Supersymmetry and other beyond the Standard Model physics: Prospects for determining mass, spin and CP properties
SSupersymmetry and other beyond the Standard Model physics:Prospects for determining mass, spin and CP properties
Wolfgang Ehrenfeld for the ATLAS Collaboration Deutsches Elektronen Synchrotron, Notkestrasse 85, 22603 Hamburg, Germany
Abstract
The prospects of measuring masses, spin and CP properties within Su-persymmetry and other beyond the Standard Model extensions at theLHC are reviewed. Emphasis is put on models with missing transverseenergy due to undetected particles, as in Supersymmetry or UniversalExtra Dimensions.
It is widely expected that the Large Hadron Collider (LHC), which started very successfully onthe 10th September 2008 with single beam injection, will uncover physics beyond the presentStandard Model (SM) of particle physics. Supersymmetry (SUSY) is one of the most promis-ing candidates for new physics. Among its virtues are the potential to overcome the hierarchyproblem, to provide a dark matter candidate and make a unification of gauge coupling constantsat a high energy scale possible. If the SUSY mass scale is in the sub-TeV range, already firstLHC data will likely be sufficient to claim a discovery of new physics although new physics donot strictly mean SUSY as other new physics scenarios can have similar features and properties.In order to distinguish different scenarios of new physics and to determine the full set of modelparameters within one scenario as many measurements of the new observed phenomena as pos-sible are needed. This includes the precise measurement of masses, spins and CP properties ofthe newly observed particles.Both multi-purpose experiments at the LHC, ATLAS [1] and CMS [2], are designed forthese measurements. They will be able to pin down the exact model of new physics, e. g. todistinguish SUSY from Universal Extra Dimensions (UED).
In the following we assume R-parity conservation. As a consequence sparticles can only beproduced in pairs and the lightest SUSY particle (LSP) is stable, which usually escapes detec-tion in high-energy physics detectors. At LHC energies mostly pairs of squarks or gluinos areproduced in proton-proton collisions, which then subsequently decay via long cascades into theLSP. Typical event topologies at the LHC are multi jet events with zero or more leptons andmissing transverse energy due to the two LSPs. In the case of ATLAS these events will be trig-gered using a combined jet and missing E T trigger. The selection is mainly based on four jets( p j T >
100 GeV , p j ,j ,j T >
50 GeV ) and missing E T ( E mis T >
100 GeV , . m eff ). The effec-tive mass, m eff , is the scalar sum of missing E T and the transverse momentum of the four leadingjets. For further details see [3]. With this kind of selection minimal Supergravity (mSUGRA)models up to m / ∼ . or m ∼ can be discovered with a luminosity of 1 fb − . a r X i v : . [ h e p - e x ] D ec .1 Mass Measurements After the discovery of new physics beyond (cid:24)(cid:24)(cid:24)(cid:58) (cid:101) q L (cid:45)(cid:3)(cid:3)(cid:3)(cid:23) q (cid:101) χ (cid:88)(cid:88)(cid:88)(cid:122)(cid:1)(cid:1)(cid:1)(cid:21) (cid:96) + (cid:101) (cid:96) − R (cid:72)(cid:72)(cid:72)(cid:106)(cid:0)(cid:0)(cid:0)(cid:18) (cid:96) − (cid:101) χ Fig. 1: Prime example of a SUSY decay chain forSUSY mass reconstruction. The first lepton in thedecay chain is called the near lepton while the otheris called the far lepton. the SM as many measurements of the productionprocess and particle properties are needed to pin-down the exact model of new physics. For exam-ple the masses of the new particles can be used todistinguish between different SUSY models. Dueto the two escaping LSPs in every SUSY event, nomass peaks can be reconstructed and masses mustbe measured by other means. In mSUGRA models the main source of mass information is pro-vided by (cid:101) χ decays, such as (cid:101) χ → (cid:101) (cid:96) ± (cid:96) ∓ → (cid:101) χ (cid:96) + (cid:96) − (see Fig. 1). First we consider the invariantmass spectrum of