Discriminating between lepton number violating scalars using events with four and three charged leptons at the LHC
Francisco del Aguila, Mikael Chala, Arcadi Santamaria, Jose Wudka
CCAFPE-173/13UG-FT-303/13FTUV-13-0516IFIC/13-25UCRHEP-T528
Discriminating between lepton number violating scalars usingevents with four and three charged leptons at the LHC
Francisco del Águila, Mikael Chala, Arcadi Santamaria, and Jose Wudka CAFPE and Departamento de Física Teórica y del Cosmos,Universidad de Granada, E–18071 Granada, Spain Departament de Física Teòrica, Universitat de València and IFIC,Universitat de València-CSIC, Dr. Moliner 50,E-46100 Burjassot (València), Spain Department of Physics and Astronomy,University of California, Riverside CA 92521-0413, USA
Abstract
Many Standard Model extensions predict doubly-charged scalars; in particular, all models withresonances in charged lepton-pair channels with non-vanishing lepton number; if these are pairproduced at the LHC, the observation of their decay into l ± l ± W ∓ W ∓ will be necessary in order toestablish their lepton-number violating character, which is generally not straightforward. Nonethe-less, the analysis of events containing four charged leptons (including scalar decays into one ortwo taus as well as into W bosons) makes it possible to determine whether the doubly-chargedexcitation belongs to a multiplet with weak isospin T = 0 , / , , / or (assuming there are noexcitations with charge > ); though discriminating between the isosinglet and isodoublet cases ispossible only if charged-current events cannot produce the doubly-charged isosinglet. O (5) = ( L cL ˜ φ ∗ )( ˜ φ † L L ) , resulting in sub-eVMajorana neutrino masses after electroweak symmetry breaking: L (5) m ν = − x ij O (5) ij /M →− ( x ij v / M ) ν cLi ν Lj with v/ √ � φ � ∼ GeV the Higgs vacuum expectation value(VEV). In this second case lepton number (LN) is broken because O (5) involves two leptondoublets with total LN equal to , and two SM Higgs doublets with vanishing LN. Thisbreaking is, however, very small because its coefficient xv/M = m ν /v is ∼ − to accountfor the observed neutrino masses, m ν ∼ . eV. This slight breaking can indicate, for exam-ple, new physics (NP) at a very high scale M ∼ GeV, if x ∼ , or at the TeV scale if x ∼ − . This last example is the scenario we are a priori interested in: new particles nearthe TeV with LN violating (LNV) decays eventually observable at the LHC.The simplest possibility results from the addition to the SM of a number of heavy RHMajorana neutrinos N , which has been extensively studied [4–7]. However, the correspond-ing LNV signal l ± l ± W ∓ (with the W decaying to jets and the background event carryingthe missing charge) does not allow for searches in a broad range of heavy neutrino massesbecause heavy neutrino production is suppressed by mixing angles [8], and the final statedoes not allow for a very efficient resonance reconstruction since only one of the two same-sign leptons comes from the N decay. The next simplest alternatives require the addition of a scalar weak triplet Δ with hypercharge Y Δ = 1 (the electric charge Q equals T + Y ,with T the third component of isospin), or of a fermion isotriplet of 0 hypercharge; thesecorrespond to the so-called see-saw models of type II and III, respectively, in contrast withtype I when the heavy mediator is the neutrino N . An essential difference in the tripletcases is that they contain new particles that are pair produced with electroweak strength,since they are charged, and they can be easily reconstructed through their leptonic decays. L cL = ( ν cL , l cL ) is the SM lepton doublet with charge conjugated fields, ψ cL = ( ψ L ) c = Cψ LT , ψ cR = ( ψ R ) c = Cψ RT , and φ = ( φ + , φ ) the SM Higgs doublet, with ˜ φ = iσ φ ∗ and σ the second Pauli matrix. In thetext we write down column doublets in a row for convenience, when no confusion is expected. In the following it should be understood that when we refer to an “addition” of certain particles or to an“extension” containing such particles, we mean the extension of the SM that is obtained by adding thecorresponding fields. ∼ GeV with an integrated luminosity of ∼ fb − at a center of mass energyof √ s = 7 TeV, although with the assumption that the doubly-charged scalar component Δ ±± only decays into two same-sign leptons of the first two families. These limits are muchless stringent when Δ ±± mainly decays into tau leptons, and even weaker if they have anappreciable branching ratio into W ± W ± ; on the other hand, the reach is so high becauseit also benefits of rather small SM backgrounds. At any rate, the outstanding