SUSY at LHC  KEK · 2008. 9. 29. · production process I nclusive SUSY Se ar ches qq~~ qq ~_~ ~~...
Transcript of SUSY at LHC  KEK · 2008. 9. 29. · production process I nclusive SUSY Se ar ches qq~~ qq ~_~ ~~...

SUSY at LHC

production process
Inclusive SUSY Searches
~~qq
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~~gg
~~gq
M(q) = 1.2 M(g)~ ~
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“Typical” SUSY model has gluinos andsquarks at O 1TeV decaying to χ̃01 atO 100GeV .
Cross sections known to NLO; typically1pb [Beenakker].
Generally decay to χ̃01 via several steps,
g̃ q̃Lq̄ χ̃02qq̄ ˜ qq̄ χ̃01 qq̄
Hence expect multiple jets plus large /ETfrom χ̃01. May also have leptons or τ’s.
Standard Model backgrounds include Z νν̄ jets, W jets, tt̄, b jetswith b νX , etc. Also backgrounds from mismeasured events.
F.E. Paige 8 BSM Flavor Physics
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Large in small M(SUSY) Large in high M(SUSY)

SUGRA parameter and cross section
S.Asai 2003 JPS meeting
cross section
large production cross sectionn expressed by mass and QCD coupling. high x PDF needed K factor is 1.4

Cross section of possible background process
S.Asai （２００7、JPS)
Production process
at 10fb^1(the first year)
Observed ever (by 2007)
/hour
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Basic objects at LHC
• jet and lepton momenta
• Jet and lepton transverse momenta (to the beam)
• ETmiss: Sum of the transverse momenta of all particles.
• Meff Sum of the transverse energies of first 4 jets + ETmiss
DM
DM
New particle
New particle
Missing PT
2
The gluino and squark decays are associated with jets with high transverse momentum (pT ). Thetransverse momentum is the order of the gluino and squark masses. Moreover, because the LSP issignificantly lighter than the gluino, the LSP from the gluino decay also has high pT . They wouldgive a large missing transverse momentum to the SUSY events. In addition, decays of the EWIsparticles may produce high PT leptons. Events from the standard model (SM) processes do nothave such high pT particles.
Motivated by these observations, following cuts are often applied to reduce the SM backgroundevents to the SUSY signal events[2];
• An event is required to have at least one jet with PT > 100 GeV and three jets with PT > 50 GeVwithin η < 3,
• The effective mass of the event must satisfy Meff > 400 GeV, where the effective mass is definedusing the transverse missing energy and the transverse momentum of four leading jets as:
Meff ≡∑
i=1,...4
pTi + ETmiss. (2)
If the event has hard isolated leptons, the effective mass may be defined as follows:
Meff ≡∑
i=1,...4
pTi +∑
leptons
pT l + ETmiss. (3)
Here sum of the lepton pT can be taken over the leptons with pT > 20 GeV and η < 2.5 GeV.
• The missing transverse energy must satisfy the relation:
ETmiss > max(0.2Meff , 100GeV). (4)
• The transverse sphericity ST must be greater than 0.2, where ST is defined as 2λ2/(λ1 + λ2),with λ1 and λ2 being the eigenvalues of the 2 × 2 sphericity tensor Sij = pkipkj formed bysumming over the tranverse momentum of all calorimeter cells.
To reduce the background further, hard, isolated lepton(s) may be required. These cuts are enoughto reduce the SM backgrounds from tt̄+njets and W (Z) +njets productions down to a manageablelevel, although the production cross section of the SM processes may be O(104) higher than signalcross sections. While the SUSY production section reduces very quickly as sparticle masses increasebeyond 1 TeV, the signature becomes more and more prominent over the background. Previousstudies show that the squark and gluino with mass around 2.5 TeV can be found at the LHC in theminimal super gravity model (MSUGRA).
In MSUGRA, the SM background after the cuts can be neglected safely. Then, the distribution ofaccepted events are also useful to determine the mass scale of SUSY particles. For example, the peakof Meff distribution is sensitive to the squark and gluino masses. For the events with same flavoropposite sign dileptons, the invarian mass distributions, mll, mjl, and mjll, are useful to reconstructthe SUSY particle masses mχ̃01 , mχ̃02 , mq̃01 and ml̃01 .
Recently it is pointed out that a string inspired model based on the flux compactification (KKLTmodels) [5] predicts the mass relation different to the MSUGRA [6–8]. The model is called mixedmodulus anomaly mediation (MMAM) model. It has a volume modulas T and a compensator fieldof minimum supergravity model C as messanger of SUSY breaking. The SUSY mass spectrumdepends on the ratio of the two SUSY breaking parameters FT and FC . The unification scale ofsparticle masses depends on the ratio. It is interesting that the unification scale of the soft SUSY
pT1, pT2, pT3.....
pj1, pj2,.... pl1, pl2....

DM and collider signature
• “SUSY signature” “Models with new colored particles decaying into a stable neutral particleLSP”
• “New physics” are migrated into SUSY category
• Little Higgs model with T parity. UED
• Signal:
High PT jets (pT1>100GeV, pT2,3,4>50GeV)
pTl>20GeV, ST>0.2
ETmiss> max(100GeV, 0.2Meff )
t̃, b̃
Lepton partners
Dark matter LSP, LKK, LOT
colored partner squark, gluino,
g1, q1, extra quarks
gauge partners
assume mass difference is large

DM
DM
quark > jet
ETmiss

Background and discovery
• The typical number of SUSY events are 105 for 10 fb1, while BG rate is 1098 for W, Z and ttbar productions. 104 rejection of SM process is required.
• Understanding of the distribution is the key issue
• PT distribution of the jets, Meff distribution. (theoretical complexities)
• Etmiss distributions(Experimental complexities)
!"#$%&$'(')*+,'./!'0#121,'34&45647'899: ;%1172?@2,'+ABC
+71$$'$4&2%1D$'('2"4')*+
EF4

Cuts on Meff
• At hadron collider, particles are produced at the energy threshold.
• The pT of the decay products are peaked at its energy.
• Therefore , sume of pT represents the scale of the produced sparticles very well
P(pT
E
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∝
2pT /E√
1 −(
pTE
)2
PT/E
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The gluino and squark decays are associated with jets with high transverse momentum (pT ). Thetransverse momentum is the order of the gluino and squark masses. Moreover, because the LSP issignificantly lighter than the gluino, the LSP from the gluino decay also has high pT . They wouldgive a large missing transverse momentum to the SUSY events. In addition, decays of the EWIsparticles may produce high PT leptons. Events from the standard model (SM) processes do nothave such high pT particles.
Motivated by these observations, following cuts are often applied to reduce the SM backgroundevents to the SUSY signal events[2];
• An event is required to have at least one jet with PT > 100 GeV and three jets with PT > 50 GeVwithin η < 3,
• The effective mass of the event must satisfy Meff > 400 GeV, where the effective mass is definedusing the transverse missing energy and the transverse momentum of four leading jets as:
Meff ≡∑
i=1,...4
pTi + ETmiss. (2)
If the event has hard isolated leptons, the effective mass may be defined as follows:
Meff ≡∑
i=1,...4
pTi +∑
leptons
pT l + ETmiss. (3)
Here sum of the lepton pT can be taken over the leptons with pT > 20 GeV and η < 2.5 GeV.
• The missing transverse energy must satisfy the relation:
ETmiss > max(0.2Meff , 100GeV). (4)
• The transverse sphericity ST must be greater than 0.2, where ST is defined as 2λ2/(λ1 + λ2),with λ1 and λ2 being the eigenvalues of the 2 × 2 sphericity tensor Sij = pkipkj formed bysumming over the tranverse momentum of all calorimeter cells.
To reduce the background further, hard, isolated lepton(s) may be required. These cuts are enoughto reduce the SM backgrounds from tt̄+njets and W (Z) +njets productions down to a manageablelevel, although the production cross section of the SM processes may be O(104) higher than signalcross sections. While the SUSY production section reduces very quickly as sparticle masses increasebeyond 1 TeV, the signature becomes more and more prominent over the background. Previousstudies show that the squark and gluino with mass around 2.5 TeV can be found at the LHC in theminimal super gravity model (MSUGRA).
In MSUGRA, the SM background after the cuts can be neglected safely. Then, the distribution ofaccepted events are also useful to determine the mass scale of SUSY particles. For example, the peakof Meff distribution is sensitive to the squark and gluino masses. For the events with same flavoropposite sign dileptons, the invarian mass distributions, mll, mjl, and mjll, are useful to reconstructthe SUSY particle masses mχ̃01 , mχ̃02 , mq̃01 and ml̃01 .
Recently it is pointed out that a string inspired model based on the flux compactification (KKLTmodels) [5] predicts the mass relation different to the MSUGRA [6–8]. The model is called mixedmodulus anomaly mediation (MMAM) model. It has a volume modulas T and a compensator fieldof minimum supergravity model C as messanger of SUSY breaking. The SUSY mass spectrumdepends on the ratio of the two SUSY breaking parameters FT and FC . The unification scale ofsparticle masses depends on the ratio. It is interesting that the unification scale of the soft SUSY

