aa r X i v : . [ h e p - e x ] F e b Summary of ILD performance at SPS1a’
Mikael Berggren, Nicola d’Ascenzo, Peter Schade, and Olga Stempel ∗ DESY -FLCNotekstr. 85, 22607 Hamburg -GermanyThe performance of the ILD detector at the ILC for the analysis of µ and τ channelsat the SUSY benchmark-point SPS1a’ has been studied with full detector simulation.It is concluded that if 500 fb − is delivered to the experiment, ∆( M ˜ χ ) = 920 MeV /c ,∆( M ˜ µ L ) = 100 MeV /c , ∆( M ˜ χ ) = 1 .
38 GeV /c , and ∆( σ ( e + e − → ˜ µ L ˜ µ L )) = 1.35 fbcan be achieved from the µ channels alone. The preliminary results from the ˜ τ channels,indicates that ∆( P τ ) = 13 % is also achievable. The SUSY benchmark point SPS1a’ [2] offers a rich phenomenology at the ILC. It is pointwith quite low mass-spectrum in the slepton sector, and heavy squarks. Bosinos up to˜ χ (in e + e − → ˜ χ ˜ χ ) would be produced at E CMS = 500 GeV. It is a pure mSUGRAmodel, hence R-parity and CP is conserved. The unification scale parameters are: M / =250 GeV , M = 70 GeV , A = −
300 GeV , tan β = 10, and sign ( µ ) = +1. The point is not incontradiction with any experimental limits [3]. The ˜ τ is the NLSP, and M ˜ τ = 107 . /c and M ˜ χ = 97 . /c , so ∆( M ) = 10 . /c . At E CMS = 500 GeV, this yields P ˜ τ ,min = 2 . /c hence γγ events will pose a problem. As SPS1a’ is a point withan important co-annihilation contribution to the dark-matter relic density, the M ˜ τ is amost important quantity to determine. An other consequence of the ˜ τ being the NLSP,is that τ :s are present in large fraction of the SUSY decays, so that SUSY itself will be amayor background source for τ channels. On the other hand, the M ˜ µ L ( M ˜ µ R ) is 189.9(125.3)GeV /c , so that the minimum µ energy is 32.1(6.6) GeV. As, in addition, the branchingratios to ˜ µ in bosino decays are quite low, the µ final states offer cleaner conditions, and arewell suited for doing the most precise measurements.The present note reports on the status of the analysis of of the µ and τ channels ofthe SPS1a’ scenario in the LDC’ detector. SPheno [4] was used to run the unification-scalemodel to the EW scale, and
Whizard [5] was the used to generate events. The
LDCPrime 02Sc detector model was fully simulated using
MOKKA [6], and the events were reconstructed with
MarlinReco [7]. The same chain was used to produce background events. µ channels Two channels containing only µ :s in the final state was chosen as a first study [8]: ˜ µ L ˜ µ L → µµ ˜ χ ˜ χ and ˜ χ ˜ χ → µ ˜ µ R ˜ χ → µµ ˜ χ ˜ χ . As mentioned in the introduction, the SUSYbackground problem is not too severe in the µ channels, and it is advantageous to runthe ILC at the polarisation giving the largest signal. Hence, these channels were studiedassuming 80 % left e − polarisation and 60 % right e + polarisation. Under these conditions,the ˜ µ L ˜ µ L process has a large cross-section, and is well suited to determine M ˜ µ L and M ˜ χ .˜ χ ˜ χ has a small cross-section × BR, but can be used to determine M ˜ χ , without the need ∗ Support by DFG through SFB 676 is acknowledged
