Measuring Slepton Masses and Mixings at the LHC
Jonathan L. Feng, Sky T. French, Iftah Galon, Christopher G. Lester, Yosef Nir, Yael Shadmi, David Sanford, Felix Yu
aa r X i v : . [ h e p - ph ] D ec UCI-TR-2009-11
Measuring Slepton Masses and Mixings at the LHC
Jonathan L. Feng, Sky T. French, Iftah Galon, ChristopherG. Lester, Yosef Nir, Yael Shadmi,
1, 3
David Sanford, and Felix Yu Department of Physics and Astronomy,University of California, Irvine, California 92697, USA Cavendish Laboratory, J. J. Thomson Avenue, Cambridge, CB3 0HE, UK Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel Department of Particle Physics, Weizmann Institute of Science, Rehovot 76100, Israel (Dated: November 2009)
Abstract
Flavor physics may help us understand theories beyond the standard model. In the contextof supersymmetry, if we can measure the masses and mixings of sleptons and squarks, we maylearn something about supersymmetry and supersymmetry breaking. Here we consider a hybridgauge-gravity supersymmetric model in which the observed masses and mixings of the standardmodel leptons are explained by a U(1) × U(1) flavor symmetry. In the supersymmetric sector, thecharged sleptons have reasonably large flavor mixings, and the lightest is metastable. As a result,supersymmetric events are characterized not by missing energy, but by heavy metastable chargedparticles. Many supersymmetric events are therefore fully reconstructible, and we can reconstructmost of the charged sleptons by working up the long supersymmetric decay chains. We obtainpromising results for both masses and mixings, and conclude that, given a favorable model, precisemeasurements at the LHC may help shed light not only on new physics, but also on the standardmodel flavor parameters.
PACS numbers: 13.85.-t, 11.30.Hv, 12.15.Ff, 14.60.Pq, 12.60.Jv . INTRODUCTION The study of flavor physics is interesting both because we do not understand why there issmallness and hierarchy in the standard model (SM) flavor parameters, and because flavorphysics holds a key to understanding theories beyond the SM. If supersymmetry is discoveredat the Large Hadron Collider (LHC), then studying its flavor properties — the masses andmixings of sleptons and squarks — may indeed take us a long way toward understanding theSM flavor parameters, and will also shed light on the underlying structure of supersymmetryand supersymmetry breaking. In this work, we take some new steps toward a quantitativeanalysis of the actual prospects for supersymmetric flavor measurements at the LHC, fol-lowing earlier studies of lepton flavor studies at the LHC [1, 2, 3, 4, 5, 6, 7, 8, 9]. Our goalis to answer the following questions: • How many sleptons might the LHC be able to identify? • How precisely can the masses of these sleptons be measured? • Can the flavor decomposition of these sleptons be determined?The answers to these questions may ultimately allow us to identify the correct theory oflepton flavor, which has eluded us for decades despite plentiful experimental data. Still,even these first questions are ambitious, and for this reason our objective here is not toundertake a comprehensive study of all supersymmetric models, but rather to work towardan existence proof that, in some well-motivated cases, significant progress is possible. To dothis, we will choose a favorable model to analyze.In Ref. [10], hybrid supersymmetric models were constructed in which sfermion massesreceive both flavor-conserving gauge-mediated contributions and flavor-violating gravity-mediated contributions governed by a U(1) × U(1) horizontal symmetry. These models satisfyall low-energy constraints obtained from flavor factories, and also explain all charged leptonand neutrino masses and mixings in terms of a few charge assignments under the flavor-symmetry. At the same time, the gravity-mediated effects, although subdominant, are largerthan Yukawa-generated renormalization group (RG) effects and predict significant flavormixing for sleptons and sneutrinos, with potentially striking implications for supersymmetricsignals at the LHC. In these models, the lightest supersymmetric particle (LSP) is thegravitino, and the next-to-lightest supersymmetric particle (NLSP) is metastable. We willexamine a model in which the NLSP is a charged slepton, the slepton mass splittings arelarge enough to be observable, and some flavor mixings are significant. Although we focuson this model, the techniques developed are also applicable to models with other forms ofhybrid supersymmetry breaking (see, e.g. , Refs. [11, 12]) and other similar frameworks.With a metastable slepton NLSP, there is no missing energy associated with the NLSP,and supersymmetric decay chains are, in principle, fully reconstructible. We choose a modelin which the lightest two sleptons are predominantly a selectron and a smuon. These featuresare favorable for our analysis. Other features of the model are not as favorable: the twolightest sleptons are quasi-degenerate, with a mass splitting of roughly 5 GeV; the mixingof these two sleptons is small; and one of the remaining sleptons is an almost pure stau, sothat its decays always involve taus which are hard to reconstruct.In this analysis, we will only use information from electrons and muons, and assume thattaus are not reconstructed at all. Even with this restrictive assumption, we find that one canextract quite a lot of information, including precision measurements of five slepton masses2nd one mixing angle, as well as O (1) estimates of the remaining mixing angles. We expectthat these results may be improved, perhaps significantly, in a full analysis optimized toextract information from tau events also. II. THE MODEL
We now specify the model precisely and explain its key features. In our model, sfermionmasses receive dominant flavor-conserving contributions from gauge-mediated supersymme-try breaking (GMSB) and smaller, but still significant, flavor-violating contributions fromgravity-mediated supersymmetry breaking. Note that the gravity-mediated contributionsare generically present, since they arise from generic K¨ahler potential contact terms be-tween the supersymmetry-breaking sector and the minimal supersymmetric standard model(MSSM).The size of the gravity-mediated contributions relative to the GMSB contributions is x ∼ ˜ m ˜ m ∼ N (cid:18) πM m F grav αM Pl F GMSB (cid:19) , (1)where N is the number of 5 + ¯5 messengers, M m is the messenger scale, M Pl is thePlanck scale, and α stands for either the SU(2) or U(1) fine-structure constant. F GMSB is the supersymmetry-breaking F -term associated with gauge-mediation. In addition, thesupersymmetry-breaking sector typically contains other F terms as well, and the gravity-mediated contributions are determined by F = F + P F i , where F i are the non-GMSB F -terms. If these other F i are negligible compared to F GMSB , Eq. (1) reduces to x ∼ ˜ m ˜ m ∼ N (cid:18) πM m αM Pl (cid:19) . (2)For the gravity contributions to be significant, either M m must be not far below αM Pl , orsome F i ’s must be larger than F GMSB .In the models we consider, we choose x <
1, so that the lightest supersymmetric particle(LSP) is the gravitino, with mass m ˜ G ∼ √ x m NLSP . The NLSP will be generically long-livedin these models even for a low messenger scale, since then its decays to the gravitino aresuppressed by the large F grav .The identity of the NLSP in these models is determined by the number of messengerfields N . For small N it is a neutralino, and for large N it is a charged slepton. We wouldlike the NLSP to be a charged slepton, with a large enough mass splitting between thelightest neutralino and the NLSP that neutralino decays to the NLSP are observable. Forvery high messenger scales, however, this requires a very large N [13]. As an alternative,we therefore choose a moderate messenger scale M m ∼ GeV, and assume additional F i ’sso that F GMSB ≪ F grav .For the gravity-mediated contributions, the constraints from low-energy flavor-changingneutral current decays, such as µ → eγ , imply that large slepton mixing is possible only ifthere is strong degeneracy, while large mass splittings require a rather precise lepton-sleptonalignment. We assume that the Froggatt-Nielsen (FN) mechanism [14] governs the flavorstructure of the gravity-mediated contributions [15]. As has been shown in Ref. [10], thereare many possible scenarios that satisfy these constraints. We are particularly interestedin models where the mass splitting between slepton generations is at least a few GeV, so3hat ATLAS/CMS will perhaps be able to measure it, and where at least some sleptonmass eigenstates have appreciable components of both electron and muon flavors, so thatATLAS/CMS will have the potential of observing mixing.Model B of Ref. [10] is optimal for our purposes. First, it has x ∼ .