performanceof these experiments will allow them to probe quite high masses at the LHC in the nearfuture. Once a doubly-charged resonance is observed in a same-sign di-lepton channel, ourpurpose is then to discuss to what extent it can be established that it is a member of thescalar triplet mediating the see-saw of type II, or whether it belongs to another multiplet.In order to address this question we will first classify the type of scalar multiplet additionsH containing such a resonance; these are characterized by their isospin T and hypercharge Y , which in turn determine the leading contribution to the total cross sections for doubly-charged scalar pair production and, if not a weak singlet, for the associated production withits singly-charged partner. This will eventually allow the measurement of both the T and Y quantum numbers of the new multiplet H.Any scalar multiplet containing a doubly-charged field can be coupled to like-charge di-leptons in a gauge invariant way by considering effective operators of high enough dimension.If we want to classify the scalar resonances coupling to lepton pairs with |LN| = 2 andobservable (though not exclusively) in the doubly-charged channel with two charged leptonsof the first two families, which will be the trigger for all these searches, we have to considerall invariant effective operators constructed with one of the two lepton bilinears with non-3anishing scalar couplings, L cL L L , l cR l R , any number of SM Higgs doublets φ and the newscalar multiplet H they belong to. There are two such operators of dimension 4 (containingno SM Higgs doublets) generating the desired di-leptonic scalar decays: in one the newscalars couple to the bilinear with left-handed (LH) lepton doublets and in the other tothe bilinear with RH lepton singlets. In the former case the new scalar multiplet will bea triplet Δ = (Δ ++ , Δ + , Δ ) with hypercharge 1 mediating the much-studied see-saw oftype II, in the latter case the new scalar will be an isosinglet κ ++ with hypercharge 2.(A realistic model of this type has been discussed in some detail in Ref. [19].) Exceptfor higher-order corrections to these renormalizable couplings, the couplings to fermions ofother multiplets with doubly-charged components do not occur in renormalizable theories,but must involve higher-dimensional operators. If this is the case, the fundamental theorymust contain additional heavier fields that upon integration give rise to the higher orderoperators (couplings) we will now classify. There are three independent operators ofdimension 5 (with one SM Higgs doublet): there is a single operator involving a quadruplet
Σ = (Σ ++ , Σ + , Σ , Σ ′− ) of hypercharge 1/2 coupling to two LH lepton doublets; and there aretwo independent operators involving a doublet χ = ( χ ++ , χ + ) of hypercharge 3/2 couplingto both |LN| = 2 lepton bilinears; the model resulting from the addition of this doubletwas briefly discussed in Ref. [14], and studied recently in Refs. [15, 16, 22]. Finally, thereis one operator of dimension 6 (containing two SM Higgs doublets) coupling a quintuplet Ω = (Ω ++ , Ω + , Ω , Ω − , Ω −− ) of hypercharge 0 to two LH lepton doublets; this field can beassumed to be real, as we do in the following. There are other operators involving quintupletsof non-zero hypercharge but these also include scalars with electric charges larger than 2; The other combination L cL l R requires a γ µ insertion because of the fermions’ chirality, and hence thepresence of a covariant derivative to ensure the operator is Lorentz invariant; through use of integrationby parts and the equations of motion the corresponding operators are then seen to be equivalent to theones considered here. This is the reason why they did not appear in the listing in [20]. Typically a heavier triplet coupling to the LH lepton bilinear, with a small VEV or/and with scalarcouplings softly breaking LN. We can also write the Weinberg operator but with one of the Higgs doublets replaced by a new heavydoublet of hypercharge 1/2, [21] but this does not contain a doubly-charged component and cannotresonate in same-sign di-lepton channels. Moreover, there is only one combination of the lepton doubletsthat gives a triplet involving the same-sign charged lepton bilinear; any other possible invariant operatorof that type must be related. Indeed, ( ˜ L L χ )( φ † L L ) = ( − a ( ˜ L L τ a L L )( φ † τ − a χ ) + ( ˜ L L L L )( φ † χ ) , wherethe last operator does not include the doubly-charged bilinear combination. imension 4 Triplet ΔSinglet κ ( ˜ L L τ a L L )Δ − a l cR l R κ Dimension 5