LCWS/ILC 2008 energy [GeV] m ) - Y i e l d ( f b · Standard Model Background ( 10) · SUSY background( 100) · ( cmm fi mm ~ fi c c fi - e + e 10) · ( c m c mfi L- m~ +L m~ fi - e + e [GeV] mm m0 50 100 150 200 250 300 350 400 450 500 ) - Y i e l d ( f b · Standard Model Background ( 10) · SUSY background( 100) · ( cmm fi mm ~ fi c c fi - e + e 10) · ( c m c mfi L- m~ +L m~ fi - e + e Figure 1: The distributions of P µ (left), and M µµ (right)to scan over the threshold. The main background processes are other SUSY giving two µ :s, mainly ˜ µ R ˜ µ R , ˜ χ ˜ χ with one ˜ χ going to ˜ µµ , the other to ˜ νν and ˜ τ ˜ τ with τ → µν µ ν τ Standard model background is mainly from
W W and ZZ . Finally, each of the two processesis background to the other one.The following kinematic variables were used to disentangle signal and background, andto separate the two signal channels: The momentum of µ :s ( P µ ), the acolinearity angle be-tween the µ :s ( θ acol ), the acoplanarity angle between them,defined as the acolinearity in theprojection perpendicular to the beam-axis ( θ acop ), the total missing transverse momentum( P T miss ) in the event, the invariant mass of the two µ :s (M µµ ), the total missing energy(E miss ), the polar angle of the missing momentum ( θ missing p ), and the velocity β of the µ system. The distributions of P µ and M µµ are shown in Fig. 1, and that of β in Fig. 2 | b |0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) - Y i e l d ( f b · Standard Model Background ( 10) · SUSY background( 100) · ( cmm fi mm ~ fi c c fi - e + e 10) · ( c m c mfi L- m~ +L m~ fi - e + e Figure 2: The distribution of the velocity β The ˜ µ L ˜ µ L channel was selected by de-manding that E miss ∈ [200 , µµ / ∈ [80 , <
30 GeV /c , and θ missing p ∈ [0 . π, . π ]. Assuming an inte-grated luminosity of 500 fb − , this leaves13000 events of SM background and 11000events of SUSY background, while 16300signal events were selected, correspondingto an efficiency of 60 %. The ˜ µ L and ˜ χ masses were then extracted by fitting theedges of the P µ distribution, see Fig. 3. Theerrors on the fitted masses are ∆( M ˜ µ L ) =100 MeV /c and ∆( M ˜ χ ) = 920 MeV /c ,respectively. The beam-energy spread dom-inates these numbers. The productioncross-section was determined using the extended likelihood formed by L ( p T µ , θ acol )), asthese two variables were not used in selecting the signal. The uncertainty on the observedvalue is ∆( σ ( e + e − → ˜ µ L ˜ µ L )) = 1.35 fb.The ˜ χ ˜ χ channel was selected by demanding that θ missing p ∈ [0 . π, . π ], β > . miss ∈ [355 , T miss >
40 GeV /c , M µµ ∈ [40 ,
85] GeV /c and E viss >
40 GeV /c . LCWS/ILC 2008 / ndf c – – – – energy [GeV] m
26 28 30 32 34 36 38 40 42 ) - Y i e l d ( f b / ndf c – – – – B+A/(1+exp(x-E)/S)signal / ndf = 8.39 / 14 c Amplitude(A) 3.51 – – – – energy [GeV] m
146 148 150 152 154 156 ) - Y i e l d ( f b / ndf = 8.39 / 14 c Amplitude(A) 3.51 – – – – B+A/(1+exp((x-E)/S))Signal
Figure 3: The fit to the lower (left) and upper (right) edges of the P µ distribution / ndf = 20.57 / 26 c Background(B) 2.93 – – – – – – – -79.82 Invariant Mass [GeV]40 50 60 70 80 90 ) - Y i e l d ( f b / ndf = 20.57 / 26 c Background(B) 2.93 – – – – – – – -79.82 Standard Model BackgroundSUSY background cmm fi mm ~ fi c Total signal
Figure 4: The fit to the M µµ distributionAt the assumed integrated luminosity,500 events of SM background and 2400events of SUSY background is expected,while 720 signal events were selected, cor-responding to an efficiency of 34 %. As-suming that the ˜ χ mass is known from theprevious channel, the mass of ˜ χ can be ex-tracted by a fit to the edge in the invariantmass spectrum, Fig. 4, and an uncertaintyof ∆( M ˜ χ ) = 1 .