1, so that the sleptonmass splittings, which are generically √ x times the slepton mass, can easily be larger than10 GeV. Second, the flavor mixing, determined by a U(1) × U(1) horizontal symmetry, issignificant. Schematically, the ( e, µ, τ ) flavor decompositions of the slepton mass eigenstatesare ˜ ℓ ∼ ( λ , , ℓ ∼ ( λ , , ℓ ∼ (1 , λ , λ )˜ ℓ ∼ ( λ , λ , ℓ ∼ ( λ , , λ )˜ ℓ ∼ (1 , λ , λ ) , (3)where λ ∼ . ℓ , the heaviest, to ˜ ℓ , the lightest. We see that there issignificant mixing in many, although not all, of the sleptons. To fully specify Model B, onemust also choose 21 O (1) coefficients, one for each independent component of the gravity-mediated contributions. We use this freedom to fix the mass ordering so that the lightersleptons are dominantly e - and µ -flavored, since this improves the prospects for precisionmass and mixing measurements.Our model, then, is completely specified by the input parameters for the GMSB “spine,”the horizontal symmetry and charge assignments of Model B, and the O (1) parametersentering the gravity-mediated sfermion mass contributions. These input parameters arelisted in Appendix A. We then give these input parameters to Spice [17], a computerprogram that determines from these parameters the masses and flavor composition of allsuperparticles, along with their flavor-general decay branching ratios.
Spice interfaces with
Softsusy [18, 19] to generate the sparticle mass spectrum, and it calls
Susyhit [20] togenerate non-flavor violating decays. The decays generated by
Spice include all possiblelepton flavor combinations for the decays of charginos, neutralinos, sleptons, and sneutrinos.All possible two-body decays are included, along with relevant three-body slepton decays ˜ ℓ → ˜ ℓℓℓ in cases where the only kinematically allowed two-body decays involve gravitinos [21].Note that, because of flavor mixing, the sleptons and leptons in these 3-body decays can,in principle, carry any flavor. Spice produces
Herwig [22, 23] and SUSY Les HouchesAccord [24] input files, which may be used to generate collider events. In this work, we use
Spice with
Softsusy
Susyhit
Spice properly accounts for full 6 × A -term contributions associated with the gravity-mediated contributions,and so the only left-right mixing is small and originates from RG evolution. Thus, the We assume that the spurion λ does not have an appreciable F -term. This may require a rather complicatedFN model [16]. IG. 1:
Slepton Mass Hierarchy.
Masses and flavor compositions of the sleptons, along with thetwo lightest neutralinos and the leptons resulting from common decay modes. Sleptons ˜ ℓ , , aredominantly right-handed, with the dotted line in ˜ ℓ demarcating a small ˜ τ L component, and ˜ ℓ , , are dominantly left-handed, with the dotted line in ˜ ℓ demarcating a small ˜ τ R component. Left-right mixing in the other sleptons is negligible. The symbols ℓ , , and ℓ a,b are used to refer toleptons produced at particular steps in the decay chain, regardless of their flavor. lighter 3 sleptons are dominantly right-handed and the heavier 3 sleptons are dominantlyleft-handed, with flavor compositions consistent with Eq. (3). Left-right mixing is small, andlimited to the stau-dominated states ˜ ℓ and ˜ ℓ . As desired, ˜ ℓ and ˜ ℓ have some ˜ e R − ˜ µ R mixingand ˜ τ R is confined primarily to ˜ ℓ . The state ˜ ℓ is dominantly ˜ e L , while ˜ ℓ , demonstrate O (1) ˜ µ L − ˜ τ L mixing.As shown in Fig. 1, the lowest lying supersymmetric states have the following hierarchy: m ˜ G ≪ m ˜ ℓ , , < m χ < m ˜ ℓ , , < m χ . (4)Here χ is the lightest neutralino, which is mostly the Bino, and χ is the second-lightestneutralino, which is, to a good approximation, the neutral Wino. The dominant decay5odes are χ → ℓ ± ˜ ℓ ∓ , , (5)˜ ℓ ± , , → ℓ ± χ (6) χ → ℓ ± ˜ ℓ ∓ , , (7)˜ ℓ ± → ℓ ± a ℓ ∓ b ˜ ℓ ± , , ℓ ± a ℓ ± b ˜ ℓ ∓ , (8)˜ ℓ ± → ℓ ± a ℓ ∓ b ˜ ℓ ± , ℓ ± a ℓ ± b ˜ ℓ ∓ . (9)These are also shown in Fig. 1. There are several noteworthy features. First, the decays of χ directly to the light sleptons ˜ ℓ , , are highly suppressed, since these sleptons are dominantlyright-handed and have no couplings to Winos. Second, the leptons in the ˜ ℓ , decays arequite soft and may be difficult to detect. Finally, the slepton-to-slepton ˜ ℓ , decays may beeither charge-preserving or charge-flipping. The charge-flipping modes are possible becausethe neutralino is a Majorana fermion, and the possibility of both kinds of decays will playa crucial role in the analysis described below. III. EVENT GENERATION
We generate our signal events for the LHC with center-of-mass energy √ s = 14 TeV using Herwig [22, 23] and pass them through a generic LHC detector simulation,
AcerDET1.0 [25]. We configure
AcerDET as follows: electrons and muons are selected with p T > | η | < .
5. Electrons and muons are considered to be isolated if they are separatedfrom other leptons and jets by ∆
R > .
4, where ∆ R = q (∆ η ) + (∆ φ ) , and if less than10 GeV of energy is deposited in a cone of ∆ R = 0 .
2. The lepton momentum resolutionswe use are parameterized from the results of Full Simulation of the ATLAS detector [26];our electrons are smeared according to a pseudorapidity-dependent parametrization, whilemuons are smeared according to the results for | η | < .
1. The leading-order two-to-twosupersymmetric cross section determined by
Herwig with CTEQ5L parton distributionfunctions is 1.154 pb. We generate 115,400 events, corresponding to 100 fb − of data. AcerDET does not take into account lepton reconstruction efficiencies. We therefore applyby hand a reconstruction efficiency of 90% to the muons and a reconstruction efficiencyof 77% to the electrons. This gives 0.86 as the ratio of electron to muon reconstructionefficiency.In a real detector or full simulation thereof, a long-lived charged slepton, such as our˜ ℓ , would be expected to produce a visible track by virtue of its charge. Measurement ofthe curvature of this track would determine the ˜ ℓ momentum . If the ˜ ℓ arrival time werealso to be measured with sufficient accuracy, the ˜ ℓ speed could also be determined. Themomentum and speed may be combined to determine the track mass , which will constitutethe primary signature for the existence of new physics ( i.e. , the ˜ ℓ ) in our signal events. AcerDET is not a full detector simulation and so, unsurprisingly, does not produce trackobjects or speed “measurements” associated with our long-lived sleptons. Strictly speaking, the curvature determines only the momentum-to-charge ratio, but we will assume unitcharges for all heavy charged tracks. ℓ are potentially very important in ourstudy, it is necessary to augment AcerDET by incorporating additional parameterizationsfor ˜ ℓ momentum and speed measurements. We used the resolutions taken from Ref. [27],based on ATLAS Muon Resistive Plate Chamber (RPC) timings. Given these results, tomodel the reconstructed ˜ ℓ momentum, we start with the momentum taken from MonteCarlo truth, and then smear the slepton’s 3-momentum magnitudes p ≡ | ~p ˜ ℓ | and speeds β by Gaussian distributions with σ p /p = 0 .
05 and σ β = 0 .
02, respectively. The slepton’senergy and direction are not smeared. Note that we could just as easily have used anotherparametrization based on ATLAS Muon Drift Tube (MDT) fits [28]. Our use of just onesuch source of timing information might therefore mean that our speed resolution can beimproved in a future study. We only consider sleptons with β > . β ,greater than 0.6.Having parametrized the slepton reconstruction process above, subsequent uses of ex-pressions like “˜ ℓ momentum” and “ β ” refer to the smeared (supposedly reconstructed)quantities rather than to Monte Carlo truth. IV. ANALYSIS
In this section we outline our approach to measuring the mixings and masses of the sixsleptons. As our NLSP is a metastable charged particle, our entire decay chain is, in prin-ciple, fully reconstructible. Our goal is therefore to reconstruct the various superpartners,starting with the slepton NLSP, by working our way up the decay chain, constructing vari-ous invariant mass distributions. In this section we explain each invariant mass distributionand in the next section we interpret the results in terms of mixings and masses.As explained in Sec. I, in this analysis we ignore tau leptons, and instead only considerwhat we can deduce about masses and mixings from observing electrons and muons. Wemake this choice because tau reconstruction is expected to be poor in comparison to electronand muon reconstruction, but the inclusion of tau reconstruction certainly merits furtherstudy.