Etmiss cut gg → T−T
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−, T− → tBH pp→ttbar
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ATLAS assumes 1 fb‐1 , detector systematics as with 1 fb‐1 background syst. uncert. with 1 fb‐1 : QCD 50%, W/Z/top 20% Significance: from Poisson probability of backgrounds, including stat.+syst. uncertainties, to fluctuate to signal
Baseline: 4 jets (>100, 50, 50, 50 GeV) ETmiss > 100 GeV, > 0.2 Meff ST > 0.2 No e or µ Δϕ(jet 1,2,3 – MET)>0.2
Alternative: 2 or 3 jets with ETmiss Cut harder on pT of jets (>150, 100 GeV) and ETmiss (>0.25 or 0.3 Meff ) somewhat better significance, but more sensitive to QCD bg.
ATLAS benchmarks (other than SU2) all > 5σ in 1 fb‐1

SUSY Searches at the LHC 14 Oleg Brandt, Univ. of Oxford
mSUGRA reach at ATLAS & CMS (1 fb1)
A0 = 0, µ > 0, tan! = 10, 5" contours (incl. systematics)
! Assumed uncertainties (ATLAS):
! QCD: 50%
! tt, V+j: 20%
1 fb1
1 fb1
! Beware:
! Different significance
definitions!
! CMS: syst. uncertainties
estimated for 10 fb1
(except 0lepton: 1 fb1)
In principle, we can say lots using first 1fb 1. understand of
background is the key.

!"#$%&'()*
! +,&./0,(PS)123Pt(456738961:;"#?@AB&(ME)1CollinearCSoft:456DEFG
! CollinearCSoft:4561PSH
7389
IJKL
PythiaCHerwig61PS6)*
M
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Pt(GeV)
OPQRQSTUVTWXYZ[\\K[\P]\[XY\S^^T[TP_S`\aY[• Bg process pp→W(Z)+X, ttbar ....
• Lowest order process (ex gq→W q) +“multiple parton final states” (ex. gq→ W+ n jet not in soft and collinear region (ME collections, CKKW, Mangano)
• Some generators(ALPGEN, MADevent..) allow to simulate multiparton final state. Matching between PS and ME. (Lessons from Tevatron)
• up to ttbar + 3 jet, W(Z) +6 jet (!) have been included in BG estimation.
Estimating background better
Asai TEV4LHC
PS(soft and collinear)
ME correction

Success of QCD simulation at Tevatron
• 2> 2 process with PS cannot reproduce Tevatron data, with PS+ME matching, it looks OK.
• Comparison of five matrix elelemnt generator with matching shows good agreement.
• After matching , predictions are independent of mtrix
Marc Buehler, UVa SUSY 06, UCIrvine 9
Z + n Jets: Jet Multiplicities
PYTHIA SHERPA
! MC normalized w.r.t. total number of events observed in data
! MC range stat: central value ±1"stat
for MC
! MC range stat & sys: central value ± stat and sys! Main data error due to jet energy scale uncertainties
 too few multijet events
Marc Buehler, UVa SUSY 06, UCIrvine 14
Leading jet pT
in events with n!1 jets2nd jet pT in events
with n!2 jets3rd jet p
T in events
with n!3 jets
Data vs MC: Jets
Jet pT data to theory (MEPS) comparison for