38 GeV /c was found. τ channels As mentioned in the introduction, SUSY it-self poses a background problem in the τ analysis, and it is therefore needed to run the ILC at the polarisation that minimises thebackground. For 100 % left e − polarisation and 100 % right e + polarisation, the cross-sections for ˜ χ ˜ χ and ˜ χ +1 ˜ χ − are several hundred fb, and the branching ratios to ˜ τ is above50 %. With the opposite polarisation, however, these cross-sections will almost vanish.Hence, these channels were studied assuming 80 % right e − polarisation and 60 % left e + polarisation.As the γγ background poses another challenge for the τ channels, quite strong criteriamust be applied: A correlated cut in ρ (the transverse momentum of the jets wrt. the thrustaxis, in the projection perpendicular to the beam) was also done: ρ > θ acop + 1 .
7. Tofurther reduce the γγ background to acceptable levels, it was demanded that there be nosignificant activity in the BeamCal, and that the φ angle of the missing momentum was notin the direction of the incoming beam-pipe.The ˜ τ mass can be extracted from the end-point of the spectrum of E τ , which is equal to E ˜ τ ,max , and the ˜ χ mass, known eg. from the ˜ µ L analysis above. In principle, the maximumof the spectrum spectrum is at P ˜ τ ,min , so that the ˜ τ can be used to find M ˜ χ as well, butdue to the large γγ background, the maximum is quite hard to observe. LCWS/ILC 2008 energy of jet[GeV] E v en t s / . G e V energy of jet[GeV] E v en t s / . G e V Figure 5: E jet distribution after all cuts in thedecay-mode independent analysisTo extract the signal in order to de-termine the end-point the following cutswere applied: E miss ∈ [430 , M jet < /c , θ jet above 20 degrees, θ acop <
160 degrees, θ acol ∈ [80 , | cos θ missingp | < .
9, and charge ofeach jet = ±
1. In addition, the anti- γγ cutdescribed above was applied. After thesecuts, the SM background was 222 events,the SUSY background was 2747, while 8262signal events remained (10.2 % efficiency).Fig. 5 shows that the end-point is almostbackground free, and also that the turn-over point (expected to be at P ˜ τ ,min =2 . /c ) is too distorted by the cuts to be useful.The ˜ τ mass-eigenstates are expected to be different from the chiral ones, and the off-diagonal term of mass-matrix is − M τ ( A ˜ τ − µ tan β ). The diagonal terms in the mass matrixare known from M ˜ µ L and M ˜ µ R , so a measurement of θ mix gives A ˜ τ − µ tan β . If ˜ χ is purelybino - it is in SPS1a’ - the τ polarisation (P τ ) depends only on θ mix . P τ can be extractedfrom spectrum for exclusive decay-mode(s). In this analysis, the τ → π + − ν τ mode hasbeen studied. The spectrum of π :s in the decay-chain ˜ τ → τ → π + − ν τ is shown in Fig. 6,with and without ISR and beam-spread. The highest sensitivity to the polarisation is in theregion with P π < P ˜ τ ,min . [GeV] p E0 5 10 15 20 25 30 35 40 R a t i o [ % ] / G e V without beam spread or ISRwith beam spread and ISR Figure 6: The P π distribution, at generatorlevel. Shaded: fixed beam-energy, open: ISRand beam-spread includedThe ˜ τ → τ → π + − ν τ signal is selectedwith a set of cuts that intend to distort thespectrum as little as possible. The followingpre-selections were first applied: The eventsshould pass the anti- γγ cut, E vis should be <
120 GeV, the number of reconstructedparticles <
20, and at least one of the twojets should contain a single particle. Thissingle particle should be identified as a π ,and have E <
43 GeV. Finally, the to-tal charge should be 0. Events passing thispreslection should then also fulfil the follow-ing criteria: The mass of the rest of theevent (ie. after removing the signal pion)should be below 2.5 GeV /c | cos θ | of bothjets should be < .