A. Reconstructing the slepton NLSP ˜ ℓ In each event, direct reconstruction of the ˜ ℓ momentum, speed, and mass is expectedto be relatively straightforward, using the slow charged track signature already describedin Sec. III. We restrict our attention to sleptons with speeds in the range 0 . < β < . ℓ mass measurement. Of the sleptons with β > .
6, 15% have β < . β limit. As expected,even ignoring background that will enter the β > . / ndf χ ± ± ± ) (GeV) l~m(
80 100 120 140 160 180 200 - E n t r i e s / G e V / f b × / ndf χ ± ± ± (a) β > . / ndf χ ± ± ± ) (GeV) l~m(
80 100 120 140 160 180 200 - E n t r i e s / G e V / f b × / ndf χ ± ± ± / ndf χ ± ± ± ) (GeV) l~m(
80 100 120 140 160 180 200 - E n t r i e s / G e V / f b × / ndf χ ± ± ± (b)0 . < β < . FIG. 2:
Reconstructed ˜ ℓ Mass Distributions.
Reconstructed ˜ ℓ masses from events with sleptonspeed (a) β > . . < β < .
8. The histograms are the distributions, and the solid linesare Gaussian fits with means and standard deviations as indicated. The Gaussian fit for (a) ispoor and is shown for comparison purposes only, as described in the text. The ˜ ℓ ’s 3-momentummagnitudes p ≡ | ~p ˜ ℓ | and speeds have been smeared by Gaussian distributions with σ p /p = 0 . σ β = 0 .
02, respectively. . < β < .
8, we assume that the efficiency for reconstructing ˜ ℓ is 100%, and we do notrequire these sleptons to pass any isolation criteria.Figure 2 tells us two valuable things. First, for any given event, the slepton mass ismeasured to an accuracy of the order of 10 GeV. Second, from taking all of the eventstogether, the statistical error on the mean mass is much smaller, of the order of 0.1 GeV.The strong agreement between the underlying ˜ ℓ mass and the fitted mean reconstructed˜ ℓ mass in Fig. 2 is perhaps misleading. Such agreement was to be expected as no sourcesof systematic offsets were introduced in our smearing process. Realistically, the fitted meanreconstructed ˜ ℓ mass will be subject to some systematic offset, even after all attempts tocalibrate the detector have been completed. The size and direction of such an offset cannotbe known in advance, so we do not attempt to simulate any systematic offset in this analysis.We can make use of the high precision (mean) mass measurement from the set of allevents to help us remove some of the momentum and time-of-flight measurement errors inindividual events, thereby reducing our exposure to the 10 GeV event-by-event variability inreconstructed slepton masses. We do this by scaling each component of the four-momentumof every slow charged track by a constant so that the track mass matches the mean massobtained from the fit to all events. After rescaling, the smeared and rescaled momentum iscentered on the true momentum with a full-width half-maximum of 27 GeV and rms of 9.9GeV, and the corresponding energy difference distribution has a full-width half-maximum of31 GeV and rms of 9.4 GeV. We find that this event-by-event rescaling process is necessaryto allow us sufficient resolution to travel up the decay chain and determine the masses ofsparticles heavier than the NLSP. 8 (GeV) T p E n t r i e s / G e V / , E v en t s
10 parent l~(e), T p parent l~), µ ( T p FIG. 3:
Three Body p T Distribution.
The p T distribution of leptons ℓ = e, µ from the three bodydecays ˜ ℓ → ℓℓ ˜ ℓ from Monte Carlo truth. B. Why it is impossible to directly reconstruct ˜ ℓ , The next most obvious particles to reconstruct are the next two lightest sleptons, ˜ ℓ , .We see in Fig. 1 that the dominant ˜ ℓ , decays are three-body. In principle, given anideal detector, we could reconstruct the ˜ ℓ , by looking at the three-particle invariant massdistributions resulting from combining the ˜ ℓ with all possible combinations of two furtherleptons which give a charged ˜ ℓ , candidate.Since in this analysis we are not reconstructing taus, we cannot detect ˜ ℓ in this way. Wewill briefly comment on the ˜ ℓ in Sec. IV D.Unfortunately, direct reconstruction of ˜ ℓ is also impossible as ˜ ℓ and ˜ ℓ are nearly degen-erate. In Fig. 3 we plot the true p T of all leptons produced in the three-body ˜ ℓ decays. Wesee that ∼
90% of all electrons and muons have p T <
10 GeV. Leptons with p T <
10 GeV,which we denote “soft” leptons, will be very difficult to reconstruct in ATLAS/CMS.To determine the mass and mixings of the ˜ ℓ , we must therefore rely on indirect mea-surements. These do, in fact, make a measurement of the ˜ ℓ mass possible, as we describein the next section. C. Reconstructing the lightest neutralino χ and ˜ ℓ In this section we describe the χ reconstruction, and explain how it can be used to detect˜ ℓ and measure its mass as well.Referring to Fig. 1, we see that the neutralino can decay to any one of the three lightsleptons. Let us first discuss neutralino decays to ˜ ℓ and ˜ ℓ , with the ˜ ℓ subsequently decayingto ˜ ℓ via a 3-body decay. Since the leptons involved in this 3-body decay, ℓ a,b , are typicallysoft, they will usually go undetected, so that one only observes the final ˜ ℓ and the hard9epton, ℓ , coming from the original neutralino decay. (Throughout this section, subscriptson the leptons are as shown in Fig. 1.) We therefore define two main categories of neutralinodecay — direct and indirect. The latter is further divided into two subcategories, which wename “OS indirect” and “SS indirect,” based on whether the final ˜ ℓ has the opposite orsame sign as the lepton ℓ : • Direct decays of χ to the slepton NLSP: χ → ˜ ℓ ± ℓ ∓ • Indirect decays of the χ to the slepton NLSP via ˜ ℓ , χ → ˜ ℓ ± ℓ ∓ , followed by athree-body ˜ ℓ decay of one of the following types: ◦ ˜ ℓ ± → ˜ ℓ ± ℓ ± a ℓ ∓ b OS indirect ◦ ˜ ℓ ± → ˜ ℓ ∓ ℓ ± a ℓ ± b SS indirectNote that in the instance of a direct decay, the ˜ ℓ and the lepton ℓ must be oppositelycharged, whereas in indirect decays, same-sign charges are also possible. Detection of same-sign events are direct evidence of the Majorana nature of the neutralino. As mentionedabove, with a hard lepton p T cut, only the lepton ℓ is observed.
