From Inclusive SignaturesFrom Inclusive Signaturesto String Theory?to String Theory?

LHC Inverse WorkshopLHC Inverse WorkshopMCTPMCTP

April 12-15, 2006April 12-15, 2006

PIYUSH KUMARPIYUSH KUMAR

Work based on Work based on G. Kane, P.K., J. ShaoG. Kane, P.K., J. Shao

hep-ph/0604…hep-ph/0604…

LHC Inverse ProblemLHC Inverse Problem

Split into three categories :Split into three categories :

1) What is the broad set of possibilities for New Physics?1) What is the broad set of possibilities for New Physics?

2) What is the specific model within this broad set?2) What is the specific model within this broad set?

Typically, more focus on the above two. Typically, more focus on the above two.

However,However,

3) What is the underlying Theoretical Framework giving rise to New 3) What is the underlying Theoretical Framework giving rise to New PhysicsPhysics

and the specific model?and the specific model?

--- Take this framework to be String theory, as it has the capability to --- Take this framework to be String theory, as it has the capability to

address all questions.address all questions.

Even within a particular scheme for new physics,Even within a particular scheme for new physics,

Inverse Map from Signatures to Parameters :Inverse Map from Signatures to Parameters : Very Challenging…. Very Challenging….

-- Degeneracies in Parameter space. Shown for the -- Degeneracies in Parameter space. Shown for the MSSM in hep-ph/0512190 MSSM in hep-ph/0512190 (Arkani-Hamed, Kane(Arkani-Hamed, Kane,,Thaler,Wang)Thaler,Wang)

To Solve ….To Solve ….

Need new independent signaturesNeed new independent signatures..

Another method to address degeneracies --- Have a Another method to address degeneracies --- Have a Theoretical model. Theoretical model.

--- Relates parameters in a non-trivial way. --- Relates parameters in a non-trivial way. --- Could resolve (or greatly reduce) degeneracies --- Could resolve (or greatly reduce) degeneracies.. --- But which model?--- But which model?

We find that :We find that :

1) Patterns of signatures 1) Patterns of signatures sensitivesensitive to the properties of the theoretical to the properties of the theoretical construction construction could distinguish different underlying theory could distinguish different underlying theory constructions constructions with limited data. with limited data. 2) Could help in solving the problem of degeneracies. 2) Could help in solving the problem of degeneracies. (within a(within a particularparticular theory)theory) Can also address the problem of degeneraciesCan also address the problem of degeneracies among different among different theoriestheories in future. in future.For concreteness, focus on For concreteness, focus on

a) Traditional low-scale supersymmetry (General MSSM) as New Physics.a) Traditional low-scale supersymmetry (General MSSM) as New Physics.

b) Underlying Theoretical framework of String Theory, with variousb) Underlying Theoretical framework of String Theory, with various constructions giving rise to it.constructions giving rise to it.

Get around the problem by Get around the problem by

--- considering many constructions (each with many --- considering many constructions (each with many models)models)

--- looking at patterns of signatures.--- looking at patterns of signatures.

In our analysis, In our analysis,

--- Have analyzed patterns of LHC signatures for seven semi-realistic --- Have analyzed patterns of LHC signatures for seven semi-realistic constructions. Have been studied in literature.constructions. Have been studied in literature.

--- Even though the constructions not fully realistic, they have the--- Even though the constructions not fully realistic, they have the potential of becoming more realistic in the future.potential of becoming more realistic in the future.

--- Also, the point of the analysis is an illustration of the approach.--- Also, the point of the analysis is an illustration of the approach.

--- Similar analysis can (and should) be carried out for more realistic --- Similar analysis can (and should) be carried out for more realistic constructions in future.constructions in future.

Next Slide --- Show results for distinguishibility of Next Slide --- Show results for distinguishibility of constructions basedconstructions based

on patterns of signatures.on patterns of signatures.

