Discovering the constrained NMSSM with tau leptons at the LHC
aa r X i v : . [ h e p - ph ] N ov LPT Orsay 10-79
Discovering the constrained NMSSM with tau leptonsat the LHC
Ulrich Ellwanger , Alice Florent , Dirk Zerwas Laboratoire de Physique Th´eorique, UMR 8627, CNRS and Universit´e Paris-Sud 11,Bˆat. 210, F-91405 Orsay, France LAL, Universit´e Paris-Sud 11, CNRS/IN2P3, Orsay, France
Abstract
The constrained Next-to-Minimal Supersymmetric Standard Model (cNMSSM)with mSugra-like boundary conditions at the GUT scale implies a singlino-like LSPwith a mass just a few GeV below a stau NLSP. Hence, most of the squark/gluinodecay cascades contain two τ leptons. The gluino mass > ∼ . > ∼ τ lepton. This dedicated analysis allows to improve on the results of genericsupersymmetry searches for a large part of the parameter space of the cNMSSM. Thedistribution of the effective mass and the signal rate provide sensitivity to distinguishthe cNMSSM from the constrained Minimal Supersymmetric Standard Model in thestau-coannihilation region. Introduction
The Next-to-Minimal Supersymmetric Standard Model (NMSSM, for recent reviews see [1,2]) provides an elegant solution to the µ -problem of the Minimal Supersymmetric StandardModel (MSSM) [3]: after the replacement of the µ -term in the superpotential of the MSSMby the coupling to a gauge singlet superfield S , the superpotential is scale invariant and theonly dimensionful parameters in the Lagrangian are soft Supersymmetry (SUSY) breakingterms.After electroweak symmetry breaking, all components of the gauge singlet superfield S mix with the components of the MSSM-like Higgs doublet superfields H u and H d . Accord-ingly NMSSM specific phenomena can take place in the CP-even Higgs sector, the CP-oddHiggs sector and the neutralino sector. In this paper we concentrate on the neutralinosector, where the 5th singlet-like neutralino (in addition to the two neutral higgsinos, theneutral wino and the bino) can be the Lightest Supersymmetric Particle (LSP) [4–8] and, si-multanously, give rise to a dark matter density in agreement with WMAP constraints [9–14].Such a scenario is not far fetched: A conceptually simple origin of soft SUSY breakingterms is a minimal coupling to supergravity (with a flavour independent K¨ahler potentialand minimal gauge kinetic terms), and the assumption of spontaneously broken SUSY ina hidden sector. Then, the soft SUSY breaking terms are universal at the Planck scale(not far from the GUT scale) in the form of universal scalar masses m , universal gauginomasses M / and universal trilinear scalar couplings proportional to A .The correspondingly constrained NMSSM (cNMSSM) has been studied first in [15–20].Since then, the precision of the radiative corrections has been considerably improved, andthe computation of the dark matter relic density has become possible [9]. Imposing therequirement of a dark matter relic density in agreement with WMAP constraints [14] aswell as present constraints on Higgs and supersymmetric particle (sparticle) masses, theparameter space of the cNMSSM has been analysed recently in [21, 22]. (For studies ofthe semi-constrained NMSSM, where the singlet-dependent SUSY breaking parameters areallowed to be non-universal, see [12, 13, 23–25].)Within the cNMSSM, the dark matter constraints require a singlino-like LSP. The originof this phenomenon is quite easy to understand: first, the CP-even scalar singlet s has toassume a non-vanishing vacuum expectation value (vev) in order to generate the required µ -term. For this reason its SUSY breaking mass squared m S at the electroweak scale mustnot be very large; otherwise the minimum of its potential is at s = 0. Second, m S is hardlyrenormalized between the GUT and the electroweak scales, which leads to m S ∼ m withthe consequence that, in the cNMSSM, m must be small compared to M / and A .It is well known that, within the cMSSM [26], a small value of m would imply a stau( e τ ) LSP, which is not a reasonable candidate for the dark matter. In the cNMSSM, thesinglino-like neutralino χ can – and must – be lighter than the e τ for this reason. In orderfor its dark matter relic density not being too large, its mass must be only a few GeV belowthe mass of the e τ such that χ − e τ coannihilation processes are sufficiently fast [12, 21, 22].1uch a scenario would necessarily have a strong impact on sparticle searches at colliders(see [27, 28] for reviews of searches at the LHC): since the e τ is the NLSP and the singlino-like neutralino χ couples only very weakly to all sparticles, the sparticles decay first intothe e τ under the emission of at least one τ -lepton. Subsequently the e τ decays into χ + τ ,hence each sparticle decay cascade contains typically two τ -leptons. In the present paperwe study, for the first time, the corresponding implications for sparticle searches at theLHC.As discussed in [21, 22], the sparticle (and Higgs) spectrum is quite constrained in thecNMSSM, and can essentially be parametrized by M / . The present lower bounds on m e τ and the lower LEP bound of ∼
114 GeV on the CP-even Standard Model like Higgsmass require M / > ∼
520 GeV which, inspite of m < ∼
50 GeV, implies a quite heavysparticle spectrum: squark masses > ∼ > ∼ . p T as well as a large missing transverse energy E missT . The sum of the squarkand/or gluino production cross sections is, however, just ∼ M / ).Each sparticle production event in the cNMSSM will contain typically four τ -leptons inthe final state: two of the τ -leptons (those originating from e τ decays into χ + τ ) will bequite soft due to the small e τ − χ mass difference < ∼ τ -leptons from decays as χ → e τ + τ are relatively energetic.The aim of the present paper is to show that a dedicated analysis allows for muchbetter signal to background ratios for the cNMSSM than standard (generic) supersymmetricanalyses. We simulate and study signals and various Standard Model backgrounds for theLHC at 14 TeV c.m. energy, and find that the signal to background ratio is sufficientlylarge allowing for the discovery of the cNMSSM for a wide range of values of M / .Events with E missT , jets and τ -leptons could also be a signal for the (c)MSSM in theso-called stau-coannihilation region [29–33]. Since the squark/neutralino spectrum of thecMSSM is necessarily different from the cNMSSM, the combination of M eff (essentially thesum of the transverse momenta and E missT ) and the signal rate has sensitivity to distinguishthe two models.In the next section we present the spectrum of the cNMSSM. In section 3 we discuss thesignal, backgrounds and appropriate cuts. Details of the simulation of the cNMSSM signaland the Standard Model backgrounds, the effect of cuts, and the resulting cross sections andsignal to background ratios are given in section 4. Section 5 is devoted to the comparisonof the cNMSSM with the cMSSM, and Section 6 to conclusions and an outlook. The NMSSM with a scale invariant superpotential W [1, 2] differs from the MSSM throughthe replacement of the µ term in W MSSM by the coupling to a gauge singlet superfield S and a trilinear S self-coupling: W MSSM = µH u H d + . . . → W NMSSM = λSH u H d + κ S + . . . , (2.1)2here we have omitted the quark/lepton Yukawa couplings. Hence, if the vev s of S isnon-zero (induced by the soft SUSY breaking terms), an effective µ term µ eff = λs of thedesired order of magnitude is generated and solves the µ problem of the MSSM [3].Apart from the Yukawa couplings in the superpotential and the gauge couplings, theLagrangian of the NMSSM depends on soft SUSY breaking scalar masses for the Higgsfields H u , H d and S , the squarks and the sleptons; trilinear couplings among the scalars(proportional to the couplings in the superpotential); and gaugino masses for the bino ( M ),the winos ( M ) and the gluino ( M ). Assuming supersymmetry breaking from a hiddensector in minimal supergravity (mSUGRA), the SUSY breaking terms are assumed to beuniversal at the scale of grand unification (near the Planck scale) and denoted as m , A and M / , respectively. Hence the parameters of the corresponding cNMSSM are, apartfrom the gauge and quark/lepton Yukawa couplings, m , A , M / , λ and κ . (2.2)It is convenient to fix κ from the requirement that the Higgs vevs h u and h d generate thecorrect value of M Z .As mentioned in the introduction and discussed in detail in [21, 22], the remainingparameters in (2.2) are strongly constrained: m must be small such that the vev s is non-zero. A small non-zero value for m affects essentially only the singlet-like CP-even Higgsmass [22], which is irrelevant for the present study; hence we assume m = 0 in the following.In order to avoid a e τ LSP, the singlino (the fermionic component of S ) must be lighter suchthat e τ is the NLSP. The singlino relic density can be reduced to an amount compatiblewith WMAP constraints, if its co-annihilation rate with the e τ is large enough, i.e. if thecorresponding mass difference is sufficiently small. This fixes A ∼ − M / [21,22]. Finally λ must also be quite small, since λ induces mixings in the CP-even Higgs sector betweenthe doublet- and singlet-like Higgs states: if the singlet-like Higgs state is heavier than the(Standard Model like) Higgs state h , the mass of h falls below the LEP bound of ∼
114 GeVif λ is too large; if the mass of singlet-like Higgs state is below m h (below 114 GeV as for thepoint P520 in Table 1 below), its coupling to the Z boson violates again LEP bounds [34]for λ too large. All in all one finds λ < ∼ .
02 [21, 22] (but λ > ∼ − in order still to allowfor singlino- e τ co-annihilation). λ induces also mixings between the singlet-like neutralino and the MSSM-like neutralinos(bino, neutral wino and higgsinos). For λ < ∼ .
02, these mixings are very small. Hence thecouplings of the singlino-like LSP χ to all MSSM-like sparticles (squarks, gluino, sleptons,charginos and neutralinos), which are induced by these mixings, are very small as well.Accordingly branching ratios of all these sparticles into the singlino-like LSP are negligiblysmall, unless a decay into χ is the only decay possible. Due to R-parity conservation thisis the case for the NLSP, the e τ . Hence sparticle decay cascades proceed as in the MSSM(with a spectrum as in the cNMSSM, but without the singlet-like states) until the e τ NLSPis produced. Depending on λ , the width of the final decay e τ → χ + τ can be so small,that the e τ decay vertex is visibly displaced [22]. This case (where the displaced vertexcorresponds to the production of a soft τ -lepton) could be another interesting signature forthe cNMSSM, but subsequently we will not assume that λ is so small that this phenomenonoccurs. 3oncerning the remaining parameter M / , we find that the LEP constraints on theHiggs sector require M / > ∼
520 GeV. Then, all bounds on sparticle masses from collidersas well as constraints from B-physics are satisfied. For the calculation of the spectrumwe use the code NMSPEC [23] within NMSSMTools [35, 36], updated including radiativecorrections to the Higgs sector from [37]. The dark matter relic density is computed withthe help of micrOMEGAs [9]. Clearly, very large values of M / are generally disfavouredby fine-tuning arguments; moreover, smaller values of M / < ∼ M / ≤ A , tan β = h u /h d and µ eff ( A is determined by the correct dark matter relicdensity, whereas tan β and µ eff are obtained as output) as well as the Higgs and sparticlespectra for M / = 520 , ,
800 GeV and 1 TeV for m = 0 and λ = 0 . m e τ − m χ < ∼ τ -leptons from thedecay e τ → χ + τ are necessarily soft. τ -leptons from the decay χ → e τ + τ (where χ isdominantly bino-like) profit at least from m χ − m e τ ∼