SUSY+jet (Madgraph V4.4)Any physics output from SUSY + jet?
15
example: degenerate SUSY > pT of jets become smallerStandard cut throw away lots of events. Alwall et al with initial state radiation,
it may be visible (at least at Tevatron. )
Out[129]=
XX
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FIG. 2: The 95% gluinobino exclusion curve for DO! at 4fb−1 for S/B > 1. The dashed line shows the correspondingexclusion region using DO! ’s nonoptimized cuts. The massesallowed in the CMSSM are represented by the dotted line; the“X” marks the current DO! limit on the gluino mass at 2.1fb−1 (see text for details) [7]. The inset shows the effect ofscaling the production cross section for the case of S/B > 1.The solid lines show the exclusion region for σ/3 (bottom)and 3σ (top).
GeV, we place tighter cuts on the monojet and dijetsamples than DO! does. While DO! technically hasstatistical significance in this region with their existingcuts, their signaltobackground ratio is low. Becauseof the admitted difficulties in calculating the StandardModel backgrounds, setting exclusions with a low signaltobackground should not be done and fortunately canbe avoided by tightening the HT and ET! cuts. Similarly,for larger gluino masses, the generic cuts are no longereffective and it is necessary to use the optimized cuts,which are tighter than DO! ’s.
IV. CONCLUSIONS AND OUTLOOK
In this paper, we describe the sensitivity that DO!has in searching for gluinos away from the CMSSM hypothesis in jets + ET! searches. It was assumed that thegluino only decayed to two jets and a stable bino. However, many variants of this decay are possible and thesearch presented here can be generalized accordingly.
One might, for example, consider the case where thegluino decays dominantly to bottom quarks and heavyflavor tagging can be used advantageously. Cascade decays are another important possibility. Decay chainshave a significant effect upon the searches because theyconvert missing energy into visible energy. In this case,additional parameters, such as the intermediate particlemasses and the relevant branching ratios, must be considered. In the CMSSM, the branching ratio of the gluino
into the wino is roughly 80%. This is the dominant decayaffecting the DO! gluino mass bound in CMSSM parameter space (see Fig. 2). While this cascade decay may berepresentative of many models that have gluinolike objects, the fixed mass ratio and branching ratio are againartifacts of the CMSSM. A more thorough examinationof cascade decays should be considered.
In addition to alternate decay routes for the gluino,alternate production modes are important when thereare additional particles that are kinematically accessible. In this paper, it was assumed that the squarks arekinematically inaccessible at the Tevatron; however, ifthe squarks are accessible, g̃q̃ and q̃q̃ production channels could lead to additional discovery possibilities. Forinstance, a gluino that is degenerate with the bino couldbe produced with a significantly heavier squark. Thesquark’s subsequent cascade decay to the bino will produce a great deal of visible energy in the event and maybe more visible than gluino pair production.3
Finally, in the degenerate gluino region, it may bebeneficial to use a monophoton search rather than amonojet search [22].4 Preliminary estimates of the reachof the monophoton search show that it is not as effective as the monojet search. This is likely due to theabsence of finalstate photon radiation from the gluinos.However, it may be possible to better optimize the monophoton search, because the Standard Model backgroundsare easier to understand in this case.
Ultimately, a modelindependent search for jets plusmissing energy would be ideal. We believe that our exclusive nj + ET! searches, with results presented in anexclusion plot as a function of HT and ET! , would provide significant coverage for these alternate channels [21].This analysis should be carried forward to the LHC toensure that the searches discover all possible supersymmetric spectra. The general philosophy of parameterizing the kinematics of the decay can be easily carriedover. The main changes are in redefining the HT and ET!cuts, as well as the hard jet energy scale. We expect asimilar shape to the sensitivity curve seen in Fig. 2, butat higher values for the gluino and bino masses. Therefore, it is unlikely that there will be a gap in gluinobinomasses where neither the Tevatron nor the LHC has sensitivity.
Acknowledgements
We would like to thank JeanFrancois Grivaz, AndyHaas, Roni Harnik, Masahiro Ibe, Greg Landsberg,Frank Petriello, and Patrice Verdier for helpful discus
3 We thank M. Ibe and R. Harnik for this observation.4 We thank F. Petriello for pointing this out
4
BA
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~g
B~
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~B
g~
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_q
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j
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_q
~B
g~ ~
g
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q_
/ET
FIG. 1: Boosted gluinos that are degenerate with the binodo not enhance the missing transverse energy when there isno hard initial or finalstate radiation. (A) illustrates thecancellation of the bino’s ET! . (B) shows how initial or finalstate radiation leads to a large amount of ET! even if thegluino is degenerate with the bino.
the search is not limited by phase space and four ormore wellseparated jets are produced, as well as largemissing transverse energy. The situation is very different for light gluinos (mg̃ ! 200 GeV) that are nearlydegenerate with the bino. Such light gluinos can be copiously produced at the Tevatron, with cross sectionsO(102 pb), as compared to O(10−2 pb) for their heavier counterparts (mg̃ " 400 GeV). Despite their largeproduction cross sections, these events are challengingto detect because the jets from the decay are soft, withmodest amounts of missing transverse energy. Even ifthe gluinos are strongly boosted, the sum of the binomomenta will approximately cancel when reconstructing the missing transverse energy (Fig. 1A). To discovera gluino degenerate with a bino, it is necessary to lookat events where the gluino pair is boosted by the emission of hard QCD jets (Fig. 1B). Therefore, initialstateradiation (ISR) and finalstate radiation (FSR) must beproperly accounted for.
The correct inclusion of ISR/FSR with parton showering requires generating gluino events with matrix elements. We used MadGraph/MadEvent [14] to computeprocesses of the form
pp̄→ g̃g̃ + Nj, (1)
where N = 0, 1, 2 is the multiplicity of QCD jets. Thedecay of the gluino into a bino plus a quark and an antiquark, as well as parton showering and hadronization ofthe finalstate partons, was done in PYTHIA 6.4 [15].
To ensure that no double counting of events occursbetween the matrixelement multiparton events and theparton showers, a version of the MLM matching procedure was used [16]. In this procedure, the matrix element multiparton events and the parton showers areconstrained to occupy different kinematical regions, separated using the k⊥ jet measure:
d2(i, j) = ∆R2ij min(p2Ti, p
2Tj)
d2(i,beam) = p2Ti, (2)
where ∆R2ij = 2(cosh ∆η − cos ∆φ) [17]. Matrixelement events are generated with some minimum cutoff d(i, j) = QMEmin. After showering, the partons areclustered into jets using the kT jet algorithm with aQPSmin > Q
MEmin. The event is then discarded unless all re
sulting jets are matched to partons in the matrixelementevent, d(parton, jet) < QPSmin. For events from the highest multiplicity sample, extra jets softer than the softest matrixelement parton are allowed. This procedureavoids doublecounting jets, and results in continuousand smooth differential distributions for all jet observables.
The matching parameters (QMEmin and QPSmin) shouldbe chosen resonably far below the factorization scale ofthe process. For gluino production, the parameters were:
QMEmin = 20 GeV and QPSmin = 30 GeV. (3)
The simulations were done using the CTEQ6L1PDF [18] and with the renormalization and factorization scales set to the gluino mass. The cross sectionswere rescaled to the nexttoleadingorder (NLO) crosssections obtained using Prospino 2.0 [19].
Finally, we used PGS [20] for detector simulation,with a cone jet algorithm with ∆R = 0.5. As a checkon this procedure, we compared our results to the signalpoint given in [7] and found that they agreed to within10%.
B. Backgrounds
The three dominant Standard Model backgroundsthat contribute to the jets plus missing energy searchesare: W±/Z0 + jets, tt̄, and QCD. There are severalsmaller sources of missing energy that include single topand diboson production, but these make up a very smallfraction of the background and are not included in thisstudy.
The W±/Z0 + nj and tt̄ backgrounds were generated using MadGraph/MadEvent and then showeredand hadronized using PYTHIA. PGS was used to reconstruct the jets. MLM matching was applied up to threejets for the W±/Z0 background, with the parametersQMEmin = 10 GeV and QPSmin = 15 GeV. The top background was matched up to two jets with QMEmin = 14 GeVand QPSmin = 20 GeV. Events containing isolated leptonswith pT ≥ 10 GeV were vetoed to reduce backgroundcontributions from leptonically decaying W± bosons. Toreject cases of ET$ from jet energy mismeasurement, alower bound of 90◦ and 50◦ was placed on the azimuthalangle between ET$ and the first and second hardest jets,respectively. An acoplanarity cut of < 165◦ was appliedto the two hardest jets. Because the DO$ analysis didnot veto hadronically decaying tau leptons, all taus weretreated as jets in this study.
2
Kawagoe Nojiri
mLSP=0.7msq

SUSY parameter measurementA brief history
• early 1990
• JLC study: define LC as the machine to measure SUSY parameters, spin, and interaction. check GUT relation M1:M2
• LHC = a discovery machine.
• Snowmass 1996:
• Trying to establish US participation at LHC, “(ex)Theorists”(Hinchliffe, Paige, ...) took LC concepts. Techniques for mass reconstruction were established at that time.
• ILC: SUSY coupling measurements (’96 Nojiri et al , Feng et al....): physics point of LC over LHC
pairproduced charginos !̃ 1! with a 10% acceptance from its
decay products,16 assuming "Ldt"100 fb#1 for bothPe"1 and 0. The errors in m !̃
1$ and m !̃
2$ were both assumed
to be 2% as long as they are accessible kinematically.17 One
can see that the upper bound practically disappears18 when
tan# exceeds 5.
C. Checking the supersymmetry relation
So far we have been assuming that new particles found at
a LC are superpartners of leptons. In other words, we have
implicitly been using supersymmetric interactions of sfermi
ons with the neutralinos of the MSSM without any attempt at
checking the nature of the interactions. Instead, we merely
used the data to determine the free parameters of the MSSM,
such as M 1 and tan# . In this subsection we are going todiscuss the possibility to probe the gauginosfermion
fermion interaction $more specifically, the B̃ẽReR coupling%and some aspects of the B̃&̃1& coupling.We start our discussion with ẽR . The production proceeds
though the schannel exchange of gauge bosons and
tchannel exchange of neutralinos, whose cross section is
shown in Appendix B. The tchannel exchange is dominated
by Binolike neutralino exchange, which led us to the
simple dependence of the cross section on the gaugino mass
M 1 as has been shown in Fig. 3$a%.The treelevel coupling of the B̃ẽReR vertex has a
simple relation to the Bee coupling in the MSSM:
gB̃ ẽ ReR"!2gtan'W"!2g!. $19%
This relation is imposed by supersymmetry. Thus the mea
surement of gB̃ ẽ e will allow us to prove that ẽ and B̃ are
indeed superpartners of eR and B .
For this test we modify the relation of Eq. $19% as
gB̃ ẽ ReR"!2g!Y B̃ $20%
and estimate the sensitivity to Y B̃ by introducing a new
(!̄2 function for the selectron pair production which depends on Y B̃ though gB̃ ẽ Re
. In the limit of mZ%M 1 and ) ,we obtain an approximate formula for the matrix element
M:
M*sin'!1# 4Y B̃21#2cos'# f!# f
2!4M 12/s
" . $21%It is apparent from Eq. $21% that one can constrain both Y B̃and M 1 by measuring the differential cross section:
d+(e!e#→ ẽR!ẽR
#)/dcos'.Figure 14 is a (!̄ ẽ
2contour plot projected on the M 1Y B̃
plane for a representative point in the parameter space of the
MSSM: m ẽR"200 GeV, )"300 GeV, M 1"99.57 GeV, and
tan#"2. One finds a good sensitivity to the coupling Y B̃ of,1% in this case. The reason why we got upper and lowerbounds on M 1 and Y B̃ is as follows: When we increase M 1!from M 1 to M 1!(M 1, the total cross section decreases. The
16The direction of a produced chargino can be solved for with a
twofold ambiguity when the chargino decays into W!̃ 10 6.. The
forwardbackward asymmetry for the final state W can also be used
even if the !̃ 1! decays into W*!̃ 1
0 25,7..17(m !̃
1$ was found to be around 5% for 50 fb#1 of data 6.. A
threshold scan for the !̃ 1!!̃ 1
# pair production might determine the
mass better.18It has been claimed that a very precise measurement of tan# ispossible when tan#,4 7. if the chargino mass errors are negligibly small. Some additional error on tan# has been introduced hereassuming a finite error on m!
i$. In Fig. 13, we have also taken a
larger value of m /̃ compared to 7., where sensitivity to tan# issmaller.
FIG. 13. 1$2%‘‘+’’ errors on tan# from chargino production asfunctions of input tan# . We used chargino distributions forPe"!1 and 0 with "Ldt"100 fb#1, and assuming that bothchargino masses are known to 2% accuracy. The upper bound prac
tically disappears when tan# exceeds 5. Input values areM 2"210 GeV, )"#195 GeV, and m /̃ 2"500 GeV.
FIG. 14. (!̄ ẽ2"1 contour in the M 1Y B̃(0gB̃ ẽ Re / !2 g!) plane.
The definition of (!̄ ẽ2has been modified to allow gB̃ ẽ Re to deviate
from !2 g!. Input values are m ẽR"200 GeV, )"300 GeV,M 1"99.57 GeV, and tan#"2. The error in the coupling is of aboutthe same order as that of the radiative correction proportional to
log10(mq̃ /m l̃ ) when mq̃ /m l̃,10.
6772 54NOJIRI, FUJII, AND TSUKAMOTOTsukamoto et al ‘93
Nojiri et al ‘96

