Discovery and exclusion prospects for staus produced by heavy Higgs bosons decays at the LHC
Ernesto Arganda, Víctor Martín-Lozano, Anibal D. Medina, Nicolás I. Mileo
IIFT-UAM/CSIC-21-4
Discovery and exclusion prospects for stausproduced by heavy Higgs bosons decays at the LHC
Ernesto Arganda , ∗ , Victor Mart´ın-Lozano † , Anibal D. Medina ‡ andNicolas I. Mileo § Instituto de F´ısica Te´orica UAM/CSIC,C/ Nicol´as Cabrera 13-15, Campus de Cantoblanco, 28049, Madrid, Spain IFLP, CONICET - Dpto. de F´ısica, Universidad Nacional de La Plata,C.C. 67, 1900 La Plata, Argentina DESY, Notkestraße 85, 22607 Hamburg, Germany
Abstract
In a previous work we developed a search strategy for staus produced by the decay of theheavy CP-even Higgs boson H within the context of the large tan β regime of the minimalsupersymmetric standard model (MSSM) in an scenario of large stau mixing. Here we study theperformance of such search strategy by confronting it with the complementary mixing pattern inwhich decays of both the CP-even and CP-odd heavy Higgs bosons contribute to the productionof (cid:101) τ (cid:101) τ ∗ + c.c pairs. Again, we focus on final states with two opposite-sign tau leptons andlarge missing transverse energy. We find that our proposed search strategy, although optimizedfor the large stau mixing scenario, is still quite sensitive to the complementary mixing pattern.For instance, with a total integrated luminosity of only 100 fb − we are able to exclude heavyHiggs masses above 850 GeV for average stau masses higher than 290 GeV. We also extendthe results reported in the preceding work for the large mixing scenario by including now theexclusion limits at 100 fb − and the prospects both for exclusion and discovery in a potentialhigh luminosity phase of the LHC (1000 fb − ). Finally, we discuss the possibility to distinguishthe two mixing scenarios when they share the same relevant mass spectrum and both reach thediscovery level with our search strategy. ∗ [email protected] † [email protected] ‡ [email protected] § [email protected] a r X i v : . [ h e p - ph ] F e b Introduction
Among the theories that extend the standard model (SM) of particle physics, supersymmetry(SUSY) remains as one of the most interesting and promising candidates (for reviews, see, e.g., [1,2]). From a phenomenological point of view, its minimal version with R -parity conservation [3],the minimal supersymmetric standard model (MSSM) [4–6], has as its main virtues a solution tothe gauge hierarchy problem, a potential unification of SM gauge couplings at high energies and aviable dark-matter candidate, the lightest supersymmetric particle (LSP) [7,8]. The MSSM predictsthe existence of superpartners (sparticles) for each SM particle: squarks/sleptons, gauginos andhiggsinos are the companions of quarks/leptons and gauge and Higgs bosons, respectively. TheMSSM Higgs sector contains two scalar doublets that under the assumption of a CP-conservingpotential leads to a physical spectrum that includes three neutral Higgs bosons (a light scalar h , aheavy scalar H , and a heavy pseudoscalar A ) and a pair of charged Higgs bosons ( H ± ), of whichthe 125-GeV SM-like Higgs boson [9,10] can be easily accommodated as the lightest CP-even Higgsboson h (see for instance [11]). Together with the phenomenological signals of these additionalHiggs bosons, the existence of sparticles produces a rich phenomenology with characteristic collidersignals that are being searched for at the Large Hadron Collider (LHC).A particular interesting example are the supersymmetric scalar partners of the tau leptons,the staus, which are being intensely searched for at the LHC by the ATLAS and CMS collabora-tions [12–19], since in many scenarios where SM gauged mediators are responsible for the trans-mission of SUSY breaking from a hidden sector to the visible sector, staus could be among thelightest sparticles. In a previous work [20], we have demonstrated that stau-pair production atthe LHC that are originated from the decay of a heavy scalar Higgs boson, and where the staussubsequently mainly decay into a tau lepton and the LSP neutralino, can be very promising in thelarge-tan β regime within MSSM scenarios with large stau mixing [21]. Indeed, we found that inthese regions of the MSSM parameter space, resonant stau-pair production cross sections are 1-2orders of magnitude larger than the usually considered electroweak (EW) production mechanism.The search strategy we developed was dedicated to scenarios with a stau mixing pattern for whichthe only relevant Higgs decay channel into staus was H → (cid:101) τ ∗ (cid:101) τ , being (cid:101) τ the lightest stau. Thisclass of stau mixing pattern occurs when the stau mixing angle is large and the diagonal entries ofthe stau mass matrix are of similar value. By means of a set of basic cuts, we obtained signal-to-background significances at the discovery level for a LHC center-of-mass energy of 14 TeV and atotal integrated luminosity of 100 fb − . For this new work we would like to extend our previousanalysis and show that our search strategy also works very well for scenarios with a complementarystau mixing pattern in which the stau mixing angle is small but the non-diagonal entries of the staumass matrix are large, mainly due to a sufficiently large stau trilinear coupling. In these latter sce-narios, contrary to the ones analyzed in our previous work, not only the CP-even Higgs contributesto the stau pair production but there is also the CP-odd Higgs contribution which in this case isnon-vanishing, potentially increasing the phenomenological signals. Furthermore, mixed combina-tions of heaviest and lightest staus are preferable produced via the heavy Higgs boson decays andthus we have the decay patterns, H/A → (cid:101) τ ∗ (cid:101) τ , (cid:101) τ ∗ (cid:101) τ , where (cid:101) τ is the heaviest stau, as the mainsource of staus. Since in this mixing pattern m (cid:101) τ can be much larger than m (cid:101) τ , we expect thatthe the collider phenomenology of the stau decays products to be quite different from the patternsanalyzed by us before and can potentially help in distinguishing both mixing patterns from eachother. From a more general approach, this search strategy could be applied to any process at theLHC with an identical topology, that is, the resonant production of a pair of charged scalars whichdecay into a tau lepton and an invisible particle, consisting of final states with a τ -lepton pair plusa large amount of missing transverse energy ( E miss T ).1he paper is organized as follows: Section 2 is devoted to review the theoretical features of thelarge stau mixing MSSM scenarios we work with, paying special attention to the main characteristicsof the H/A decays into a stau pair. The collider analysis we develop along this work is presented inSection 3, together with the description of our search strategy for stau pairs, originated from heavyHiggs boson resonances and decaying into the lightest neutralino and a tau lepton. A compendiumof the obtained results is presented in Section 4, for both classes of stau scenarios and with a finalstudy of the potential discrimination between them, leaving Section 5 for a discussion of our mainconclusions. H/A decays into stau leptons within the MSSM
