We review the use of invariant mass distributions in cascade decays to
measure the masses of New Physics (NP) particles in scenarios where the final
NP cascade particle is invisible. We extend earlier work by exploring further
the problem of multiple solutions for the masses.Comment: 4 pages, 4 figures, to appear in the proceedings of the XXXIII
  International Conference on High Energy Physics (ICHEP'06), July 26 - August
  2 2006, Mosco

Gjelsten, B. K.

Miller, D. J.

Osland, P.

Raklev, A. R.

English

arXiv

Gjelsten, Borge K.

Osland, S.

Bern Open Repository and Information System (BORIS)

arXiv:hep-ph/0611080v1  7 Nov 2006December 21, 2013 20:39 WSPC/Trim Size: 10in x 7in for Proceedings ICHEP06MASS AMBIGUITIES IN CASCADE DECAYSB. K. GJELSTENLaboratory for High Energy Physics, University of Bern, CH-3012 Bern, SwitzerlandD. J. MILLERDepartment of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, U.K.P. OSLANDDepartment of Physics and Technology, University of Bergen, N-5020 Bergen, NorwayA. R. RAKLEVTheory Division, Physics Department, CERN, CH-1211 Gene`ve, SwitzerlandWe review the use of invariant mass distributions in cascade decays to measure the masses of NewPhysics (NP) particles in scenarios where the final NP cascade particle is invisible. We extendearlier work by exploring further the problem of multiple solutions for the masses.Keywords: SUSY; BSM; MSSM.1. IntroductionInspired by the precise determination ofthe dark matter relic density made possiblewith data from the WMAP satellite1,2,3 NewPhysics (NP) models with a weakly interact-ing massive particle have flourished over thelast years. Such particles, whether they ap-pear in models of supersymmetry, universalextra dimensions or little Higgs theories, areinvisible to the detectors of collider experi-ments, and to be viable dark matter candi-dates, certainly stable on the scale of the cur-rent age of the universe. The conservation ofa NP quantum number, be it R-parity, KK-parity or T-parity, ensures a cascade decay ofall heavier NP particles into the lightest NPparticle. Measuring NP particle masses insuch scenarios by reconstructing mass peaksis then in general no longer possible.The well studied alternative to this is touse measurements of the endpoints of invari-ant mass distributions.4,5,6,7,8,9,10 As we canexpress endpoint positions in terms of theNP masses, we can in principle solve for themasses if we have at least as many endpointsas unknown masses. However, there are non-trivial problems with this method. Generallythe expressions for the endpoints are com-plicated functions, leading to possible mul-tiple solutions, and strong correlations be-tween the measured masses.11 As an illustra-tion of this problem, we consider the decaychainq˜L → χ˜02q → ℓ˜Rℓnq → χ˜01ℓf ℓnq (1)and show in Fig. 1 the quantityµ =∑i|mfalsei −mtruei |/mtruei (2)for a scan over the SPS1a12 mSUGRA scalar(m0) and gaugino (m1/2) mass plane for atrilinear coupling A0 = −m0, tanβ = 10 andµ > 0. The sum in (2) runs over the squark,slepton and neutralino masses in the decaychain (1).We find that for virtually all points inthe mass plane where the decay chain (1) ex-ists, and where the lightest supersymmetricparticle (LSP) is not the stau (at lowm0), we1source: https://doi.org/10.7892/boris.20726 | downloaded: 8.5.2016December 21, 2013 20:39 WSPC/Trim Size: 10in x 7in for Proceedings ICHEP062 [GeV]1/2m100 200 300 400 500 600 700 800 900 1000 [GeV]0m10020030040050060070001234567 LSPτ∼)αSPS1a  ()βSPS1a  (1/2=0.4m0SPS1 slope, mFig. 1. Scan of µ, as given by Eq. (2), over theSPS1a mass plane. In the top white area the de-cay chain (1) is not kinematically accessible, whilethe bottom white area has a charged stau LSP.get a false solution from the set of endpoints.Along the middle of the physical wedge inthis plane, and intersecting the SPS1a line,the above quantity can become rather large.In an experiment one might also encounterthe problem of “feet”, i.e. structures in thedistributions near the endpoints that