RESULTS

HM-AHM-A HM-BHM-B HM-CHM-C PH-APH-A PH-BPH-B II-AII-A II-BII-B

HM-AHM-A ______

HM-BHM-B PYPY ______ symmetricsymmetric

HM-CHM-C PYPY PYPY ______

PH-APH-A YesYes YesYes YesYes ______

PH-BPH-B YesYes YesYes YesYes YesYes ________

II-AII-A YesYes YesYes YesYes YesYes YesYes ______

II-BII-B YesYes YesYes YesYes YesYes YesYes YesYes ________

• HM-A HM-A : Heterotic M-theory constructions with one kahler modulus.: Heterotic M-theory constructions with one kahler modulus.

• HM-B HM-B : Heterotic M-theory constructions with one kahler modulus and one five-brane.: Heterotic M-theory constructions with one kahler modulus and one five-brane.

• HM-C HM-C : Herterotic M-theory constructions with multiple kahler moduli.: Herterotic M-theory constructions with multiple kahler moduli.

• PH-APH-A : Pert. Heterotic string theory constructions with kahler stabilization of dilaton. : Pert. Heterotic string theory constructions with kahler stabilization of dilaton.

• PH-B PH-B : Pert. Heterotic string theory constructions with multiple gaugino condensates.: Pert. Heterotic string theory constructions with multiple gaugino condensates.

• II-A II-A : Type II A string theory constructions with Intersecting D-branes.: Type II A string theory constructions with Intersecting D-branes.

• II-B II-B : Type II B string theory constructions with KKLT-like moduli stabilization.: Type II B string theory constructions with KKLT-like moduli stabilization.

Example – the PH-B constructionExample – the PH-B construction

Perturbative Heterotic String compactified on toroidal orbifolds.Perturbative Heterotic String compactified on toroidal orbifolds.

Tree Level kahler potential.Tree Level kahler potential.

Presence of a Green-Schwarz (GS) mechanism to cancel anomalies.Presence of a Green-Schwarz (GS) mechanism to cancel anomalies.

Multiple gaugino condensates (typically two) to stabilize the dilaton Multiple gaugino condensates (typically two) to stabilize the dilaton and breakand break

supersymmetry --- “racetrack mechanism”.supersymmetry --- “racetrack mechanism”.

Supersymmetry breaking mediated by gravity.Supersymmetry breaking mediated by gravity.

Minimum preferred with <FMinimum preferred with <FSS> = 0; <F> = 0; <FTT> ≠ 0; Re(t) ≥ 1; m> ≠ 0; Re(t) ≥ 1; m3/23/2 ~ 10 ~ 10 TeV.TeV.

(Carlos et al hep-th/9204012, de la Macorra et al hep-ph/9210219, etc.)(Carlos et al hep-th/9204012, de la Macorra et al hep-ph/9210219, etc.)Tree level contribution to soft terms vanishing. (if all nTree level contribution to soft terms vanishing. (if all n ii = -1) = -1)

Both Green-Schwarz counter-term and superconformal anomaly Both Green-Schwarz counter-term and superconformal anomaly contribute tocontribute toone-loop gaugino masses. One loop contribution one-loop gaugino masses. One loop contribution non-universalnon-universal..

For phenomenological analysis : For phenomenological analysis : {m{m3/23/2, , δδGSGS, Re(t), tan(, Re(t), tan(ββ)})} calculate soft terms as a function of thesecalculate soft terms as a function of these

Next slideNext slide ------ present pattern table of important signatures useful inpresent pattern table of important signatures useful in distinguishing different constructions.distinguishing different constructions.

--- Actually have more distinguishing signatures than --- Actually have more distinguishing signatures than what will be shown.what will be shown.

--- Naively can construct many signatures. --- Naively can construct many signatures.