Quadruplet ΣDoublet χ ( − − b C × → a,b ( ˜ L L τ a L L ) φ b Σ − a − b ( − − a ( ˜ L L τ a L L )( φ † τ − a χ ) , l cR l R ( ˜ φ † χ ) Dimension 6 � Quintuplet Ω C × → a,b ( ˜ L L τ a L L )( ˜ φ † τ b φ )Ω − a − b Table I: Lowest-dimension, independent, gauge invariant effective operators coupling scalar multi-plets H in the text with charges | Q | ≤ to lepton pairs with |LN| = 2, observable in same-signdi-lepton channels. ˜ L L = iσ L cL , C j × j → jm ,m are the corresponding Clebsch-Gordan coefficients and τ a the Pauli matrices in the spherical basis, A +1 = − √ ( A − iA ) , A = A , A − = √ ( A + iA ) ,times C × → a, − a , up to a global factor and sign: τ ± = ± ( σ ∓ iσ ) / , τ = σ / √ . the same is true of multiplets with isospin > 2. We collect the corresponding operators inTable I.In the following we will concentrate on the additions to the SM listed in Table I which arethose with the lowest isospin and requiring lower dimension effective operators. They alsoexhaust the models with doubly-charged scalars resonating in same-sign di-lepton channelsbut without scalars with larger electric charges, that is, these multiplets satisfy T + Y = 2 . (1)The explicit expressions of the operators in Table I will not be needed in the simulationsperformed in this note. Indeed, the decay of a scalar into two leptons can be in generalparametrized (after spontaneous symmetry breaking) by two independent couplings corre-sponding to the two fermion chiralities: ψ cL ψ ′ L H ++ , and ψ cR ψ ′ R H ++ . (2)Thus, all operators containing L cLi L Lj ( l cRi l Rj ) reduce to the first (second) times a small (ingeneral, flavor-dependent) coupling constant. Since the helicity of the final leptons cannotbe measured, except eventually for the tau lepton [25], then although the operators in TableI involve definite fermion chiralities, we could use any of the two couplings above in the Scalars with larger electric charges have a rich variety of striking decays, especially if they are mass degen-erate with their doubly-charged partners [23, 24]. But these models are in general also more complicated. τ case, the dependence of the total cross section on the τ helicity due to theexperimental cuts is anyway negligible. On the other hand, although the relative strength ofthe lepton couplings to different components within a given scalar multiplet is fixed by gaugeinvariance (inherent to the explicit form of the operators), we will not use these relationseither in this letter. In a companion paper we will provide the missing details, including alsothe Feynman rules, the details of the applied cuts and of the event reconstruction procedureswe will refer to later, as well as the discussion of other related signatures not studied here;we shall also provide the code we used to perform the corresponding simulations.Two remarks are in order to justify the way we proceed: (i) LNV doubly-charged scalarsare expected to decay slowly . Although present limits on Δ ±± look quite stringent, the physicsinvolved is quite rare. in the sense that LN breaking is very small, as already emphasized.This necessarily translates into very small decay widths into lepton pairs and/or gauge bosonpairs (implying displaced vertices [10]) because both channels have different LN and theirproduct must reflect the fact that LNV amplitude is minuscule, m ν /v ∼ − . Similarly,the stringent limits on lepton flavor violation also strongly restricts the decay width at leastinto some lepton pairs. Hence, it also makes sense in general to look for decays into leptonsthat are as slow as into gauge bosons, which appreciably reduces present Δ ±± mass limits asstressed above. (ii) The effective Lagrangian approach is the appropriate way of describingthese extension of the SM . Indeed, specific models may not look simple because they have toexplain these small numbers, which can be the (joint) result of small couplings, of quantumloop suppression factors, or of multiple layers of NP. So, in this context, once the SM has beenlargely confirmed, also including the Higgs sector, as well as the gap between the electroweakscale and the scale of NP, we have to consider all higher order effective operators couplingthe new scalars H to like-charge di-leptons, although they may be suppressed by severalpowers of a heavy scale, as long as they are dominant.Let us now discuss how to discriminate among the different H additions by exploiting theimplications of gauge invariance, which completely fixes the scalar production cross sections.As a matter of fact, these cross sections are in general not only of electroweak size but are In the see-saw of type II if both channels have the same partial decay width, which implies � Δ � ∼ × − GeV for m Δ = 500 GeV, then the decay length is ∼ µ m; see Ref. [11] for the explicit decay widthexpressions and further discussion. In general, for doubly-charged scalar masses heavier than few hundredsof GeV, �� i,j = e,µ,τ Γ(Δ → l i l j )Γ(Δ → W W ) � − ≈ − �� i =1 , , m ν i � − m W m > m W m µ m . -5 -4 -3 -2 -1