Mass reconstruction at LHC
• Invariant mass distributions instead of energy distribution
• Tag particles from a SUSY particle decay chains (jet selections are essential)
• end point of distributions or distributions near the end point (momentums are aligned )
• Exact Kinematical relation (long decay chains)
• PT of the jets ( Peaks at typical scale) ⇒ MT2
mass information
}

golden channel
• BG (from lepton from charginos, top production ) can be estimated from eμ distribution.
• m(jll), m(jl) and m(ll) contains mass information
• Single channel should be dominated
q̃ → χ̃02j → l̃jl → χ̃0
1jll
source particle
{
high PT jets is recognized “from squarks”
same flavor odd sign letpons with high PT
m(ll) smaller than
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Mass measurement end point method
• proton is composite paraticle. The energy of hard scattering cannot be fixed.
• However there are relation among the momenta of particles from a single cascade decay. This can be used as initial state energy constraint.
• The constraint is stronger as decay cascade is longer. (see later slide. )
• Experimental:How to find correct jets and leptons from a decay.
χ̃02 → (l1 l̃) → l1l2χ01
p2χ̃01
= m2χ̃01
(p2 + pχ̃1)2 = m2
l̃
(p1 + p2 + pχ̃1)2 = m2χ̃0
2
3 body mll = M2 − M1
2body × 2 mll = M2
√
1 −M2
l̃
M22
√
1 −M2
1
M2l̃
max value

BG subtraction
• BG in 2 lepton channel, SUSY chargino production. sqL> χ+/ q (60%) or χ02> tau tau χ01 (often dominant mode)
• BG e+e:μ+μ::e+μ :eμ+=1:1:1:1 with exactly same therefore it is possible to subtract the background reliably.
LHC Point 5
0
100
200
300
400
500
0 100 200 300 400 500
Mll (GeV)
Events
/10 G
eV
/10 fb
1
Figure 26: M!! for the Point 5 signal (open histogram) and the sum of all backgrounds(shaded histogram).
LHC Point 5
0
20
40
60
80
0 200 400 600 800 1000
11.50 / 9
P1 32.18
P2 623.5
P3 64.11
P4 24.03
P5 .1042
P6 .7275E04
Mllj! (GeV)
Events
/20 G
eV
/10 fb
1
Figure 27: M!!jχ̃01
for events with 86 < M!! < 109 GeV using !pχ̃01
= Mχ̃01/M!!!p!! for the
Point 5 signal (open histogram) and the Standard Model background (shaded histogram).
34
LHC Point 4
0
50
100
150
200
250
0 50 100 150 200
Mll (GeV)
(ee +
µµ
) E
vents
/5 G
eV
/10 fb
1
Figure 15: M!+!− distribution for oppositesign, sameflavor dileptons for the Point 4 signal(solid histogram), oppositesign, oppositeflavor dileptons (dashed histogram), and StandardModel background (shaded histogram).
LHC Point 4
50
0
50
100
150
200
250
0 50 100 150 200
Mll (GeV)
(ee +
µµ
 eµ
) E
vents
/5 G
eV
/10 fb
1
Figure 16: Difference of the M!+!− distribution for oppositesign, sameflavor dileptons andoppositesign, oppositeflavor dileptons for the Point 4 signal (open histogram) and theStandard Model background (shaded histogram).
23
LHC Point 4
0
50
100
150
200
250
0 50 100 150 200
Mll (GeV)
(ee
+ µµ
) E
ve
nts
/5 G
eV
/10
fb
1
Figure 15: M!+!− distribution for oppositesign, sameflavor dileptons for the Point 4 signal(solid histogram), oppositesign, oppositeflavor dileptons (dashed histogram), and StandardModel background (shaded histogram).
LHC Point 4
50
0
50
100
150
200
250
0 50 100 150 200
Mll (GeV)
(ee
+ µµ
 eµ
) E
ve
nts
/5 G
eV
/10
fb
1
Figure 16: Difference of the M!+!− distribution for oppositesign, sameflavor dileptons andoppositesign, oppositeflavor dileptons for the Point 4 signal (open histogram) and theStandard Model background (shaded histogram).
23
tree body decay two body decays
three body ＋BG
The contribution from heavy sparticle.

Jetlepton combinations are also useful
Interaction point
m(jll)
decay
lepton
LSP
squark
Take the two highest pTjets. Take min(Ｍ(j1ll), M(j2ll) so that end point is not disturbed.
Jets
lepton

Jetlepton combinations are also useful
Interaction point
m(jll)
decay
lepton
LSP
squark
Take the two highest pTjets. Take min(Ｍ(j1ll), M(j2ll) so that end point is not disturbed.
Jets
lepton

Jetlepton combinations are also useful
Interaction point
m(jll)
decay
lepton
LSP
squark
Take the two highest pTjets. Take min(Ｍ(j1ll), M(j2ll) so that end point is not disturbed.
Jets
lepton

LSP
squark m(jll)
m(ll)
m(jl)
m(jll) with mll>0.5 mll(max)
LHC mass measurement using end points.
jet
lepton
lepton
ee+μμeμ subtraction is effective to select
single channel
Hinchliffe et al (97)

event by event parameter counting
• Single decay cascade. unknown 4(a LSP momentum)
• n mass shell constraints
• if n> 4, each events give one constraint to mass relation. ( mass relation method Nojiri Polesello Tovey, Kawagoe)
• At the end point, several momentum go colinear, reducing the unknown degree of freedom. (end point method)
• Sparticle pair production. unknown 8, n1+n2 mass shell constraint, 2 Etmiss constraint. n1+n2>6 is enough to get event by event mass constraint.
m2i = (p1 + .... + pi)
2, p1 = pLSP
(p0, p1, p2, p3)

Neutralino mass matrix revisited
M1 0 O(mZ) O(mZ)0 M2 O(mZ) O(mZ)
O(mZ) O(mZ) 0 µO(mZ) O(mZ) µ 0
The positive and negative eigenvalue one of them will be pure Higgsino state
Yukawa interaction to the matter partner
Mixing among gaugino is small
gauginoHiggsino mix(especially wino )
gauge interaction to the matter partners
GUT relation among gauginos M1:M2:M3= α1:α2:α3by the effect of anomaly mediated sectors.
coupling to the Higgs boson . Important for DM detection

Parameters behind the decay.
• decay from heavier ino give us μ parameters.
R
χ̃01 = B̃+ H̃
χ̃02, χ̃±1
= W̃+ H̃
χ̃04, χ̃±2
= H̃+ W̃
ignored higgsino
χ̃03
L µ > M2 > M1 case
slepton prove