1. Direct and OS-indirect χ decays: measuring the χ and ˜ ℓ masses For both the direct and OS indirect decays, the ˜ ℓ and the lepton ℓ have opposite signs.These channels therefore have identical signatures and are therefore reconstructed in tandem.We take all OS ˜ ℓ ± e ∓ and ˜ ℓ ± µ ∓ combinations and reconstruct the invariant masses m ˜ ℓ ± e ∓ and m ˜ ℓ ± µ ∓ .When our OS ˜ ℓ and lepton are from a direct decay, we expect to reconstruct the χ massexactly. However, when the ˜ ℓ results from an indirect decay, we do not expect to correctlyreconstruct the χ as we are missing the two soft leptons produced in the decay ˜ ℓ ± → ˜ ℓ ± ℓ + a ℓ − b .Such events nevertheless contain valuable information: as shown in Ref. [33], the ˜ ℓ -leptoninvariant mass then exhibits a “shifted peak,” somewhat lower than the neutralino mass, byan amount E shift ≃ M + m M m ∆ m . (10)Here M is the neutralino mass, the mean of the ˜ ℓ ℓ invariant mass distribution, m is thereconstructed mean of the ˜ ℓ mass, and ∆ m ≡ m ˜ ℓ − m ˜ ℓ . For our model parameters wepredict E shift ≃ . m and determine themass of the ˜ ℓ indirectly.We plot these OS slepton-lepton invariant mass distributions in Fig. 4 for both p T >
10 GeV and p T >
30 GeV. The harder p T cut effectively removes the soft leptons produced inthree-body ˜ ℓ , decays that have not already failed reconstruction from the lepton collections(see Fig. 3). We decompose these distributions (and the distributions that follow) intothe sum of an exponentially falling background and one or more Gaussian peaks. Theexponentially falling background is designed to model the combinatoric background fromsupersymmetric events. The fitting function has the form dNdm = N tot − X i f i ! ( − a i ) e a i m + X i f i s π σ i e − ( m − ¯ mi )22 σ i , (11)10 e)>30GeV T ) (GeV) p -+ e l~m(
100 120 140 160 180 200 220 240 260 280 300 - E n t r i e s / G e V / f b × = 2.55 +/- 0.04 σ a = -0.01115 +/- 0.0005 = 0.547 +/- 0.006 sig fmean = 225.10 +/- 0.04(200 to 300 GeV) = 11340.6 entries N (e)>30GeV T ) (GeV) p -+ e l~m(
100 120 140 160 180 200 220 240 260 280 300 - E n t r i e s / G e V / f b × (e)>10GeV T p (e)>30GeV T p (a) ℓ = e (e)>30GeV T ) (GeV) p -+ e l~m(
100 120 140 160 180 200 220 240 260 280 300 - E n t r i e s / G e V / f b × = 2.55 +/- 0.04 σ a = -0.01115 +/- 0.0005 = 0.396 +/- 0.010 sig fmean = 225.10 +/- 0.04(200 to 300 GeV) = 5510.71 entries N (e)>30GeV T ) (GeV) p -+ e l~m(
100 120 140 160 180 200 220 240 260 280 300 - E n t r i e s / G e V / f b × (e)>10GeV T p (e)>30GeV T p )>30GeV µ ( T ) (GeV) p -+ µ l~m(
100 120 140 160 180 200 220 240 260 280 300 - E n t r i e s / G e V / f b × = 4.1 +/- 0.1 σ a = -0.00552 +/- 0.0007 = 0.396 +/- 0.010 sig fmean = 220.6 +/- 0.1(200 to 300 GeV) = 5510.71 entries N )>30GeV µ ( T ) (GeV) p -+ µ l~m(
100 120 140 160 180 200 220 240 260 280 300 - E n t r i e s / G e V / f b × )>10GeV µ ( T p )>30GeV µ ( T p (b) ℓ = µ FIG. 4: OS ˜ ℓ ± ℓ ∓ Invariant Mass Distributions.
Invariant mass distributions of OS ˜ ℓ ± ℓ ∓ pairsfor (a) ℓ = e and (b) ℓ = µ , requiring p T >
10 GeV and p T >
30 GeV. The p T >
30 GeVdistributions in the range 200 GeV < m <
300 GeV have been fit with a Gaussian peak on topof an exponentially decaying background as given by the red (lighter) solid and purple (lighter)dashed contours, respectively. The sum of these fits is given by the blue (darker) solid line. Thefit parameters, defined in Eq. (11), are as indicated. where N tot is the total number of events in the distribution, a i is the exponential decayparameter with units of GeV − , f i is the fraction of the total number of events in peak i ,and ¯ m i and σ i are the center and width of peak i .Indeed, we see two different peaks: a higher one at 225.1 GeV in the ˜ ℓ ± e ∓ sample,corresponding to the true neutralino mass, and the lower shifted peak centered at 220.6 GeVin the ˜ ℓ ± µ ∓ sample. Of course, in the model we are considering, each one of these samplescontains both these peaks, but because of the flavor compositions of ˜ ℓ and ˜ ℓ , the ˜ ℓ ± e ∓ sample is dominated by direct decays, and therefore seems to exhibit just the unshifted peakat ∼
225 GeV, while the ˜ ℓ ± µ ∓ sample is dominated by indirect decays, and therefore seemsto exhibit just the shifted peak at ∼
220 GeV. In a general model, with larger mixings, onewould see a double-peak structure, which might be harder to disentangle. Then, however,the SS decays can come to our aid: these can only originate from indirect decays, and thuswill cleanly exhibit only the shifted peak, with no contamination from direct decays.
2. SS indirect χ decays: a clean measurement of the ˜ ℓ mass As explained above, the SS ˜ ℓ ± ℓ ± sample cleanly probes the indirect neutralino decaysthrough ˜ ℓ , and exhibits just the neutralino shifted peak. Here we take all SS ˜ ℓ ± e ± and˜ ℓ ± µ ± combinations and reconstruct the invariant masses m ˜ ℓ ± e ± and m ˜ ℓ ± µ ± . Again we doso for both p T >
10 GeV and p T >
30 GeV. The invariant mass distributions are shownin Fig. 5, and indeed, we only see the neutralino shifted peak at around 219 GeV. It is notsurprising that the peaks in these distributions are somewhat lower than the shifted peak11 e)>30GeV T ) (GeV) p +- e l~m(
100 120 140 160 180 200 220 240 260 280 300 - E n t r i e s / G e V / f b = 2.4 +/- 0.3 σ a = -0.00815 +/- 0.0005 = 0.052 +/- 0.007 sig fmean = 219.2 +/- 0.3(200 to 300 GeV) = 5072.8 entries N (e)>30GeV T ) (GeV) p +- e l~m(
100 120 140 160 180 200 220 240 260 280 300 - E n t r i e s / G e V / f b (e)>10GeV T p (e)>30GeV T p (a) ℓ = e (e)>30GeV T ) (GeV) p +- e l~m(
100 120 140 160 180 200 220 240 260 280 300 - E n t r i e s / G e V / f b σ a = -0.00815 +/- 0.0005 = 0.551 +/- 0.008 sig fmean = 219.2 +/- 0.3(200 to 300 GeV) = 7915.55 entries N (e)>30GeV T ) (GeV) p +- e l~m(
100 120 140 160 180 200 220 240 260 280 300 - E n t r i e s / G e V / f b (e)>10GeV T p (e)>30GeV T p )>30GeV µ ( T ) (GeV) p +- µ l~m(
100 120 140 160 180 200 220 240 260 280 300 - E n t r i e s / G e V / f b × = 3.36 +/- 0.06 σ a = -0.00673 +/- 0.0007 = 0.551 +/- 0.008 sig fmean = 219.39 +/- 0.06(200 to 300 GeV) = 7915.55 entries N )>30GeV µ ( T ) (GeV) p +- µ l~m(
100 120 140 160 180 200 220 240 260 280 300 - E n t r i e s / G e V / f b × )>10GeV µ ( T p )>30GeV µ ( T p (b) ℓ = µ FIG. 5: SS ˜ ℓ ± ℓ ± Invariant Mass Distributions.