200 300 400 500 600 700 80010 σ ( pb ) e v e n t s ( f o r f b ) m H ++ (GeV) quintuplet (NC)quadruplet (NC)triplet (NC)doublet (NC)singlet (NC) 10 -4 -3 -2 -1
200 300 400 500 600 700 80010 σ ( pb ) e v e n t s ( f o r f b ) m H ++ (GeV) quintuplet (CC)quadruplet (CC)triplet (CC)doublet (CC) Figure 1: Doubly-charged scalar pair (left) and single (right) production at LHC for √ s = 14 TeV,with scalars H belonging to a real quintuplet Ω , a quadruplet Σ , a triplet Δ , a doublet χ or asinglet κ with hypercharge Y = 0 , / , , / and , respectively. For a complex quintuplet thecross sections are double because there are two doubly-charged scalars, obviously, if mass degenerate.On the other hand, the singlet has no single production of doubly-charged scalars because it doesnot have a singly-charged component. generated by the same types of couplings independently of the multiplet H, and differ only inthe coupling strength, which only depends on the hypercharge and isospin of the multiplet.In our case, the doubly-charged scalar is either pair produced or produced in associationwith its singly-charged partner through the gauge couplings: L H ±± γ = ieQ ( ∂ µ H −− )H ++ A µ + h . c . , (3) L H ±± Z = igc W ( T − Qs W )( ∂ µ H −− )H ++ Z µ + h . c . , (4) L H ±± W = ig √ � ( T − T + 1)( T + T )[H ++ ( ∂ µ H − ) − ( ∂ µ H ++ )H − ] W − µ + h . c . , (5)where Q = 2 and T = Q − Y , and c W ( s W ) the cosine (sine) of the Weinberg angle.Thus, measuring the total pair production cross section (generated by the Z/γ couplings)we can determine the hypercharge, and hence T ; this, together with the total associatedproduction cross section (generated by the W coupling), will allow an estimate of T . InFig. 1 we plot the corresponding cross sections for the five cases listed in Table I. It isimportant to note that since the hypercharge and the isospin are related by Eq. (1), it is Higher order contributions to doubly-charged scalar pair production as, for instance, those generated byvector boson fusion may need to be eventually considered for larger doubly-charged scalar masses. Butin this case we can use the extra quarks in the forward direction to isolate this new type of events. The Z couplings in Eq. (4), which are not sodifferent in strength from the photon one. Although they also involve the quark couplings,which when properly taken into account make, for instance, the singlet and doublet casesindistinguishable. Thus, one must also rely on the absence of the associated production ofa doubly and a singly-charged scalar in the singlet case to discriminate between them.Any final mode requires not only the production but the subsequent decay of the newscalars. So, no particular channel allows the determination of the strength of the couplingsinvolved in the production, but only their product by the corresponding branching ratios.Hence, although the production cross sections are fixed by gauge symmetry, we have torely on measuring several (preferably all) decay channels in order to estimate the total crosssection, and determine which of the scalar multiplets is being produced. Obviously, the scalarproduction in all cases is kinematically identical, except for the charge distribution which isrelated to the quark parton distribution functions. On the other hand, one can not rely onpossible differences in the di-lepton branching ratios or in the kinematical distributions ofthe decay, because the former are model-dependent and the coupling constants multiplyingthe different operators in Table I can always be arranged to fit the observed number of eventsin a given final state; while the only kinematical observable which can be used to distinguishbetween operators is the tau lepton helicity, and taus do not need to be the most frequentdecay product.There is one last and essential point to discuss further before illustrating how to dis- vector boson fusion cross section also depends on T and T only, and the analysis below goes throughaccordingly (we will provide the details in a forthoming publication). Single doubly-charged productionthrough vector boson fusion may be only dominant for unusual models evading the stringent electroweakconstraints on the VEV of the neutral scalar partner of the doubly-charged scalar boson [26]. In this casethe doubly-charged scalar only decays into W pairs, and does not resonate in the