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

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SUSY at LHC

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

    qq_~~

    ~~gg

    ~~gq

    M(q) = 1.2 M(g)~ ~

    M(GeV)200 400 600 800 1000

    1000

    100

    10

    1

    0.1

    σ (p

    b)

    “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

    g

    g

    g

    g

    g

    q

    u

    u

    q̃∗

    ũu d

    g

    u

    g̃d̃

    d

    d

    d

    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

    /hour

  • 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 particle--LSP”

    • “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 fb-1, while BG rate is 109-8 for W, Z and ttbar productions. 10-4 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

    )

    2pT /E√

    1 −(

    pTE

    )2

    PT/E

    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

  • Etmiss cut gg → T−T

    −, T− → tBH pp→ttbar

    Tmiss

    E

    (GeV

    )

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    400

    600

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    M (GeV)eff600 1000 1400 1800

    M (GeV)eff600 1000 1400 1800

    Signal

    Tmiss

    E

    (GeV

    )

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    600

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    Signal Background

    jets

    jets

    t

    !

    !

    t!

    (T T production) (t t production)! !

    T T!

    A AH H

    jets jets

  • 
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 fb-1)

    A0 = 0, µ > 0, tan! = 10, 5" contours (incl. systematics)

    ! Assumed uncertainties (ATLAS):

    ! QCD: 50%

    ! tt, V+j: 20%

    1 fb-1

    1 fb-1

    ! Beware:

    ! Different significance

    definitions!

    ! CMS: syst. uncertainties

    estimated for 10 fb-1

    (except 0-lepton: 1 fb-1)

    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

    M

    M

    N

    N

    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 multi-parton 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 (ME-PS) 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

    100 200 300 400 5000

    50

    100

    150

    200

    Gluino Mass !GeV"

    BinoMass!GeV

    "

    Out[112]=

    100 200 300 400 5000

    50

    100

    150

    200

    Gluino Mass !GeV"

    BinoMass!GeV

    "

    FIG. 2: The 95% gluino-bino exclusion curve for DO! at 4fb−1 for S/B > 1. The dashed line shows the correspondingexclusion region using DO! ’s non-optimized 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 signal-to-background ratio is low. Becauseof the admitted difficulties in calculating the StandardModel backgrounds, setting exclusions with a low signal-to-background 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 hy-pothesis in jets + ET! searches. It was assumed that thegluino only decayed to two jets and a stable bino. How-ever, 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 de-cays 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 con-sidered. 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 param-eter space (see Fig. 2). While this cascade decay may berepresentative of many models that have gluino-like ob-jects, 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 accessi-ble. In this paper, it was assumed that the squarks arekinematically inaccessible at the Tevatron; however, ifthe squarks are accessible, g̃q̃ and q̃q̃ production chan-nels 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 pro-duce 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 mono-photon search rather than amonojet search [22].4 Preliminary estimates of the reachof the mono-photon search show that it is not as effec-tive as the monojet search. This is likely due to theabsence of final-state photon radiation from the gluinos.However, it may be possible to better optimize the mono-photon search, because the Standard Model backgroundsare easier to understand in this case.

    Ultimately, a model-independent search for jets plusmissing energy would be ideal. We believe that our ex-clusive nj + ET! searches, with results presented in anexclusion plot as a function of HT and ET! , would pro-vide significant coverage for these alternate channels [21].This analysis should be carried forward to the LHC toensure that the searches discover all possible supersym-metric spectra. The general philosophy of parameter-izing 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. There-fore, it is unlikely that there will be a gap in gluino-binomasses where neither the Tevatron nor the LHC has sen-sitivity.

    Acknowledgements

    We would like to thank Jean-Francois 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

    TE/

    ~g

    B~

    q_

    ~B

    g~

    q

    _q

    qq

    j

    q

    _q

    ~B

    g~ ~

    g

    B~

    q_

    /ET

    FIG. 1: Boosted gluinos that are degenerate with the binodo not enhance the missing transverse energy when there isno hard initial- or final-state radiation. (A) illustrates thecancellation of the bino’s ET! . (B) shows how initial- or final-state 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 well-separated jets are produced, as well as largemissing transverse energy. The situation is very differ-ent for light gluinos (mg̃ ! 200 GeV) that are nearlydegenerate with the bino. Such light gluinos can be co-piously produced at the Tevatron, with cross sectionsO(102 pb), as compared to O(10−2 pb) for their heav-ier 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 reconstruct-ing 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 emis-sion of hard QCD jets (Fig. 1B). Therefore, initial-stateradiation (ISR) and final-state radiation (FSR) must beproperly accounted for.

    The correct inclusion of ISR/FSR with parton show-ering requires generating gluino events with matrix ele-ments. 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 anti-quark, as well as parton showering and hadronization ofthe final-state partons, was done in PYTHIA 6.4 [15].

    To ensure that no double counting of events occursbetween the matrix-element multi-parton events and theparton showers, a version of the MLM matching proce-dure was used [16]. In this procedure, the matrix el-ement multi-parton events and the parton showers areconstrained to occupy different kinematical regions, sep-arated 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]. Matrix-element events are generated with some minimum cut-off 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 matrix-elementevent, d(parton, jet) < QPSmin. For events from the high-est multiplicity sample, extra jets softer than the soft-est matrix-element parton are allowed. This procedureavoids double-counting jets, and results in continuousand smooth differential distributions for all jet observ-ables.