70 GeV (for P520), or more energyfrom the decays of other sparticles into e τ . Note that right-handed sleptons e e R and e µ R decay essentially via the three-body channel as e e R → e + e τ + τ . In fact, apart from theNMSSM-specific decay e τ → χ + τ (with a branching ratio of 100 %), the correspondingsparticle decay branching ratios can be obtained from the code SUSY-HIT [38] and theMSSM with a corresponding spectrum, which is used for the simulations of events below.At the LHC, the dominant sparticle production processes are of course squark-gluinoand squark-(anti-)squark pair productions. Subsequently a typical squark decay cascadelooks like e q → q + χ → q + τ + e τ → q + τ + τ + χ , (2.3)but many more possibilities exist. Their simulation, together with the simulation of Stan-dard Model background processes, will be discussed in the next sections. As for most SUSY models, the production of squarks of the first generation and of gluinoswill be the dominant sparticle production processes at the LHC. Their total productioncross sections are obtained at NLO (QCD) from PROSPINO [39], and are also shown inTable 1. The dominant contributions originate from squark + gluino production ( ∼ ∼ ∼ ∼ ∼
19% to the totalsparticle production cross sections.The dominant background processes for SUSY searches are well-known: top-antitoppair production, W+n-jet production, Z+n-jet production, W+Z production and WW+n-jet production. Since we will compare the performance of our simulation with the resultsof standard SUSY searches by ATLAS [40], we assume the same production cross sectionsfor these background processes as in [40] (given in Table 2 below).Given that gluinos (whose decay generates typically two hard jets) are even somewhatheavier than the first generation squarks (generating typically one hard jet), we require at4520 P600 P800 P1000 M / (GeV) 520 600 800 1000 A (GeV) -142 -166 -225 -282tan β µ eff (GeV) 666 757 977 1190 m h (GeV) 100 115 117 118 m h (GeV) 115 118 159 199 m h (GeV) 654 738 937 1127 m a (GeV) 174 203 275 345 m a (GeV) 654 738 937 1127 m h ± (GeV) 667 751 951 1140 m χ (GeV) 142 166 225 282 m χ (GeV) 215 250 338 427 m χ (GeV) 404 471 636 801 m χ , (GeV) 680 770 990 1200 m χ ± (GeV) 404 471 636 801 m χ ± (GeV) 684 773 992 1203 m ˜ g (GeV) 1192 1361 1777 2187 m ˜ u L (GeV) 1082 1234 1607 1973 m ˜ u R (GeV) 1044 1189 1546 1895 m ˜ d L (GeV) 1085 1237 1609 1974 m ˜ d R (GeV) 1040 1184 1539 1886 m ˜ t (GeV) 825 947 1246 1538 m ˜ t (GeV) 1032 1165 1492 1816 m ˜ b (GeV) 973 1109 1444 1772 m ˜ b (GeV) 1020 1158 1496 1826 m ˜ e L (GeV) 347 399 527 654 m ˜ e R (GeV) 196 224 296 368 m ˜ ν l (GeV) 338 391 521 650 m ˜ τ (GeV) 147 171 229 286 m ˜ τ (GeV) 353 403 525 647 m ˜ ν τ (GeV) 332 383 509 633 σ (pb) 1.36 0.70 0.134 0.035Table 1: Input parameters, tan β , µ eff and low-energy spectra for four points of thecNMSSM with m = 0 and λ = 0 . E missT .For the τ -leptons we consider their hadronic decays only. For their transverse momentawe require at least 30 GeV, which allows to assume an efficiency of ∼
40% [40] (and a τ -fakerate of jets of ∼ − τ -leptons perevent are sufficiently energetic and the total signal cross sections are already quite small,we require one identified τ -lepton only.Additional standard cuts are a lower limit on the angle ∆Φ between the hard jets and E missT , as well as a cut on the transverse mass M T formed from E missT and the identified τ -lepton (in order remove semileptonically decaying W+jets events). Altogether, the list ofour cuts is given by:1. At least two jets, one with p T >
300 GeV and one with p T >
150 GeV2. E missT >
300 GeV3. At least one τ -lepton with p T >
30 GeV4. ∆Φ( j i , E missT ) > . M T >