--- However, as emphasized in hep-ph/0512190, many--- However, as emphasized in hep-ph/0512190, many signatures signatures notnot independent ; in fact, highly correlated. independent ; in fact, highly correlated. So, many signatures not helpful in distinguishing moreSo, many signatures not helpful in distinguishing more and more constructions.and more constructions.

--- As will see later, having a high scale theory helps --- As will see later, having a high scale theory helps to find distinguishing signatures .to find distinguishing signatures .

Pattern Pattern TableTable

Const./Const./SignaturesSignatures

AA BB CC DD EE FF GG

ConditionCondition > 4000> 4000 > 0.13> 0.13 > 5.0> 5.0 >0.02>0.02 > 8> 8 > 1.2> 1.2 > 45> 45

HM-AHM-A √√ XX √√ √√ √√ √√ √√

HM-BHM-B BothBoth XX √√ BothBoth √√ √√ √√

HM-CHM-C BothBoth XX BothBoth √√ √√ BothBoth BothBoth

PH-APH-A XX XX √√ XX N.ON.O √√ XX

PH-BPH-B N.O.N.O. N.O.N.O. XX N.O.N.O. N.ON.O XX N.O.N.O.

II-AII-A N.ON.O √√ XX N.O.N.O. N.ON.O XX BothBoth

II-BII-B N.O.N.O. N.O.N.O. N.O.N.O. N.O.N.O. N.O.N.O. N.O.N.O. N.O.N.O.

AA – # of events with – # of events with OS dileptonsOS dileptons and ≥2 jets. and ≥2 jets. BB – – (X-15∙Y), X=ratio of(X-15∙Y), X=ratio of # of events # of events with with 0 leptons and 4 jets and total # of events.0 leptons and 4 jets and total # of events. Y=ratio of # of events with 2 leptons and 4 jets and total # of events.Y=ratio of # of events with 2 leptons and 4 jets and total # of events.

CC – (X/Y), X= – (X/Y), X= ## of events with of events with OSDF dileptons andOSDF dileptons and ≥2 jets.≥2 jets. Y= ratioY= ratio of ( of (# of # of events withevents with 1 tau, 1 tau, ≥2 jets≥2 jets) and (# of events with and (# of events with ≥≥3 b jets, 3 b jets,

≥2 jets)≥2 jets).. DD – (X/Y), X= # of events with – (X/Y), X= # of events with 2 leptons and 02 leptons and 0 b jets and b jets and ≥≥ 2 2 jets. jets. Y = total # Y = total # of events.of events.EE – – # of events with# of events with clean dileptons. clean dileptons.F F – – (X/Y), X=ratio of (# of events with 0 lepton and 4 jets) and (total # of events). (X/Y), X=ratio of (# of events with 0 lepton and 4 jets) and (total # of events).

Y=ratio of (# of events with 1 lepton) and (# of events with 0 lepton and Y=ratio of (# of events with 1 lepton) and (# of events with 0 lepton and ≥≥ 2 jets). 2 jets).

GG – – endpoint of the OS dilepton endpoint of the OS dilepton invariant massinvariant mass ((mmllll) distribution.) distribution.

Some DetailsSome Details

--- Simulated ~ 50 “models” for each construction.--- Simulated ~ 50 “models” for each construction. “ “Model” – defined by a set of input parameters for each Model” – defined by a set of input parameters for each

construction. construction. Expect that results are robust (confirm for one case).Expect that results are robust (confirm for one case).

--- Counting signatures denote # of events --- Counting signatures denote # of events in excess ofin excess of the the Standard Model.Standard Model.

--- Signatures presented are for a luminosity of 5 fb--- Signatures presented are for a luminosity of 5 fb-1-1 at the LHC. at the LHC. Want to focus on early results. More data will give better Want to focus on early results. More data will give better

results.results.

--- Criteria for an observable signature:--- Criteria for an observable signature:

a) Na) Nsignalsignal/√N/√Nbkgdbkgd > 4 ; b) N > 4 ; b) Nsignalsignal/N/Nbkgdbkgd > 0.1 ; c) N > 0.1 ; c) Nsignal signal > 5.> 5.