    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 factoriza-tion scales set to the gluino mass. The cross sectionswere rescaled to the next-to-leading-order (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 di-boson 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 gen-erated using MadGraph/MadEvent and then showeredand hadronized using PYTHIA. PGS was used to recon-struct 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 back-ground 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

    pair-produced 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 gaugino-sfermion-

    fermion interaction $more specifically, the B̃-ẽR-eR coupling%and some aspects of the B̃-&̃1-& coupling.We start our discussion with ẽR . The production proceeds

    though the s-channel exchange of gauge bosons and

    t-channel exchange of neutralinos, whose cross section is

    shown in Appendix B. The t-channel exchange is dominated

    by B-ino-like 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 tree-level coupling of the B̃-ẽR-eR vertex has a

    simple relation to the B-e-e 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 de-pends 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 1-Y 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

    forward-backward 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 negligi-bly 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 1-Y 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

    missing transverse momentum

    mχ̃02− mχ̃0

    1

  • 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

    (p1 + p2 + pχ̃1)2 = m2χ̃0

    2

    3 body mll = M2 − M1

    2body × 2 mll = M2

    1 −M2

    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- :e-μ+-=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 -.7275E-04

    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 opposite-sign, same-flavor dileptons for the Point 4 signal(solid histogram), opposite-sign, opposite-flavor 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 opposite-sign, same-flavor dileptons andopposite-sign, opposite-flavor 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 opposite-sign, same-flavor dileptons for the Point 4 signal(solid histogram), opposite-sign, opposite-flavor 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 opposite-sign, same-flavor dileptons andopposite-sign, opposite-flavor 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.

  • Jet-lepton 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

  • Jet-lepton 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

  • Jet-lepton 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+μμ-eμ 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

    gaugino-Higgsino 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 co-annihilation excluded (^^; in co-annihilation region because dependence is so large. (Discussed in Baltz et al)

    • higgs s-channel exchange (; ;) Get lower limit of HIggs mass Heavy higgs is not accessible in many cases.

    • higgsino component (^^) Figure 17: Spin-independent neutralino-proton 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 un-certainty 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 con-strained value of tan β. In the interval allowed by the non-observation 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 cross-sections (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 s-wave part of the pair anni-hilation 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 cross-section on m(τ̃2). The mixing

    14

    MN, Polesello and Tovey hep-ph/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 non-trivial structure which will be discussed in thefollowing. Fig. 1 shows an example of such process in which mother superparticles werepair-produced 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 0.1947E-02

    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 SUSY-breaking (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 config-uration 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 back-to-backtransverse 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 partonic-level, 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 chan-nel[? ]. When mR < mg̃, q̃R dominantly decays into thelightest neutralino χ̃01 and a jet, therefore q̃Rq̃R produc-tion 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 neg-ligible. The right-handed 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 produc-tion and the decay pp → g̃g̃ → j j j jχ̃01 χ̃01 . The mT 2 vari-able 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 con-tribute 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 aris-ing from g̃ decay. At m = mLSP, the endpoints of bothof the events should be at mg̃ becuase the true LSP mo-menta 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 algo-rithm, 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 gluino-gluino or squark-squark) contributes to the four jet + missing ET channel,and a gluino decays dominantly into j jχ̃01 . It is not sat-isfactory 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 gen-eral MSSM points. They are also generally co-produced.When mg̃ ∼ mq̃, the squark-gluino co-production 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 − |pk|cosθ 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

    b-1

    FIGURE 3. The signal(solid) and background(dashed) dis-tributions 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 distri-butions 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 in-volving 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 pro-duced sparicle decays are identified. Several groups stud-ied 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 promis-ing. The LFV in SUSY processes might come from right-handed 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 non-zero inmodels with non-zero LFV. The sensitivity to the massdifference is recently discussed in [? ].

    The masses of the third generation squarks and slep-tons 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 = −√

    2/3|p|

    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)

    gravitino-goldstino 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 ‘right-handed’ 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 spin-3/2 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.

    -12-10

    -8-6

    -4-2

    02

    46

    810

    12-10

    -8-6-4-20246810

    -8

    -6

    -4

    -2

    0

    2

    4

    6

    8

    -12-10

    -8-6

    -4-2

    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 un-naturally 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 5-plet MDM prediction, at thebest-fit 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 AMS-08 (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 X-ray 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 re-gion 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 param-eters, 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 10-60 GeV which matches the MDM prediction. Let us compare with supersymmetry,the theoretically favored scenario: slepton masses can be fine-tuned to be quasi-degenerate withthe lightest neutralino in order to enhance 3-body annihilations obtaining the correct relic abun-dance 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 ..

    10-8

    10-7

    10-6

    10-5

    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

    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: Gamma-ray 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

    10-8

    10-7

    10-6

    10-5

    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 cosmic-ray 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, Gamma-ray

    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 cosmic-ray 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 gamma-ray (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 R-parity violating interactions

    originate from bi-linear terms of Higgs and lepton doublet. In the original basis, the

    R-parity violating interactions are assumed to be bi-linear terms in superpotential

    and supersymmetry (SUSY) breaking terms [20]. Without loss of generality, we

    can always eliminate the bi-linear R-parity violating terms from the superpotential

    by the redefinition of the Higgs and lepton-doublet 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 R-parity

    violating terms are only in the soft-SUSY breaking terms, which are given by

    LRPV = BiL̃iHu + m2L̃iHd

    L̃iH∗d + h.c., (3.1)

    where L̃i is left-handed slepton doublet in i-th generation, while Hu and Hd are up-

    and down-type Higgs boson doublets, respectively. In the following, we study the

    phenomenological consequences of the R-parity violating terms given in Eq. (3.1).

    With these R-parity violating terms, the vacuum expectation values (VEVs) of

    left-handed sneutrino fields ν̃i are generated as

    〈ν̃i〉 =Bi sin β + m2L̃iHd

    cos β

    m2ν̃iv, (3.2)

    where v # 174 GeV is the VEV of standard-model-like 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 R-parity 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 Dirac-type 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?