the two leptons m (cid:96)(cid:96) from the decay chain in Fig. 1. Due to the scalar natureof the slepton, the invariant mass exhibits a triangular shape with a sharp drop-off at a maximalvalue m max (cid:96)(cid:96) . The position of this endpoint depends on the masses of the involved sparticles: m max (cid:96)(cid:96) = m e χ (cid:118)(cid:117)(cid:117)(cid:116) − (cid:32) m e (cid:96) R m e χ (cid:33) (cid:118)(cid:117)(cid:117)(cid:116) − (cid:32) m e χ m e (cid:96) R (cid:33) . (1)Combinatorial background from SM and other SUSY processes is subtracted using the flavor-subtraction method. The endpoint is measured from the di-lepton (electron and muon) massdistribution N (e − e + ) /β + βN ( µ − µ + ) − N (e ± µ ∓ ) , where N is the number of selected eventsand β is the ratio of the electron and muon reconstruction efficiency ( β (cid:39) . ) [3]. Figure 2shows the mass distribution for different mSUGRA benchmark points . The SU3 point is anexample of a simple two-body decay (Fig. 2(b)), SU4 illustrates a more complex three-bodydecay (Fig. 2(c)) and SU1 two two-body decays (Fig. 2(a)). In all cases the m (cid:96)(cid:96) endpoint can bemeasured without a bias although the needed luminosity is quite different. Further, the fit functionto extract the endpoint(s) needs to be adjusted to the underlying mass spectrum. The expectedsensitivity is summarized in Tab. 1 including the assumed luminosity. A similar analysis canbe performed if we replaced electrons and muons by taus. Due to the additional neutrinos fromthe tau decay, the visible di-tau mass distribution is not triangular any more (see Fig. 2(d)). Thiscomplicates measuring the endpoint of the spectrum. A solution to this problem is to fit a suitablefunction to the trailing edge of the visible di-tau mass spectrum and use the inflection point as anendpoint sensitive observable, which can be related to the true endpoint using a simple MC basedcalibration procedure. Figure 2(d) shows the charge subtracted visible di-tau mass distribution N ( τ − τ + ) − N ( τ ± τ ± ) which is used to suppress background from fake taus and combinatorialbackground. The expected sensitivity is listed in Tab. 1. Please note, that the third error is due tothe SUSY-model dependent polarization of the two taus. On the other hand this influence of thetau polarization on the di-tau mass distribution can be used to measure the tau polarization fromthe mass distribution and distinguish different SUSY models from each other.By including the jet produced in association with the (cid:101) χ in the (cid:101) q L decay (see Fig. 1), sev-eral other endpoints of measurable mass combinations are possible: m max q(cid:96) (low) , m max q(cid:96) (high) , m min q(cid:96)(cid:96) , m max q(cid:96)(cid:96) . The label min/max denotes the upper/lower endpoint of the spectrum. In the case of m max q(cid:96) the near and the far lepton can not be distinguished in most of the SUSY models and instead the Within ATLAS the mSUGRA benchmark points are called SU X . SU1: m = 70 GeV , m / = 350 GeV , A =0 , tan β = 10 , µ > SU3: m = 100 GeV , m / = 300 GeV , A = − , tan β = 6 , µ > SU4: m =200 GeV , m / = 160 GeV , A = − , tan β = 10 , µ > / ndf c – – – – m(ll) [GeV]0 20 40 60 80 100 120 140 160 180 200 - E n t r i e s / G e V / f b -20020406080100 / ndf c – – – – ATLAS / ndf c – – – – m(ll) [GeV]0 20 40 60 80 100 120 140 160 180 200 - E n t r i e s / G e V / f b -1001020304050 / ndf c – – -0.3882 Smearing 1.339 – c – – -0.3882 Smearing 1.339 – ATLAS m(ll) [GeV]0 20 40 60 80 100 120 140 160 180 200 - E n t r i e s / G e V / . f b -40-20020406080100120 / ndf c – – – c – – – ATLAS [GeV] tt M0 20 40 60 80 100 120 140 160 180 - en t r i e s / G e V / f b -505101520 ATLAS (a) (b)(c) (d)