ExampleExample

Details of ProcedureDetails of Procedure

Obtain Effective Action of the ConstructionObtain Effective Action of the Construction --- --- 10D 10D 4D. 4D. ( at Unification Scale) SUSY breaking, Mediation.( at Unification Scale) SUSY breaking, Mediation. Soft SUSY breaking terms in terms of theory input parametersSoft SUSY breaking terms in terms of theory input parameters

RG Evolution from Unification Scale to Electroweak scale RG Evolution from Unification Scale to Electroweak scale --- Using SuSPECT, only a subset compatible with low energy constraints --- Using SuSPECT, only a subset compatible with low energy constraints onon superpartner masses, higgs mass, relic density, bsuperpartner masses, higgs mass, relic density, bssγγ, (g, (gμμ-2).-2). --- For simplicity, we assume no intermediate scale physics. Interesting --- For simplicity, we assume no intermediate scale physics. Interesting subject subject on its own. on its own. David Morrissey’s talk. David Morrissey’s talk. Event Generation – PYTHIA 6.324.Event Generation – PYTHIA 6.324.

Detector Simulation – Modified Version of PGSDetector Simulation – Modified Version of PGS (developed by (developed by Stephen Mrenna).Stephen Mrenna). --- Definitions and Trigger-level cuts, as in the LHC Olympics.--- Definitions and Trigger-level cuts, as in the LHC Olympics. --- Event selection cuts : Lepton, Photon P--- Event selection cuts : Lepton, Photon PTT > 10 GeV. > 10 GeV. Jet PJet PTT > 100 GeV. > 100 GeV. Missing EMissing ET T > 100 GeV.> 100 GeV.Standard Model BackgroundStandard Model Background --- tt background, diboson background. W+jets not included in the --- tt background, diboson background. W+jets not included in the interest of time.interest of time. --- However, Missing E--- However, Missing ET T threshold -- 100 GeV. From hep-ph/ 9512383, threshold -- 100 GeV. From hep-ph/ 9512383, clear that clear that tt background either biggest or comparable to W+jets.tt background either biggest or comparable to W+jets.

Distinguishibility of ConstructionsDistinguishibility of Constructions

1) Why possible? 1) Why possible? -- Soft terms for different constructions related to “theory” -- Soft terms for different constructions related to “theory”

input parameters in different ways. input parameters in different ways.

-- Relations -- Relations amongamong soft terms different for different constructions soft terms different for different constructions..

2) Naively, one can have many inclusive signatures.2) Naively, one can have many inclusive signatures. -- Many of them correlated with each other.-- Many of them correlated with each other.

-- Effective dimensionality of signature space much smaller.-- Effective dimensionality of signature space much smaller.

-- Having a theory helps!-- Having a theory helps!

In the following, explain why particular signatures useful.In the following, explain why particular signatures useful. SignaturesSignatures Spectrum Parameters Parameters Soft Terms Model Spectrum Parameters Parameters Soft Terms Model

(low scale) (high scale) (high scale)(low scale) (high scale) (high scale)

a) Explain signatures from spectrum/low scale parameters.a) Explain signatures from spectrum/low scale parameters.

b) Explain spectrum from high scale theoretical setup.b) Explain spectrum from high scale theoretical setup.

a) Explanation from the Spectrum a) Explanation from the Spectrum (few examples)(few examples)

a) HM-A -- a) HM-A -- universaluniversal boundary conditions. boundary conditions. -- alllowed spectrum - light or moderately heavy gluinos -- alllowed spectrum - light or moderately heavy gluinos (550-(550-

700 GeV)700 GeV)

slightly lighter squarks, light sleptons.slightly lighter squarks, light sleptons. -- Both ~gg and ~gq pair production comparable.-- Both ~gg and ~gq pair production comparable.