As mentioned in the introduction, we work in the context of the MSSM in the large tan β (cid:29) H k = H, A to the down-type sfermions ofmixed chiralities are given by, g H (cid:101) d L (cid:101) d R = − m d [ − µ + A d tan β ] , (1) g A (cid:101) d L (cid:101) d R = − m d [ µ + A d tan β ] , (2)where m d is the mass of the down-type fermion, µ is the Higgsino mass and A d is the trilinearcoupling given in the soft SUSY breaking Lagrangian. The couplings involving the same chiralstates are proportional to SM fermion and gauge boson masses, do not involve soft SUSY breakingparameters and therefore cannot be enhanced [22]. In contrast, the couplings involving differentchiral states depend not only on the SM fermion mass but also on SUSY parameters, namely,the trilinear soft breaking parameter A d and the µ parameter. In Ref. [21] it was shown thatin a regime where tan β (cid:29) A d , the couplings of Eqs. (1) and (2) canin fact be enhanced in the case of staus in particular. This is translated into larger branchingfractions to staus, BR( H k → (cid:80) i,j =1 , (cid:101) τ ∗ i (cid:101) τ j ), implying consequentially that the branching ratio totaus, BR( H k → τ + τ − ), decreases. It is this what allows for the resurrection of certain regions ofthe MSSM that seem at first sight to be excluded from di-tau searches at the LHC. In this regimewe can find two scenarios with sizable branching fraction into staus: in one of them (cid:101) τ ∗ (cid:101) τ is thedominant decay mode (Scenario I), while in the other the (cid:101) τ ∗ (cid:101) τ + c.c. mode gives the dominantcontribution (Scenario II). Let us take a closer look at these scenarios in terms of the stau massmatrix and the corresponding mixing patterns.The stau mass matrix is defined as, M (cid:101) τ = (cid:18) m (cid:101) τ m (cid:101) τ m ∗ (cid:101) τ m (cid:101) τ (cid:19) = (cid:32) m L + m τ + ( − / / θ w ) m Z cos 2 β m τ ( A τ − µ tan β )( m τ ( A τ − µ tan β )) ∗ m E + m τ + 1 / θ w m Z cos 2 β (cid:33) , (3)where the trilinear coupling, A τ , comes from the soft Lagrangian term L soft ⊃ y τ A τ ˜¯ e ˜ L H d + c.c. The diagonalization of the mass matrix leads to the following mass eigenvalues and eigenstates: m (cid:101) τ , (cid:101) τ = 12 ( m (cid:101) τ + m (cid:101) τ ± ∆ (cid:101) τ ) , (4) (cid:101) τ = (cid:101) τ L cos θ (cid:101) τ + (cid:101) τ R sin θ (cid:101) τ , (5) (cid:101) τ = − (cid:101) τ L sin θ (cid:101) τ + (cid:101) τ R cos θ (cid:101) τ . (6)2here ∆ (cid:101) τ ≡ (cid:112) ( m (cid:101) τ − m (cid:101) τ ) + 4 m (cid:101) τ , assuming that m ∗ (cid:101) τ = m (cid:101) τ , and the mixing angle can bewritten as tan 2 θ (cid:101) τ = 2 m (cid:101) τ m (cid:101) τ − m (cid:101) τ . (7)Now that we have defined the stau sector, let us study the decay of a heavy Higgs boson, H k = H, A , into staus. The decay width is given byΓ( H k → (cid:101) τ ∗ i (cid:101) τ j ) = G F √ M H k λ / (cid:101) τ i (cid:101) τ j H k g H k (cid:101) τ i (cid:101) τ j ( i, j = 1 , , (8)where λ ijk = (cid:32) − m i m k − m j m k (cid:33) − m i m j m k , (9)is the kinematic factor in a two-body decay, and g H k (cid:101) τ i (cid:101) τ j is the coupling of the Higgs H k to the staus (cid:101) τ i and (cid:101) τ j . It is important to note that this coupling is a combination of the chiral couplings givenin Eqs. (1) and (2), and then can be written as g H k (cid:101) τ i (cid:101) τ j = (cid:88) α,β = L,R T ijαβ g H k (cid:101) τ α (cid:101) τ β , (10)where the T ijαβ are the elements of a 4 × θ (cid:101) τ ∼ π/
4. Inthis case, according to Eq. (7), it is not only important that m (cid:101) τ is large but it is also requiredthat m (cid:101) τ ∼ m (cid:101) τ . In such case, there is a cancellation of the contributions that mix chiralities inthe coupling g H (cid:101) τ (cid:101) τ involving different staus, leaving them only proportional to the chiral diagonalcouplings that as we mentioned before cannot be enhanced. The mass diagonal couplings g H (cid:101) τ (cid:101) τ and g H (cid:101) τ (cid:101) τ on the other hand do not present this cancellation and depend on the parameters that mixeschiralities, which can be increased by our choice of parameters. Therefore, the Higgs couplings to (cid:101) τ ∗ (cid:101) τ and (cid:101) τ ∗ (cid:101) τ suffer a cancellation, while the couplings to (cid:101) τ ∗ (cid:101) τ and (cid:101) τ ∗ (cid:101) τ are maximal. Since in thissituation the decays into pairs of heavier staus (cid:101) τ are usually not kinematically available, the decayof H is dominated by the decays into (cid:101) τ ∗ (cid:101) τ . Furthermore, as a consequence of the fact that themixed-mass couplings are suppressed, the couplings involving the CP-odd Higgs A to staus are alsosuppressed, and the stau production via Higgs boson decays is dominated by the heaviest CP-evenHiggs H .The situation that characterizes Scenario II arises when the mixing angle is small but m (cid:101) τ islarge due to the A τ term [22]. In this case the mixed chiral couplings are maximized, such that theleft-right part of the coupling of H to (cid:101) τ ∗ (cid:101) τ and the right-left part of the coupling of H to (cid:101) τ ∗ (cid:101) τ aremaximal. This latter pattern of decay also shows up for the supersymmetric decays of the CP-oddHiggs A to staus due to CP conservation. In Ref. [20] we developed a search strategy that proved to be very efficient as a discovery toolwithin the context of what we call here Scenario I. In this section we will apply the same analysiswhich was optimized for Scenario I to both scenarios in order to test its discovery potential not3nly for Scenario I but also for Scenario II. In the two scenarios the staus are resonantly producedthrough a heavy Higgs boson: H , in the case of Scenario I, and H/A in the case of Scenario II.As it was mentioned in Ref. [20], the cross section of the resonant production is significantly largerthan that corresponding to the EW pair production in the mass range m H/A ∈ [800 − β ∈ [25 − β regions compared to the EW-size production via SM electroweak gauge bosons, andthe large values of A τ that enhance the decays of the heavy Higgs bosons, allowing non-negligiblevalues of the branching ratios to staus, BR( H → (cid:101) τ ∗ (cid:101) τ ) ∼ . − . H/A → (cid:101) τ ∗ i (cid:101) τ j ) ∼ . − . i, j = 1 , i (cid:54) = j ) for Scenario II.Our analysis focuses on the process b ¯ b → H/A → (cid:101) τ ∗ i (cid:101) τ j → τ + (cid:101) χ τ − (cid:101) χ , with taus decayinghadronically for both scenarios. Regardless on which stau mass state is produced, the final stateinvolves two opposite-sign tau leptons and a large amount of missing energy, that comes fromthe two LSP neutralinos, (cid:101) χ . In order to test the two stau mixing scenarios, we have taken thebenchmarks points used in Ref. [20] for Scenario I and new ones produced in such a way thatfulfill the requirements of Scenario II, but were included already in Ref. [21]. A caveat is in ordergiven that the parameter space considered for our scenarios I and II may be already excludedby the most recent LHC searches for Higgs bosons decaying into two tau leptons [23, 24], evenwhen considering the additional decays into staus [21]. However, as mentioned in the conclusionof Ref. [21], points of parameter space that have just been excluded by the recent di-tau searchescan once again be resurrected considering the supersymmetric decays of the heavy Higgs bosonsinto staus in a completely analogous manner. We will therefore continue our analysis with theseolder points given that our conclusions regarding the strength of the search strategies proposedand the possible phenomenological signals will remain the same as for newly equivalent resurrectedparameter points that are allowed to evade the latest ditau searches.All the points were computed using SPheno 3.3.8 [25,26], from which we obtain all the spectraand phenomenological properties, like the branching ratios. To test the different points, we produceMonte Carlo events for the b -quark fusion process that dominates the heavy Higgs production in thelarge tan β limit, b ¯ b → H/A → (cid:101) τ ∗ i (cid:101) τ j → τ + (cid:101) χ τ − (cid:101) χ , at a center-of-mass energy of √ s = 14 TeV usingthe tool MadGraph aMC@NLO 2.6 [27]. In order to compute the signal cross section we make use ofthe tool
SusHi [28,29] that gives the results for Higgs boson production cross sections at NNLO forthe different production modes. The obtained values confirm that the dominant production modeis b -quark annihilation, with a cross section at least two orders of magnitude larger than the gluonfusion mode.In Table 1 we show two particular benchmark points that are representative of each scenarioand that we use to prove our search strategy. In Scenario I we use a point with a heavy Higgs mass m H = 947 . β = 33 .