χ̃2 → l̃R → χ̃1
χ̃4 → l̃L → χ̃1
χ̃i → χ̃1Z0
mll

Parameter behind decay II
• parameter Determination using end point only is dangerous. Relative weights, additional particles are important.
RL caseM2 > M1 > µ
χ̃04, χ̃±2
= W̃+H̃
ignored higgsino χ̃03 = B̃+H̃

summary of SPS 1a
• Most of mass error is LSP mass error. Mass differences are known rather precisely
• Access to 3 neutralino mass, information on 3 of (M1,M2,µ, tanβ)
• selectron and smuon mass error is about same to that of N02
• stau mass also can be measured from tau tau end point. many fake tau background. Need more study, but don’t be nervous.
particle mass error(low) error(high)gluino 595 16.3 8.0 bbll
squark(L) 540 21.2 8.7
squark(R) 520 17.7 11.8 MT2 10GeV sys
378 14.6 5.1177 13.4 4.796 13.2 4.7
from LHC/LC study
χ̃04
χ̃0
2
χ̃0
1
MMN SUSY06

Trying to pin downDark matter nature
• DM density: for SPS1a
• slepton exchange (^^)v but we need to find if slepton is left handed as cross section is proportional to Y^4
• stau coannihilation excluded (^^; in coannihilation region because dependence is so large. (Discussed in Baltz et al)
• higgs schannel exchange (; ;) Get lower limit of HIggs mass Heavy higgs is not accessible in many cases.
• higgsino component (^^) Figure 17: Spinindependent neutralinoproton direct detection cross section for pointLCC1. See Fig. 8 for description of histograms.
efficiency.
In Fig. 20, we show the likelihood distribution for the effective local flux, obtainedby combining the distribution of values of the cross section with the statistical uncertainty of the direct detection measurement. Using the data from the ILC at 1000GeV, this property of the dark matter halo at the Earth would be measured to 28%accuracy.
4.6 Constraints from relic density and direct detection
If LCC1 is the correct theory of Nature, it is possible that, by the end of thedecade, the LHC will have observed missing energy events and a convincing signal ofdark matter from annihilation to gamma rays will also have been observed. Values ofthe WIMP mass will have been obtained from the LHC and from the endpoint of thegamma ray spectrum, and these values will have been seen to agree. Undergrounddirect detection experiments in the 25 kg range such as SuperCDMS may also givethe WIMP mass and flux at the Earth. Further, the Planck measurements of theCMB will have provided a very accurate measurement of the cosmic density of darkmatter. Under these circumstances, it would be very tempting to use the Planck andSuperCDMS measurements to constrain the parameters of supersymmetry model.
This analysis would depend on very strong assumptions whose status would still
46
LHC+ILC(1000)
LHC+ILC(500)
Probability density
P! scattering cross section(pb)
LHC
Baltz et al (2006)
0.08
0.1
0.12
0.14
80 100 120
m(LSP) (GeV)
!h
2
Figure 9: Value of the predicted relic density Ωχh2 as a function of the measured χ̃01 mass.
the Higgs mass is fixed, and its experimental uncertainty does not contribute to the error onthe relic density prediction, as for high Higgs masses the contribution of channels involvinghiggses to the neutralino annihilation is negligible.
In this case the dominant contribution to the uncertainty will come from the poorly constrained value of tan β. In the interval allowed by the nonobservation of theSM decays of thehiggs, the relic density varies by ∼11%, as shown in the right side of Figure 11. It is interestingto disentangle the contributions of the different annihilation processes to the variation. In theright side of Figure 11 we show the annihilation crosssections (in units of their contributionto 1/Ω). For the different processes. The spread is dominated by the χ̃01χ̃01 → τ+τ− process.The reason is that for each value of tan β we recalculate the soft parameters in such a way thethe sparticle masses, and the branching ratios which are measured experimentally are keptconstant. Therefore the composition of the χ̃01 and the value of θτ vary as shown in Figures 3,producing the dependency observed in the full line in the left side of Figure 11.
An additional uncertainty will come from the value of m(τ̃2), which contributes a ∼ 7%spread to the result, as shown in Figure 12. This is because the τ̃2 exchange contribution isopposite to the τ̃1 contribution. The cancellation appear in the swave part of the pair annihilation cross section, which is chirality suppressed. In the limit where Higgsino component ofthe lightest neutralino can be ignored, the τ̃i contribution to the amplitude can be expressedas
M(swave) ∝ sin θτ cos θτ [1/(1 + m2τ̃1/m2χ̃01
) − 1/(1 + m2τ̃2/m2χ̃01
)]Z211 (2)
yielding the observed dependence of the annihilation crosssection on m(τ̃2). The mixing
14
MN, Polesello and Tovey hepph/0512204
Fake peak from Markovchain analysis

not so many sqL*because pp collider
LSP
sqL
lepton (h=1/2)
lepton
qL
lepton (h=1) orantilepton (h=1/2)
scalar decay.
Fiding slepton chirality
h=+1/2
30

• Pmiss is the sum of two LSP momentum.
• Px(missing)= Px(LSP1)+Py(LSP2)
• Py(missing) =Py(LSP1)+Py(LSP2)
• A complex quantity.
• Example ：squarkR pair production followed by squark R > LSP+q
• The end point of the distribution agree with squark mass if mχ =LSP mass
MT2 distribution
the final state†. In this paper, we will concentrate on the case that each mother particledecays into the same set of daughter particles, since such symmetric decay typically hashigher event rate while showing the nontrivial structure which will be discussed in thefollowing. Fig. 1 shows an example of such process in which mother superparticles werepairproduced and each of them decays into one neutralino LSP (χ̃01) and some visibleparticles. While the invisible part of each decay consists of only one particle (neutralinoLSP), the visible part might contain one or more visible particle(s) in general.
Figure 1: Kinematic situation for mT2 where pmissT denotes the total missing transversemomentum.
With two invisible LSPs in the final state, each LSP momentum can not be determinedalthough the total missing transverse momentum pmissT can be measured experimentally.Furthermore, the LSP mass might not be known in advance. In such situation, one canintroduce a trial LSP mass mχ, and define the mT2 variable as follows [10, 11]:
mT2(pvis(1)T , m
(1)vis, p
vis(2)T , m
(2)vis, mχ) ≡ min
{pχ(1)T +pχ(2)T =−p
vis(1)T −p
vis(2)T }
[
max{m(1)T , m(2)T }
]
, (5)
where the minimization is performed over trial LSP momenta pχ(i)T constrained as
pχ(1)T + p
χ(2)T = p
missT ,
†In Ref.[11], mT2 has been further generalized to the case involving more missing particles than two.
3
5 Supersymmetric Models
MT2 (GeV)
Eve
nts
/8 G
eV
/30
fb
1
0
50
100
150
0 200 400 600 800
Figure 5.15: Distribution of MT2 for the events passing the cuts. In red is shown the StandardModel background. The integrated statistics in the plot is 30 fb−1.
0
50
100
150
0 200 400 600 800
30.73 / 28
P1 0.1947E02
P2 511.7
P3 39.75
MT2 (GeV)
Eve
nts
/8 G
eV
/30
fb
1
Figure 5.16: Distribution of MT2 for events passing the cuts. Superimposed is the fit describedin the text.
230