-- Both ~g and ~q decay to N-- Both ~g and ~q decay to N22 and C and C1.1.

-- N-- N22 and C and C11 decay via sleptons. decay via sleptons.

-- M-- MN2N2 ~ M ~ MC1C1 ~ 2 M ~ 2 MLSPLSP leptons pass the cuts. leptons pass the cuts.

So, the HM-A construction has many events for leptons; distinguishing it So, the HM-A construction has many events for leptons; distinguishing it fromfrom

the PH-A, PH-B and II-A constructions (non-universal soft terms).the PH-A, PH-B and II-A constructions (non-universal soft terms). The above figure just one example.The above figure just one example. These constructions typically have -- heavy scalars, varying gluino.These constructions typically have -- heavy scalars, varying gluino.

-- N-- N22 and C and C11 decay via Z and W. decay via Z and W.

-- -- ΔΔMMN2-N1 N2-N1 & & ΔΔMMC1-N1 C1-N1 comparatively smaller comparatively smaller leptons softer on leptons softer on average.average.

b) HM-C – Contains HM-A as a subset, can also be seen from the figure. b) HM-C – Contains HM-A as a subset, can also be seen from the figure. Non-universal soft terms.Non-universal soft terms. Origin of “PY” in the Pattern Table results.Origin of “PY” in the Pattern Table results.

c) HM-B – Also contains the HM-A as a subset. c) HM-B – Also contains the HM-A as a subset. Universal soft terms. Universal soft terms. Contains two regions, seen from Figure. Contains two regions, seen from Figure. Region II – “focus point region”, scalars heavier compared to Region II – “focus point region”, scalars heavier compared to gauginos.gauginos. can be understood from high-scale theory. can be understood from high-scale theory. can be distinguished from HM-A. Origin of “PY”. can be distinguished from HM-A. Origin of “PY”.

d) II-B -- very heavy spectrum (Falkowski et al – hep-ph/0507110) d) II-B -- very heavy spectrum (Falkowski et al – hep-ph/0507110) gluino ≥ 3 TeV; squarks, sleptons ≥ 2 TeV.gluino ≥ 3 TeV; squarks, sleptons ≥ 2 TeV.

Not ObservableNot Observable with 5 fb with 5 fb-1-1 of data. of data.

Still useful as distinguishable from other constructions which are Still useful as distinguishable from other constructions which are observable.observable.Look at more specific signatures -- to distinguish more Look at more specific signatures -- to distinguish more

constructions.constructions.

Explain one more example.Explain one more example.

PH-A, HM-C, II-APH-A, HM-C, II-A

-- -- All haveAll have heavy scalars and heavy scalars and lighter gluinos.lighter gluinos. -- ~g -- ~g N N22, C, C11 ; N ; N22, C, C11 decay decay via Z and W similarly.via Z and W similarly. -- Therefore, compare fraction -- Therefore, compare fraction of gluinos decaying to Nof gluinos decaying to N22, C, C1.1.

---- Also look at Also look at ΔΔMMN2-N1N2-N1 & & ΔΔMMC1-C1-

N1 N1

II-A -- distinguishable from PH-A, PH-B and HM-C .II-A -- distinguishable from PH-A, PH-B and HM-C .

PH-B – Signature not observable. PH-B – Signature not observable. -- Two possible LSPs . a) Wino LSP -- Two possible LSPs . a) Wino LSP M MLSPLSP ≈ M ≈ MC1C1 No (hard) leptons. No (hard) leptons. Also MAlso MN2N2 >> M >> MLSPLSP N N22 production suppressed. production suppressed.

b) Bino LSP -- heavy gluinos (> 900 GeV).b) Bino LSP -- heavy gluinos (> 900 GeV). heavy Nheavy N22 & C & C11, but , but ΔΔMMN2-N1N2-N1 & & ΔΔMMC1-N1C1-N1 quite small. quite small. soft leptons.soft leptons. -- Can be understood from high scale construction.-- Can be understood from high scale construction.

b) Explanation from the Underlying Theory setupb) Explanation from the Underlying Theory setup

Helpful to understand the origin of the spectrum pattern from the highHelpful to understand the origin of the spectrum pattern from the highscale theoretical setup.scale theoretical setup. --- As an illustration, carry out exercise for the PH-B construction.--- As an illustration, carry out exercise for the PH-B construction.