are hid-den by background.8,13We have previously started an investiga-tion into the possible improvements to thismethod that can result from fitting the wholeinvariant mass distribution to an analyticalexpression derived for its shape.13 We foundthat knowledge of the shape will predict anypossible irregular features at the endpointsfor a measured set of masses, thus essentiallyremoving the problem of feet. Here we wantto investigate further what effect knowledgeof the shape of the invariant mass distribu-tion has on the problem of multiple solutions.2. Multiple solutionsUsing as our example the four possiblea in-variant mass distributions for the SUSY de-aWe can form the invariant mass of the two leptons,the two leptons and a jet, but assuming that we can-not, in general, identify which lepton is the leptonnearest to the squark in the decay chain, we use jet-0 20 40 60 0 200 400 6000 100 200 0 200 400 600Fig. 2. Invariant mass distributions for the SU1benchmark point and the decay chain (1) with ar-bitrary normalisation. In blue (solid) are the distri-butions for the nominal masses, in red (dashed) arethe distributions for the masses in the false solution.cay chain (1) we show in Fig. 2 the shape ofthese distributions, as found in Ref. 13, forthe nominal masses of the ATLAS SU1 stau-coannihilation benchmark point. (One mayconstruct other invariant mass distributionby imposing cuts, but for simplicity we willneglect them here.)For SU1 there is also another set ofmasses that give the same endpoints for theinvariant mass distributions. If only end-points are measured we have two indistin-guishable solutions for the SUSY masses.The two sets are given in Table 1 as the nom-inal masses of the benchmark point, and thefalse solution from the nominal endpoints ofthe benchmark point.In Fig. 2 we see that there are only smallvisible differences in the shapes between thetwo mass sets of SU1 for three of the distri-butions, but for mql(low) there is a markedlepton combinations that give the highest and lowestinvariant mass.December 21, 2013 20:39 WSPC/Trim Size: 10in x 7in for Proceedings ICHEP063Table 1. Nominal and false sets ofmasses for benchmark points [GeV].Set mχ˜01ml˜Rmχ˜02mq˜LSU1 nom. 137 254 264 760SU1 false 122 127 246 744SU3 nom. 118 155 219 631SU3 false 347 411 452 900change. Similar differences in the shapescan also be seen in three of the distributionsfor SU3, the bulk-region benchmark point,shown in Fig. 3, although they are individu-ally somewhat less distinct than for SU1. Forboth cases it seems likely that the false so-lution could be ruled out, with the expectedhigh statistics at the LHC for SUSY scenar-ios with sub-TeV squark masses. For theSU3 benchmark point the large differences inmass between the solutions should also showup clearly in the measured cross sections.This is unfortunately not the situationfor all models. For the SPS1a bulk-regionbenchmark point12 the differences in theshapes are very small. After adding smear-0 50 100 0 200 4000 100 200 300 0 200 400Fig. 3. Invariant mass distributions for the SU3benchmark point. See caption of Fig. 2 for details.ing from detector effects, combinatorics frompicking the correct jet, initial and final stateradiation etc., separating the two mass setsfor SPS1a will be very difficult and requirevery large statistics and an extremely goodunderstanding of the detector, if at all possi-ble.It is then natural to ask how effectivethe shape can be in distinguishing multiplesolutions over a wide range of SUSY models.In Fig. 4 we show a scan over the SPS1a massplane. We plot the value ofD =12NN∑i=1∫ mmaxi0|fi(m)− gi(m)| dm (3)where fi and gi are the invariant mass distri-butions for the false and nominal sets of masssolutions (normalized to∫dmf(m) = 1,∫dmg(m) = 1), with the i-index runningover the number of distributions N (hereN = 4), and where mmaxi is the endpointof the i-th distribution. The numerical pre-factor ensures that D ≤ 1.The difference in shape between thenominal and false solutions, as