As in Fig. 4, but for SS ˜ ℓ ± ℓ ± pairs. of Fig. 4b. The SS samples necessarily come from neutralino decays through ˜ ℓ , which onlyexhibit the shifted peak, whereas the OS ˜ ℓ µ sample, although dominated by such decays,also contains some events in which the neutralino decays directly to ˜ ℓ . The latter lead tothe correct neutralino peak at 225 GeV. D. Indirectly reconstructing the remaining light slepton ˜ ℓ Inspecting Figs. 4 and 5 also reveals a smaller peak around 160 GeV. It is easy to seethat this peak corresponds, at least partially, to ˜ ℓ . Consider ˜ ℓ decays to ˜ ℓ . These aredominantly ˜ ℓ → ˜ ℓ eτ . The tau decay could give another charged lepton, but this chargedlepton would typically be softer than the original electron produced in the ˜ ℓ decay. Thus,when we consider the invariant mass of this electron paired with the ˜ ℓ , we should find apeak somewhat below the ˜ ℓ mass, much like the shifted neutralino peak discussed in theprevious two sections. An analogous peak should also occur for ˜ ℓ µ pairs, coming eitherfrom direct ˜ ℓ → ˜ ℓ µτ decays, or from indirect decays through ˜ ℓ → ˜ ℓ µτ .However, this peak starts at around 140 GeV, which, as we already know, is the ˜ ℓ mass.We therefore expect another peak around 140 GeV, originating from ˜ ℓ → ˜ ℓ decays withone soft lepton. In a real detector, smearing effects would then make it hard to conclusivelyestablish the identity of the 160 GeV peak. We therefore leave the question of ˜ ℓ identificationfor future work, in which tau leptons are carefully treated. E. Reconstructing the heavy sleptons ˜ ℓ , , Once the χ is reconstructed, we can use it as a base for reaching higher up the decaychain. As evident in Fig. 1, the heavier sleptons dominantly decay through ˜ ℓ , , → χ ℓ .Since in our case no heavy slepton is purely stau, all three of the sleptons are in principle12 >30GeV µ (e, T ) (GeV) p µ )+ -+ e l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b µ (e, T ) (GeV) p µ )+ -+ e l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b (a) ( ℓ , ℓ ′ ) = ( e, µ ) )>30GeV µ (e, T ) (GeV) p µ )+ -+ e l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b µ (e, T ) (GeV) p µ )+ -+ e l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b T )+e) (GeV) p -+ e l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b T )+e) (GeV) p -+ e l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b (b) ( ℓ , ℓ ′ ) = ( e, e ) )>30GeV µ , µ ( T ) (GeV) p µ )+ -+ µ l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b µ , µ ( T ) (GeV) p µ )+ -+ µ l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b (c) ( ℓ , ℓ ′ ) = ( µ, µ ) )>30GeV µ , µ ( T ) (GeV) p µ )+ -+ µ l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b µ , µ ( T ) (GeV) p µ )+ -+ µ l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b µ ( T )+e) (GeV) p -+ µ l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b µ ( T )+e) (GeV) p -+ µ l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b (d) ( ℓ , ℓ ′ ) = ( µ, e ) FIG. 6:
OS Slepton-Dilepton Invariant Mass Distributions.
Invariant mass distributions of(˜ ℓ ± ℓ ∓ ) ℓ ′ , where the ˜ ℓ ± ℓ ∓ pair reconstructs χ as described in the text, and ( ℓ , ℓ ′ ) = (a) ( e, µ ),(b) ( e, e ), (c) ( µ, µ ), and (d) ( µ, e ). Both ℓ and ℓ ′ are required to have p T >
30 GeV. Thesedistributions in the range 250 GeV < m <
400 GeV have been fit with Gaussian peaks on topof an exponentially decaying background as given by the green (lighter) solid and purple (lighter)dashed contours, respectively. The sum of these fits is given by the blue (darker) solid line. accessible even by reconstructing only electrons and muons.We take all ˜ ℓ ± ℓ ∓ combinations lying within 2 σ of the mean of the OS ˜ ℓ ℓ invariantmass distributions of Fig. 4 and combine them with yet another lepton ℓ ′ = e, µ to obtain(˜ ℓ ± ℓ ∓ ) ℓ ′ invariant mass distributions. Here and in the following we enclose ˜ ℓ ℓ in parenthesesto indicate a ˜ ℓ -lepton pair that reconstructs the χ . We require that both ℓ and ℓ ′ have p T >
30 GeV. This essentially gives us the m χ ℓ ′ invariant mass distribution. These invariantmass distributions, with fitted peaks, are shown in Fig. 6.13 >30GeV µ (e, T ) (GeV) p µ )+ +- e l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b µ (e, T ) (GeV) p µ )+ +- e l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b (a) ( ℓ , ℓ ′ ) = ( e, µ ) )>30GeV µ (e, T ) (GeV) p µ )+ +- e l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b µ (e, T ) (GeV) p µ )+ +- e l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b T )+e) (GeV) p +- e l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b T )+e) (GeV) p +- e l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b (b) ( ℓ , ℓ ′ ) = ( e, e ) )>30GeV µ , µ ( T ) (GeV) p µ )+ +- µ l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b µ , µ ( T ) (GeV) p µ )+ +- µ l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b (c) ( ℓ , ℓ ′ ) = ( µ, µ ) ,e)>30GeV µ ( T )+e) (GeV) p +- µ l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b µ ( T )+e) (GeV) p +- µ l~ → χ m((
260 280 300 320 340 360 380 400 - E n t r i e s / G e V / f b (d) ( ℓ , ℓ ′ ) = ( µ, e ) FIG. 7:
SS Slepton-Dilepton Invariant Mass Distributions.
As in Fig. 6, but for SS slepton-dileptoncombinations (˜ ℓ +1 ℓ ) ℓ ′± and (˜ ℓ − ℓ − ) ℓ ′± . We can also take all combinations of SS ˜ ℓ -lepton pairs with invariant masses falling within2 σ of the SS primary ˜ ℓ -lepton invariant mass distribution means and combine them withanother lepton. The resulting invariant mass distributions, with fitted peaks, are plottedin Fig. 7. Again we require that both leptons have p T >
30 GeV. We know that thesecombinations give a poorer reconstruction of ˜ ℓ , , than the OS combinations, since SS ˜ ℓ ℓ pairs reconstruct not the neutralino mass but the neutralino shifted peak, but we includethese plots for completeness. Note that there is another reason why we expect these plotsto give an inferior reconstruction of the heavier sleptons compared to the OS plots of Fig. 6.The combinatoric background is larger here, since it includes ˜ ℓ plus two lepton combinationswith charges summing to either ± ±
3, whereas the OS plots only include the former.14 rue Measured Observation˜ ℓ . ± . ℓ with 0 . < β (˜ ℓ ) < . χ . ± .
04 GeV χ peak in the ˜ ℓ ± e ∓ invariant mass distribution (Fig. 4a)∆ m (˜ ℓ , ) 4.95 GeV 5 . ± .
06 GeV ˜ ℓ ± e ∓ minus ˜ ℓ ± µ ± peak positions (Fig. 4a, Fig. 5b)˜ ℓ . ± . ℓ ∓ e ± ) e invariant mass distribution (Fig. 6b)˜ ℓ ± ℓ ∓ e ± ) µ invariant mass distribution (Fig. 6a)˜ ℓ . ± . ℓ ∓ e ± ) µ invariant mass distribution (Fig. 6a) | U e /U µ | . ± . N (˜ ℓ ± e ± ) /N (˜ ℓ ± µ ± ) (Fig. 5)TABLE I: Results.
Best measurements of slepton masses and mixings in our model. The mea-surement for ˜ ℓ is given under the assumption that the excess of events we see is indeed a massresonance, and not a fluctuation of the background. F. Reconstructing the heavier neutralino χ With every step up the chain, the reconstruction errors compound, making χ recoveryharder than χ . In this analysis we do not attempt to reconstruct the heavier neutralino.Nevertheless, we note that imposing the additional constraint that some lepton combina-tions reconstruct the χ may provide additional information and allow constraints on flavormixings among the heavy sleptons. V. RESULTS
We now take our invariant mass distributions and interpret them in terms of sleptonmasses and mixings. Our best measurements of slepton masses and mixings in this model aresummarized in Table I, and the individual entries are supported by the detailed discussionsbelow.
A. The light sleptons ˜ ℓ , , and the lightest neutralino χ As explained in Sec. IV D we do not attempt to measure the ˜ ℓ mass in this analysis,although we see hints that its mass lies somewhat above 160 GeV. We therefore only presenthere measurements of the masses of ˜ ℓ and ˜ ℓ . The lack of direct observation of a thirdslepton is entirely to be expected for a spectrum with mixings such as ours, and for ananalysis not attempting to reconstruct taus.From the distribution given in Fig. 2, we measure m ˜ ℓ = 135 . ± . − , the high number of reconstructed ˜ ℓ allows us to measurethe ˜ ℓ mass with small statistical error.We expected to be able to measure the ˜ ℓ indirectly using indirect SS and indirect OS χ decays. In Fig. 4a we see the invariant mass distribution of OS ˜ ℓ e pairs. This distributionis peaked at 225 . ± .
