In SUSY scenarios with invisible LSP, sparticle masses can be determined from
fits to the endpoints of invariant mass distributions. Here we discuss possible
improvements by using the shapes of the distributions. Positive results are
found for multiple-minima situations and for mass regions where the endpoints
do not contain sufficient information to obtain the masses.Comment: to appear in Proceedings of SUSY06, the 14th International Conference
  on Supersymmetry and the Unification of Fundamental Interactions, UC Irvine,
  California, 12-17 June 200

Gjelsten, B. K.

Miller, D. J.

Osland, P.

Raklev, A. R.

English

arXiv

B. K. Gjelsten

D. J. Miller

P. Osland

A. R. Raklev

Crossref

Mass Determination in Cascade Decays Using Shape Formulas

In SUSY scenarios with invisible LSP, sparticle masses can be determined from fits to the endpoints of invariant mass distributions. Here we discuss possible improvements by using the shapes of the distributions. Positive results are found for multiple-minima situations and for mass regions where the endpoints do not contain sufficient information to obtain the masses.In SUSY scenarios with escaping LSP, sparticle masses can be determined from fits to the endpoints of invariant mass distributions. Here we discuss possible improvements by using the shapes of the distributions. Interesting results are found for multiple‐minima situations and for mass regions where the endpoints do not contain sufficient information to obtain the masses.In SUSY scenarios with invisible LSP, sparticle masses can be determined from fits to the endpoints of invariant mass distributions. Here we discuss possible improvements by using the shapes of the distributions. Positive results are found for multiple-minima situations and for mass regions where the endpoints do not contain sufficient information to obtain the masses

Gjelsten, B.K.

Miller, D.J.

Raklev, A.R.