8, and a lightest stau mass m (cid:101) τ = 367 . H is σ bbH = 194 . b -quark annihilationand σ ggH = 3 . β value makes the b -quarkannihilation cross section larger than gluon fusion. The values of the branching fraction of theheavy Higgs boson H decaying into staus and tau leptons are 0.17 and 0.09, respectively. As wecan see here, the enhancement of the decay into staus leads to a decrease in the branching ratio totau leptons. The branching fraction of the lightest stau into a tau lepton and the lightest neutralinois BR( (cid:101) τ → τ (cid:101) χ ) = 0 .
98. Thus the total cross section for the process pp → H → (cid:101) τ ∗ (cid:101) τ → τ (cid:101) χ τ (cid:101) χ at √ s = 14 TeV is σ totalS − I = 31 . m H = 1149 GeV, m A = 1148 . β = 45 .
33. In this benchmark point the production cross section isroughly σ bbH ∼ σ bbA ∼
120 fb. The relatively large production cross section despite the value ofthe masses is due to the large value of tan β that enhances the b -quark annihilation production4 arameter Scenario I Scenario II m A [GeV] 947.5 1148.9tan β M [GeV] 100 100 M , M [GeV] 2200 2200 µ [GeV] -327.2 -273.13 A τ [GeV] -859.4 1125 m ˜ L [GeV] 412.9 591.9 m ˜ E [GeV] 393.8 363.1 m H [GeV] 947.6 1149 m (cid:101) τ [GeV] 367.5 350.7 m (cid:101) τ [GeV] 408.4 583.9 m (cid:101) χ [GeV] 99 98.2 Table 1: Benchmark points of Scenario I and Scenario II that are used to develop the collider analysis. for both CP-even and CP-odd Higgs bosons. For this scenario the stau masses are m (cid:101) τ = 350 . m (cid:101) τ = 583 . A → (cid:80) i (cid:54) = ji,j =1 , (cid:101) τ ∗ i (cid:101) τ j ) = 0 .
25 and BR( H → (cid:80) i (cid:54) = ji,j =1 , (cid:101) τ ∗ i (cid:101) τ j ) = 0 .
22. We can notice that for thisbenchmark point the decay of the heavy Higgs bosons to a lightest stau pair is zero in the case ofthe CP-odd Higgs boson and BR( H → (cid:101) τ ∗ (cid:101) τ ) = 0 .
01 for the CP-even one. This is just a realizationof the properties of this scenario where there is an enhancement of the chiral couplings and the non-mixed states of the staus. The branching ratios for both stau states are BR( (cid:101) τ → τ (cid:101) χ ) = 0 .
28 andBR( (cid:101) τ → τ (cid:101) χ ) = 0 .
82 respectively. Therefore, the total cross section of the process pp → H/A → (cid:80) i,j =1 , (cid:101) τ ∗ i (cid:101) τ j → τ (cid:101) χ τ (cid:101) χ for this Scenario-II benchmark point at √ s = 14 TeV is σ totalS − II = 13 . m H/A is lighter than it is in Scenario II and, on top of that, the branching ratioof staus is almost saturated by the τ (cid:101) χ channel, which is not the case in Scenario II. Background Cross section [fb] t ¯ t W +jets 6.257 × Z +jets 4.254 × W W ZZ Table 2: List of backgrounds and their cross sections to the process b ¯ b → H/A → (cid:101) τ ∗ i (cid:101) τ j → τ + (cid:101) χ τ − (cid:101) χ at theLHC at a center-of-mass energy of √ s = 14 TeV. t ¯ t , W +jets, Z +jets, W W and ZZ , andthey are listed in Table 2 with their cross sections at √ s = 14 TeV. In principle, one has toinclude the QCD multijet background as well, however this is highly suppressed once the cutsinvolving large amounts of E miss T are applied, as shown in Ref. [20]. Although all the eventscorresponding to the background processes have been generated at leading order, the cross sectionsfor t ¯ t , W W and ZZ have been rescaled with K-factors of 1.5, 1.4, and 1.3, respectively, extractedfrom Ref. [27]. In addition, the cross sections for the W +jets and Z +jets backgrounds have beenestimated by considering up to two light jets. It is important to note that for the t ¯ t , W +jets,and W W backgrounds we have included only the decay of the W boson into τ ν τ , while in thecase of the ZZ and Z +jets backgrounds, we have considered the decays ZZ → τ + τ − ν ¯ ν and Z → τ + τ − , respectively. Both the signal and the different backgrounds have been generated with MadGraph aMC@NLO 2.6 [27] and showered with
PYTHIA 8 [30], while the detector response has beensimulated with
Delphes 3 [31]. The implementation of the different cuts of the search strategythat we present below have been carried out with
MadAnalysis 5 [32] in the expert mode.