di-leptonic channel. Wealso assume that the SM Higgs does not have a large coupling to doubly-charged scalar pairs, and thus,that its contribution to doubly-charged pair production is negligible. Pair production through mixingwith other scalars [27] is not considered either. W ± W ± if the scalar is doubly-charged. However, the correspond-ing branching ratio can be larger, of the same order or negligible when compared to thedi-leptonic one, as already discussed above (see footnote 8) for the triplet case. This is sobecause LN must be broken if neutrino masses are Majorana, as we assume, and thereforethese new scalars must exhibit both decay modes at some level: if they decay into two lep-tons with the same leptonic charge, their LN would be well-defined and different from zeroby 2 units, and if they only decay into a pair of gauge bosons, their LN would be preservedand equal to 0; only by having both decay channels their LN is not well-defined and LNviolated. This is in practice realized by ensuring a small LNV VEV, for instance, when atriplet is added to the SM, by requiring � Δ � � = 0 , and then inducing through the kineticterm the coupling g � Δ � W ∓ µ W ∓ µ Δ ±± . (6)The models with multiplets without neutral components which can acquire a VEV mustinclude mixing terms violating LN in the scalar potential in order to generate this couplingto some order [29]. As indicated above, LN is violated very weakly and this small numberis in general proportional to yη , where y is the effective di-lepton Yukawa coupling in Eq.(2) and η is proportional to a LNV VEV (similarly to the triplet case in Eq. (6)), � H � /v ,and/or to a small mixing angle, possibly times a loop suppression factor. (This product alsoenters in the amplitude for neutrino-less double beta decay, and this further restricts themodels [19, 20].) The constraint yη ≪ encompasses all scenarios found in specific models: η much larger than, of the same order as or much smaller than y . In the first case the newscalars decay mainly into gauge bosons and their signals do not emerge from the backgroundbecause their invariant masses can not be efficiently reconstructed [30]. In the other twocases the analysis we proposed can be carried out. If both decay channels are comparable,LNV could be experimentally confirmed by observing l ± l ± W ∓ W ∓ events (and/or l ± l ± W ∓ Z if H ±± is single produced). If only di-lepton channels are observable, LNV may not beestablished at the LHC but the type of scalar multiplet could be still determined. Experimental limits [17, 18] are in general given assuming that the doubly and singly-charged scalarsonly decay into leptons. As pointed out, we allow these scalars also to decay into gauge bosons. But weneglect mass splittings within multiplets due to mixing with other scalars. If not, decay chains must bealso considered [28]. � a = ll,lτ,ττ,W W z a , z a ≡ Br (H → a ) . Hence, as already emphasized, the total H ±± production cross section cannotbe inferred from the observation of a single decay mode. However, one can try to measureit accounting for different channels. Indeed, the four charged lepton ( e or µ ) cross sectionfor any given channel ab can be written σ ab = (2 − δ ab ) σz a z b , where σ is the total scalarpair production cross section we want to measure and z a,b the corresponding branchingratios, which in general include cascades into two leptons plus missing energy; note that weare dealing with extremely narrow resonances. Thus, the doubly-charged pair productioncross section with both scalars decaying into two leptons of the first two families reads σz ll ; whereas, for instance, the doubly-charged pair production cross section with one scalardecaying into two leptons of the first two families and the other to anything giving twocharged leptons of the first two families, too, plus missing energy is written σ llllp missT = σ llll + 2 � a = lτ,ττ,W W σz ll z a Br ( a → ll + p missT ) . Hence, if we are able to reconstruct andestimate all σ lla ≡ σz ll z a , a � = ll , besides σ llll , we can then evaluate σ = � σ llll + 12 � a � = ll σ lla � /σ llll . (7)In the following we argue that this is feasible, knowing that experimentalists will easilyimprove on the assumptions being made here, especially when using real data. Assuming aheavy scalar mass m H ±± = 500 GeV, doubly-charged scalar pairs are generated at LHCfor a center of mass energy √ s = 14 TeV using MADGRAPH5 [31], after implementingEqs. (3 − m H ±± ± GeV. We find thatthe number of background events is ∼ for an integrated luminosity of 300 fb − , and that Note that present limits are weakened when z ll + z lτ is appreciably smaller than 1.
