s θ (cid:0) u † /ZU (cid:1) + h.c. (A5)Now consider the W -boson couplings. The right-handedup quark does not couple to the W in the gauge basis,so the relevant couplings are simply: L W = − g √ (cid:16) U † /W − D + X † /W − U (cid:17) + h.c. (A6) ⊂ − gs θ (cid:16) u † /W − D + X † /W − u (cid:17) + h.c. (A7)where we moved to the mass basis in the last line.
2. Decay rates
In this section, we present formulae for the different decayrates used in the text for both the scalar resonance andthe U quark. a. φ decays We begin by considering the tree-level decays of φ . The0dominant contribution is Γ( φ → Zu ¯ u ) = m φ N c π ) m Q v s θ y φ g Z ( τ ) (A8)where N c is the number of colors, τ ≡ m Q /m φ , and g Z ( τ ) ≡ (cid:90) dx (cid:90) − x d ¯ x (1 − x )(1 − ¯ x )(2 − x − ¯ x − τ ) (1 − x − τ ) (1 − ¯ x − τ ) . (A9)The other conceivable -body decays, φ → hu ¯ u , φ → W d ¯ u , and φ → W u ¯ d vanish identically due to the cus-todial production.In addition φ has several loop induced decays to vectorbosons as well as the Higgs. All the loop induced decaysdecays violate custodial symmetry. This can easily beseen at the operator level, where the terms Φ B µν B µν , Φ W aµν W µνa , and Φ G µνA G Aµν (A10)(where B µν , W aµν , and G Aµν represent the hypercharge,SU(2) L , and QCD field strength tensors respectively)all violate custodial symmetry and Tr (cid:2) H † Φ H (cid:3) vanishesidentically. There is a large breaking of this symmetryfrom gauging hypercharge, which induces decays into γγ , γZ , and ZZ . Since gauging hypercharge only breaks SU (2) R , the Z interactions are suppressed by powers ofthe Weinberg angle, resulting in these being genericallysubdominant to the photon decays. The general compu-tation of these decay rates is made complicated due tothe mixing of the VLQs with the up quark, however sincethese contributions are suppressed by powers of the mix-ing angle they are generically small. We have checkedthe size of these corrections by computing the rates nu-merically using FeynArts3 , FormCalc8 , and
Loop-Tools2 [36, 37] and we find that the effect is at most in the interesting region of parameter space (thoughoften much smaller), and we neglect these effects for sim-plicity.The decay rate of a scalar into two photons mediated byVLQs with mass m i is [38] Γ( φ → γγ ) = m φ N c π ) e (cid:16) (cid:88) i y iφ m i Q i A / ( x i ) (cid:17) , (A11)where x i ≡ m i /m φ and (for m i > m φ / ) A / ( x ) =2 x (1 + (1 − x ) arcsin(1 / √ x ) ) . The sum runs over allVLQs and for a bidoublet the sum is (cid:88) i y iφ m i Q i A / ( x i ) = (cid:20) y φ m V (cid:21) A / ( x V ) , (A12)where the only non-zero contribution arises from the D and X quarks.The decay to two gluons mediated by VLQs is Γ( φ → gg ) = m φ π ) g s (cid:16) (cid:88) i y iφ m i A / ( x i ) (cid:17) , (A13) where g s is the strong coupling constant. For a bidou-blet of VLQs with a triplet scalar, the sum is equal tozero showing that gluon fusion is custodially protectedas expected.The decay to ZZ mediated by VLQs is Γ( φ → ZZ ) = m φ N c π ) e s w c w (cid:16) (cid:88) i y iφ m i A / ( x i )( T i − Q i s w ) (cid:17) . (A14)The sum for the bidoublet is: (cid:88) i y iφ m i A / ( x i )( T i − Q i s w ) = (cid:20) y φ m V s w (cid:21) A / ( x V ) . (A15)The decay to Zγ is Γ( φ → Zγ ) = 8 m φ N c (4 π ) e s w c w (cid:18) (cid:88) i y i ( T i − Q i s w ) Q i m i × ( I ( x i , λ i ) − I ( x i , λ i )) (cid:19) (A16)where λ i ≡ m i /m Z and I ( a, b ) ≡ ab a − b ) + a b a − b ) (cid:2) f ( a ) − f ( b ) (cid:3) + a b ( a − b ) [ g ( a ) − g ( b )] , (A17) I ( a, b ) ≡ − ab a − b ) (cid:2) f ( a ) − f ( b ) (cid:3) , (A18)and f ( x ) ≡ sin − (1 / √ x ) and g ( x ) ≡ √ x − f ( x ) . Forthe bidoublet, (cid:88) i y i m i Q i ( T i − Q i s w )( I ( x i , λ i ) − I ( x i , λ i )) = − (cid:20) y φ m i s w (cid:21) ( I ( x V , λ V ) − I ( x V , λ V )) . (A19)The Φ → γγ, Zγ, ZZ decays obey the expected rela-tionship when they all arise from Φ B µν B µν : θ w : tan θ w (A20)The decay of φ to W + W − is Γ( φ → W + W − ) = m φ N c (4 π ) e s w (cid:16) (cid:88) i y iφ m i A / ( x i ) (cid:17) . (A21)For a bidoublet the sum vanishes identically as expected.Lastly, the φhh operator vanishes at tree-level and atone-loop by custodial symmetry but will be generated attwo-loops by custodial symmetry breaking. b. U − decays
800 1000 1200 1400 1600 1800 20000.000.020.040.060.080.100.12
FIG. 8: Branching ratio of the U → uφ decay fordifferent value of the couplings. The fraction isindependent of the mixing angle.The vector-like quarks can decay in a couple ways. Wewill assume m Q > m φ such that the VLQs can decay tothe scalar. Furthermore, we will focus on U since that’sthe only VLQ that will play a role in the phenomenology.The decays rates are Γ( U → uZ ) ≈ m V π e s θ s w c w m V m Z (A22) Γ( U → uφ ) = m V π y φ s θ (cid:32) − M φ m V (cid:33) (A23)Notice that the uZ decay is enhanced by m V /m Z due tothe longitudinal polarization of the Z . Thus in order forthe φ decay to be substantial one needs larger Yukawas.The branching ratio into φ u is shown in figure 8 for dif-ferent Yukawas.
3. Custodial symmetry breaking
In this work we have assumed that the couplings andmasses of the VLQs and the triplet Φ preserve the custo-dial symmetry, which enforces a cancellation in the loopamplitudes corresponding to the gluon fusion productionof φ as well as the decays to gg , hh , and W W . Assum-ing no cancellations or large mass hierarchies, a genericscalar φ coupling to N f VLQs with coupling y φ wouldacquire an effective coupling to gluons of the form L generic ⊃ − π N f g s y φ m φ φ G µν,A G Aµν , (A24)with similar expressions for the other amplitudes. Theexplicit breaking of custodial symmetry due to the gaug-ing of hypercharge means that these amplitudes willstill be generated, but with an additional suppression of O ( α/c w ) compared to the above estimate.In particular, the VLQ mass renormalization and therenormalization of the Tr (cid:2) V Φ V (cid:3) couplings due to hy-percharge gauge boson loops, illustrated in Figure 9, FIG. 9: Prototypical loop contributions to the custodialsymmetry breaking amplitudes. Such two-loopcontributions can induce gluon fusion production anddecays two gluons. Similar diagrams can give rise todecays to W + W − and hh .will contribute operators of the form Tr [ T R Φ] G µν,A G Aµν .Since the mass and vertex renormalizations are logarith-mically divergent, they require counterterms which arenot calculable in the effective theory. Instead, we calcu-late the size of the IR contributions and take this as anestimate of the overall size of the irreducible contribu-tions.The mass renormalization of the VLQs introduces a masssplitting between the different T R states of size δm V m V (cid:39) g (cid:48) π log (cid:18) Λ m V (cid:19) ∆ (cid:0) Y (cid:1) (A25) (cid:39) απc w log (cid:18) Λ m V (cid:19) . Similarly, the vertex and wavefunction renormalizationprovide a contribution to the operator δy φ Tr (cid:2) V T R Φ V (cid:3) of size δy φ y φ (cid:39) g (cid:48) π log (cid:18) Λ m V (cid:19) ∆ (cid:0) Y (cid:1) (A26) (cid:39) απc w log (cid:18) Λ m V (cid:19) . where g (cid:48) is the