We will describe here the search strategy that we follow which was first proposed in Ref. [20]. Firstof all, we apply some basic selection cuts that define the final state that we are searching for. Werequire that both signal and background events exhibit two opposite-sign tau leptons and we alsodemand that they have the following properties: p τ T >
50 GeV , p τ T >
40 GeV , | η τ | < . . (11)Here we define τ and τ as the leading and subleading tau leptons, respectively, p T is the transversemomentum of the corresponding tau lepton and η τ is its pseudorapidity. Given the topology of thesignal process, one must rely on the large amount of transverse missing energy, E miss T , coming fromthe two LSP neutralinos escaping the detector in order to discriminate it from the background.For such reason, in this analysis we take into account kinematic variables that depend directly on E miss T :1. The transverse mass m T , defined as m T ( (cid:126)p iT , (cid:126)p inv T ) = (cid:115) m i + 2 (cid:18)(cid:113) m i + | (cid:126)p iT | E miss T − (cid:126)p iT · (cid:126)p inv T (cid:19) , (12)where i denotes the detected particle with transverse momentum (cid:126)p iT and mass m i , and (cid:126)p inv T is the total missing transverse momentum.2. The stransverse mass m T , which is designed to target events with two sources of missingtransverse momentum: m T = min /(cid:126)p + /(cid:126)p = (cid:126)p inv T (cid:110) max (cid:104) m T ( (cid:126)p iT , /(cid:126)p ) , m T ( (cid:126)p jT , /(cid:126)p ) (cid:105)(cid:111) , (13)where i and j are the two visible states from the parent decays, and /(cid:126)p and /(cid:126)p are thecorresponding missing transverse momenta. The power of the m T variable comes from thefact that its distribution presents an endpoint around the mass of the parent decaying particle.This feature makes this variable quite efficient to discriminate between the signal and the t ¯ t and W W backgrounds. 6
200 400 600 800 m τ T [GeV]0 . . . . . . . . . F r a c t i o n o f e v e n t s Scenario IScenario II t ¯ tW + jets Z + jets WWZZ m τ T [GeV]0 . . . . . . . . . F r a c t i o n o f e v e n t s Scenario IScenario II t ¯ tW + jets Z + jets WWZZ m ττ [GeV]0 . . . . . . . . . F r a c t i o n o f e v e n t s Scenario IScenario II t ¯ tW + jets Z + jets WWZZ m T [GeV]0 . . . . . . . . . . F r a c t i o n o f e v e n t s Scenario IScenario II t ¯ tW + jets Z + jets WWZZ
Figure 1: Four different distributions of kinematic variables after the selection cuts are applied to the signaland background events. On each case we show the distribution of the signal for the two scenarios along withthose corresponding to the backgrounds listed in Table 2. Top left panel: Transverse mass of the leadingtau lepton, m τ T . Top right panel: Transverse mass of the subleading tau lepton, m τ T . Bottom left panel:Invariant mass of the two tau leptons, m ττ . Bottom right panel: Stransverse mass m T . In Fig. 1 we depict the distributions of several variables after applying the selection cuts definedabove to the signal and background events. The two top panels represent the transverse mass ofthe leading and the subleading tau leptons. From these two distributions we can see that thebackground events concentrate in the low transverse mass region, m τT (cid:46)
200 GeV for the leadingtau lepton and m τT (cid:46)
120 GeV in the case of the subleading tau lepton. On the other hand, thedistribution of the signal events reaches heavier transverse masses due to the fact that there is moremissing transverse energy coming from the neutralinos. For that reason we require the transversemass of the two tau leptons to be greater than 120 GeV. The bottom left panel shows the invariantmass of the tau lepton pair. We see that it is easy to discriminate the events coming from the ZZ and Z +jets backgrounds since they peak at m ττ ∼ m Z . Therefore, we set a cut on the invariantmass of the two tau leptons of m ττ >
100 GeV. The bottom right panel depicts the m T variable.From the shape of the distribution, it is clear that this variable is crucial to discriminate betweenthe signal and the background events. The aim of the m T variable is to select the processesin which there is a large amount of missing transverse energy, E miss T , coming from at least twosources. Moreover, recall that this variable exhibit an endpoint around the mass of the parentdecaying particle. These features explain the quick decrease for the background distributions,7hich are mostly concentrated at m T <
150 GeV. On the other hand, the signal distributionextends towards higher values of m T . Based on this we impose the cut m T >
180 GeV that hasa significant impact on the background events. In addition to the cuts already explained, we havealso included a cut in the angular separation of the two tau leptons, ∆ R ( τ , τ ), and imposed a b -jet veto along with the requirement that the number of light jets is smaller than 2. All the cutsare summarized in Table 3, where the left column contains the selection cuts and the right columnincludes the cuts that define our signal region. It is important to emphasize here that the factthat our search strategy for stau pairs is based on their production through heavy resonances ( H and A Higgs bosons) allows us to impose a much more restrictive cut on the m T variable than instrategies based on the usual electroweak stau production (see for example Table 1 of [19]). In thelatter case, the background is much less suppressed and unfortunately mimics the signal better. Selection Cuts Signal Region Cuts N b = 0 & N j < p τ T >
50 GeV ∆ R ( τ , τ ) < . p τ T >
40 GeV m τ T , m τ T >
120 GeV | η τ | < . m ττ >
100 GeV m T >
180 GeV
Table 3: List of cuts performed in the collider analysis. The first column shows the selection cuts that definethe process. In the second column we depict the selected cuts in order to discriminate the signal from thebackground.
We can now test the efficiency of the search strategy by applying it to the benchmark points ofScenarios I and II given in Table 1. In order to simulate the background, we have followed the sameprocedure as in Ref. [20], generating the same number of events as it is indicated in Table 4 for everybackground source. Following similar searches [12, 14] we assume a systematic uncertainty of 30%on the estimated sum of all backgrounds. In order to compute the significance of the signal events, S , with respect to the background events, B , including the potential systematic uncertainties weuse [33] S dis = (cid:115) (cid:18) ( B + S ) log (cid:18) ( S + B )( B + σ B ) B + ( S + B ) σ B (cid:19) − B σ B log (cid:18) σ B SB ( B + σ B ) (cid:19)(cid:19) , (14)where σ B = (∆ B ) B , with ∆ B being the relative systematic uncertainty, in our case ∆ B = 30%. InTable 4 we show the number of events for every source of background and the signal events of bothscenarios at a LHC center-of-mass energy of √ s = 14 TeV and for a total integrated luminosity of L = 100 fb − . For each scenario we show a column with the number of events if no cut is appliedand a second column with the number of events after applying the cuts. We see that with a 30% ofsystematic uncertainties, a signal significance of 6.62 σ for Scenario I and 5.24 σ for Scenario II areobtained for a luminosity of 100 fb − . In spite of the differences between the two scenarios in terms Given that in our scenarios the main production mechanism of the resonances is the b -quark annihilation, it couldbe interesting to study the signal process without imposing the b -jet veto. In principle, one could define differentsignal regions according to the number of b -tagged jets, allowing for a better discovery rate and efficiency. However,the proper identification of b -jets arising from the initial state is a complex task and would require a detailed studyon its own, which is out of the scope of this paper.
8f the nature of the stau states, the decaying resonance and the Higgs-stau coupling, the analysisappears to be efficient in both cases.
Scenario I Scenario IINo Cuts SR No Cuts SR
Signal 3171 28.78 1317 21.16 t ¯ t W +jets 6 . × . × Z +jets 4 . × . × W W ZZ S dis O (10 − ) 6.62 O (10 − ) 5.24 Table 4: Number of signal and background events at √ s = 14 TeV for an integrated luminosity of L = 100fb − before and after applying cuts. The last line represents the signal significance obtained using Eq. (14). One can also think the other way around and imagine that no significant signal events arefound for a given luminosity. In that situation, one can set 95% C.L. exclusion limits by using theexclusion significance as follows [33]: S exc = (cid:115) (cid:18) B log (cid:18) BS + B (cid:19) + S (cid:19) ≤ . , (15)where B is the total number of background events and S is the number of signal events at a givenluminosity L . In the next section we will analyze a set of points for each scenario in terms ofexclusion and discovery significances using this search strategy. In this section we use the search strategy described above and test it against several benchmarkpoints from both Scenario I and Scenario II. For each benchmark point we study the efficiency of theanalysis in terms of potential exclusion at 95% C.L. and discovery signal significance by consideringtwo values of integrated luminosity at √ s = 14 TeV, L = 100 fb − , to be easily reached at the nextrun of the LHC, and L = 1000 fb − , corresponding to the high-luminosity LHC (HL-LHC). Withthese two values of the luminosity we can explore the future prospects and the reach of this searchstrategy in terms of physical parameters such as the mass of a new heavy (pseudo) scalar. H → (cid:101) τ (cid:101) τ ∗ → τ + (cid:101) χ τ − (cid:101) χ From Scenario I we take 27 benchmark points that were described in Ref. [20]. These points arecharacterized by different values of m H , tan β , A τ , and m (cid:101) τ . We have applied the search strategydescribed in Section 3.1 and we have studied the exclusion power of the analysis as well as the signalsignificance of discovery. The results are shown in Fig. 2, where the orange points correspond to9xcluded benchmarks and the blue ones to the benchmarks that cannot be ruled out at 95% C.L.by our analysis.