Features of Spectrum:Features of Spectrum:-- Heavy squarks ( ≥ 1 TeV), moderately heavy sleptons (light stau), gluinos -- Heavy squarks ( ≥ 1 TeV), moderately heavy sleptons (light stau), gluinos varying from light to heavy.varying from light to heavy.-- Light gluinos -- Light gluinos always always give rise to agive rise to a Wino LSP, while heavy gluinos to a Bino Wino LSP, while heavy gluinos to a Bino LSP.LSP.

Soft terms depend on the following theory input parameters :Soft terms depend on the following theory input parameters :

{m{m3/23/2, , δδGSGS,, Re(t), tan(Re(t), tan(ββ)}; <F)}; <FSS> = 0 > = 0 (hep-ph/0209061)(hep-ph/0209061) ((Kane, Lykken, Mrenna, Nelson, Wang, WangKane, Lykken, Mrenna, Nelson, Wang, Wang) ) Scalars -- mScalars -- m22

ii ≈ ≈ γγii m m223/23/2

(One loop, Tree level vanishing.)(One loop, Tree level vanishing.) Trilinears -- ATrilinears -- Aijkijk ≈ m ≈ m3/2 3/2 ((γγii+ + γγjj + + γγkk ) )

Gauginos -- MGauginos -- Ma a = g= gaa22/2 {2[(/2 {2[(δδGSGS/16/16ππ22)+b)+baa] G] G22(t,t) F(t,t) FTT- 2 b- 2 baa m m3/23/2 } }

γγi i (squarks) > (squarks) > γγi i (sleptons) , In particular (sleptons) , In particular γγi i (Q(Q33) ≈ 3 ) ≈ 3 γγi i (E(E33) )

sleptons lighter than squarks, with stau the lightest.sleptons lighter than squarks, with stau the lightest.

Since Soft terms arise at one loop, need heavy mSince Soft terms arise at one loop, need heavy m3/2 3/2 ≈ 20-30 TeV.≈ 20-30 TeV.

--- Explains the squark and slepton spectrum.--- Explains the squark and slepton spectrum.

Gaugino Sector --- worthwhile to look at some plots Gaugino Sector --- worthwhile to look at some plots

(at unification scale) (at unification scale)

Variation of MVariation of Maa as a function of Re(t). ( as a function of Re(t). (δδGSGS=-15, m=-15, m3/2 3/2 = 20 TeV )= 20 TeV )

(at unification scale)(at unification scale)

Variation of MVariation of M11/M/M22 as a function of Re(t). ( as a function of Re(t). (δδGSGS=-15, m=-15, m3/2 3/2 = 20 TeV )= 20 TeV )

--- M3 smallest of the three --- as b3 is the largest.--- M3 smallest of the three --- as b3 is the largest.

--- --- Also, MAlso, M1low1low ≈ 0.45 M ≈ 0.45 M1unif 1unif ; M; M2low2low ≈ 0.9 M ≈ 0.9 M2unif2unif

Thus, for Re(t) < Re(tThus, for Re(t) < Re(t00) (≈ 1.4) , we have M) (≈ 1.4) , we have M1unif1unif/M/M2unif2unif > 2 > 2 Wino LSP; Wino LSP; otherwise Bino LSP.otherwise Bino LSP.

For those values of Re(t), M3 quite small For those values of Re(t), M3 quite small light gluino. light gluino.