mT2 end points. m
T2(gluino) (GeV)
Ev
ents
/10
GeV
(G
eV)
m! = 10 GeV
0
500
1000
1500
2000
2500
3000
3500
0 100 200 300 400 500 600 700 800 900
mT2
(gluino) (GeV)
Ev
ents
/10
GeV
(G
eV)
m! = 350 GeV
0
500
1000
1500
2000
2500
3000
3500
300 400 500 600 700 800 900 1000 1100 1200
Figure 9: mT2 distribution with (a) mχ = 10 GeV and (b) mχ = 350 GeV for the AMSBparameter point (71).
650
700
750
800
850
900
950
1000
1050
1100
0 50 100 150 200 250 300 350
(GeV)m!
(GeV
)m
T2
max
(g~)
mAMSB(heavy squark)
Figure 10: mmaxT2 as a function of the trial LSP mass mχ for the AMSB parameter point(71).
parameter point in a minimal anomaly mediated SUSYbreaking (AMSB) scenario [16],which give
mg̃ = 780 GeV, mχ̃01 = 98 GeV, (71)
21
Figure 8: Extreme momentum configuration providing mmaxT2 as an unbalanced solutionfor mχ > mχ̃01 .
Therefore, m(2)T > m(1)T if mχ > mχ̃01 , though m
(2)T is at the unconstrained minimum value,
so that we have unbalanced mT2 solution, i.e. mT2 = (mg̃−mχ̃01)+mχ for this momentumconfiguration. The same unbalanced mT2 solution is obtained for the momentum configuration with other values of m(1)vis because those cases also give m
(2)T ≥ m
(1)T when m
(2)T
is at the unconstrained minimum. Such momentum configurations and the backtobacktransverse boosted ones would have a sizable pmissT , so can be used to determine mmaxT2from real collider data.
To summarize the extremal features of mT2 for the decay of gluino pair when mq̃ > mg̃,the maximum of mT2 over all events is given by
mmaxT2 (mχ) =m2g̃ − m2χ̃01
2mg̃+
√
√
√
√
(
m2g̃ − m2χ̃012mg̃
)2
+ m2χ if mχ < mχ̃01 ,
mmaxT2 (mχ) =(
mg̃ − mχ̃01)
+ mχ if mχ > mχ̃01 (70)
as obtained in (45) and (47) in more generic context. Thus, there is a level crossing ofmmaxT2 at mχ = mχ̃01 , yielding a kink structure as shown in Fig. 4(a). If such m
maxT2 curve
can be constructed from collider data, which will be examined in the next subsection, thiskink structure will enable us to determine the true LSP mass mχ̃01 and the gluino massmg̃ = mmaxT2 (mχ = mχ̃01) simultaneously.
To see explicitly the extremal features of gluino mT2, a Monte Carlo event sampleof the signal pp → g̃g̃ → qqχ̃01qqχ̃01 has been generated in partoniclevel, for a SUSY
20
gluino 3 body decay.
LSP mass can be determined from jet system.take the higest pT jet and jet with largest Delta R Xp_Tassign other jet
Cho et al
large mjj events
small mjj events
increase
test mass
MT2test LSP mass
pp → g̃g̃ → 4jχ̃01χ̃0
1

hemisphere method. Assume the event has structure pp→ AB→D1 D2 XX. 1)separate jets into two visible object. 2) calculate MT2 using the momenta of visible objects. → heaviest sparticle mass (squark mass) is recovered.
For arbitrary SUSY process
33
trial LSP momenta of Eq. (??), therefore, mT 2 is boundedfrom above,
mT 2 < max(m1,m2) (3)
where m1 and m2 are the masses of the primary producedSUSY particles. This is because the mT 2 is defined as theminimum of the maximum of the two mT , therefore iteffectively takes the minimum of the transverse mass ofthe decay products of the heavier sparticle[? ].
The mT 2 distribution can be used for the determinationthe right handed squark mass (mR) in j j+ET miss channel[? ]. When mR < mg̃, q̃R dominantly decays into thelightest neutralino χ̃01 and a jet, therefore q̃Rq̃R production can be tagged by requiring two very high pT jetsin the final state. When m = mLSP, the endpoint of mT 2is equal to mR. The selected events are populated nearthe mT 2 endpoint, therefore the SM background is negligible. The righthanded squark mass mR is determinedwith the error of 3% at SPS1a[? ].
Recently, Cho et al[? ? ] investigated the mT 2 variableas a function of a test LSP mass for gluino pair production and the decay pp → g̃g̃ → j j j jχ̃01 χ̃01 . The mT 2 variable is constructed from two jet pairs so that p1(2)vis is amomentum of one of the jet pairs arising from a gluinodecay. The endpoint of the mT 2 distribution as a functionof a test LPS mass has a kink exactly at m = mLSP. Thisis because two different sets of the SUSY events contribute to the endpoint of mT 2 variable. For m < mLSP, theevents with m j j ∼ mminj j give mmaxT 2 , while for m > mLSP,the events with m j j ∼ mmaxll give it, where m
min(max)j j is
the minimum (maximum) jet pair invariant mass arising from g̃ decay. At m = mLSP, the endpoints of bothof the events should be at mg̃ becuase the true LSP momenta can be the test momenta that satisfy Eq.(2). Thus,the endpoint becomes a function which has a kink atm = mLSP. This means that one can determine the LSPmass from the kink position experimentally.
In [? ? ], it is shown that the mT 2 endpoint is sensitiveto the both LSP and gluino masses for several modelpoints by explicit MC simulations. They select the fourhighest pT jets of the events, and divide them into two jetpairs using some distance measure, and regarded the jetpair momentum as two visible momenta pivis in Eq. (??).
In the previous analyses, the endpoint method has beenused to determine the sparticle masses. For example, inthe SUSY cascade decay q̃ → χ02 → l̃ → χ01 , the sparticlemasses are solved analytically from the endpoints of mll ,m jl and m jll distributions. The lepton channel is veryclean but the branching ratio is rather small in wideregion of the parameter space. This was a problem inthe SUSY parameter determination at the LHC—we didnot know how to fix the LSP mass kinematically whenχ̃02 → l̃l is closed. It should be noted that the decayg̃ → j jχ01 for the mT 2 study involves only jets, and it has
Point b
0
50
100
150
200
250
300
350
400
450
0 500 1000 1500 [GeV]
FIGURE 1. A parton level inclusive mT 2 distribution at amodel point with mq̃ = 1342 GeV and mg̃ = 785 GeV. The solidline correspond to the distribution using the hemisphere algorithm, while the dotted line correspond to those with correctparton assignments.
significant branching ratio. The LSP mass determinationusing the mT 2 kink method could be applied in widerparameter region.
The inclusive mT 2
The proposal in [? ? ] is still limited to the case thatonly a single channel (either gluinogluino or squarksquark) contributes to the four jet + missing ET channel,and a gluino decays dominantly into j jχ̃01 . It is not satisfactory because gluino and squark can decay into thechannel involving multiple jets. The number of high pTjets are larger than four, and there are no good reason toselect the first four jets to study mT 2 distributions for general MSSM points. They are also generally coproduced.When mg̃ ∼ mq̃, the squarkgluino coproduction is thedominant part of the colored SUSY particle productions.
In [? ? ], we proposed an inclusive definition of mT 2,which can be calculated for events with any numberof jets in the final state. The quantity is defined firstby dividing the jets into two hemisphere which satisfyfollowing conditions,
p(i)hemi = ∑k∈Hi
pk
d(pk, p(i)hemi) < d(pk, p
( j)) for k ∈ Hi and k /∈ Hjwhere,
d(pk, p j) ≡ (Ek − pkcosθ jk)Ek
(E j +Ek)2(4)
The hemisphere axes (momenta) may be found by takingthe highest pT jet i and the jet j with max(∆Ri j pT j) asinitial axes. Jets are first associated with one of the initialaxes with smaller d. The new hemisphere momenta iscalculated under the assignments, and the procedure is
hemisphere
correct assignments
Nojiri, Shimizu,Kawagoe, Okada Nojiri Sakurai, Shimiru,Takeuchi
parton level check it looks good!

subsystem MT2(for msq>mgl
• At LHC σ（squark gluino）>σ（gluino gluino）
• squark > j +chargino/neutralino/gluino. • Subsystem mT2 (remove highest pTjet ) end point gives gluino mass
nu
mb
er
of
ev
en
ts/b
in/f
b1
FIGURE 3. The signal(solid) and background(dashed) distributions at the same model point. Here we apply a cut m1(2)hemi >200 GeV. We produced 50,000 SUSY events for this study, andthe distribution is normalized to 1fb−1
FIGURE 4. The msubT 2 distributions at the same model point.The endpoint is consistent with the input gluino mass mg̃ =785 GeV. The distribution is normalized to 1fb−1.
squark and gluino masses in Fig. ??.
Exact relations
In the endpoint method, endpoints of the several distributions are solved to obtain the sparticle masses involvedin the events. Each endpoint gives one constraint amongthe sparticle masses. It is known that a decay cascade involving at least three SUSY cascade decaies are requiredto determine the all sparticle masses from the endpoints.
FIGURE 5. The fitted mT 2 and msubT 2 endpoints(solid lines)and mq̃ and mg̃ (dashed lines) at each model point. The barsshow statistical errors for 50,000 events.
The results in [? ? ] shows that ETmiss constrain the LSPmomenta, and the spartice masses are solved even thoughthere are only two sparticles involved in the decays. Ingeneral, pTmiss provides an independent constraint to thesparticle mass determination when both of the pair produced sparicle decays are identified. Several groups studied the case involving q̃ → χ̃02 → l̃ → χ̃01 . By using theexact relation among the visible and missing momentaevent by event, the errors on the LSP mass is improvedby factor of 30% in [? ]
MORE FAVORITE TOYS
If SUSY particles are found in the early phase of theLHC experiments, we would be able to access variousdecay chains of SUSY particles in the later stage of theexperiment.
The channel involving χ0i → l̃l is experimentallyclean, therefore search of lepton flavor violation (LFV)in neutralino cascade decays are experimentally promising. The LFV in SUSY processes might come from righthanded neutrino Yukawa couplings. Gauge mediationmodels may also lead experimentally acceptable LFVif the planck scale soft masses violate lepton flavor[?]. By measuring difference of the two lepton endpoints∆mll = mee −mµµ arising from χ̃02 → l̃l→ llχ̃01 , one candetect/set the lower limit to the slepton mass difference∆ml = mẽ −mµ̃ . The ∆ml is expected to be nonzero inmodels with nonzero LFV. The sensitivity to the massdifference is recently discussed in [? ].
The masses of the third generation squarks and sleptons are also important in distinguishing SUSY models.They are expected to be lighter than the first and secondgeneration squarks if the SUSY mediation scale is nearthe planck scale. In addition, stop mass and its mixing
gluino
squark
neutralino chargino
highest pT jets