800 900 1000 1100 m H [GeV] − − − − A τ [ G e V ]
95% C.L. exclusion √ s = 14 TeV and L = 100 fb −
800 900 1000 1100 m H [GeV] − − − − A τ [ G e V ]
95% C.L. exclusion √ s = 14 TeV and L = 1000 fb −
800 900 1000 1100 m H [GeV]25 . . . . . . . . . t a n β
95% C.L. exclusion √ s = 14 TeV and L = 100 fb −
800 900 1000 1100 m H [GeV]25 . . . . . . . . . t a n β
95% C.L. exclusion √ s = 14 TeV and L = 1000 fb − Figure 2: Potential exclusion at 95% C.L. obtained from Eq. (15) in the [ m H , A τ ] plane (top) and [tan β , A τ ] plane (bottom), within Scenario I, for a center-of-mass energy of √ s = 14 TeV and total integratedluminosities of 100 fb − (left panel) and 1000 fb − (right panel). We display in orange the benchmark pointsthat are excluded at 95% C.L. and in blue those that are allowed. For L = 100 fb −
23 of the 27 benchmarks points are excluded. All the points with heavy Higgsboson mass smaller than 1000 GeV are ruled out. Above this value, m H > m H = 1075 GeV that can be excluded, while the remaining 4 benchmarks inthis mass region are allowed. This is due to the fact that the benchmark point with m H = 1075GeV has also a value of A τ large enough to enhance the coupling g Hdd and then the branching ratiointo staus, which is ∼ µ and then its contributionto the coupling in Eq. (1) adds to that corresponding to the A τ . Finally, as can be seen in the plane[tan β , A τ ], this benchmark point includes a large value of tan β which increases the productioncross section compensating the suppression due to the large value of m H . Furthermore, a largevalue of tan β also enhances g Hdd .Within the high-luminosity phase of the LHC, it could be possible to exclude benchmark pointswith heavy Higgs boson masses above 1 TeV. However, as can be seen from the right panel ofFig. 2, it seems that for trilinear couplings smaller than 1 TeV, our analysis cannot probe heavyHiggs boson masses above 1.1 TeV, even with values of tan β as large as 42.In Fig. 3 we show the discovery prospects for each of the 27 benchmarks in the [ m H , A τ ] and10
00 900 1000 1100 m H [GeV] − − − − A τ [ G e V ] √ s = 14 TeV and L = 100 fb − S < σ σ < S < σ S > σ
800 900 1000 1100 m H [GeV] − − − − A τ [ G e V ] √ s = 14 TeV and L = 1000 fb − S < σ σ < S < σ S > σ
800 900 1000 1100 m H [GeV]25 . . . . . . . . . t a n β √ s = 14 TeV and L = 100 fb − S < σ σ < S < σ S > σ
800 900 1000 1100 m H [GeV]25 . . . . . . . . . t a n β √ s = 14 TeV and L = 1000 fb − S < σ σ < S < σ S > σ Figure 3: Signal significance in the [ m H , A τ ] plane (top) and [tan β , A τ ] plane (bottom), within Scenario Ifor a center-of-mass energy of √ s = 14 TeV and total integrated luminosities of 100 fb − (left panel) and1000 fb − (right panel). Red circles correspond to significances below the evidence level ( S < σ ), bluecircles to significances between the evidence level and the discovery one (3 σ < S < σ ), and green circles tosignificances larger than the discovery level ( S > σ ). [ m H , tan β ] planes. Signal significances in the ranges S < σ , 3 σ < S < σ (evidence level) and S > σ (discovery level) are displayed in red, blue and green, respectively. We see that most of thebenchmarks with m H below 1 TeV lie in the evidence or the discovery level. Only those around m H = 910 GeV with a trilinear coupling A τ = 720 GeV are below the evidence level due to thesmall branching ratio of H into staus, which is almost 10%. Among these benchmark points, solelyone could be tested by increasing the luminosity to 1000 fb − . The benchmarks in the mass region m H > L = 1000 fb − . Again the exception is the point with m H = 1075 GeV, due to the combination of a large trilinear coupling ( A τ = 1 TeV) that leads toa branching ratio of 16%, and a value of tan β = 43 that is large enough to increase the productioncross section despite the large heavy Higgs boson mass. From the low panels of Fig. 3, we seethat there is a region with tan β ∈ (37-41) and m H ≥ m H grows, and thebenchmarks in the mass region above 1 TeV correspond to tan β values that are not large enough tocompensate this trough their impact on the production cross section and the decay rate. It seemsthat values of tan β above 41 are required in order to test the region m H >
50 800 850 900 950 1000 1050 1100 m H [GeV]200250300350400450 m ˜ τ [ G e V ] m ˜ τ > m H
95% C.L. limits of exclusion for √ s = 14 TeVExclusion: L = 100 fb − L = 1000 fb − Figure 4: Potential areas of exclusion at 95% C.L. within Scenario I for a center-of-mass energy of √ s = 14TeV. The area above the full line, here in dark gray, represents the one that could be possibly excluded bythis analysis at 100 fb − of integrated luminosity if no evidence of signal is found. The area below it, here inlight gray, that is defined by the dashed line shows the potentially excluded range at 1000 fb − of integratedluminosity. However, the dashed line here is not visible since it goes below masses of the lightest stau of m (cid:101) τ <
200 GeV. The shaded red area is forbidden because the decay mode H → ˜ τ ˜ τ ∗ is kinematically closed. By performing an interpolation based on the 27 benchmark points studied above, we can nowinterpret the obtained results in the [ m H , m (cid:101) τ ] plane. This is shown in Fig. 4, where we displaythe 95% C.L. exclusion limits for L = 100 fb − (dark gray) and L = 1000 fb − (light gray). Thered area on the left top corner is kinematically forbidden. We see that the search strategy is ableto probe most of the [ m H , m (cid:101) τ ] plane with a luminosity of L = 100 fb − . On the other hand,a higher luminosity is required to gain sensitivity in the region at m H >
930 GeV and m (cid:101) τ <
260 GeV because the large values of m H reduces the production cross section and also the smallvalues of m (cid:101) τ lead to a substantial decrease in the amount of E miss T , which makes the m T cut lesspowerful. The last explains the fact that for a given heavy Higgs boson mass above 930 GeV we canmove from the allowed to the excluded region by increasing the stau mass. With L = 1000 fb − ,the search strategy becomes sensitive to the whole area comprised by heavy Higgs boson massesbetween 750 GeV and 1100 GeV and stau masses between 200 GeV and 450 GeV.In Fig. 5 we present the same contour plot in the [ m H , m (cid:101) τ ] plane as in Fig. 2 but for thediscovery prospects of the signal, for a total integrated luminosity of L = 100 fb − (left panel ) and1000 fb − (right panel). We depict the evidence level (3 σ ) as a light green area limited by a solidblack line whereas the discovery level (5 σ ) is shown as a darker green area limited by a dashed blackline. From the left panel we see that for L = 100 fb − the search strategy is sensitive to m H <