At Unification scaleAt Unification scale

Regions not allowed:

a) For Re(t) ≈≈ Re(tc) (≈ 1.2) , MM33 almost vanishing excluded by low energy constraints.

b) For Re(t) ≈≈ 0, M2 very small excluded by chargino bounds.

Soft Terms from the Theoretical setup

-- Moduli stabilized such that <FS>=0, modular weights ni = -1.

SUSY breaking moduli dominated. All soft terms zero at tree level.

-- Different for different constructions. Can be understood. For PH-A, <FS> ≠ 0, <FT> = 0; Different expresions for K, W, f. For HM-A, Both <FS>,<FT> ≠ 0; Different expressions for K, W, f.

DegeneraciesDegeneracies

For the MSSM --- O(50) degeneracyFor the MSSM --- O(50) degeneracy (hep-ph/0512190)(hep-ph/0512190)

Degeneracies characterized as follows : Degeneracies characterized as follows :

a) Flipper (cycler) -- Mass eigenvalues of two inos same, identity swapped.a) Flipper (cycler) -- Mass eigenvalues of two inos same, identity swapped.

b) Squeezer – Mass separation between inos very close in one model, while b) Squeezer – Mass separation between inos very close in one model, while very different in another.very different in another.

c) Slider -- Masses of many states move collectively in one direction.c) Slider -- Masses of many states move collectively in one direction.

-- Highly unlikely that all 50 degenerate MSSMs from the -- Highly unlikely that all 50 degenerate MSSMs from the samesame high scale high scale construction. construction.

-- By definition, a theoretical model relates parameters non-trivially. -- By definition, a theoretical model relates parameters non-trivially.

-- Having a model can thus remove (or greatly reduce) degeneracies.-- Having a model can thus remove (or greatly reduce) degeneracies.

A Simple ExampleA Simple Example

There exists no degeneracy in the HM-A construction !There exists no degeneracy in the HM-A construction !

Can carry out similar exercise for other constructions. MostCan carry out similar exercise for other constructions. Most degeneracies removed in all constructions.degeneracies removed in all constructions.

HM-A constructionHM-A construction --- Universal soft terms.--- Universal soft terms. Hierarchy between gauginos fixed. Hierarchy between gauginos fixed. (M(M11<M<M22<M<M33)) Flipper degeneracy Flipper degeneracy notnot possible. possible.

Since MSince M22 ≈ 2 M ≈ 2 M11 at low scale, squeezer at low scale, squeezer degeneracy also degeneracy also not not possible.possible.

Turns out that slider degeneracy also not Turns out that slider degeneracy also not allowed. allowed.

--- Cannot compensate for change in gluino --- Cannot compensate for change in gluino mass by changing squark masses in themass by changing squark masses in the opposite way.opposite way.

--- Do not want to vary the gluino and squark --- Do not want to vary the gluino and squark masses a lot.masses a lot.

--- The electroweak-ino spectrum also more --- The electroweak-ino spectrum also more or less or less fixed by the universality of gaugino fixed by the universality of gaugino masses.masses.

--- Cannot get a “big-enough” slider.--- Cannot get a “big-enough” slider.

For our set of high scale constructions, didn’t find anyFor our set of high scale constructions, didn’t find any

degeneracy coming from degeneracy coming from differentdifferent high scale constructions.. high scale constructions..

However, still possible to have them.However, still possible to have them.

Have not studied them yet, but expect that possible to distinguish Have not studied them yet, but expect that possible to distinguish

them also in future.them also in future.

--- Constructions should be made more and more realistic.--- Constructions should be made more and more realistic.

--- Since have a high scale theory, can be brought to confront data --- Since have a high scale theory, can be brought to confront data

in different fields like cosmology, flavor physics, rare decays, etc.in different fields like cosmology, flavor physics, rare decays, etc.

--- Thinking of new clever orthogonal signatures from a bottom-up point of --- Thinking of new clever orthogonal signatures from a bottom-up point of

view can help a lot --- Tom Hartman’s talk.view can help a lot --- Tom Hartman’s talk.