U (1) Y coupling constant. Now, custo-dial symmetry violating amplitudes of the kind in Figure9 can be generated either with an insertion of δm V in-stead of m V , or with the coupling δy φ . Therefore, theamplitude is suppressed by a factor δ AA (cid:39) δm V m V + δy φ y φ (A27) (cid:39) απc w log (cid:18) Λ TeV (cid:19) (A28)In the same spirit, one can also generate a mixing be-tween the Higgs and the new scalar φ . Such a mixingis induced at two loops from the operator of the form, y Φ HH m φ Tr (cid:2) H † T R Φ H (cid:3) . The coefficient of this operatoris of order y Φ HH (cid:39) y φ λ V π απc w log (cid:18) Λ TeV (cid:19) , (A29)2which results in a mixing angle between the Higgs and φ of order (cid:39) m V tan θ √ vm φ y φ π απc w log (cid:18) Λ TeV (cid:19) ∼ O (10 − − − ) , (A30)where we have substituted λ V for the mixing angle. Thismixing will induce decays of φ to t ¯ t , but due to the small-ness of the coupling, we do not expect this decay to beobservable in the near future.
4. Down-type model
We now present the down-type model which can havemixing between the SM down-type quarks and the VLQs.The model is identical to the up-type model but assigningthe V bidoublet a U(1) X charge of − / (as opposed to +2 / ). This gives the following fields V = (cid:32) D UY D (cid:33) V = (cid:32) D YU D (cid:33) (A31)where Q D = Q D = − / , Q U = +2 / , and Q Y = − / . As in the up-mixing case, a mixing is generatedbetween a SM quark and a VLQ through: L V LQ = m V Tr (cid:2) V V (cid:3) + λ V Tr (cid:2) H † V (cid:3) d (0) + h.c. (A32)where d (0) denotes the down quark in the SM mass basisof the down-type sector. The mixing produces a ZDd coupling resulting in electroweak production of D , whichcan decay into the diphoton resonance. Appendix B: Experimental constraints
The LHC has performed searches with significant sen-sitivity to models with light-quark mixing. The con-straints were studied in detail in [14] for both up-quarkmixing and charm-quark mixing in the context of a com-posite model and in [23] for the up-type mixing model.The dominant constraints arise from charged current pro-duction of D and X quarks. There are additional con-straints from production of the charged +2 / quarks, butsince they are always subdominant, we omit these. In-stead of recasting the constraints ourselves we make useof the recast performed in Ref. [14]. The authors re-cast two searches: a 7 TeV search by ATLAS searchingfor the bidoublet model (without the additional scalartriplet) [39] and an TeV search for excited quarks [41]with a similar final state which is not optimized for thesingle production of vector-like-quarks but shares a sim-ilar final state. The two searches have competitive lim-its. Additionally there are constraints on pair production of VLQs, however these are subdominant in the mass
800 1000 1200 1400 1600 1800 20000.00.20.40.60.81.0
FIG. 10: The constraints on the bidoublet model(reinterpreted from the work of [14]) arising from anATLAS 7 TeV dedicated search for single production ofVLQs [39], a CMS 8 TeV search for W / Z -tagged dijetresonances [40], and electroweak precision (EWP).Areas above the lines are excluded. Here we neglectedeffects due to additional decay channels of thevector-like-quarks into the scalars in our model.ranges we are interested in. In particular ATLAS hasperformed a search for VLQs decaying to W j finding alimit around
GeV for a single VLQ [42]. With twocopies of such VLQs the limits strengthen but do not ex-tend past