CERN Document Server

arXiv:hep-ph/0611259v1  20 Nov 2006Mass Determination in Cascade Decays UsingShape FormulasB. K. Gjelsten, D. J. Miller†, P. Osland and A. R. Raklev‡Laboratory for High Energy Physics, University of Bern, CH-3012 Bern, Switzerland†Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, U.K.Department of Physics and Technology, University of Bergen, N-5007 Bergen, Norway‡Theory Division, Physics Department, CERN, CH-1211 Genève, SwitzerlandAbstract. In SUSY scenarios with invisible LSP, sparticle masses can be determined from fits tothe endpoints of invariant mass distributions. Here we discuss possible improvements by using theshapes of the distributions. Positive results are found for multiple-minima situations and for massregions where the endpoints do not contain sufficient information to obtain the masses.Keywords: BSM, SUSY, MSSM, MSUGRAPACS: 11.80.Cr, 12.60.Jv, 14.80.LyINTRODUCTIONIn R-parity conserving supersymmetric models sparticles are produced in pairs at thecollision point, then decay in cascades, resulting in a number of Standard Model particlesas well as two Lightest Supersymmetric Particles (LSPs), one for each primary sparticle.If the LSPs leave the detector without a trace, as is the case in most scenarios of thistype, the event cannot be fully reconstructed. This in turn prevents a direct measurementof the sparticle masses from mass peaks. The foreseen way to obtain these massesin such scenarios, is through endpoint measurements of invariant mass distributions[1, 2, 3, 4, 5, 6, 7]. Particularly suited is the cascade decay q˜L ! χ˜02 q ! ˜lRlnq ! χ˜01 lflnqwhich for a large share of SUSY models and parameters is kinematically allowed andappears at a rate sufficient for study. Four invariant mass distributions can be constructedfrom the visible decay products, mll, mqll, mql(high)and mql(low)1.Once the endpoints have been measured, the masses can be found. However, measur-ing an endpoint is not trivial. A fit must be made to the edge region of the distribution.Such a fit necessarily involves a signal and a background hypothesis. If these are not ingood correspondence with the true shapes, it is expected that the endpoint fitting may in-troduce large systematic uncertainties. While a straight-line hypothesis sometimes per-forms well, the fact that each distribution can take on a large variety of shapes [5, 7]really is a limiting factor, especially since a mismeasurement of an endpoint by 10 GeVcan easily multiply to 40 GeV in the resulting masses. Without an appropriate signal hy-1 Additional constrained mass distributions can be constructed, e.g. mqll for events with mll > mmaxll =p2.The corresponding endpoint measurements however usually involve large errors. Although relevant, suchdistributions have not been considered in this study.pothesis the endpoint method is incomplete. The many studies undertaken so far reflectthis in that they have mainly focused on determining the statistical error, which can befairly well estimated by a straight line, putting off the systematics of the fitting procedurefor later investigations. With the recent advent of an analytic description of the shapesof these mass distributions [8], the time for such investigations has come closer.MASSES FROM SHAPESThe completion of the endpoint method requires formulas for the edge-region part ofthe distributions expressed by the endpoints. The shape formulas are however writtenin terms of the sparticle masses. Fitting the distributions gives the masses directlywithout any recourse to the endpoints. The considerable difference in approach asks for acomparison between the two methods. We here investigate the matter for the mSUGRApoint SPS 1a [9]. In order for the characteristics of the methods to easily shine through,we make a simple comparison, with no background included, and no detector effects.The comparison is based on histograms generated randomly from the shape formulastaken from [8] convoluted with a gaussian of width 2 GeV for mll and 10 GeV for theother distributions. The selected procedure and numbers mimic the effect of sparticlewidths, initial and final-state radiation, detector effects etc. The same procedure is alsoinvoked for the shape-fitting process. The normalisation of the histograms correspondsroughly to the ultimate statistics expected for an LHC experiment.TABLE 1. Endpoint values and errors [in GeV] forSPS 1a.Nominal Fitted Error Inflated errormmaxll 77.07 77.13 0.04 0.04mmaxql(high) 375.8 378.9 0.4 1.2mmaxql(low) 298.5 304.2 0.8 2.4mmaxqll 425.9 432.3 0.3 0.9Endpoint method. For the endpoint analysis a straight-line fit is used to obtain thestatistical uncertainty. Table 1 shows the nominal values together with the fitted valuesand the errors obtained. A second set of errors, three times the statistical ones, exceptfor mmaxll , is included to give a slightly more realistic situation. The discrepancy betweenthe nominal and the fitted endpoints reminds us of the problem with endpoint fitting.Figure 1 (left and middle) shows the resulting 1, 2 and 3σ contours in the mχ˜01 –m˜lRplane for the two sets of errors. The nominal endpoint values are used, not the fittedones. From these figures the main characteristics of the endpoint method are apparent:the occurrence of multiple solutions [5, 10] and strong mass correlation reflecting thefact that mass differences are accurately determined while the overall scale only poorlyso.Shape method. Since the background is expected to be more prominent for lowerinvariant masses, only the higher part of the distributions are used in the shape fit.) [GeV]10χ∼m(70 75 80 85 90 95 100) [GeV]Rl~m(110115120125130135140145150) [GeV]10χ∼m(50 60 70 80 90 100 110 120) [GeV]R l~m(8090100110120130140150160) [GeV]10χ∼m(85 90 95 100 105 1102 χ2829303132333435363738σ1 σ2 σ3 FIGURE 1. SPS 1a comparison. Left (Middle): endpoint method for the first (second) set or errors. Twominima are found, the correct one situated at mχ˜01 = 96 GeV, the false at mχ˜01 = 80 GeV. Right: shape fitto the same distributions. The false minimum is not present.The result of the fit is given by the χ2-function in Fig. 1 (right). Notice that the falsesolution is absent. The shape difference for the two mass sets is apparently sufficientto discriminate between them. Whether or not this situation holds for a more realisticanalysis remains to be seen. The