100 GeV, where M T is computed from the visible momenta of the hardest τ -lepton and E missT .Below we will denote this set of cuts as cNMSSM analysis. Both the signal and the top quark background were generated by PYTHIA 6.4 [41], whichwas in charge of generation and phase-space decays. PYTHIA performed the parton show-ering as well as the matching procedure according to the MLM prescription including initialand final state radiation. TAUOLA [43–45] was employed for the τ -decays. All other back-grounds (involving at least one W or Z-boson) were generated with ALPGEN [42]. In orderto keep the statistics manageable, preselection cuts were applied on the ALPGEN sam-ples. Since event generation was performed by leading order generators, the cross sectionswere scaled according to the NLO cross sections in Table 1 for the signal, as in [40] to theNLO+NLL calculation for top production, and to NLO (or NNLO level, where available)for electroweak boson(s) production.For the detector simulation we employed AcerDet [46]. AcerDet is a fast detector sim-ulation which provides a reasonable description of the performance of an LHC detector.The events generated by PYTHIA and ALPGEN+PYTHIA were all passed through Ac-erDet. AcerDet reconstructs jets, leptons and the missing transverse energy, it also labelsthe origin of the jets, e.g., those coming from a tau lepton. The efficiency and the corre-sponding background rejection for a working point of 40% τ identification efficiency wereimplemented at reconstruction level.One of the issues to be checked is the energy of the reconstructed tau-jets. For thisinitial check we used PYTHIA to produce Z bosons and their subsequent decay to tauleptons. The hadron-hadron as well as the lepton-hadron final states were reconstructed6nd compared to the results of the ATLAS collaboration presented in [40]. Reasonableagreement at the level of a few percent (about 3 GeV) was found.A fast detector simulation as AcerDet will not be able to simulate the non-Gaussiantails, e.g., in the transverse missing energy distribution. Simulation and reconstructionresults without full detector simulation and reconstruction are therefore not expected tobe perfectly reproduced. To get a feeling of how well the background can be modeled withAcerDet, two signatures of Ref. [40] have been implemented and analysed in addition to thededicated cNMSSM analysis: the four-jet SUSY search (4j0l) and the SUSY search with atleast one tau in the final state (4jtau).Events cross section (pb) 4j0l (fb) 4jtau (fb) cNMSSM (fb)tt 2110000 833 350 ±
12 50 ± ± ± ± ±
16 9.6 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
21 61 ± ± j i , E missT ), the remaining QCD background was found to be small in [40]. In ourcase, QCD events could pass the cNMSSM cuts only if a very large value of E missT and a τ -lepton would be faked simultaneously. Assuming a jet → τ fake rate up to ∼
2% (for anacceptance of 40%), and that the suppression rate of QCD events without missing energyfor E missT ) >
150 GeV is 1% [40] while we cut at 300 GeV, we should be safe of the QCD7ackground.Whereas the two ATLAS analyses are designed to cover a large variety of supersym-metric signals, the signatures discussed above are chosen specifically for heavy squarks andgluinos as well as τ -rich final states as in the cNMSSM. The background cross sectionsfor this analysis are shown in the last column of Table 2. The total background, alreadydecreased from the 4-jet-0-lepton to the 4-jet-tau analysis by an order of magnitude, isreduced by another factor four to ∼
16 fb.Typically the overall efficiency for all SUSY processes weighted by the cross sectionvaries between 7% and 10%. The cross section for the cNMSSM benchmark points afterall cuts are shown in Table 3 for the three analyses. The S/B ratio, the ratio S/ √ B for anintegrated luminosity of 1 fb − as well as for 30 fb − are shown.4j0l 4jtau cNMSSMP520 1.36pb 101 ± ± ± √ B 1 fb − √ B 30 fb −
22 19 136P600 0.70pb 47 ± ± ± √ B 1 fb − √ B 30 fb − ± ± ± √ B 1 fb − √ B 30 fb − ± ± ± √ B 1 fb − √ B 30 fb − √ B for an integrated luminosity of 1 fb − and 30 fb − are shown.Table 3 clarifies the advantage of the cNMSSM cuts with respect to the general analysis:the ratio S/ √ B is 7 −