04 GeV. We expect this peak to be a combination of pure χ fromdirect decays and off-reconstructed χ from indirect decays. The OS ˜ ℓ µ distribution ofFig. 4b peaks at a mass roughly 5 GeV lower. In Fig. 5 we see that both SS slepton-leptoninvariant mass distributions have a mean close to the lower of the two OS peak positions.15e therefore have a measurement consistent with Ref. [33]: nearly degenerate ˜ ℓ and ˜ ℓ with the ˜ ℓ having a much greater selectron component than the ˜ ℓ (seen from the minimalcontamination of the χ peak in the OS ˜ ℓ e distribution). With this hypothesis we canidentify the position of the higher peak, namely the OS ˜ ℓ e peak, as the χ . This gives us a χ mass of 225 . ± .
04 GeV.As explained in Sec. IV C 2, it is better to extract E shift from the SS distributions, asthese only come from indirect decays. From Fig. 5b, we see that the shifted peak is at219 . ± .
06 GeV. We then find E shift = 5 . ± .
07 GeV. Using Eq. (10), we then find∆ m ≡ m ˜ ℓ − m ˜ ℓ = 5 . ± .
06 GeV, and so m ˜ ℓ = 141 . ± . m ˜ ℓ is dominantly from the uncertainty in m ˜ ℓ .Since the shifted neutralino peak appears in both the ˜ ℓ ± µ ± and ˜ ℓ ± e ± invariant massdistributions, we have strong evidence that ˜ ℓ has both smuon and selectron components.Similarly, since we see peaks in both the ˜ ℓ ± e ∓ and ˜ ℓ ± µ ∓ distributions, we conclude that ˜ ℓ has both selectron and smuon components. It is still unclear whether these states also havestau components. As we will see in Sec. VI B 1, we cannot rule out this possibility, but withsome mild assumptions about the neutralino couplings to ˜ ℓ , we can show that if there arenon-zero stau components in ˜ ℓ , , they must be equal to each other.The cleanest “flavor” measurement we can extract is based on the SS shifted neutralinopeaks in Fig. 5, since these are only sensitive to ˜ ℓ . If we assume that the neutralino couplingsto the first two generations are the same, then dividing the number of events N SSe in the ˜ ℓ e peak of Fig. 5a by the number of events N SSµ in the ˜ ℓ µ peak of Fig. 5b, and adjusting forthe different reconstruction efficiencies for electrons and muons, we find the ratio of selectronto smuon components of ˜ ℓ to be | U e /U µ | = N SSe /N SSµ = 0 . ± . , (12)in good agreement with our input model.One could try to rule out a third light slepton with a selectron or smuon component,based on the absence of a clear peak in our distributions. This would support the hypothesisthat ˜ ℓ , are selectron-smuon mixtures. Indeed, the fact that we only observe one shiftedneutralino peak in the ˜ ℓ e and ˜ ℓ µ distributions indicates that there is no such third sleptonwhich is close in mass to ˜ ℓ . Furthermore, although we have not shown these distributionshere, if one does not impose the requirement that ˜ ℓ and one lepton reconstruct the neutralinopeak, there is no clear peak in the ˜ ℓ ℓℓ ′ invariant mass distributions, with ℓ, ℓ ′ = e, µ .However, the peak we see near 160 GeV makes it hard to conclusively exclude such a thirdslepton, although, as we explained in Sec. IV D, this peak seems consistent with a pure staustate with mass above 160 GeV. B. The heavy sleptons ˜ ℓ , , In principle, the invariant mass distributions of (˜ ℓ ℓ ) ℓ ′ combinations contain a lot of in-formation about ˜ ℓ , , . There is however a lot of supersymmetric background which makesthe identification of the peaks challenging. The cleanest peaks are obtained from OS com-binations (˜ ℓ ± e ∓ ) ℓ ′ , where the ˜ ℓ ± e ∓ pair reconstructs m χ , as shown in Fig. 6ab. The OScombinations (˜ ℓ ± µ ∓ ) ℓ ′ of Fig. 6cd also yield useful information, although the peaks are notas clean. Similarly, useful but not particularly clean peaks are found in the SS invariantmass distributions of Fig. 7. 16hen we consider the invariant mass distributions of χ e ± combinations for χ recon-structed from ˜ ℓ ∓ e ± (Fig. 6b), we obtain a very clear peak which identifies ˜ ℓ , with a meanvalue of 283 . ± . ℓ mass produced by considering these com-binations is questionable and contains much fewer events than the ˜ ℓ peak. The ˜ ℓ peak isnegligible. This strongly suggests that ˜ ℓ has a dominant selectron component. The invari-ant mass distributions of χ e ± combinations for χ reconstructed from ˜ ℓ ∓ µ ± (Fig. 6d) arenot as convincing, but the presence again of a dominant peak near ˜ ℓ further supports ˜ ℓ having a strong selectron component.When we consider the invariant mass distributions of χ µ ± combinations (Fig. 6a), onepeak is present, which identifies ˜ ℓ . We see an additional excess of events at a lower mass,which could be evidence for ˜ ℓ . In Fig. 7c a similar excess, shifted to lower mass, supportsthe hypothesis that this excess of events is more than just a fluctuation of the backgroundand is indeed ˜ ℓ . We have already described a lack of evidence for selectron components inthese two mass states. The mass of the clear heavier peak, ˜ ℓ , is 343 . ± . ℓ , then the peak describes a mass of 307 ± ℓ and not fluctation of thebackground.Assuming that χ is predominantly gaugino, and that ˜ ℓ and ˜ ℓ have identical quantumnumbers, the χ branching ratios to these two sleptons can only differ due to phase spaceeffects. We know that ˜ ℓ , have negligible selectron components, so can only be smuon-staumixtures. The ratio of the number of events in the ˜ ℓ peak to the number of events in the ˜ ℓ peak of Fig. 6a therefore gives the smuon-stau mixing in these states up to the phase-spacefactor. Although the compounded reconstruction errors and ignorance of systematics makeexact results from this analysis suspect, we can conclude that this mixing is O (1), if wesupport the excess of events near 307 GeV being a ˜ ℓ mass peak. VI. DISCUSSION
We now reflect on the measurements we have made and on the measurements we havebeen unable to make. In what follows, we consider how the lessons learned from consideringthis particular supersymmetry model generalize to a wider range of supersymmetric models.We also consider in this section what we might be able to deduce if, in addition to theseexperimental observations, we make the assumption that we are expecting to observe thesix slepton states of an MSSM-type model.