gravitino LSP and NLSP
• gravitino is spin 3/2 particle
• no renormalizable interactions.
• spin 3/2 → spin 1 X spin 1/2
• If it is LSP. NLSP decays into gravititino
ψ0 = −√
2/3p
mψ−1/2
(ψ1, ψ2, ψ3) =1√
3e2ψ+1/2 −
√
2
3
E
me3ψ−1/2
∂µψµ
= 0, γµψµ
= 0
χ̃01 → γψµ τ̃1 → τψ
µ
L ∝ κ
(
ψ̄Lγµγν∂νφ −
i
4√
2λaF aµργ
µσνρ)
ψµ
h=1/2

Super Higgs mechanism
massless goldstino and background fild＜Ｆ＞
supersymmetric vacuum Ｆ＝０（unstable)
gravitinogoldstino mixing
Supersymmetric has sensible mass spectrum if gravity sector also has supersymmetry. gravitino can couple matter due to susy breaking. “gravitino LPS” is the case that we can study gravity sector using collider.

Gravitino mass and NLSP life time
NLSP life time measurement → Hidden sector determination F0
NLSP fly and decay
mG̃ [GeV]
τ̃ 1lif
etim
e[s
ec]
10 yrsyrmonth
day
hour
min
secm τ̃
1=
100 G
eV
200 G
eV
400 G
eV
10−3 10−2 10−1 1 10 102 103
108
106
104
102
1
10−2
Life time +Mass measurement→ Planck scale measurement
mG̃
[GeV]
τ̃1
life
tim
e[s
ec]
10 yrsyr
month
day
hour
min
secm
τ̃1=
100 G
eV
200 G
eV
400 G
eV
10−3 10−2 10−1 1 10 102 103
108
106
104
102
1
10−2
FIG. 4: The lifetime of the CNLSP τ̃ in the case of gravitino LSP, as a function of the gravitino
mass, for the stau mass 100, 200, and 400 GeV (from top to bottom).
width into a gravitino and lepton is given by [8]
Γτ̃ (τ̃ → G̃τ) =m5τ̃
48πm2G̃M2pl
(1 −
m2G̃
+ m2τm2τ̃
)4 [1 −
4m2G̃m2τ
(m2τ̃ − m2G̃ − m2τ )
2
]3/2.
= (68 days)−1( mτ̃
100 GeV
)5 (10 GeVmG̃
)2×
(1 −
m2G̃
+ m2τm2τ̃
)4 [1 −
4m2G̃m2τ
(m2τ̃ − m2G̃ − m2τ )
2
]3/2. (5)
We show the dependence of the stau lifetime on the gravitino mass in Fig. 4.
The decay τ̃ → Xτ can be triggered by a single tau jets initiating from the position where
τ̃ is stopped. The tau energy is monochromatic and expressed as
Eτ =m2τ̃ + m
2τ − m2X
2mτ̃. (6)
Here X is the invisible particle in the τ̃ decay, for this case X = G̃. If one can measure
the lifetime and the mass of the stau, the gravitino mass can be determined assuming that
eq.(5) is correct. Then the total SUSY breaking scale F0 =√
3mG̃Mpl is also determined,
which is important to understand the hidden sector physics.
LHC detectors can determine the mass of τ̃ through the stau velocity measurement βτ̃
in the muon system of the CMS detector . The measurement of the lifetime may not be
easy at main detectors if lifetime is too much longer then detector size. The cross section
12
weakly to the MSSM particle with comparable strength to the gravitino.
For simplicity, we will assume the NLSP is pure ‘righthanded’ stau, τ̃ = τ̃R throughout
this section. Extension to the case with mixing with τ̃L is straightforward, but it will
introduce the additional parameter to the model, where the dependence is expected to be
small.
The gravitino is a spin3/2 particle. However, in the limit where mG̃ ! mτ̃ , the effective
interaction to MSSM particles would be reduced to that of spin 1/2 particle, goldstino χ̃.
The effective action relevant to the τ̃R decay is given as follows,
L =m2τ̃√
3m3/2Mpl( ¯̃χτRτ̃
∗R + H.c.) +
−mB̃4√
6m3/2Mpl¯̃χ[γµ, γν ]B̃(cos θW Fµν − sin θW Zµν). (26)
The action is similar to that of axino given in Eqs.(9) and (10) except the coupling coeffi
cients. The relative weight of the two terms in eq.(26) are fixed by the supergravity, while
for the axino the coefficient in eq.(10) is induced from Eqs.(9) by the radiative corrections.
Note that the term proportinal to X[γµ, γν ]B̃Fµν is a non renormalizable coupling of the
photon to gravitino or axino and induces significantly different γ, τ distribution.
The axino three body decay τ̃ → γτ ã proceeds through the diagrams shown in Fig.14,
where the hatched triangle express the effective vertex shown in Eq. (10). On the other
hand The relevant diagrams for the three body decay into goldstino τ̃ → γτχ̃, are given
in Fig.??. the diagram corresponding to the top right of Fig. 14 does not exists for the
goldstino case. The difference of the action and the relevant diagrams will appear as the
deviation of the three body decay distributions. In the Appendix, we list the three body
decay differential width into gravitino/axino in the limit where the gravitino/axino mass can
be neglected compared to mτ̃ . The formula for the massive gravitino and axino are given in
Ref. [11].
B. Numerical results
The three body decay τ̃ → τγX should be visible in the stopper detector if it has an
ability to measure charged tracks, and also segmented in small units. The position where
τ̃ decays in the detector will be identified by measuring the position where the charged
track by the π+, µ and e from τ is initiated. For hadronic tau decays, a π± is always in the
decay products, sometimes with photons coming from π0 decays. Photons are converted into
27

NLSP Signal in the detector
NLSP decay appear as 1)Displaced vertex (reduced resolutions….) only up to
c! ~106m2)ionizing trac for CNLSP
2.5 Kg /cm2

CNLSP stopper at LHC
• CNSP reduces its momentum by ionization and stop ultimately
use stopped CNLSP? For M=100 GeV CNLSP with βγ＜0.54 stops inside main detector.
•But the detector is noisy underLHC operation.
・Use the events stopped in the surrounding rock? (muon) no energy measurements then.
Range/Mass as function of βγ
Range of the particle in the unit of g /cm3
=material that particle have to go though to be stopped.

LHC as NLSP factory
• LHC is SUSY factory 105 SUSY partcile for 1pb
• If dark matter is outside MSSM sector, NLSP provide us ballpark for
• the sector that couple through supergravity
• highly suppressed interactions but stronger than supergravity
• If NLSP is charged, we will see the CNLSP at low luminsity run. We can propose dedicated study at high luminosity run or super LHC.