Combining all the above can help in eventually resolving Combining all the above can help in eventually resolving degeneracies.degeneracies.

Possible LimitationsPossible Limitations

1) 1) Sampling IssuesSampling Issues

-- Sampling only ~50 models for each construction not enough.-- Sampling only ~50 models for each construction not enough.

Relation of soft terms to input parameters as well asRelation of soft terms to input parameters as well asamong themselves properly understood. among themselves properly understood.

-- expect that qualitative features of signatures and results-- expect that qualitative features of signatures and results do not change. do not change.

Explicitly confirmed expectation for one construction PH-A. Explicitly confirmed expectation for one construction PH-A.

-- simulated ~300 more models for the PH-A construction and -- simulated ~300 more models for the PH-A construction and

compared compared with ~50 models. Results don’t change.with ~50 models. Results don’t change.

-- In the future, plan to do a much more dense sampling of parameter -- In the future, plan to do a much more dense sampling of parameter space space

for other constructions also.for other constructions also.

2) 2) Method of distinguishing signaturesMethod of distinguishing signatures

-- Method of distinguishing signatures naïve could lead to

misleading results.

Our results seem to be robust.

Typically, find more than one signature distinguishing constructions.

Gives us confidence our results are reliable.

In future, can do a precise analysis with a χ2-like variable for each

signature. Can construct the quantity :

ΔSiAB = min { [(si

A (x) – siB (y)) /σi

AB]2 } for the ith signature.

w.r.t parameter vectors x & y.

Point of ViewPoint of View

Useful toUseful to apply approach at various stagesapply approach at various stagesStage IStage I : : Distinguish broad classes of constructions with limited data and simple Distinguish broad classes of constructions with limited data and simple

signaturessignatures and analysis techniques. and analysis techniques. Could still rule out many classes of constructions and learn about the onesCould still rule out many classes of constructions and learn about the ones consistent with limited data.consistent with limited data.

This was the goal of the present analysis.This was the goal of the present analysis. To make further progress, need more data, more exclusive To make further progress, need more data, more exclusive signatures and special analysis techniques (suitable to favorable signatures and special analysis techniques (suitable to favorable constructions)constructions)

--- --- Techniques present in literature (but mostly for mSUGRA, GMSB, etc.) Techniques present in literature (but mostly for mSUGRA, GMSB, etc.) --- Techniques used recently for solving the “Blackboxes”.--- Techniques used recently for solving the “Blackboxes”.

Suitable for subsequent stages.Suitable for subsequent stages.

Combining above techniques with knowledge of connection Combining above techniques with knowledge of connection between theory and databetween theory and data can help make a lot of can help make a lot of progress.progress.

CONCLUSIONSCONCLUSIONS

Have explored a technique whichHave explored a technique which

1) may help distinguish different high scale string constructions1) may help distinguish different high scale string constructions with limited data.with limited data.

2) addresses the problem of degeneracies and may help in eventually 2) addresses the problem of degeneracies and may help in eventually solvingsolving

them.them.

UPSHOTSUPSHOTS --- LHC signatures can be directly related to high scale theoretical --- LHC signatures can be directly related to high scale theoretical

models.models. --- Can combine both --- Can combine both top-downtop-down and and bottom-upbottom-up approaches. approaches. --- Can thus get insights about the nature of the underlying--- Can thus get insights about the nature of the underlying (string) theoretical framework itself.(string) theoretical framework itself.

HM-CHM-CHM-BHM-B …………

low scale low scale parameter parameter

spacespace

Signature Signature spacespace

PH-APH-A II-BII-B

HM-AHM-A parameterparameter spaces of high scale constructionsspaces of high scale constructions

low scale low scale parameter parameter

spacespace

Signature Signature spacespace

highhigh scalescale parameterparameter spacespace

AA BB