1, 0, 0) ( , ,
0) ( , , ) ( , , ) Quintuplet ( l ± l ± ) l ∓ l ∓ p missT ( l ± l ± )( l ∓ l ∓ ) 1307 ± ±
32 501 ± ±
16 362 ± ±
16 238 ± ± Quadruplet ( l ± l ± ) l ∓ l ∓ p missT ( l ± l ± )( l ∓ l ∓ ) 765 ± ±
24 293 ± ±
12 212 ± ±
12 139 ± ± Triplet ( l ± l ± ) l ∓ l ∓ p missT ( l ± l ± )( l ∓ l ∓ ) 383 ± ±
18 147 ± ± ± ± ± ± Doublet ( l ± l ± ) l ∓ l ∓ p missT ( l ± l ± )( l ∓ l ∓ ) 189 ± ±
12 73 ± ± ± ± ± ± Singlet ( l ± l ± ) l ∓ l ∓ p missT ( l ± l ± )( l ∓ l ∓ ) 168 ± ±
12 64 ± ± ± ± ± ± Table II: Number of expected signal events with four charged leptons, electrons or muons, at LHCwith √ s = 14 TeV and an integrated luminosity of 300 fb − for a doubly-charged scalar mass of 500GeV belonging to an electroweak quintuplet, quadruplet, triplet, doublet or singlet with hypercharge0, 1/2, 1, 3/2 and 2, respectively, and different branching ratio ( z ll , z lτ , z ττ + z W W ) assumptions.After applying standard cuts, we require that two same-sign leptons reconstruct the scalar mass ± GeV and the other two reconstruct none, one or two taus, as well as the second doubly-chargedscalar mass, or are compatible with its decay to
W W . We also specify the number of events withthe two same-sign pairs reconstructing both scalars. Only statistical errors are included. the number of signal events also depends on the multiplet the doubly-charged scalar belongsto, and on the assumed branching ratios z a . In Table II we gather 4 different cases forillustration: ( z ll , z lτ , z ττ + z W W ) = (1 , , , (1 / , / , , (1 / , , / , (1 / , / , / , foreach multiplet addition. We specify in each case the total number of events passing thecuts, ( l ± l ± ) l ∓ l ∓ p missT , and also have both like-charge pairs reconstructing the doubly-chargedscalar mass, ( l ± l ± )( l ∓ l ∓ ) . We sum τ τ and W W events because we can easily disentanglethe τ τ + W W sample (with a very similar efficiency for both types of events) from the ll and lτ ones, while distinguishing between both subsamples requires more sophisticated In definite models as in the see-saw of type II, the Yukawa couplings giving neutrinos a mass are the samemediating the like-charge di-leptonic scalar decay, and they are then constrained, [11] but this is not soin general. l ± l ± W ∓ W ∓ and measuringits cross section in this final mode, we obtain the best sensitivity by subtracting from thecommon sample those events consistent with the second same-sign lepton pair reconstruct-ing two τ leptons with the doubly-charged scalar invariant mass. This is possible becausethere are 2 unknowns and 3 constraints when p missT is also measured. In contrast, the
W W reconstruction cannot be done on an event-by-event basis because in this case thereare 6 unknowns but only 5 constraints.Looking at Table II it is clear that the addition of a doublet and of a singlet cannotbe distinguished in doubly-charged pair production in any channel (sum). Analogously,comparing the fourth column for the triplet (quadruplet) to the second one for the doublet(triplet) it is apparent that using only one channel we cannot always differentiate betweenthe various multiplet extensions. But, as we have stressed before, counting the number ofevents in the three subsets, we can discriminate between the different scalar multiplets H,except between the doublet and the singlet. The three sub-samples are classified accordingto their kinematical properties (mainly the invariant mass of two same-sign leptons, m ll ,the missing momentum, p missT , and the momentum fraction, x , carried out by the chargedlepton in tau decays, as defined in footnote 13). Once the efficiency ǫ of the analysis foreach sub-sample, ( l ± l ± )( l ∓ l ∓ ) , ( l ± l ± )( l ∓ τ ∓ ) , ( l ± l ± )( τ ∓ τ ∓ + W ∓ W ∓ ) , is known, the crosssection for each subset, σ llll,lllτ,llττ + llW W , and thus, the total cross section, can be obtainedfrom real data. In Fig. 2 we plot the error estimate in the determination of σ in Eq.