GeV. Furthermore, electroweak precisionplaces an additional constraint from additional contribu-tions to the S parameter [17]. One might worry thatthe additional scalar would complicate the limits, in par-ticular the VLQs can decay to the scalar weakening theconstraints. In general these branching ratios are (cid:46) and we ignore such effects in our discussion.Our goal is now to convert the single production limitsquoted Ref. [14] into our (closely related) framework. InRef. [14] the authors study a bidoublet model but withan additional VLQ singlet which they denote as ˜ U . Wecan decouple the particle to match with our framework.Multiplying their cross sections by the correction factor, s θ (cid:20) cos vf sin (cid:18) tan − (cid:18) y R fm V sin vf (cid:19)(cid:19)(cid:21) − (B1)with f = 600 GeV, v (cid:39) GeV, and y R = 1 gives thecross sections in our case. Employing this procedure weobtain the limits shown in figure 10.3 [1] ATLAS collaboration,
Search for resonances decayingto photon pairs in 3.2 fb − of pp collisions at √ s = 13TeV with the ATLAS detector , Tech. Rep.ATLAS-CONF-2015-081, CERN, Geneva, Dec, 2015.[2] CMS collaboration,
Search for new physics in highmass diphoton events in proton-proton collisions at √ s = 13 TeV , Tech. Rep. CMS-PAS-EXO-15-004,CERN, Geneva, 2015.[3] R. Franceschini, G. F. Giudice, J. F. Kamenik,M. McCullough, A. Pomarol, R. Rattazzi et al.,
What isthe gamma gamma resonance at 750 GeV? , .[4] S. Knapen, T. Melia, M. Papucci and K. Zurek, Rays oflight from the LHC , .[5] X.-F. Han, L. Wang, L. Wu, J. M. Yang and M. Zhang, Explaining 750 GeV diphoton excess from top/bottompartner cascade decay in two-Higgs-doublet modelextension , .[6] F. P. Huang, C. S. Li, Z. L. Liu and Y. Wang,
750 GeVDiphoton Excess from Cascade Decay , .[7] J. Liu, X.-P. Wang and W. Xue, LHC diphoton excessfrom colorful resonances , .[8] A. Berlin, Diphoton and diboson excesses in a left-rightsymmetric theory of dark matter , Phys. Rev.
D93 (2016) 055015, [ ].[9] J. Bernon, A. Goudelis, S. Kraml, K. Mawatari andD. Sengupta,
Characterising the 750 GeV diphotonexcess , .[10] V. De Romeri, J. S. Kim, V. Martin-Lozano,K. Rolbiecki and R. R. de Austri, Confronting darkmatter with the diphoton excess from a parent resonancedecay , .[11] P. Agrawal, J. Fan, B. Heidenreich, M. Reece andM. Strassler, Experimental Considerations Motivated bythe Diphoton Excess at the LHC , .[12] A. Kobakhidze, F. Wang, L. Wu, J. M. Yang andM. Zhang,
750 GeV diphoton resonance explained as aheavy scalar in top/bottom seesaw model , .[13] P. S. B. Dev, R. N. Mohapatra and Y. Zhang, QuarkSeesaw, Vectorlike Fermions and Diphoton Excess , .[14] C. Delaunay, T. Flacke, J. Gonzalez-Fraile, S. J. Lee,G. Panico and G. Perez, Light Non-degenerateComposite Partners at the LHC , JHEP (2014) 055,[ ].[15] K. Agashe, R. Contino, L. Da Rold and A. Pomarol, ACustodial symmetry for Zb ¯ b , Phys. Lett.
B641 (2006)62–66, [ hep-ph/0605341 ].[16] A. Atre, M. Carena, T. Han and J. Santiago,
HeavyQuarks Above the Top at the Tevatron , Phys. Rev.
D79 (2009) 054018, [ ].[17] A. Atre, G. Azuelos, M. Carena, T. Han, E. Ozcan,J. Santiago et al.,
Model-Independent Searches for NewQuarks at the LHC , JHEP (2011) 080, [ ].[18] M. Redi and A. Weiler, Flavor and CP InvariantComposite Higgs Models , JHEP (2011) 108,[ ].[19] T. Flacke, J. H. Kim, S. J. Lee and S. H. Lim, Constraints on composite quark partners from Higgssearches , JHEP (2014) 123, [ ].[20] M. Redi, V. Sanz, M. de Vries and A. Weiler, StrongSignatures of Right-Handed Compositeness , JHEP (2013) 008, [ ].[21] N. Vignaroli, Early discovery of top partners and test ofthe Higgs nature , Phys. Rev.