850 GeV regardless the value of the stau mass (within the considered range). For m H >
850 GeVthe sensitivity is lost for stau masses below 300 GeV due to the same two reasons discussed beforein the case of the exclusion plot: on the one hand, the signal cross section decreases considerablyfor large values of m H , and on the other one, small stau masses produce a final state with lessenergetic tau leptons and lower E miss T , which in turn reduces the discrimination power of crucialkinematic variables as m T or m T . This high m H range can still be probed if larger values of thestau mass are considered. In particular, the discovery level is reached for m (cid:101) τ > − , our analysis cover most of the considered area in the [ m H ,12
50 800 850 900 950 1000 1050 1100 m H [GeV]200250300350400450 m ˜ τ [ G e V ] m ˜ τ > m H Significance for √ s = 14 TeV and L = 100 fb − Significance: σ σ
750 800 850 900 950 1000 1050 1100 m H [GeV]200250300350400450 m ˜ τ [ G e V ] m ˜ τ > m H Significance for √ s = 14 TeV and L = 1000 fb − Significance: σ σ Figure 5: Signal significance in the [ m H , m ˜ τ ] plane, within Scenario I, for a center-of-mass energy of √ s =14 TeV and total integrated luminosities of 100 fb − (left panel) and 1000 fb − (right panel). The dark grayarea above the dashed line is the discovery level region ( ≥ ≥ σ and the red area is kinematically forbidden. m (cid:101) τ ] plane. However, its sensitivity is not enough to reach the region with m H >
900 GeV and m (cid:101) τ <
260 GeV. We see that this region of high m H and low m (cid:101) τ is very challenging even withinthe context of the HL-LHC. H/A → (cid:101) τ , (cid:101) τ ∗ , → τ + (cid:101) χ τ − (cid:101) χ The parameters involved in Scenario II are m H , m A , tan β , A τ , m (cid:101) τ , and m (cid:101) τ . Thus, we have inthis case an additional parameter arising from the stau sector, namely, m (cid:101) τ . We select in this case228 benchmark points. We explore the results obtained for each of them in terms of the parameters A τ , tan β , and m A first and then in the stau sector, that we characterize by using the average ofthe two stau masses and their difference m (cid:101) τ = m (cid:101) τ + m (cid:101) τ , ∆ m = m (cid:101) τ − m (cid:101) τ . (16)We choose m A instead of m H because it is a natural parameter in the MSSM and also one canobtain m H making use of m A . Furthermore, as we move in the decoupling limit we find usuallythat m A ∼ m H .In Fig. 6 we show the results of applying the 95% C.L. exclusion condition of Eq. (15) to theScenario-II benchmarks in the [ m A , A τ ] (top) and [tan β , A τ ] (bottom) planes for total integratedluminosities of 100 fb − (left) and 1000 fb − (right). From the plots on the top panel we see thatthe exclusion power of the search strategy extends to masses up to 1200 GeV. Again, for a givenmass, the sensitivity increases for higher values of | A τ | . For L = 100 fb − all the points with m A (cid:46)
840 GeV are excluded even for the lowest values of A τ considered here ( | A τ | ∼
500 GeV).For L = 1000 fb − this conclusion is valid for masses below 860 GeV. Above these masses thesensitivity depends on the specific values of A τ and tan β . Regarding this last parameter, we seefrom the bottom panels that all the points with tan β ≥
47 (tan β ≥
42) are excluded for L = 10013
00 900 1000 1100 1200 m A [GeV] − − − A τ [ G e V ]
95% C.L. exclusion √ s = 14 TeV and L = 100 fb −
800 900 1000 1100 1200 m A [GeV] − − − A τ [ G e V ]
95% C.L. exclusion √ s = 14 TeV and L = 1000 fb −
25 30 35 40 45 50tan β − − − A τ [ G e V ]
95% C.L. exclusion √ s = 14 TeV and L = 100 fb −
25 30 35 40 45 50tan β − − − A τ [ G e V ]
95% C.L. exclusion √ s = 14 TeV and L = 1000 fb − Figure 6: Potential exclusion at 95% C.L. in the [ m A , A τ ] plane (top plots) and [tan β , A τ ] plane (bottomplots), within Scenario II, for a center-of-mass energy of √ s = 14 TeV and total integrated luminositiesof 100 fb − (left panels) and 1000 fb − (right panels). Benchmarks excluded by the analysis are shown inorange, while the allowed ones are shown in blue. fb − (1000 fb − ). The main reason for this behavior is the fact that larger values of tan β enhancethe b -quark annihilation production cross section and the coupling with the staus at the same time,so that the search strategy is quite efficient even for benchmark points with large m A and m H andrelatively low values of A τ ( | A τ | ∼
500 GeV).In Fig. 7 we depict, in the same parameters planes as in Fig. 6, the results corresponding to thesignal significance prospects for L = 100 fb − (left) and 1000 fb − (right). Similarly to the resultsdiscussed above for the exclusion limits, benchmarks with higher values of | A τ | are more likely tobe detected by the search strategy. Specifically, all the benchmarks with | A τ | ≥ σ , with most of them reaching the discovery level. We note that for L = 1000 fb − some of these benchmarks lie in the high mass region with m A ≥ A τ ( ∼
500 GeV). The same conclusions aboutthe impact of the value of A τ in the significance can be read off on the lower panels. In addition, wealso see that for the case of L = 1000 fb − all the points with tan β ≥
46 reach significances above3 σ . In fact, more than half of the benchmarks lying in that region correspond to significances atthe discovery level.Let us turn now to the results in terms of the stau variables defined in Eq. (16). These are14
00 900 1000 1100 1200 m A [GeV] − − − A τ [ G e V ] √ s = 14 TeV and L = 100 fb − S < σ σ < S < σ S > σ
800 900 1000 1100 1200 m A [GeV] − − − A τ [ G e V ] √ s = 14 TeV and L = 1000 fb − S < σ σ < S < σ S > σ
25 30 35 40 45 50tan β − − − A τ [ G e V ] √ s = 14 TeV and L = 100 fb − S < σ σ < S < σ S > σ
25 30 35 40 45 50tan β − − − A τ [ G e V ] √ s = 14 TeV and L = 1000 fb − S < σ σ < S < σ S > σ Figure 7: Signal significance in the [ m A , A τ ] plane (top plots) and [tan β , A τ ] plane (bottom plots), withinScenario II for a center-of-mass energy of √ s = 14 TeV and total integrated luminosities of 100 fb − (leftpanels) and 1000 fb − (right panels). Benchmarks with significances below the evidence level ( S < σ ),between the evidence level and the discovery level (3 σ < S < σ ) and above the discovery level ( S > σ )are shown in red, blue and green, respectively. shown in Fig. 8 in the planes [ m A , m (cid:101) τ ] (top panels) and [∆ m , m (cid:101) τ ] (bottom panels) for L = 100fb − (left) and L = 1000 fb − (right). We see that all the points with m (cid:101) τ ≥
300 GeV are excludedin the case of L = 100 fb − , while this value decreases to m (cid:101) τ ≥
270 GeV for L = 1000 fb − .This conclusion is also visible in the [∆ m , m (cid:101) τ ] plane, from which we also note that in the case of L = 100 fb − the points with m (cid:101) τ ≥