(7) combining the three previous measurements for the quintuplet, quadruplet, triplet anddoublet additions relative to the singlet one for an integrated luminosity of 100, 300 and3000 fb − . It is apparent from this Figure and Table II that only a few hundred eventsare needed to distinguish between different multiplets. Hence, if a doubly-charged scalaris discovered, it will be possible to also decide which multiplet it belongs to by collectingenough statistics.In order to distinguish the singlet from the doublet extensions we must look at theassociated (charged) production, which is absent in the former case, and bounded from below The momentum of an energetic τ can be assumed to align with the charged-lepton momentum it decaysto: xp µτ = p µl , with < x < . From our Monte Carlo simulations we estimate the sub-sample efficiencies including the correspondingbranching ratios: ǫ llll = 0 . , ǫ lllτ = 0 . and ǫ llττ = ǫ llW W = 0 . , respectively. / / / / / / / σ / σ s i ng l e t doublet/singlettripletquadrupletquintuplet Figure 2: Error estimate for the measurement of the total cross section for doubly-charged scalarpair production in Eq. (7) for m H ±± = 500 GeV at LHC with √ s = 14 TeV and an integratedluminosity of 100, 300 and 3000 fb − (from left to right), assuming it belongs to a weak quintuplet,quadruplet, triplet or doublet (singlet) with hypercharge 0, 1/2, 1 and 3/2 (2), respectively. in the latter one (assuming a signal is observed in pair production). It is then sufficient tosearch for three charged leptons plus missing energy, requiring two same-sign leptons toreconstruct the doubly-charged scalar, and requiring the other opposite-charged lepton andthe missing momentum be compatible with a singly-charged scalar of similar mass. Thisis also illustrated in Table III when assuming the same branching ratios for singly anddoubly-charged scalars. Although when dealing with specific models one must calculatethe different partial decay widths and sum them up to obtain the corresponding branchingratios for singly and doubly-charged scalars; for they are in general correlated.Finally, one can wonder about other final states; for instance, including semi-leptonic This test makes use of the distribution of the transverse mass of the opposite-sign lepton and p missT , andof the number of jets. l ± l ± )( l ∓ p missT ) (1, 0, 0) ( , ,
0) ( , , ) ( , , ) Quintuplet ±
34 283 ±
21 261 ±
20 130 ± Quadruplet ±
27 166 ±
18 153 ±
17 76 ± Triplet ±
21 83 ±
15 77 ±
15 38 ± Doublet ±
17 41 ±
13 38 ±
14 19 ± Singlet ±
12 0 ±
12 0 ±
12 0 ± Table III: As in Table II but for for the produciton of a single doubly-charged scalar in associationwith a singly-charged scalar of a similar mass. We also require that the opposite sign lepton(electron or muon) and the missing momentum (corresponding to a neutrino) are compatible withthe di-leptonic decay of the singly-charged scalar.
W W decays for the second doubly-charged scalar. This signal, however, cannot be separatedfrom the same final state from single production with the associated singly-charged scalardecaying into
W Z ; this and other examples allowing for consistent checks will be also studiedin detail in the companion paper. Obviously, once the possibility of discriminating amongdifferent H multiplets is established, there will be many other cross-checks that will lead toalternative ways of discriminating among the scalar multiplet additions.
Acknowledgements