Fig. 2: Flavour subtracted di-lepton mass spectrum for different mSUGRA benchmark points: (a) SU1( (cid:96) = e, µ ), (b)SU3( (cid:96) = e, µ ), (c) SU4( (cid:96) = e, µ ), (d) SU3( (cid:96) = τ ). minimum/maximum of the mass m q(cid:96) ± is used. As in the di-lepton case a suitable fit function foreach observable is needed. The expected sensitivity to the different mass combinations for theSU3 model are summarized in Tab. 1.These five mass combinations can be used to extract the underlying high mass modelparameters using fitting programs like Fittino [4] or SFitter [5]. Measuring the number of new particles and their masses will give us enough information toextract model parameters for a certain extension of the SM. However, the mass information willnot always be enough to distinguish different scenarios of new physics. For example, UED withKaluza-Klein (KK) parity can be tuned in such a way that it reproduces the mass spectrum ofcertain SUSY models. However, the spin of the new particles is different and can be used todiscriminate between these models.The standard SUSY decay chain (see Fig. 1) can also be used to measure the spin of (cid:101) χ [6].A charge asymmetry A is expected in the invariant masses m q(cid:96) near( ± ) formed by the quark andthe near lepton. It is defined as A = ( s + − s − ) / ( s + + s − ) , where s ± = dσ/dm q(cid:96) near( ± ) . Inmost of the cases it is experimentally not possible to distinguish between near and far lepton andhence only m q(cid:96) ± can be measured, diluting A . Further, the asymmetry from the corresponding m q(cid:96) ∓ charge distribution is the same as the asymmetry for m q(cid:96) ± , but with opposite sign. Usuallyit is not possible to distinguish q jets from q jets at the LHC. On the other side more squarksthan anti-squarks will be produced. The expected asymmetry A for SU3 is shown in Fig. 3 for a bservable benchmark point true mass [GeV] expected mass [GeV] luminosity [fb − ] m (cid:96)(cid:96) SU1 56.1 . ± . ± . m (cid:96)(cid:96) SU1 97.9 . ± . ± . m (cid:96)(cid:96) SU3 100.2 . ± . ± . m ττ SU3 98 ± ± . ± m (cid:96)(cid:96) SU4 53.6 . ± . ± . m max q(cid:96) (low) SU3 325 ± ± ± m max q(cid:96) (high) SU3 418 ± ± ± m min q(cid:96)(cid:96) SU3 249 ± ± ± m max q(cid:96)(cid:96) SU3 501 ± ± ± β . In case of m ττ the third error is due to the uncertainty in thetau polarization. luminosity of 30 fb − , where already 10 fb − are sufficient to exclude the zero spin hypothesis at99% CL [7]. In the case of SU1 far and near leptons are distinguishable on kinematic grounds.On the other hand, cross section times branching ratio of this decay chain is much lower than theSU3 case, so that 100 fb − are needed to exclude the zero spin hypothesis at 99% CL.The slepton spin can be measured in direct di-slepton production qq → Z γ → (cid:101) (cid:96) (cid:101) (cid:96) → (cid:101) χ (cid:96) (cid:101) χ (cid:96) . In UED the corresponding process is qq → Z γ → (cid:96) (cid:96) → γ (cid:96)γ (cid:96) , where (cid:96) and γ arethe KK-lepton and -photon, respectively. Both have spin / , the same as their SM partners. Inboth decay chains a SM lepton-pair is produced, all other particles escape undetected. Althoughthe involved new particle masses can be the same, the slepton spin ( ) and KK-lepton spin ( / )are different. The angle θ ∗ , as defined between the incoming quark and the slepton/KK-lepton,can be used to discriminate between both model. The pure phase space (PS) distribution wouldbe flat. In SUSY and UED models it is proportional to A cos θ ∗ , where A = − for SUSYand A = ( E (cid:96) − m (cid:96) ) / ( E (cid:96) + m (cid:96) ) for UED. However, θ ∗ is not directly accessible. Experimen-tally only θ ∗ ll ≡ cos (cid:0) − exp (cid:0) ∆ η (cid:96) + (cid:96) − / (cid:1)(cid:1) = tanh (cid:0) ∆ η (cid:96) + (cid:96) − / (cid:1) , the angle between the twoleptons, can be measured. Note, that θ ∗ ll is invariant under boosts along the beam axis. Still, θ ∗ ll has some correlation with θ ∗ . Events with two good leptons ( p l ,l T > ,