quantifiedby the D-value is fairly constant at aroundD ≈ 0.07, except for a wedge in the massplane, where we have a transition between [GeV]1/2m100 200 300 400 500 600 700 800 900 1000 [GeV]0m10020030040050060070000.020.040.060.080.10.12 LSPτ∼)αSPS1a  ()βSPS1a  (1/2=0.4m0SPS1 slope, mFig. 4. Scan of D, as given by Eq. (3), over theSPS1a mass plane. In the top white area the decaychain (1) is not kinematically accessible, while thebottom white area has a charged stau LSP.December 21, 2013 20:39 WSPC/Trim Size: 10in x 7in for Proceedings ICHEP064different forms for the analytical expressionsfor the mql(low) and mql(high) distributions.13In this region the D-value changes rapidlyfrom low to high values, and from Fig. 4we see that the SPS1a benchmark point suf-fers from an unfortunate position, giving ita value of D = 0.016. Comparing to Fig. 1we find that while large mass differences cangive large differences in shape, there are cer-tainly areas where the correct solution couldbe readily identified from the shape, evenwhen the mass differences are small, and thuswhere a comparison of cross sections wouldbe difficult.Due to smearing from the experimentaleffects mentioned above, it is difficult to cal-culate exactly for what D-value two sets ofsolutions can be distinguished for some givenintegrated luminosity at the LHC. However,assuming that the two distributions of SU1are distinguishable, and using as a basis forcomparison that we find a D-value of D =0.070 for SU1, this suggests that we shouldbe able to distinguish between the nominaland false solutions in most of the parameterspace shown in Fig. 4. We have performedsuch scans for different values of A0 andtanβ, in the mass planes of the SPS1b, SPS3and SPS5 benchmark points,12 and find sim-ilar results there.3. ConclusionsWe have discussed aspects of the use of an-alytical expressions for invariant mass distri-butions in determining masses in NP scenar-ios, using a well studied SUSY decay chainas our example. We have focused on the pos-sibility of using differences in the shapes ofdistributions to remove false solutions thatappear if only the endpoints of the invari-ant mass distributions are used to determinethe NP masses. Our results from scans ofthe mSUGRA parameter space indicate thatwith the exception of certain limited areas,the shapes of the distributions should in gen-eral be well suited to reject the false solu-tion, given that enough statistics are avail-able, and may be applied even when a com-parison of cross sections would be difficult.AcknowledgmentsARR acknowledges support from the Euro-pean Community through a Marie Curie Fel-lowship for Early Stage Research Training.This research has been supported in partby the Research Council of Norway and theSwiss National Science Foundation.References1. C. L. Bennett et al., Astrophys. J. Suppl.148, 1 (2003) [arXiv:astro-ph/0302207].2. D. N. Spergel et al., Astrophys. J. Suppl.148, 175 (2003) [arXiv:astro-ph/0302209].3. D. N. Spergel et al., arXiv:astro-ph/0603449.4. I. Hinchliffe, F. E. Paige, M. D. Shapiro,J. Soderqvist and W. Yao, Phys. Rev. D55,5520 (1997) [arXiv:hep-ph/9610544].5. H. Bachacou, I. Hinchliffe and F. E. Paige,Phys. Rev. D62, 015009 (2000) [arXiv:hep-ph/9907518].6. B. C. Allanach, C. G. Lester, M. A. Parkerand B. R. Webber, JHEP 0009, 004 (2000)[arXiv:hep-ph/0007009].7. C. G. Lester, CERN-THESIS-2004-003.8. B. K. Gjelsten, D. J. Miller and P. Osland,JHEP 0412, 003 (2004) [arXiv:hep-ph/0410303].9. G. Weiglein et al. [LHC/LC Study Group],Phys. Rept. 426, 47 (2006) [arXiv:hep-ph/0410364].10. B. K. Gjelsten, D. J. Miller and P. Osland,JHEP 0506, 015 (2005) [arXiv:hep-ph/0501033].11. B. K. Gjelsten, D. J. Miller and P. Osland,arXiv:hep-ph/0507232;arXiv:hep-ph/0511008.12. B. C. Allanach et al., in Proc. of theAPS/DPF/DPB Summer Study on the Fu-ture of Particle Physics (Snowmass 2001),ed. N. Graf, Eur. Phys. J. C25, 113 (2002)[arXiv:hep-ph/0202233].13. D. J. Miller, P. Osland and A. R. Rak-lev, JHEP 0603, 034 (2006) [arXiv:hep-ph/0510356].