We thank J. Santiago and A. Aparici for useful discussions and the careful reading of themanuscript. This work has been supported in part by the Ministry of Economy and Com-petitiveness (MINECO), under the grant numbers FPA2006-05294, FPA2010-17915 andFPA2011-23897, by the Junta de Andalucía grants FQM 101 and FQM 6552, by the “Gen-eralitat Valenciana” grant PROMETEO/2009/128, and by the U.S. Department of Energygrant No. DE-FG03-94ER40837. M.C. is supported by the MINECO under the FPU pro-gram. [1] G. Aad et al. [ATLAS Collaboration], Phys. Lett. B (2012) 1 [arXiv:1207.7214 [hep-ex]].[2] S. Chatrchyan et al. [CMS Collaboration], Phys. Lett. B (2012) 30 [arXiv:1207.7235 hep-ex]].[3] S. Weinberg, Phys. Rev. Lett. (1979) 1566–1570.[4] W. -Y. Keung and G. Senjanovic, Phys. Rev. Lett. (1983) 1427.[5] T. Han and B. Zhang, Phys. Rev. Lett. (2006) 171804 [hep-ph/0604064].[6] F. del Aguila, J. A. Aguilar-Saavedra and R. Pittau, JHEP (2007) 047[hep-ph/0703261].[7] A. Atre, T. Han, S. Pascoli and B. Zhang, JHEP (2009) 030 [arXiv:0901.3589 [hep-ph]].[8] F. del Aguila, J. de Blas and M. Perez-Victoria, Phys. Rev. D78 (2008) 013010[arXiv:0803.4008 [hep-ph]].[9] A. Hektor, M. Kadastik, M. Muntel, M. Raidal and L. Rebane, Nucl. Phys. B (2007) 198[arXiv:0705.1495 [hep-ph]].[10] R. Franceschini, T. Hambye and A. Strumia, Phys. Rev. D (2008) 033002[arXiv:0805.1613 [hep-ph]].[11] F. del Aguila and J. A. Aguilar-Saavedra, Nucl. Phys. B813 (2009) 22–90, [arXiv:0808.2468[hep-ph]].[12] F. del Aguila and J. A. Aguilar-Saavedra, Phys. Lett. B (2009) 158 [arXiv:0809.2096[hep-ph]].[13] A. Arhrib, B. Bajc, D. K. Ghosh, T. Han, G. -Y. Huang, I. Puljak and G. Senjanovic, Phys.Rev. D (2010) 053004 [arXiv:0904.2390 [hep-ph]].[14] J. F. Gunion, C. Loomis and K. T. Pitts, eConf C (1996) LTH096 [hep-ph/9610237].[15] V. Rentala, W. Shepherd and S. Su, Phys. Rev. D (2011) 035004 [arXiv:1105.1379[hep-ph]].[16] K. Yagyu, arXiv:1304.6338 [hep-ph].[17] S. Chatrchyan et al. [CMS Collaboration], Eur. Phys. J. C (2012) 2189 [arXiv:1207.2666[hep-ex]].[18] G. Aad et al. [ATLAS Collaboration], Eur. Phys. J. C (2012) 2244 [arXiv:1210.5070[hep-ex]].[19] F. del Aguila, A. Aparici, S. Bhattacharya, A. Santamaria and J. Wudka, JHEP (2012)133 [arXiv:1111.6960 [hep-ph]].[20] F. del Aguila, A. Aparici, S. Bhattacharya, A. Santamaria, J. Wudka and , JHEP (2012) 146 [arXiv:1204.5986 [hep-ph]].
21] J. F. Oliver and A. Santamaria, Phys. Rev. D (2002) 033003 [hep-ph/0108020].[22] M. Aoki, S. Kanemura and K. Yagyu, Phys. Lett. B (2011) 355 [Erratum-ibid. B (2012) 495] [arXiv:1105.2075 [hep-ph]].[23] K. S. Babu, S. Nandi and Z. Tavartkiladze, Phys. Rev. D (2009) 071702 [arXiv:0905.2710[hep-ph]].[24] G. Bambhaniya, J. Chakrabortty, S. Goswami and P. Konar, arXiv:1305.2795 [hep-ph].[25] H. Sugiyama, K. Tsumura and H. Yokoya, Phys. Lett. B (2012) 229 [arXiv:1207.0179[hep-ph]].[26] C. -W. Chiang, T. Nomura and K. Tsumura, Phys. Rev. D (2012) 095023[arXiv:1202.2014 [hep-ph]].[27] A. G. Akeroyd and S. Moretti, Phys. Rev. D (2011) 035028 [arXiv:1106.3427 [hep-ph]].[28] M. Aoki, S. Kanemura and K. Yagyu, Phys. Rev. D (2012) 055007 [arXiv:1110.4625[hep-ph]].[29] M. Gustafsson, J. M. No and M. A. Rivera, Approved for Phys.Rev.Lett.,2013[arXiv:1212.4806 [hep-ph]].[30] S. Kanemura, K. Yagyu and H. Yokoya, arXiv:1305.2383 [hep-ph].[31] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer and T. Stelzer, JHEP (2011) 128[arXiv:1106.0522 [hep-ph]].[32] M. L. Mangano, M. Moretti, F. Piccinini, R. Pittau and A. D. Polosa, JHEP (2003)001 [hep-ph/0206293].[33] T. Sjostrand, S. Mrenna and P. Z. Skands, JHEP (2006) 026 [hep-ph/0603175].[34] S. Ovyn, X. Rouby and V. Lemaitre, arXiv:0903.2225 [hep-ph].(2006) 026 [hep-ph/0603175].[34] S. Ovyn, X. Rouby and V. Lemaitre, arXiv:0903.2225 [hep-ph].