A. Mass Measurements
Out of the six sleptons, we have been able to identify in a rather convincing way the massesof four: ˜ ℓ , ˜ ℓ , ˜ ℓ and ˜ ℓ . We have evidence for ˜ ℓ , though given the statistics available itis not clear that were this peak truly observed in an experiment it would necessarily bemore than background fluctuations. The ˜ ℓ mass has been determined indirectly using theneutralino shifted peak, whereas the other sleptons are found by direct measurement. In allfive cases the masses we obtain are in reasonable or good agreement with the true slepton17asses. We see hints for ˜ ℓ but cannot measure its mass conclusively because of its dominantstau component, and because it happens to be close in mass to ˜ ℓ .The correct determination of as many as five of the six sleptons tells us that for fullyreconstructible supersymmetric decay chains ending in stable charged NLSPs, working upthe decay chain and reconstructing invariant mass distributions in stages is a promisingway of measuring superpartner masses in the slepton sector. We have seen that, even withnearly degenerate states, indirect methods do exist which may still render these sleptonmasses measurable. B. Mixings
1. Light sleptons
Our best mixing measurement is of the e − µ ratio in ˜ ℓ , shown in Eq. (12). If we assumethat ˜ ℓ , are selectron-smuon mixtures, with no stau components, we have ˜ ℓ ˜ ℓ ! = cos θ R sin θ R − sin θ R cos θ R ! ˜ e R ˜ µ R ! . (13)With this assumption, our measurement of Eq. (12) impliessin θ R = 0 . ± . . (14)How well can we test the assumption that ˜ ℓ , have no stau component? Clearly a directdetermination cannot be done in an analysis that does not look at τ leptons, but it isinteresting to ask whether we can use the information we have on ˜ ℓ and ˜ ℓ to argue this.As we will now see, with some mild assumptions about the model, we can show that ˜ ℓ and˜ ℓ can only have equal stau components, i.e., | U τ | = | U τ | . We cannot exclude, however, | U τ | = | U τ | 6 = 0.We begin by assuming that the neutralino coupling to the three light sleptons is flavor-blind, an assumption that is valid not only in our model, but generically in the types ofmodels we are considering. In the mass distributions of Figs. 4 and 5, we take the numberof events in the OS electron (muon) peak to be N OSe ( N OSµ ). Then N SSe = N f SS | U e | (15) N SSµ = N f SS | U µ | (16) N OSe = N h f | U e | + (1 − f SS ) | U e | i (17) N OSµ = N h f | U µ | + (1 − f SS ) | U µ | i , (18)where N is the total number of neutralino decays to ˜ ℓ , and f SS is the fraction of ˜ ℓ → ˜ ℓ decays in which the slepton charge flips sign (˜ ℓ ± → ˜ ℓ ∓ ). We include the factor f ≈ ℓ and ˜ ℓ . Assuming that we already know that theneutralino is a fermion and the sleptons are scalars, we have f = − m /M − m /M ! , (19)18here one power comes from phase space, and the other one from the matrix element forthe χ → ˜ ℓℓ decay.It is useful to combine these four equations to obtain two combinations that are indepen-dent of N and f SS . One such combination is the ratio N SSe /N SSµ , which we already usedto extract | U e | / | U µ | . The other one is N e N µ = N SSe + N OSe N SSµ + N OSµ = f | U e | + | U e | f | U µ | + | U µ | . (20)For the 2-state assumption, using the value of sin θ R we found above, the theoretical pre-diction is N e /N µ ≈ f = 1 .
09, in reasonable agreement with the data, N e /N µ = 1 . ± . . (21)It is easy to see, however, that this agreement would persist for any | U e | , | U µ | ≪ | U e | ≃ | U µ | , (22)which, for | U τ | , | U τ | 6≪ | U e | , | U µ | , implies (by unitarity) that | U τ | ≃ | U τ | .
2. Heavy sleptons
It is encouraging that, despite the ˜ ℓ being produced high up in our decay chains, wehave good evidence that ˜ ℓ has a very strong selectron component and negligible smuoncomponent from the strong peaks in the χ e invariant mass distributions and the absenceof a peak in the χ µ invariant mass distributions. For ˜ ℓ and ˜ ℓ we know that these havestrong smuon components but negligible selectron components. Assuming that these statesare left-handed sleptons, and that the χ is a gaugino, we can deduce that the smuon-staumixing in these states is of O (1). Assuming further that ˜ ℓ is a left-handed slepton, we canalso conclude that it is predominantly a selectron. VII. CONCLUSIONS
The understanding of slepton masses and mixings that we have arrived at, based onexperimental evidence, is summarized in Table I. The results are very close to the assumedunderlying input model. We have taken a “data-driven” approach, in which we try to inferfrom the data the masses and flavor compositions of new particles, rather than fitting theparameters of a particular model to the data. The methods we described are specific tomodels with metastable charged particles and, therefore, no missing energy.The most obvious way to identify the sleptons in our model (which we initially tried)would be to look for peaks in the NLSP plus two leptons invariant-mass distributions. Thisdoes not work very well, however, either because some of the relevant leptons are too soft orbecause of the large supersymmetric combinatoric backgrounds. Instead, we showed that thebest mass measurements in these scenarios can be obtained by reconstructing the spectrumin stages, starting from the bottom up. For example, rather than discovering a heavy sleptonby searching for a peak in the invariant mass distribution of the NLSP plus two leptons,we first identify the lightest neutralino as a peak in the NLSP plus lepton distribution, and19hen combine this neutralino with one additional lepton to obtain the heavier slepton peak.We also demonstrated that nearly-degenerate particles can be resolved indirectly, using theshifted peak of their mother particle.We then outlined methods for measuring the slepton flavor compositions, essentially bycounting experiments. We were able to qualitatively infer the flavor makeup of the sleptons,and to quantitatively measure one mixing.The charged NLSP is a crucial ingredient in our analysis, yet the model we chose alsohas some unfavorable features:1. The two lightest sleptons are almost degenerate.2. The e − µ mixing in these sleptons is small.3. One slepton, ˜ ℓ , is an almost pure stau state, and is quite close in mass to ˜ ℓ , , so thatthe peak it gives in the NLSP plus e/µ distributions is very close to the ˜ ℓ peak.We have also not used any information from tau leptons. Given these difficult features andthe pessimistic assumption about taus, the amount of information we were able to extractis encouraging.The analysis we presented is certainly preliminary. If our toy model were real data, onewould want to perform detailed measurements to confirm that the observed events weresupersymmetric, establish the gaugino identities of the neutralinos, and explore the squarkand gluino sector. One could then fit the flavor parameters of the model to the data, andflesh out the details of the picture we outlined here.We conclude that, under favorable but not outrageously optimistic circumstances (un-less we think of discovering supersymmetry as outrageously optimistic), it is possible thatmeasurements made at the Large Hadron Collider will allow us to determine a great dealabout the slepton spectrum and flavor decomposition, and constrain, and possibly clarify,the flavor structures of both supersymmetry and the standard model. Acknowledgments
We thank James Frost and Are Raklev for technical assistance and Kfir Blum for dis-cussions. YS thanks the Aspen Center for Physics, where part of this work was completed.The research of JLF, YN, YS and IG was supported in part by the United States-IsraelBinational Science Foundation (BSF) under Grant No. 2006071. The work of JLF, DS, andFY was supported in part by NSF Grant No. PHY–0653656. STF and CGL acknowledgethe support of the United Kingdom’s Science and Technology Facilities Council, Peterhouseand the University of Cambridge. The work of IG and YS was supported in part by theIsrael Science Foundation (ISF) under Grant No. 1155/07. The work of YN is supported bythe Israel Science Foundation (ISF) under Grant No. 377/07, the German-Israeli Foundationfor scientific research and development (GIF), and the Minerva Foundation.20
PPENDIX A: MODEL DETAILS1. Input Parameters
As discussed in Sec. II, the model used for this analysis is a hybrid model in which sleptonmasses receive contributions from both gauge- and gravity-mediated supersymmetry break-ing. Gauge-mediation provides the primary, flavor-universal contributions to soft masses,and gravity-mediation supplements these with flavor-violating contributions. The sleptonsoft mass matrices then have the form M ν = m ℓ + xm ℓ X L (A1) M ℓ L = m ℓ + m E m † E + xm ℓ X L (A2) M ℓ R = m R + m † E m E + xm ℓ X R , (A3)where m ℓ and m R are the gauge-mediated, flavor-conserving contributions to the left- andright-handed sleptons, m E is the lepton mass matrix, and x is the ratio between gravity-and gauge-mediated contributions. The symmetric matrices X L and X R parameterize thegravity-mediated flavor-violating effects for left- and right-handed sleptons, with the flavorstructure determined by the Froggatt-Nielsen mechanism [14].For the model analyzed here, the flavor-conserving gauge-mediated contributions arespecified by the standard GMSB parameters N = 5 , M m = 4 . · GeV , Λ = 3 . · GeV , C grav = 1 , tan β = 10 , µ > . (A4)The gravity-mediated, flavor-violating contributions are governed by a U(1) × U(1) hori-zontal symmetry under which the lepton superfields have the charges L (2 , , L (0 , , L (0 , E (2 , , E (2 , − , E (0 , − . (A5)The resulting flavor-violating masses are generated using appropriate powers of the Froggatt-Nielsen expansion parameter λ with O (1) coefficients for each term in the matrix. Theresulting flavor-violating contributions for the sleptons are X L = − . λ − . λ . λ − . λ − . λ . λ . λ . λ . λ (A6) X R = − . λ . λ − . λ . λ − . λ . λ − . λ . λ . λ , (A7)and the lepton mass matrix is given by m E = h φ d i λ − . λ . λ − . λ − . λ . λ . λ . λ . (A8)We ignore the neutrino mass matrix for our purposes, as neutrino flavor is unobservable incolliders and thus unimportant for this study. We take x = 0 . λ = 0 . ass (GeV) ˜ e R ˜ µ R ˜ τ R ˜ e L ˜ µ L ˜ τ L ˜ ℓ − . − . − . . . ℓ . − . − . − . . ℓ − . . . ℓ − . . . − . . ℓ − . . − . . − . ℓ . . − . . − . Physical Slepton Masses and Flavor Composition.