30 GeV ) and missing ) (GeV) near m(jl m ( jl ) c h a r g e asy mm e t r y -0.8-0.6-0.4-0.2-00.20.40.60.8 asymmetryEntries 25Mean 84.4RMS 69.65 = 19.1 % c CL = 0.234 % RT CL = 0.390 % comb CL m(jl) (GeV) m ( jl ) c h a r g e asy mm e t r y -0.5-0.4-0.3-0.2-0.100.10.20.30.40.5 asymmetryEntries 40Mean 204RMS 153 = 4.22e-09 c CL = 0.621 % RT CL = 6.64e-10 comb CL Fig. 13: Charge asymmetries for lepton-jet invariant masses after SFOS-OFOS sub-traction. Left: using the near lepton from the chain involving ˜ l L in SU1 point.Right: using both near and far leptons in SU3 point.As already discussed, subtracting OFOS entries to the initial m ( jl ) SFOS distri-butions has the advantage of statistically removing the contribution of the reducibleSFOS background. To prove that this procedure does not affect the observabilityof a non-zero charge asymmetry, confidence levels are calculated also starting fromthe m ( jl ) distributions in all the selected OFOS events, as illustrated in Fig. 14for SU1 and SU3 points. The combined confidence level measured in both cases is m(jl) (GeV) m ( jl ) c h a r g e asy mm e t r y -0.8-0.6-0.4-0.2-00.20.40.60.8 asymmetryEntries 25Mean 66.71RMS 65.34 = 57.1 % c CL = 92.1 % RT CL = 86.4 % comb CL m(jl) (GeV) m ( jl ) c h a r g e asy mm e t r y -0.5-0.4-0.3-0.2-0.1-00.10.20.30.40.5 asymmetryEntries 38Mean 254RMS 134.2 = 19.3 % c CL = 93.3 % RT CL = 48.9 % comb CL Fig. 14: Charge asymmetries for m ( jl ) obtained in SUSY events with OFOS leptonspairs. Left: using the near lepton from the chain involving ˜ l L in SU1 point. Right:using both near and far leptons in SU3 point.larger than 50%, giving quantitative evidence for the flatness of the plots.Another test against background is given in Fig. 15, where in both SU1 and SU3samples the charge asymmetries have been reported for SFOS background events19 ATLAS
Fig. 3: Expected charge asymmetry A for SU3 and 30 fb − . cos q *ll F r a c t i o n o f e v e n t s , F / b i n SUSYUEDPS`Data´
200 fb -1 S5 ATLAS
Fig. 4: Expected θ ∗ ll distribution for the S5bench mark point and 200 fb − . T >
100 GeV are selected. Further, events with b-jets and high p T jets ( p T >
100 GeV ) are re-jected [8]. The expected θ ∗ ll distribution for a luminosity of 200 fb − is shown in Fig. 4 includingthe predictions for the SUSY, UED and PS case. Clearly, the difference between all three casescan be see. For a five sigma significance 200 fb − are needed to distinguish between SUSY andUED and 350 fb − to distinguish between SUSY and PS. The previous section was devoted to the measurement of masses and spins in the case of missingenergy due to non detectable new particles within cascade decays. Without this complication themeasurement of masses and spins of new particles is straight forward. As an example we willdiscuss the graviton case [9]. The graviton, which should be a spin 2 particle, can be produceddirectly in proton-proton collisions at the LHC. The decay channel G → e − e + can be cleanlyselected. The mass of the graviton resonance can be directly measured from the di-electroninvariant mass distribution. For a given luminosity of 100 fb − the graviton with m G up to2080 GeV can be discovered. θ ∗ , the angle between the electron and the beam axis, can be usedto measure the spin of the observed resonance. The general form of the cos θ ∗ distribution is A cos θ ∗ + B cos θ ∗ . For graviton production via gluons or quarks the factors are A =0 , B = − and A = − , B = 4 , respectively. Further, the SM background is only flat ( A =0 , B = 0 ) for electron-pair production via a scalar resonance. In the case of a vector resonance A = α, B = 0 , where α = 1 in the SM. For a given luminosity of 100 fb − the spin 2 nature ofthe graviton can be determined at 90% CL up to graviton masses of 1720 GeV, which also meansthat the spin 1 case is ruled out. Provided new particles are in the sub-TeV regime, already first LHC data will allow to performa rough spectroscopy of these. In the case of no missing energy due to invisible particles atthe end of a decay chain, the experimental methods for mass and spin measurements are verywell established and can be applied at the LHC. In the case of missing energy the experimentalmethods to measure mass and spin of the new particles are quite advanced and will be neededto distinguish for example SUSY from UED. Clearly, some of the more difficult measurementsneed high luminosity.
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