Mass ambiguities in cascade decays

Gjelsten, B.K.

Miller, D.J.

Raklev, A.R.

Enlighten

Mass Ambiguities in Cascade Decays

We review the use of invariant mass distributions in cascade decays to measure the masses of New Physics (NP) particles in scenarios where the final NP cascade particle is invisible. We extend earlier work by exploring further the problem of multiple solutions for the masses.We review the use of invariant mass distributions in cascade decays to measure the masses of New Physics (NP) particles in scenarios where the final NP cascade particle is invisible. We extend earlier work by exploring further the problem of multiple solutions for the masses.We review the use of invariant mass distributions in cascade decays to measure the masses of New Physics (NP) particles in scenarios where the final NP cascade particle is invisible. We extend earlier work by exploring further the problem of multiple solutions for the masses.We review the use of invariant mass distributions in cascade decays to measure the masses of New Physics (NP) particles in scenarios where the final NP cascade particle is invisible. We extend earlier work by exploring further the problem of multiple solutions for the masses

CERN Document Server

arXiv:hep-ph/0611080v1  7 Nov 2006O ctober 22,2013 21:26 W SPC/Trim Size: 10in x 7in forProceedings ICH EP06M A SS A M B IG U IT IES IN C A SC A D E D EC AY SB.K .G JELSTENLaboratory for High Energy Physics,University ofBern,CH-3012 Bern,SwitzerlandD .J.M ILLERDepartm entofPhysics and Astronom y,University ofG lasgow,G lasgow G 12 8Q Q ,U.K .P.O SLANDDepartm entofPhysics and Technology,University ofBergen,N-5020 Bergen,NorwayA.R.RAK LEVTheory Division,Physics Departm ent,CERN,CH-1211 G eneve,SwitzerlandW e review the use ofinvariantm assdistributionsin cascade decaysto m easure the m assesofN ewPhysics (N P) particles in scenarios where the nalN P cascade particle is invisible. W e extendearlierwork by exploring furtherthe problem ofm ultiple solutions forthe m asses.K eywords:SU SY ;BSM ;M SSM .1. IntroductionInspired by the precise determ ination ofthe dark m atter relic density m ade possiblewith datafrom theW M AP satellite1;2;3 NewPhysics(NP)m odelswith a weakly interact-ing m assiveparticlehave ourished overthelastyears. Such particles,whetherthey ap-pear in m odels ofsupersym m etry,universalextra dim ensionsorlittle Higgstheories,areinvisible to the detectors ofcollider experi-m ents,and to be viable dark m atter candi-dates,certainlystableon thescaleofthecur-rentageoftheuniverse.Theconservation ofa NP quantum num ber,be itR-parity,K K -parity orT-parity,ensuresacascadedecayofallheavierNP particlesinto the lightestNPparticle. M easuring NP particle m asses insuch scenariosby reconstructing m asspeaksisthen in generalno longerpossible.Thewellstudied alternativeto thisistousem easurem entsoftheendpointsofinvari-antm assdistributions.4;5;6;7;8;9;10 Aswecanexpress endpoint positions in term s of theNP m asses,we can in principle solve forthem assesifwehaveatleastasm any endpointsasunknown m asses.However,therearenon-trivialproblem swith thism ethod.G enerallythe expressions for the endpoints are com -plicated functions,leading to possible m ul-tiple solutions, and strong correlations be-tween them easured m asses.11 Asan illustra-tion ofthis problem ,we consider the decaychain~qL ! ~02q!~‘R ‘nq! ~01‘f‘nq (1)and show in Fig.1 the quantity =Xijmfalsei   mtruei j=mtruei (2)fora scan overtheSPS1a12 m SUG RA scalar(m 0) and gaugino (m 1=2) m ass plane for atrilinearcouplingA 0 =   m 0,tan = 10and > 0.The sum in (2)runsoverthe squark,slepton and neutralino m asses in the decaychain (1).W e  nd that for virtually allpoints inthem assplanewherethedecay chain (1)ex-ists,and where the lightestsupersym m etricparticle(LSP)isnotthestau (atlow m 0),we1O ctober 22,2013 21:26 W SPC/Trim Size: 10in x 7in forProceedings ICH EP062 [GeV]1/2m100 200 300 400 500 600 700 800 900 1000 [GeV]0m10020030040050060070001234567 LSPτ∼)αSPS1a  ()βSPS1a  (1/2=0.4m0SPS1 slope, mFig. 1. Scan of , as given by Eq. (2), over theSPS1a m ass plane. In the top white area the de-cay chain (1) is not kinem atically accessible, whilethe bottom white area has a charged stau LSP.geta falsesolution from thesetofendpoints.Along the m iddle ofthe physicalwedge inthis plane,and intersecting the SPS1a line,the abovequantity can becom e ratherlarge.In an experim ent one m ight also encounterthe problem of\feet",i.e. structuresin thedistributionsneartheendpointsthatarehid-den by background.8;13W ehavepreviously started an investiga-tion into the possible im provem ents to thism ethod thatcan resultfrom  ttingthewholeinvariant m ass distribution to an analyticalexpression derived foritsshape.13 W e foundthatknowledgeoftheshapewillpredictanypossible irregular features at the endpointsfora m easured setofm asses,thusessentiallyrem oving the problem offeet.Herewe wantto investigate furtherwhate ectknowledgeofthe shape ofthe invariantm ass distribu-tion hason theproblem ofm ultiplesolutions.2. M ultiple solutionsUsing as our exam ple the four possiblea in-variantm assdistributionsforthe SUSY de-aW e can form the invariantm assofthe two leptons,the two leptonsand a jet,butassum ing thatwe can-not, in general, identify which lepton is the leptonnearestto the squark in the decay chain,we use jet-0 20 40 60 0 200 400 6000 100 200 0 200 400 600Fig. 2. Invariant m ass distributions for the SU 1benchm ark point and the decay chain (1) with ar-bitrary norm alisation. In blue (solid) are the distri-butions for the nom inalm asses,in red (dashed) arethe distributionsforthe m assesin the false solution.cay chain (1)weshow in Fig.2 the shape ofthese distributions,as found in Ref.13,forthenom inalm assesoftheATLAS SU1 stau-coannihilation benchm ark point. (O ne m ayconstruct other invariant m ass distributionby im posing cuts,butfor sim plicity we willneglectthem here.)For SU1 there is also another set ofm assesthatgive the sam e endpointsfortheinvariant m ass distributions. If only end-points are m easured we have two indistin-guishable solutions for the SUSY m asses.Thetwosetsaregiven in Table1asthenom -inalm assesofthebenchm ark point,and thefalse solution from the nom inalendpointsofthe benchm ark point.In Fig.2weseethatthereareonly sm allvisible di erencesin the shapesbetween thetwo m asssetsofSU1 forthree ofthe distri-butions,but for m ql(low ) there is a m arkedlepton com binationsthatgive thehighestand lowestinvariantm ass.O ctober 22,2013 21:26 W SPC/Trim Size: 10in x 7in forProceedings ICH EP063Table 1. N om inal and false sets ofm asses forbenchm ark points [G eV ].Set m~ 01m ~lRm~ 02m ~qLSU 1 nom . 137 254 264 760SU 1 false 122 127 246 744SU 3 nom . 118 155 219 631SU 3 false 347 411 452 900change. Sim ilar di erences in the shapescan also beseen in threeofthedistributionsfor SU3, the bulk-region benchm ark point,shown in Fig.3,although they areindividu-ally som ewhatlessdistinctthan forSU1.Forboth cases it seem s likely that the false so-lution could be ruled out,with the expectedhigh statisticsatthe LHC forSUSY scenar-ios with sub-TeV squark m asses. For theSU3 benchm ark pointthelargedi erencesinm assbetween thesolutionsshould also showup clearly in the m easured crosssections.This is unfortunately not the situationfor allm odels. For the SPS1a bulk-regionbenchm ark point12 the di erences in theshapes are very sm all. After adding sm ear-0 50 100 0 200 4000 100 200 300 0 200 400Fig. 3. Invariant m ass distributions for the SU 3benchm ark point. See caption ofFig.2 fordetails.ing from detectore ects,com binatoricsfrompicking the correctjet,initialand  nalstateradiation etc.,separating the two m ass setsfor SPS1a willbe very di cult and requirevery large statistics and an extrem ely goodunderstanding ofthedetector,ifatallpossi-ble.It is then naturalto ask how e ectivethe shape can be in distinguishing m ultiplesolutionsovera widerangeofSUSY m odels.In Fig.4weshow ascan overtheSPS1am assplane.W e plotthe value ofD =12NNXi= 1Z mm axi0jfi(m )  gi(m )jdm (3)wherefi and gi aretheinvariantm assdistri-butionsforthefalseand nom inalsetsofm asssolutions (norm alized toRdm f(m ) = 1,Rdm g(m ) = 1), with the i-index runningover the num ber of distributions N (hereN = 4), and where m m axi