Elements of the mixing matrix withvalues less than 10 − have been set to zero.Mass (GeV) ˜ ν e ˜ ν µ ˜ ν τ ˜ ν − . . . ν − . − . . ν . . Physical Sneutrino Masses and Flavor Composition.
Elements of the mixing matrixwith values less than 10 − have been set to zero.
2. Spectrum
Given these input parameters, the full supersymmetric spectrum and flavor-general decaybranching ratios are generated by the program
Spice [17]. The
Spice input file used is gmsb 5 4.6e6 3.4e4 1.0 10 1x 0.1lambda 0.2nCharges 2L1 2 0L2 0 2L3 0 2E1 2 1E2 2 -1E3 0 -1Lep -0.3838 0 0 0.8706 -1.8682 -1.5408 1.0450 0.3574 1.8554XL -3.4989 -1.2001 0.4059 -1.2001 -1.2705 1.1746 0.4059 1.1746 1.4293XR -1.0368 0.9976 -0.06188 0.9976 -0.8616 0.2204 -0.06188 0.2204 0.6544
The masses of the six slepton mass eigenstates, as well as the rotation matrix relatingthe slepton mass and gauge eigenstates, are presented in Table II. These are discussed in22 ass (GeV) Mass(GeV)˜ d L h u L H s L A c L H + b χ t χ d R χ u R χ s R χ +1 c R χ +2 b g t G ∼ Particle Spectrum.
Physical masses of the squarks, gluino, Higgs bosons, charginos,neutralinos, and gravitino.
Sec. II, with a graphical representation given in Fig. 1. The sneutrino masses and flavorcompositions are given in Table III.The masses of the remaining MSSM particles are given in Table IV. The SM-like Higgsboson is below the current bounds, but it and its precise mass play no role in the signalsstudied here. The gravitino mass is not precisely specified. The dominant contribution toits mass is from gravity-mediation, and so we expect m ˜ G ∼ √ xm ˜ ℓ . This guarantees thatdecays to the gravitino take place outside collider detectors and the signals we study areinsensitive to the precise value of m ˜ G . The general mass ordering of the lightest states istherefore m ˜ G ≪ m ˜ ℓ , , < m χ < m ˜ ℓ , , < m χ . (A9)The decays from the lightest neutralino to the light sleptons, and from the light sleptons toother light sleptons, are also shown in Fig. 1. [1] N. Arkani-Hamed, H. C. Cheng, J. L. Feng and L. J. Hall, Phys. Rev. Lett. , 1937 (1996)[arXiv:hep-ph/9603431].[2] N. Arkani-Hamed, J. L. Feng, L. J. Hall and H. C. Cheng, Nucl. Phys. B , 3 (1997)[arXiv:hep-ph/9704205].[3] K. Agashe and M. Graesser, Phys. Rev. D , 075008 (2000) [arXiv:hep-ph/9904422].[4] J. Hisano, R. Kitano and M. M. Nojiri, Phys. Rev. D , 116002 (2002)[arXiv:hep-ph/0202129].[5] T. Goto, K. Kawagoe and M. M. Nojiri, Phys. Rev. D , 075016 (2004) [Erratum-ibid. D , 059902 (2005)] [arXiv:hep-ph/0406317].[6] R. Kitano, JHEP , 023 (2008) [arXiv:0801.3486 [hep-ph]].[7] B. C. Allanach, J. P. Conlon and C. G. Lester, Phys. Rev. D , 076006 (2008)[arXiv:0801.3666 [hep-ph]].
8] S. Kaneko, J. Sato, T. Shimomura, O. Vives and M. Yamanaka, Phys. Rev. D , 116013(2008) [arXiv:0811.0703 [hep-ph]].[9] A. De Simone, J. Fan, V. Sanz and W. Skiba, Phys. Rev. D , 035010 (2009) [arXiv:0903.5305[hep-ph]].[10] J. L. Feng, C. G. Lester, Y. Nir and Y. Shadmi, Phys. Rev. D , 076002 (2008)[arXiv:0712.0674 [hep-ph]].[11] Z. Chacko and E. Ponton, Phys. Rev. D , 095004 (2002) [arXiv:hep-ph/0112190].[12] R. N. Mohapatra, N. Okada and H. B. Yu, Phys. Rev. D , 075011 (2008) [arXiv:0807.4524[hep-ph]].[13] See, e.g. , Fig. 1 of J. L. Feng and T. Moroi, Phys. Rev. D , 035001 (1998)[arXiv:hep-ph/9712499].[14] C. D. Froggatt and H. B. Nielsen, Nucl. Phys. B , 277 (1979).[15] Y. Nir and N. Seiberg, Phys. Lett. B , 337 (1993) [arXiv:hep-ph/9304307].[16] G. G. Ross and O. Vives, Phys. Rev. D , 095013 (2003) [arXiv:hep-ph/0211279].[17] G. Engelhard, J. L. Feng, I. Galon, D. Sanford and F. Yu, to appear in Comput. Phys.Commun., arXiv:0904.1415 [hep-ph].[18] B. C. Allanach, Comput. Phys. Commun. , 305 (2002) [arXiv:hep-ph/0104145].[19] B. C. Allanach and M. A. Bernhardt, arXiv:0903.1805 [hep-ph].[20] A. Djouadi, M. M. Muhlleitner and M. Spira, Acta Phys. Polon. B , 635 (2007)[arXiv:hep-ph/0609292].[21] J. L. Feng, I. Galon, D. Sanford, Y. Shadmi and F. Yu, Phys. Rev. D , 116009 (2009)[arXiv:0904.1416 [hep-ph]].[22] G. Marchesini, B. R. Webber, G. Abbiendi, I. G. Knowles, M. H. Seymour and L. Stanco,Comput. Phys. Commun. , 465 (1992).[23] G. Corcella et al. , JHEP , 010 (2001) [arXiv:hep-ph/0011363].[24] P. Skands et al. , JHEP , 036 (2004) [arXiv:hep-ph/0311123].[25] E. Richter-Was, arXiv:hep-ph/0207355.[26] G. Aad et al. [ATLAS Collaboration], JINST , S08003 (2008).[27] J. R. Ellis, A. R. Raklev and O. K. Oye, JHEP , 061 (2006) [arXiv:hep-ph/0607261].[28] S. Tarem, S. Bressler, H. Nomoto and A. Di Mattia, Eur. Phys. J. C , 281 (2009).[29] J. L. Feng, A. Rajaraman and B. T. Smith, Phys. Rev. D , 015013 (2006)[arXiv:hep-ph/0512172].[30] A. Rajaraman and B. T. Smith, Phys. Rev. D , 115015 (2007) [arXiv:hep-ph/0612235].[31] A. Rajaraman and B. T. Smith, Phys. Rev. D , 115004 (2007) [arXiv:0708.3100 [hep-ph]].[32] See, for example, CMS Collaboration, Physics Analysis Summary, CMS-EXO-08-003.[33] J. L. Feng, S. T. French, C. G. Lester, Y. Nir and Y. Shadmi, arXiv:0906.4215 [hep-ph]., 115004 (2007) [arXiv:0708.3100 [hep-ph]].[32] See, for example, CMS Collaboration, Physics Analysis Summary, CMS-EXO-08-003.[33] J. L. Feng, S. T. French, C. G. Lester, Y. Nir and Y. Shadmi, arXiv:0906.4215 [hep-ph].