9, and θ acop should beabove 85 degrees. Finally, the sum over the two jets of the p T of one jet wrt. the directionof the other should be below 30 GeV /c .With these cuts, 134 SM jets remain, and 373 SUSY jets, while 2311 signal-jets areretained (13 %). The initial and final π spectra are shown in Fig. 7. The procedure toextract the polarisation in the presence of background is to first fit the simulated back-ground alone to a heuristic function. a The signal selections cuts are then applied to the a When real data is available, the simulation of the background can be verified by reversing cuts to select
LCWS/ILC 2008 [GeV] signal candidate
E0 5 10 15 20 25 30 35 40 45 e n t r i es / [ G e V ]
10 [GeV] signal candidate
E0 5 10 15 20 25 30 35 40 45 e n t r i es / [ G e V ] t t e+e- + fi e^+e^- e+e- + X fi e+e- SM backgroundother SUSYSignal type backg. p Signal [GeV] p E0 5 10 15 20 25 30 35 40 45 e n t r i es / [ G e V ] p Signal Reconstructed data pointsFit to dataMC spectrum
Figure 7: Distribution of P π before (left) and after (right) cuts. The right-hand plot alsoshows the spectrum after background-subtraction and efficiency correction (dots), and thefinal fit.signal+background sample, and the function is subtracted from the observed distribution.An efficiency correction function, determined from signal-only simulation, is applied. Theresulting distribution is then fitted with the theoretical spectrum, corrected for ISR andbeam-spread, and the polarisation is obtained, see Fig. 7, right. Assuming an integratedluminosity of 500 fb − , the value found is P τ = (93 ±
13) %, where the error also includesthe uncertainty of the background parametrisation.
A study of some channels in SPS1a’ SUSY scenario fully simulated in the LDC’ detectorat the ILC was presented. By analysing the channel e + e − → ˜ µ L ˜ µ L , it was concluded that∆( M ˜ χ ) = 920MeV /c , ∆( M ˜ µ L ) = 100MeV /c and ∆( σ ( e + e − → ˜ µ L ˜ µ L )) = 1.35 fb, couldbe attained with an integrated luminosity of 500 fb − with 80 % left e − polarisation and 60% right e + polarisation. In the channel ˜ χ ˜ χ → µ ˜ µ R ˜ χ → µµ ˜ χ ˜ χ , ∆( M ˜ χ ) = 1 .
38 GeV /c ,was found, under the same conditions. It should be noted that this value is comparable towhat a dedicated scan of the ˜ χ ˜ χ threshold would give.In addition, a progress report on ˜ τ production was given. The preliminary result on themeasurement of the τ polarisation gives ∆(P τ ) = 13 %. Note, however, that this requiresthat the beam-polarisations are opposite to what the was used in the µ channel. References [1] Presentation: http://ilcagenda.linearcollider.org/materialDisplay.py?contribId=173&sessionId=17&materialId=slides&confId=2628 [2] J. A. Aguilar-Saavedra & al., Eur.Phys.J.
C46 (2006) 43, arXiv:hep-ph/0511344.[3] C. F. Berger, J. S. Gainer, J. L. Hewett, T. G. Rizzo, arXiv:0812.0980.[4] W. Porod, Comput. Phys. Commun. (2003) 275, arXiv:hep-ph/0301101.[5] W. Kilian, T. Ohl, J. Reuter, arXiv0708.4233.[6] P. M. Freitas, MOKKA http://mokka.in2p3.fr/ [7] http://ilcsoft.desy.de/portal/software_packages/marlin/index_eng.html [8] N. d’Ascenzo, PhD thesis, DESY Thesis-2009-004 (2009)a signal-free, but SUSY-dominated region in the parameter-space.[8] N. d’Ascenzo, PhD thesis, DESY Thesis-2009-004 (2009)a signal-free, but SUSY-dominated region in the parameter-space.