10 times larger for the cNMSSM cuts even with respect to the standard4-jet-tau signature, which originates both from the larger background suppression and thelarger efficiency on the signal. Correspondingly the cNMSSM cuts allow for a sensitivity,for a given luminosity, on a much larger part of the cNMSSM parameter space (for heaviersquarks/gluinos). The point P800 (with squark/gluino masses of 1.6/1.7 TeV) is hardlyvisible within the standard analysis even for 30 fb − , whereas the ratio S/ √ B is still ∼
18 forthe cNMSSM cuts. Only for the point P1000 (with squark/gluino masses of 1.9/2.2 TeV)a larger luminosity and/or even harder cuts seem to be required for detection.8n Figure 1 we show the spectrum of the effective mass M eff ≡ P p jetsT + P p lepT + E missT after all cuts of the cNMSSM analysis are applied, normalised to an integrated luminosityof 1 fb − . Typically, the spectrum of the effective mass peaks at a value corresponding tothe masses of the pair produced sparticles [40]. Here the maxima of M eff are shifted tosomewhat larger values due to the cuts on p jetsT and E missT . As expected, the spectrum of M eff is harder for the points with heavier squarks/gluinos. Meff/GeV0 500 1000 1500 2000 2500 3000 3500 4000 E n t r i es / G e V / f b - ProcessSMP520P600P800P1000
Figure 1: The effective mass distribution for the SM background and the cNMSSM pointsfrom Table 1, after all cuts of the cNMSSM analysis are applied, normalised to an integratedluminosity of 1 fb − .For completeness we show in Figure 2 the transverse momentum of the leading taucandidate (after the cNMSSM cuts). Modulo the rate, the spectrum of the leading taucandidate is slightly harder for the points with heavier squarks/gluinos. It is well-known that τ -rich final states from squark or gluino production would also begenerated in the so-called stau coannihilation region of the (c)MSSM [29–33]. Hence thequestion arises, by which signatures this region of the cMSSM can be distinguished fromthe cNMSSM. 9 T/GeV0 50 100 150 200 250 300 350 400 450 500 E n t r i es / G e V / f b - ProcessSMP520P600P800P1000
Figure 2: The transverse momentum distribution of the leading tau after all cuts of thecNMSSM analysis are applied, normalised to an integrated luminosity of 1 fb − .Clearly, the neutralino/ e τ spectrum of the cMSSM is different from the one of the cN-MSSM: in the cMSSM (in the stau coannihilation region, which we assume henceforth) thelighter e τ has a mass close to the bino-like neutralino LSP χ , whereas the neutralino χ is typically wino-like. At first sight, a squark decay cascade as in Eq.(2.3) is also possiblewithin the cMSSM, with corresponding replacements of the neutralinos χ and χ . How-ever, all right-handed squarks (and sleptons) would not couple to the wino-like χ , andprefer to decay directly into the bino-like χ . These decays do not lead to two τ -leptons inthe cascade. As a consequence, the τ -rich cascades hardly occur for right-handed squarkdecays, and are thus less frequent (relative to the total squark production cross section)than in the cNMSSM.On the other hand, squarks and gluinos can be considerably lighter in the cMSSM thanin the cNMSSM, since smaller values of M / – together with larger non-zero values of m – are allowed. In particular this is the case, if we look for a point in the cMSSM parameterspace with similar χ and e τ masses as the point P520 of the cNMSSM. It turns out that,for the corresponding values of M / and m (we take A = 0 for simplicity), the squarksand gluinos are considerably lighter than for the point P520. Hence we denote this pointas MSSMl (“l” for “light”). Its parameters and sparticle masses are given in Table 4 below.As indicated in the last line in Table 4, the lighter squarks and gluinos imply considerablylarger production cross sections for the point MSSMl compared to P520. As a consequence,10SSMl MSSMh M / (GeV) 360 520 m (GeV) 210 200 A (GeV) 0 0tan β