Max stopper(?) at CMSAlbert De Roeck, K.Hamaguchi MN 06
Kuno, Hamaguchi, Nakaya, Nojiri 04 (yes, we are seriously joking )
3.5m x 15m x 15m x 2 =1.6 x 109cm3
5g/cm3 x 1.6 x 109=8 x 109g ~8Kton
8.5 m from IP Ground conditions is OK in CMS for “a few KT detector ” both side because the cavern is planed from fat CMS detector(12Kton detector).
Less flux in ATLAS cavern because the Detector is bigger(23m for diameter)no space because cryostat +complicated construction strategies.
1210
86
42
02
46
810
1210
86420246810
8
6
4
2
0
2
4
6
8
1210
86
42
02
46
810

cosmic ray anomaly and gravitino
• gravitino can be dark matter but it does not pair annihilate in our universe once it is created. On the other hand, DM in MSSM sector can pair annihilate to make fantastic signal
• NEW twist, gravlino LSP + small R parity violation. gravitino decays to give anomaly
• R parity coupling must be unnaturally small but it put gravitino into indirect detection game.

How gravitino can commit to cosmic ray anomaly
43
Minimal Dark Matter and PAMELA Marco Cirelli
!!!
!!!!!!!!
!!!!!
! """""""" "
#
#######
#
#
$
$$
$
$$
$
$
$
!
!
!
!
1 10 102 103 104
1!
10!
0.3!
3!
30!
Positron energy in GeV
Positronfraction
background?
PAMELA 08
preliminary
!
!!!!!!!!!!!!!!!
!!
1 10 102 103 10410"5
10"4
10"3
10"2
p kinetic energy in GeV
p!p
background?
PAMELA 08
preliminary
Minimal Dark Matter fermion 5"plet
Figure 1: The PAMELA preliminary data [3] compared with the fermion 5plet MDM prediction, at thebestfit point for the astrophysical parameters.
Secondly, we varied M in order to see if the MDM value M ∼ 10TeV is preferred by data.We find that increasing the DM mass above 10TeV starts to give a poorer fit of the e+ spectrum.Lowering the DM mass, one needs to increasingly reduce free parameters such as Bp/Be in orderto generate the e+ excess without giving at the same time an unseen p̄ excess.
The e+ and p̄ spectra will be measured by PAMELA (possibly up to 270 GeV for e+ and 150GeV for p̄) and later by AMS08 (up to about 1 TeV). MDM predicts that the positron fractionshould continue to grow, and that an anomaly should appear in the p̄ spectrum, unless p̄ have anunfavorable boost factor or propagation in our galaxy.
Collateral constraints must be considered. The e± from DM annihilations lead to a synchrotronradiation [5] at the level of ‘WMAP haze’ anomaly [12]. Ref. [10] claims that very strong boundson the DM annihilation cross section can be inferred from infrared and Xray observations ofthe galactic center region, modeled assuming a certain magnetic field and DM density, that getsextremely high close to the central black hole leading to a high rate of DM annihilations. In this region DM becomes relativistic, and in the MDM case this means that the Sommerfeld enhancementdisappears, leaving a small annihilation cross section, σ ∼ α22/M2 ∼ 10−28 cm3/sec that would notcontradict the strong bounds of [10]. A dedicated computation of the MDM prediction togetherwith a precise description of the galactic center is necessary to quantitatively clarify this issue.
To conclude: we presented Minimal Dark Matter. Like string theory, MDM has no free parameters, and thereby makes univocal predictions, falsifiable by any single experimental result. Thepreliminary data from PAMELA, presented during idm08, show an excess in the flux of cosmic raypositrons at 1060 GeV which matches the MDM prediction. Let us compare with supersymmetry,the theoretically favored scenario: slepton masses can be finetuned to be quasidegenerate withthe lightest neutralino in order to enhance 3body annihilations obtaining the correct relic abundance and a e+ spectrum that, with a boost factor of >∼104, can be compatible with the PAMELAexcess [13]: in such a case the e+ fraction should decrease at higher energy. MDM predicts thecontinuing rise of fig. 1a. The nearby pulsars Geminga or B0656+14 could also produce a risinge+ fraction, together with an angular anisotropy [14].
Upcoming data at higher energies from PAMELA will hopeully clarify the issue.
5
gravitino dark matter → γν,Zν, Wl ..
108
107
106
105
0.1 1 10 100 1000E (GeV)
E d
J/d
E (G
eV
/cm
st
r se
c)2
2
Gravitino mass = 150 GeVLifetime = 2.2 x 10 secData: EGRET
26
total
γν
Wl
Zν
BG
0.01
0.1
1
0.1 1 10 100 1000
e
µτ
BG
Φe+
/ (Φ
+
e)
e+Φ
E (GeV)
Gravitino mass = 150 GeVLifetime = 2.2 x 10 secData: HEAT
26
Figure 5: Gammaray flux (left figure) and positron fraction (right figure). Here, we take
m3/2 = 150 GeV, τ3/2 = 2.2 × 1026 sec, and MSSM parameters as Fig. 2.
total
γν
Wl
Zνhν
BG
Gravitino mass = 300 GeVLifetime = 1.5 x 10 secData: EGRET
26
108
107
106
105
0.1 1 10 100 1000E (GeV)
E d
J/d
E (G
eV
/cm
st
r se
c)2
2
e
µ
τ
BG
0.01
0.1
1
0.1 1 10 100 1000
Φe+
/ (Φ
+
e)
e+Φ
E (GeV)
Gravitino mass = 300 GeVLifetime = 1.5 x 10 secData: HEAT
26
Figure 6: Same as Fig. 5, except for m3/2 = 300 GeV and τ3/2 = 1.5 × 1026 sec.
that the uncertainties of the cosmicray spectra observed by the past observations
are relatively large at the energy range of E ∼ O(10 GeV). Thus, it is desirable to
test the scenario of gravitino dark matter with RPV with better observations.
Fortunately, in the near future, new observations of cosmic rays, Gammaray
Large Area Space Telescope (GLAST) and Payload for Antimatter Matter Explo
ration and Light nuclei Astrophysics (PAMELA), are expected to provide results
of new measurements of the cosmicray fluxes. These experiments are designed to
detect cosmic rays with energy up to a few hundreds GeV. Thus, they will give us
better test of the scenario. Since GLAST (PAMELA) has better energy range and
resolution than EGRET (HEAT) in the measurement of gammaray (positron) flux,
20
3 Framework and Decay Rates
In this section, we introduce the supersymmetric model that we consider. Then, we
summarize the decay rates of the gravitino and the NLSP, which are important for
our study.
3.1 Model
In this article, we concentrate on the case where the Rparity violating interactions
originate from bilinear terms of Higgs and lepton doublet. In the original basis, the
Rparity violating interactions are assumed to be bilinear terms in superpotential
and supersymmetry (SUSY) breaking terms [20]. Without loss of generality, we
can always eliminate the bilinear Rparity violating terms from the superpotential
by the redefinition of the Higgs and leptondoublet multiplets. Then, the mixing
terms between the Higgsino and lepton doublets are eliminated from the fermion
mass matrix. In the following, we work in such a basis. Then, the relevant Rparity
violating terms are only in the softSUSY breaking terms, which are given by
LRPV = BiL̃iHu + m2L̃iHd
L̃iH∗d + h.c., (3.1)
where L̃i is lefthanded slepton doublet in ith generation, while Hu and Hd are up
and downtype Higgs boson doublets, respectively. In the following, we study the
phenomenological consequences of the Rparity violating terms given in Eq. (3.1).
With these Rparity violating terms, the vacuum expectation values (VEVs) of
lefthanded sneutrino fields ν̃i are generated as
〈ν̃i〉 =Bi sin β + m2L̃iHd
cos β
m2ν̃iv, (3.2)
where v # 174 GeV is the VEV of standardmodellike Higgs boson, tan β =
〈H0u〉/〈H0d〉, and mν̃i is the mass of ν̃i. The VEVs of the sneutrinos play impor
tant role in the following analysis. We parametrize the VEVs of the sneutrinos as
κi ≡〈ν̃i〉
v, (3.3)
and consider the case that κi % 1.
One important constraint on the size of the Rparity violation is from the neutrino
masses. Here, we assume that the neutrino masses are mainly from some other inter
action, like the seesaw mechanism [21] or Diractype Yukawa interaction. However,
4
New Pamela Data from “a theoriest paper”
arXiv:0808.3867
corresponding NLSP life time is around 10^5~6sec (detectable) general importance to think about R parity violation at collider?