shape difference between these two points is belowmSUGRA average [11]. The precision on the overall mass scale returned by the shapefit is roughly as for the endpoint approach using the second error set, except for the falsesolution present in the endpoint case which stretches to very low masses. Finally it isfound that also for the shape fitting method the resulting masses are very correlated,constraining mass differences much more than masses. More study is however neededto compare the degree of correlation to that obtained from the endpoint method.WHEN ENDPOINTS ARE NOT ENOUGHIn some regions of mass space the four endpoints are no longer linearly independentdue to (mmaxqll )2 = (mmaxll )2+ (mmaxql(high))2. When this happens, which is for regions (2,3),(3,1) and (3,2) in the notation of [5], curves exist in the four-dimensional mass space onwhich all mass points produce the same endpoints. In region (3,2) the curve is given bym2˜lR=m2χ˜012  A; m2χ˜02= m2˜lR+(mmaxll )2A  1; m2q˜L = m2˜lR+(mmaxqll )2A  1; A = mmaxql(high)mmaxql(low)! 2(1)From one mass set new mass sets on the curve can be generated by keeping the end-points fixed, then changing mχ˜01 and calculating the other masses. Under these circum-stances four endpoint measurements do not impose sufficient constraints to obtain themasses. Extra information is however available from the shapes. Figure 2 (three left-most) shows the relevant gaussian-convoluted (width 10 GeV) mass distributions for themass set (mχ˜01;m˜lR;mχ˜02;mq˜L)= (100;300;500;600)GeV (black, solid), and two setson the line (1) defined by increasing (blue, dotted) and decreasing (red, dashed) mχ˜01by 30 GeV. While the endpoints are the same, the shapes are seen to differ. (The mllm(ql(high)) [GeV]0 100 200 300 400 500 6000200400600800100012001400m(ql(low)) [GeV]0 100 200 300 400 500 6000100200300400500600700800900m(qll) [GeV]0 100 200 300 400 500 60005001000150020002500) [GeV]10χ∼m(60 70 80 90 100 110 120 130 1402 χ012345678910σ1 σ2 σ3 FIGURE 2. Left to right: mql(high), mql(low) and mqll for three points in region (3,2), all having thesame endpoints, but different distributions. Right: χ2-function from fitting the shapes has minimum at thecorrect mχ˜01 . Only smearing is applied, no statistical fluctuations, therefore χ2min = 0.distribution is not shown as its shape is always the same.)Based on the distributions of the original mass set (mχ˜01 = 100 GeV, black solid), his-tograms are generated, assuming a similar number of events as for the previous SPS 1ainvestigations. Figure 2 (right) shows the χ2 function from a shape fit to these distri-butions. The histograms contain no statistical fluctuations, which is why the minimumis at χ2 = 0. Adding statistical fluctuations will lift χ2min from zero, but the conclusionstays the same: A clear minimum is found for the correct masses in this region wherethe endpoints alone can not bring the masses.CONCLUSIONWe have investigated the use of shape formulas to obtain the sparticle masses in sce-narios where the LSP is undetected. Comparison with the standard endpoint methodwas made for the mSUGRA point SPS 1a. The extra solution at mχ˜01 = 80 GeV whichis returned by the endpoint inversion, is absent in the shape-fitting results. The strongcorrelation in the resulting masses remains: Mass differences are accurately determinedwhile the overall mass scale has larger uncertainties. It was furthermore shown that theuse of shapes allows for masses to be determined in regions of mass space where theendpoints alone do not suffice due to linear interdependence. In conclusion, the use ofshapes to determine masses constitute a very promising approach. More study is needed.It is particularly important to understand what impact the distortion of the invariant massdistributions, particularly from selection cuts and various backgrounds, will have on theproposed shape fitting technique.ACKNOWLEDGMENTSBKG would like to thank Bern LHEP colleagues for useful discussions. ARR acknowl-edges support from the European Community through a Marie Curie Fellowship forEarly Stage Research Training. This research has been supported in part by the ResearchCouncil of Norway and the Swiss National Science Foundation.REFERENCES1. I. Hinchliffe, F. E. Paige, M. D. Shapiro, J. Soderqvist and W. Yao, Phys. Rev. D 55 (1997) 5520[arXiv:hep-ph/9610544].2. H. Bachacou, I. Hinchliffe and F. E. Paige, Phys. Rev. D 62 (2000) 015009 [arXiv:hep-ph/9907518].3. B. C. Allanach, C. G. Lester, M. A. Parker and B. R. Webber, JHEP 0009 (2000) 004[arXiv:hep-ph/0007009].4. C. G. Lester, CERN-THESIS-2004-003.5. B. K. Gjelsten, D. J. Miller and P. Osland, JHEP 0412 (2004) 003 [arXiv:hep-ph/0410303].6. G. Weiglein et al. [LHC/LC Study Group], Phys. Rept. 426 (2006) 47 [arXiv:hep-ph/0410364].7. B. K. Gjelsten, D. J. Miller and P. Osland, JHEP 0506 (2005) 015 [arXiv:hep-ph/0501033].8. D. J. Miller, P. Osland and A. R. Raklev, JHEP 0603 (2006) 034 [arXiv:hep-ph/0510356].9. B. C. Allanach et al., in Proc. of the APS/DPF/DPB Summer Study on the Future of Particle Physics(Snowmass 2001) ed. N. Graf, Eur. Phys. J. C 25 (2002) 113 [eConf C010630 (2001) P125][arXiv:hep-ph/0202233].10. B. K. Gjelsten, D. J. Miller and P. Osland, arXiv:hep-ph/0507232; arXiv:hep-ph/0511008.11. B. K. Gjelsten, D. J. Miller, P. Osland, A. R. Raklev, to appear in Proc. of the XXXIII Interna-tional Conference on High Energy Physics (ICHEP’06), Moscow, Russia, 26 July–2 August 2006[arXiv:hep-ph/0611080].

Gjelsten, Borge

BORIS Portal  Bern Open Repository and Information System

Mass Determination in Cascade Decays using Shape Formulas

In SUSY scenarios with escaping LSP, sparticle masses can be determined from fits to the endpoints of invariant mass distributions. Here we discuss possible improvements by using the shapes of the distributions. Interesting results are found for multiple‐minima situations and for mass regions where the endpoints do not contain sufficient information to obtain the masses

Enlighten

Mass determination in cascade decays using shape formulas

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.346.6377

Mass Determination in Cascade Decays Using Shape Formulas

Abstract

Similar works

Full text

Available Versions

Crossref

Crossref

CERN Document Server

Crossref

BORIS Portal Bern Open Repository and Information System

Crossref

Enlighten

Crossref

Crossref