300 GeV appear to be easily tested when the value of ∆ m is smaller. The same conclusion can be drawn from the plots corresponding to L = 1000 fb − forpoints with average stau masses below 270 GeV. This behaviour is due to the fact that the m T cut is more efficient for smaller values of ∆ m since this kinematic variable was originally designedto tag a pair of decaying particles with equal mass.The results of the signal significance in terms of stau variables are shown in Fig. 9. In this casemost of the points with m (cid:101) τ ≥
300 GeV reach the discovery level. In contrast, all the points withstau masses below this value cannot be probed with the analysis at L = 100 fb − . This situationimproves only a bit at L = 1000 fb − , since in this case some points with m (cid:101) τ ≤
300 GeV showevidence level. However, there are no points reaching the discovery level in this region. The increasein luminosity from 100 fb − to 1000 fb − also makes that a considerable number of points in themass region above 300 GeV with large values of m A or ∆ m become accessible. In the case of the15
00 900 1000 1100 1200 m A [GeV]100200300400500600 m ˜ τ [ G e V ]
95% C.L. exclusion √ s = 14 TeV and L = 100 fb −
800 900 1000 1100 1200 m A [GeV]100200300400500600 m ˜ τ [ G e V ]
95% C.L. exclusion √ s = 14 TeV and L = 1000 fb − m [GeV]150200250300350400450500550 m ˜ τ [ G e V ]
95% C.L. exclusion √ s = 14 TeV and L = 100 fb − m [GeV]150200250300350400450500550 m ˜ τ [ G e V ]
95% C.L. exclusion √ s = 14 TeV and L = 1000 fb − Figure 8: Potential exclusion at 95% C.L. in the [ m A , m ˜ τ ] plane (top) and [∆ m , m ˜ τ ] (bottom), withinScenario II, for a center-of-mass energy of √ s = 14 TeV and total integrated luminosities of 100 fb − (leftpanels) and 1000 fb − (right panels). Benchmarks excluded by the analysis are shown in orange, while theallowed ones are shown in blue. parameter ∆ m , the behaviour is the same as in the exclusion plots. For a given m (cid:101) τ value, theefficiency of the search strategy increases for smaller ∆ m values.As we did in Section 4.1, we can interpolate the obtained results and show them in contour-lineplots. In Fig. 10 the contour-line plot of the exclusion potential at 95% C.L. in the [ m A , m ˜ τ ]plane is depicted. In this figure the dark gray area represents the exclusion region for L = 100 fb − ,while the light gray area corresponds to L = 1000 fb − . We can observe that the search strategyis able to exclude the region with m A ≤
850 GeV. This region is slightly increased to m A ≤ L = 1000 fb − . Above these masses, the search strategy excludes in general average staumasses that are greater than 275-290 GeV and 250-275 GeV for L = 100 fb − and L = 1000 fb − ,respectively. As in the case of Scenario I, the proposed search strategy is not sensitive to the regionof low values of stau masses due to the specific kinematic variables that drive its discriminationpower.In Fig. 11 we show a similar contour-line plot as in Fig. 10 but for the signal significancesat L = 100 fb − (left) and L = 1000 fb − (right). The dark (light) gray area corresponds tosignificances at the discovery (evidence) level. For L = 100 fb − the evidence level is reached formasses m A ≤
825 GeV regardless the value of m (cid:101) τ , while for masses above 825 GeV the averagestau mass needs to be larger than 300 GeV. For values of m A below ∼
780 GeV significances at16
00 900 1000 1100 1200 m A [GeV]100200300400500600 m ˜ τ [ G e V ] √ s = 14 TeV and L = 100 fb − S < σ σ < S < σ S > σ
800 900 1000 1100 1200 m A [GeV]100200300400500600 m ˜ τ [ G e V ] √ s = 14 TeV and L = 1000 fb − S < σ σ < S < σ S > σ m [GeV]150200250300350400450500550 m ˜ τ [ G e V ] √ s = 14 TeV and L = 100 fb − S < σ σ < S < σ S > σ m [GeV]150200250300350400450500550 m ˜ τ [ G e V ] √ s = 14 TeV and L = 1000 fb − S < σ σ < S < σ S > σ Figure 9: Signal significance in the [ m A , m ˜ τ ] plane (top) and [∆ m , m ˜ τ ] (bottom), within Scenario II fora center-of-mass energy of √ s = 14 TeV and total integrated luminosities of 100 fb − (left panels) and 1000fb − (right panels). Benchmarks with significances below the evidence level ( S < σ ), between the evidencelevel and the discovery level (3 σ < S < σ ) and above the discovery level ( S > σ ) are shown in red, blueand green, respectively. the discovery level are obtained within all the considered m (cid:101) τ range. It is interesting to note thatthe discovery contour line drastically grows towards large values of m (cid:101) τ for m A > m A , stau masses above 450 GeV are required in order to reach5 σ significances (see the upper left panel of Fig. 9). For L = 1000 fb − the 3 σ region extends to m A ∼
850 GeV regardless the value of m (cid:101) τ , and for m A ≥
850 GeV significances at the evidencelevel are obtained for m (cid:101) τ above 275-290 GeV. By looking at the 5 σ contour line, we concludethat significances at the discovery level can be obtained for m A <
815 GeV for any m (cid:101) τ withinthe range under study. Moreover, larger masses can still reach significances at the discovery levelif m (cid:101) τ is approximately above 300-320 GeV. This is in contrast to the case of L = 100 fb − , wherethe region in which m A > m (cid:101) τ in order to reach the discovery level. We explore now the possibility to distinguish the two mixing scenarios once they reach the discoverylevel with our search strategy and in the specific case in which they exhibit similar relevant mass17
50 800 850 900 950 1000 1050 1100 m A [GeV]200225250275300325350375400 m ˜ τ [ G e V ]
95% C.L. limits of exclusion for √ s = 14 TeVExclusion: L = 100 fb − L = 1000 fb − Figure 10: Exclusion limits at 95% C.L. in the [ m A , m ˜ τ ] plane, within Scenario II, for a center-of-massenergy of √ s = 14 TeV and total integrated luminosities of 100 fb − (dark gray) and 1000 fb − (light gray). spectra ( m H , m (cid:101) τ , and m (cid:101) τ ). As stated above, in Scenario I the tau leptons in the final state arisefrom the decay of a pair of (cid:101) τ , while in Scenario II they originate from the decay of the pair (cid:101) τ (cid:101) τ ∗ or its conjugate ( (cid:101) τ ∗ (cid:101) τ ). Thus, the main difference between the signals associated to these scenariosrelies on the difference between the stau masses. In this sense, one may expect that kinematicvariables such as m τ T , m τ T , and m T will be sensitive to the mass splitting and therefore be wellsuited to discriminate between scenarios.Benchmark m H m (cid:101) τ m (cid:101) τ SI-7 951 GeV 367 GeV 409 GeVSI-20 1075 GeV 320 GeV 388 GeVSII-47 951 GeV 367 GeV 409 GeVSII-82 1099 GeV 352 GeV 583 GeV
Table 5: List of the relevant parameters of the four benchmarks used for the comparison between ScenariosI and II.