D86 (2012) 075017,[ ].[22] N. Vignaroli,
Discovering the composite Higgs throughthe decay of a heavy fermion , JHEP (2012) 158,[ ].[23] A. Atre, M. Chala and J. Santiago, Searches for NewVector Like Quarks: Higgs Channels , JHEP (2013)099, [ ].[24] J. F. Kamenik, B. R. Safdi, Y. Soreq and J. Zupan, ’Comments on the diphoton excess: critical reappraisalof effective field theory interpretations , .[25] A. Alloul, N. D. Christensen, C. Degrande, C. Duhr andB. Fuks, FeynRules 2.0 - A complete toolbox fortree-level phenomenology , Comput. Phys. Commun. (2014) 2250–2300, [ ].[26] J. Alwall, R. Frederix, S. Frixione, V. Hirschi,F. Maltoni, O. Mattelaer et al.,
The automatedcomputation of tree-level and next-to-leading orderdifferential cross sections, and their matching to partonshower simulations , JHEP (2014) 079, [ ].[27] A. Falkowski, O. Slone and T. Volansky, Phenomenology of a 750 GeV Singlet , JHEP (2016)152, [ ].[28] J. Gao, H. Zhang and H. X. Zhu, Diphoton excess at750 GeV: gluon-gluon fusion or quark-antiquarkannihilation? , .[29] C. Csáki, J. Hubisz and J. Terning, Minimal model of adiphoton resonance: Production without gluon couplings , Phys. Rev.
D93 (2016) 035002, [ ].[30] S. Fichet, G. von Gersdorff and C. Royon,
ScatteringLight by Light at 750 GeV at the LHC , .[31] C. Csaki, J. Hubisz, S. Lombardo and J. Terning, Gluonvs. Photon Production of a 750 GeV DiphotonResonance , .[32] ATLAS collaboration, “Diphoton searches in ATLAS.”Rencontres de Moriond, 2016.[33] T. Sjostrand, S. Mrenna and P. Z. Skands,
A BriefIntroduction to PYTHIA 8.1 , Comput. Phys. Commun. (2008) 852–867, [ ].[34]
DELPHES 3 collaboration, J. de Favereau, C. Delaere,P. Demin, A. Giammanco, V. Lemaître, A. Mertenset al.,
DELPHES 3, A modular framework for fastsimulation of a generic collider experiment , JHEP (2014) 057, [ ].[35] R. D. Ball et al., Parton distributions with LHC data , Nucl. Phys.
B867 (2013) 244–289, [ ].[36] T. Hahn and M. Perez-Victoria,
Automatized one loopcalculations in four-dimensions and D-dimensions , Comput. Phys. Commun. (1999) 153–165,[ hep-ph/9807565 ].[37] T. Hahn,
Generating Feynman diagrams and amplitudeswith FeynArts 3 , Comput. Phys. Commun. (2001)418–431, [ hep-ph/0012260 ].[38] J. F. Gunion, H. E. Haber, G. L. Kane and S. Dawson,
The Higgs Hunter’s Guide , Front. Phys. (2000)1–448.[39] ATLAS collaboration,
Search for Single Production ofVector-like Quarks Coupling to Light Generations in . fb − of Data at √ s = 7 TeV , . [40] CMS collaboration,
Search for heavy resonances in theW/Z-tagged dijet mass spectrum in pp collisions at 8TeV , Tech. Rep. CMS-PAS-EXO-12-024, CERN,Geneva, 2013.[41]
CMS collaboration, CMS,
Search for heavy resonancesin the W/Z-tagged dijet mass spectrum in pp collisions at 8 TeV , .[42]
ATLAS collaboration, G. Aad et al.,
Search for pairproduction of a new heavy quark that decays into a W boson and a light quark in pp collisions at √ s = 8 TeVwith the ATLAS detector , Phys. Rev.
D92 (2015)112007, [1509.04261