is the endpointofthe i-th distribution. The num ericalpre-factorensuresthatD  1.The di erence in shape between thenom inal and false solutions, as quanti edby the D -value is fairly constant at aroundD  0:07,except for a wedge in the m assplane,where we have a transition between [GeV]1/2m100 200 300 400 500 600 700 800 900 1000 [GeV]0m10020030040050060070000.020.040.060.080.10.12 LSPτ∼)αSPS1a  ()βSPS1a  (1/2=0.4m0SPS1 slope, mFig. 4. Scan of D , as given by Eq. (3), over theSPS1a m ass plane. In the top white area the decaychain (1) is not kinem atically accessible, while thebottom white area has a charged stau LSP.O ctober 22,2013 21:26 W SPC/Trim Size: 10in x 7in forProceedings ICH EP064di erentform sfortheanalyticalexpressionsforthem ql(low ) and m ql(high) distributions.13In this region the D -value changes rapidlyfrom low to high values, and from Fig. 4weseethattheSPS1a benchm ark pointsuf-fers from an unfortunate position,giving ita value ofD = 0:016. Com paring to Fig.1we nd thatwhilelargem assdi erencescangivelargedi erencesin shape,therearecer-tainly areaswherethecorrectsolution couldbe readily identi ed from the shape, evenwhen them assdi erencesaresm all,and thuswhere a com parison ofcross sections wouldbe di cult.Due to sm earing from the experim entale ectsm entioned above,itisdi cultto cal-culate exactly for what D -value two sets ofsolutionscan bedistinguished forsom egivenintegrated lum inosity atthe LHC.However,assum ing that the two distributions ofSU1are distinguishable,and using asa basisforcom parison that we  nd a D -value ofD =0:070 for SU1,this suggests that we shouldbe able to distinguish between the nom inaland false solutionsin m ostofthe param eterspace shown in Fig.4. W e have perform edsuch scans for di erent values of A0 andtan,in them assplanesoftheSPS1b,SPS3and SPS5 benchm ark points,12 and  nd sim -ilarresultsthere.3. C onclusionsW e have discussed aspects ofthe use ofan-alyticalexpressionsforinvariantm assdistri-butionsin determ ining m assesin NP scenar-ios,using a wellstudied SUSY decay chainasourexam ple.W ehavefocused on thepos-sibility ofusing di erences in the shapes ofdistributions to rem ove false solutions thatappear if only the endpoints of the invari-antm assdistributionsareused to determ inethe NP m asses. O ur results from scans ofthem SUG RA param eterspaceindicatethatwith the exception ofcertain lim ited areas,theshapesofthedistributionsshould in gen-eralbe wellsuited to reject the false solu-tion,given that enough statistics are avail-able,and m ay be applied even when a com -parison ofcrosssectionswould be di cult.A cknow ledgm entsARR acknowledges support from the Euro-pean Com m unity through aM arieCurieFel-lowship for Early Stage Research Training.This research has been supported in partby the Research CouncilofNorway and theSwissNationalScience Foundation.R eferences1. C.L.Bennett et al., Astrophys. J. Suppl.148,1 (2003)[arXiv:astro-ph/0302207].2. D . N.Spergel et al., Astrophys. J. Suppl.148,175 (2003)[arXiv:astro-ph/0302209].3. D . N. Spergel et al., arXiv:astro-ph/0603449.4. I. Hinchlie, F. E. Paige, M . D . Shapiro,J.Soderqvistand W .Yao,Phys.Rev. D 55,5520 (1997)[arXiv:hep-ph/9610544].5. H.Bachacou,I.Hinchlie and F.E.Paige,Phys.Rev. D 62,015009 (2000)[arXiv:hep-ph/9907518].6. B.C.Allanach,C.G .Lester,M .A.Parkerand B.R.W ebber,JHEP 0009,004 (2000)[arXiv:hep-ph/0007009].7. C.G .Lester,CERN-THESIS-2004-003.8. B.K .G jelsten,D .J.M iller and P.O sland,JHEP 0412, 003 (2004) [arXiv:hep-ph/0410303].9. G .W eiglein etal.[LHC/LC Study G roup],Phys. Rept. 426, 47 (2006) [arXiv:hep-ph/0410364].10. B.K .G jelsten,D .J.M iller and P.O sland,JHEP 0506, 015 (2005) [arXiv:hep-ph/0501033].11. B.K .G jelsten,D .J.M iller and P.O sland,arXiv:hep-ph/0507232;arXiv:hep-ph/0511008.12. B. C. Allanach et al., in Proc. of theAPS/DPF/DPB Sum m er Study on the Fu-ture ofParticle Physics (Snowm ass 2001),ed.N.G raf,Eur.Phys.J. C 25,113 (2002)[arXiv:hep-ph/0202233].13. D . J. M iller, P. O sland and A. R. Rak-lev, JHEP 0603, 034 (2006) [arXiv:hep-ph/0510356].

Mass ambiguities in cascade decays

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