In order to establish the extent of the above statement, we will compare the two stau mixingscenarios by considering two benchmarks belonging to Scenario I and two ones corresponding toScenario II. The relevant parameters of these four benchmarks are listed in Table 5. Note that thebenchmarks SI-7 and SII-47 have the same relevant mass spectrum whereas this is not the case forSI-20 and SII-82. However, we can justify the use of this pair for the sake of comparison as follows.First of all, for Scenario I, the considerable difference in the value of m (cid:101) τ is not relevant since onlythe light stau contributes to the process, and then a benchmark belonging to it with exactly thesame value of m (cid:101) τ than the benchmark SII-82 would have exactly the same distributions as theSI-20. Second, the differences in m H (24 GeV) and m (cid:101) τ (32 GeV) are significantly smaller than themass splitting present in SII-82 (231 GeV) and then will not affect the main conclusions arising18
50 800 850 900 950 1000 1050 1100 m A [GeV]200225250275300325350375400 m ˜ τ [ G e V ] Significance for √ s = 14 TeV and L = 100 fb − Significance: σ σ
750 800 850 900 950 1000 1050 1100 m A [GeV]200225250275300325350375400 m ˜ τ [ G e V ] Significance for √ s = 14 TeV and L = 1000 fb − Significance: σ σ Figure 11: Signal significance in the [ m A , m ˜ τ ] plane, within Scenario II, for a center-of-mass energy of √ s = 14 TeV and total integrated luminosities of 100 fb − (left panel) and 1000 fb − (right panel). Thedark green and light green areas correspond to significances at the evidence level (3 σ ) and at the discoverylevel (5 σ ). from the comparison between the distributions.In Fig. 12 we show the distributions corresponding to m τ T , m τ T , and m T after applying the cutsof our search strategy (see Table 3). On the left panels (right panels) we compare the distributionsof the benchmarks SI-7 and SII-47 (SI-20 and SII-82). In the case of benchmarks SI-7 and SII-47, wesee that out of the three considered variables only the m τ T exhibits some sensitivity to the mixingpattern, with the peaks of the distributions of SI-7 and SII-47 shifted by approximately 80 GeV.The difficulty to distinguish these two benchmarks comes from the fact that the splitting betweenthe stau masses in SII-47 (∆ m = 42 GeV) is too small to produce traceable changes in distributionsbased on the tau leptons in the final state. The case of the benchmarks SI-20 and SII-82 is morepromising since now the mass splitting is significantly higher (∆ m = 231 GeV). In fact, as wecan see from the right panels of Fig. 12, not only the m τ T distributions are shifted but also boththe m τ T and m T distributions present different endpoints according to the benchmark. The m τ T distribution for SI-20 has an endpoint in ∼
400 GeV, while for SII-82 the distribution extends until ∼
600 GeV. Thus, a cut such as m τ T >
350 GeV rejects the majority of SI-20 events while retaininga significant number of SII-82 events. The same behaviour occurs in the m T distributions, withthe endpoint being ∼
275 GeV for SI-20 and around 475 GeV for SII-82. Again, we see that bymeans of requiring m τ T to be above 275 GeV, we are able to get rid off all the SI-20 events while stillkeeping a substantial amount of SII-82 events. As expected, we see that the higher the stau masssplitting the better the chance of distinguishing between mixing patterns through the inspection ofkinematic distributions in the proposed signal region. For the two comparisons between scenarios presented in this section we have also explored many other distri-butions of variables such as E miss T , | p τ T /p τ T | , m ττ or ∆ R ( τ , τ ). Since none of these distributions has proven to beuseful to discriminate between the stau mixing scenarios we do not include any results in this regard.
00 300 400 500 600 700 800 m τ T [GeV]0 . . . . . . F r a c t i o n o f e v e n t s SI-7SII-47
200 300 400 500 600 700 800 m τ T [GeV]0 . . . . . . . F r a c t i o n o f e v e n t s SI-20SII-82
150 200 250 300 350 400 450 500 m τ T [GeV]0 . . . . . . . . F r a c t i o n o f e v e n t s SI-7SII-47
200 300 400 500 600 700 m τ T [GeV]0 . . . . . . . . F r a c t i o n o f e v e n t s SI-20SII-82
150 200 250 300 350 400 m T [GeV]0 . . . . . . . . . F r a c t i o n o f e v e n t s SI-7SII-47
150 200 250 300 350 400 450 500 m T [GeV]0 . . . . . . F r a c t i o n o f e v e n t s SI-20SII-82
Figure 12: Distributions of the kinematic variables m τ T , m τ T and m T (from top to bottom) after applyingthe cuts listed in Table 3 for benchmarks SI-7 and SII-47 (left panels) and SI-20 and SII-82 (right panels). Conclusions
In this paper we have proven that our stau pair search strategy, developed in [20] and applied to atype of MSSM scenario in the large-tan β regime with large stau mixing, dominated by decays ofthe heavy CP-even Higgs H to a pair of lightest staus, (cid:101) τ (cid:101) τ ∗ (Scenario I), is also very efficient in thecomplementary scenario in which decays of both the CP-even and CP-odd heavy Higgs contributemainly to the production of (cid:101) τ (cid:101) τ ∗ + c.c pairs (Scenario II), and focusing also on the stau decays thatdrive to final states made up of a τ -lepton pair and a large amount of missing transverse energy.This search strategy, with a luminosity of L = 100 fb − , allows us to set exclusion limits atthe 95% C.L. for most of the [ m H , m (cid:101) τ ] parameter space of Scenario I, if m H <
930 GeV and m (cid:101) τ >
260 GeV. With a HL-LHC luminosity of 1000 fb − the search strategy is able to exclude thewhole Scenario-I area comprised by heavy-Higgs masses between 750 GeV and 1100 GeV and staumasses between 200 GeV and 450 GeV. On the other hand, for L = 100 fb − , we can reach signalsignificances at the evidence level if m H <
850 GeV regardless the value of the stau mass (withinthe considered range). If one requires discovery level significances, stau masses above 350 GeV areneeded. For L = 1000 fb − , our analysis is sensitive to most of the considered area in the [ m H , m (cid:101) τ ] plane, although not enough to reach the region with m H >
900 GeV and m (cid:101) τ <
260 GeV.With regard to Scenario II, the search strategy excludes the region with m A ≤
850 GeV at the95% C.L with L = 100 fb − . This region extends slightly to m A ≤
870 GeV for L = 1000 fb − .Above these masses, the search strategy sets 95% C.L exclusion limits for average stau masses thatare greater than 275-290 GeV (250-275 GeV) for L = 100 fb − ( L = 1000 fb − ). Considering aluminosity of 100 fb − , significances at the discovery level are obtained for masses m A ≤
780 GeVregardless the value of m (cid:101) τ , while for masses above 780 GeV the average stau mass needs to belarger than 300-320 GeV or even higher ( ∼
450 GeV) when m A is above 1090 GeV. In the caseof the HL-LHC with L = 1000 fb − , 5 σ significances can be reached for m A <
815 GeV for any m (cid:101) τ within the range under study. In addition, larger masses can still give rise to discovery-levelsignificances if m (cid:101) τ is approximately above 300-320 GeV.Finally, under the assumption that the LHC will be able to discover staus by means of our searchstrategy, we have outlined the potential for discriminating between the two possible scenarios of staumixing within the large-tan β regime, when they share the same relevant mass spectrum and bothreach 5 σ significances with our search strategy. We have shown that kinematic cuts in variablessensitive to the stau mass splitting, such as m τ T , m τ T , and m T , may be useful to discern which ofthese two types of MSSM scenario is realized in nature. By comparing two pairs of benchmarks,one with ∆ m = 42 GeV and the other with ∆ m = 231 GeV, we have illustrated the fact that thediscrimination power of these variables depends essentially on how large the mass splitting is.As a main conclusion, we can say that our search strategy is really efficient for the discovery orfor the exclusion of heavy (scalar or pseudoscalar) Higgs bosons decaying into a stau pair. Froma more general point of view, our collider analysis could be applied to any process at the LHCwith the resonant production of a pair of charged scalars which decay into a tau lepton and adark-matter candidate, resulting in final states with a τ -lepton pair plus a large amount of E miss T . Acknowledgments
The work of EA is supported by the “Atracci´on de Talento” program (Modalidad 1) of the Co-munidad de Madrid (Spain) under the grant number 2019-T1/TIC-14019. This work has beenalso partially supported by CONICET and ANPCyT under projects PICT 2016-0164 (EA, AM,NM), PICT 2017-2751 (EA, AM, NM), PICT 2017-2765 (EA), and PICT 2017-0802 (AM). VMLacknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research Founda-21ion) under Germany‘s Excellence Strategy – EXC 2121“Quantum Universe” – 390833306. VMLthanks warmly IFLP in La Plata for kind hospitality hosting him during the completion of thiswork.
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