40 30 µ eff (GeV) 466 649 m h (GeV) 114 117 m χ (GeV) 146 215 m χ (GeV) 274 406 m χ , (GeV) 480 660 m χ ± (GeV) 274 406 m χ ± (GeV) 486 666 m ˜ g (GeV) 851 1191 m ˜ u L (GeV) 800 1100 m ˜ u R (GeV) 776 1062 m ˜ d L (GeV) 804 1103 m ˜ d R (GeV) 774 1058 m ˜ t (GeV) 598 843 m ˜ t (GeV) 765 1038 m ˜ b (GeV) 688 984 m ˜ b (GeV) 749 1033 m ˜ e L (GeV) 322 401 m ˜ e R (GeV) 252 280 m ˜ ν l (GeV) 312 393 m ˜ τ (GeV) 156 222 m ˜ τ (GeV) 332 405 m ˜ ν τ (GeV) 294 382 σ (pb) 9.44 1.40Table 4: SUSY breaking parameters, tan β , µ eff , sparticle spectra and total sparticle crosssections for the cMSSM points MSSMl and MSSMh.the number of events passing our cNMSSM analysis above is larger than for P520, in spiteof the absence of τ -leptons in right-handed squark decays.There exist also points in the cMSSM parameter space where the squark and gluinospectrum resembles the one of P520, implying similar production cross sections. Such pointscorrespond to larger values of M / and m ; an example is given by the point MSSMh (“h”for “heavy”), whose squark and gluino masses are similar to those of the cNMSSM pointP520 (see Table 4).The signal rates after the cNMSSM cuts for the points MSSMl and MSSMh are givenin Table 5: these are considerably larger (as compared to P520) for the point MSSMl, butsmaller for the point MSSMh in spite of the similar squark/gluino masses and hence the11imilar total sparticle cross section (see Table 4). The reason was mentioned above: right-handed squarks do not decay via τ -rich cascades and, hence, right-handed squark decaysdo not contribute to the signal after the cNMSSM analysis.4j0l 4jtau cNMSSM analysisMSSMl 9.4pb 1429 ± ± ± √ B 1 fb −
58 15 42S/ √ B 30 fb −
320 84 227MSSMh 1.40pb 242 ± ± ± √ B 1 fb − √ B 30 fb −
54 15 56Table 5: Signal expectation for the MSSM points at NLO after all cuts. 120000 events perpoint minimum were generated. The error is the statistical error.
Meff/GeV0 500 1000 1500 2000 2500 3000 3500 4000 E n t r i es / G e V / f b - ProcessSMP520P600MSSMhMSSMl
Figure 3: The effective mass distribution for the points P520, P600, MSSMl and MSSMhafter all cuts of the cNMSSM analysis are applied.The M eff spectrum for the MSSM points, together with P520, P600 and the SM back-ground, is shown in Fig. 3. First, the point MSSMl (with similar χ and e τ masses as the12oint P520) has not only a larger signal cross section as compared to P520, but we see thatits maximum of M eff is visibly shifted towards smaller values.Can we distinguish the point MSSMh from any of the cNMSSM points? Due to thesimilar squark/gluino masses as P520, MSSMh has its maximum of M eff in the same regionas P520, but a significantly smaller signal rate. The signal rate for the cNMSSM point P600of about 58 fb is still larger than 41 fb for MSSMh. (The difference is slightly larger than aconservative error of 20-30% on the theoretical cross section prediction.) On the other handwe see in Fig. 3 that the maximum of M eff for P600 is shifted towards larger values due tothe heavier squarks/gluinos: the root mean square of the distributions is about 500 GeVand the difference of the average effective mass is about 130 GeV, so that the error on theaverage effective mass for 1 fb − is about 70 GeV, i.e., about two times smaller than thedifference. The average effective mass is affected somewhat by the tails for large effectivemass. Using a simple fit of the distributions, the peak to peak difference increases slightlyto about 150 GeV providing for a stronger separation of MSSMh and P600. Any cNMSSMpoint with still heavier squarks/gluinos (such that the signal rate coincides with the one forMSSMh) will imply a maximum for still larger values of M eff . Hence, the cNMSSM pointshave either measurably larger signal rates after applying the cNMSSM cuts (if the maximaof M eff coincide with a MSSM point), or maxima at measurably larger values of M eff (if thesignal rates coincide with a MSSM point).Additionally one can compare the cross section ratios after the generic supersymmetric4j0l cut, which are 242 fb (MSSMh, where squarks are somewhat lighter than gluinos)as compared to 47 fb (P600, where gluinos are somewhat heavier than squarks). Hence,given a corresponding signal in the data, a careful comparison of both the signal rates forgeneric and dedicated searches and the maximum of M eff (possibly including in additionthe transverse momentum of the tau lepton) should allow to distinguish the cNMSSM fromthe MSSM in the stau coannihilation region. In the present paper we have proposed criteria for the search for the fully constrainedNMSSM at the LHC. In view of the relatively heavy squarks and gluinos in the cNMSSMand correspondingly small production cross sections, this task is not quite trivial. On theother hand, due to the large number of τ -leptons in the final states, signatures involvinghadronic τ decays are relatively efficient. Whereas the soft τ -leptons in the final states aredifficult to use, the requirement of at least one hard τ -lepton has a relatively large signalacceptance.Combining this requirement with relatively hard cuts on the transverse momenta of twojets and E missT as specified at the end of section 3, the signal to background ratio is signifi-cantly improved with respect to the more standard 4j0l or 4jtau analyses. This result wasobtained after simulations including detector effects and a τ acceptance, which we com-pared with and checked against the analysis of SUSY signals by the ATLAS group. Hence,already an integrated luminosity of 1 fb − (at 14 TeV c.m. energy) becomes sensitive topart of the parameter space of the cNMSSM whereas, trivially, more luminosity is requiredin case of heavier squarks and gluinos. In any case we believe that the cuts proposed here13re the most sensitive ones to the parameter space of the cNMSSM. In addition we havediscussed in how far a refined analysis employing both the signal rate and the maximum of M eff allows to distinguish the cNMSSM from the MSSM in the stau coannihilation region.In the near future the LHC is on track to accumulate an integrated luminosity of 1 fb − at 7 TeV c.m. energy at the end of 2011. We have estimated the number of signal eventsfor the point P520, if we lower the cNMSSM cuts correspondingly: for two jets we require p T >
50 and 20 GeV, respectively, and E missT >
200 GeV. We obtain about 5 signal eventspassing these cuts.For our analysis of signals of the cNMSSM at 14 TeV c.m. energy we have left asidethe presence of two soft τ leptons per event which represent, in principle, a spectacularsignature for this class of models. In some regions of the parameter space of the cNMSSM– for very small values of λ and/or a small e τ - χ mass difference – the life time of e τ can bevery small leading to displaced vertices of the decay e τ → τ + χ into these soft τ -leptons.Using dedicated track-based algorithms, the search for these soft τ -leptons originating fromdisplaced vertices is perhaps not completely hopeless.In the framework of the general NMSSM, a singlino-like LSP can be accompagnied by aNLSP different from e τ . The signatures of these scenarios would be very different from theones discussed here (depending on the nature of the NLSP), and should also be investigatedin the future. Acknowledgments
We would like to thank T. Plehn and P. Wienemann for numerous discussions, K. Mawatarifor help in interfacing PYTHIA with TAUOLA for supersymmetric models, and SebastienBinet (LAL) for his invaluable help in automizing the production of the Alpgen samples.U.E. wishes to thank the Institut f¨ur Theoretische Physik in Heidelberg, where this workwas started, for hospitality.
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