Search for Gravitinos in R-Parity violating Supersymmetry at HERA

Search for Gravitinos in R-Parity violating

Supersymmetry at HERA

IntroductionHERA & ZEUSSUSY processes at HERAAnalysisSummary & Outlook

SLAC experimental seminarClaus Horn (DESY / Univ. Hamburg)

May 9/2006 SLAC Seminar: Search for Gravitinos Claus Horn (DESY) 2

SUSY Motivation

• Coleman-Mandula theorem / Haag-Lopuszanski-Sohnius theorem

• Unification of the forces • Solution of the hierarchy problem • Candidates for dark matter • Necessary for quantum-gravity

SUSY is our last chance to discover a fundamental space-time symmetry!


HERA acceleratore± p collider, in HamburgProtons: 920 GeVLeptons: 27.5 GeVCMS-Energy: 320 GeVLength: 6.3km

HERA I (1992-2000) L=1.6 1031 cm-2s-1

HERA II (2002-2007) L=7.0 1031 cm-2s-1

p 920 GeV 27.5 GeV e±

HERA II: polarised lepton beam also at H1 & ZEUS.


Calorimeter: Uranium Scintillator 3° < < 178° EMC E/E = 18%/(E/GeV)

1% HAC E/E = 35%/(E/GeV)

1%

P e±

ZEUS detector

Central Tracking Detector:Drift Chamber 15° < < 164° 1.4 T magnetic field

Weight: 3500T, Size: 12m ×10m ×19m


Supersymmetry

Q|boson> = |fermion> Q+|fermion> = |boson> [H,Q]=0

Postulate superpartner for each SM particle withsame QNs but spin different by ½.

No superpartners with same masses are observed.SUSY is a broken symmetry.

MSSM: Minimal number of sparticles and couplings.

In MSSM SUSY breaking is introduced “by hand“ via soft terms. over 100 free parameters!


Gauge Mediated SUSY Breaking Model

LSP is always gravitino.

Candidate for dark matter (even in RPV models).

Typically very light:

GMSB parameters: sqrt(F), Mmess, N, , tan(), sign()

Possible NLSPs: neutralino, stau, (right-handed slepton)

Distinct event signature: photon/tau + missing energy.

Example for generationof sfermion masses:

Super trace theorem: SUSY breaking not possible in visible sector. Hidden Sector Models


R-Parity

Former analyses looked for resonant squark production.

Multiplicative discrete symmetry: RP=(-1)3B+L+2S+1 for SM particles -1 for sparticles

Most general Lagrangian contains additional trilinear terms in superpotential which violate RP:

RPC: sparticles pair-produced, LSP stable

Unique initial state HERA ideal place to look for ‘ couplings.

squarks are heavy.


SUSY Classification Scheme

Particles are produced on-shell (same for all SUSY models).Decay depends on sparticle spectra of SUSY model.

HERA topologies Abstract notation

SUSY-flow graphsFundamental vertices} Abstract diagrams

Systematic approach:• List all possible diagrams with potentially high cross section.• Include also R-parity violating vertices.

Motivation: Check all possible SUSY channels at HERA before start of LHC.

Sparticle creation at HERA:


HERA Topologies• All topologically distinct graphs with up to three outgoing (s)particle lines• Initial state is fixed to electron+quark (g and from proton are only considered with 2 outgoing lines)


SUSY-flow Graphs

Number of SUSY propagatorsNumber of SUSY particles

discarded

Choose RPV verticesMark sparticle lines with a „~“. In the case of RPC: C-like loops result.

ExampleF, RPC:


Abstract Notation & Fundamental VerticesPhysics description on an abstract level to reduce complexity.

All vertices of the MSSM ! (neglecting pure bosonic SM vertices and Higgs)


ResultsAfter all cuts: 55 abstract diagrams of sparticle production.

Example of new found diagram:

Additionally consider dominant sparticle decays:

Complete list of SUSY signatures at HERA.

Characteristic signatures for different SUSY models / scenarios.

Single slepton production.Only SM propagators.All ‘ couplings can be investigated.Signature e.g. in GMSB: l+G

~

=0.2pb for m(l)=100 GeV.~

(now investigated by new PhD student)


Investigated data set (1996-2005) e- p : L=155 pb-1

e+ p : L=145 pb-1 Total: L=300 pb-1 (HERA I and HERA II)

Analysis

First ZEUS thesis with complete data set!

• Signal processes & Topologies • Event selection• Discriminant method• GMSB phenomenology• Limits


Signal Processes

R-parity violating decay channelsGravitino channel

Gaugino productionvia slepton exchange:

Electron channel

Neutrino channelSignature:

e± + multiple jets

+ multiple jetsjet + + missing energy


Signal TopologiesSimulated events (SUSYGEN+Geant detector simulation)

GMSB decay RPV decay

• 3 hard forward jets• low pT electron or neutrino (missing PT)• jets nearly isotropic in r- plane

• 1 hard forward jet• isolated, high pT photon• missing energy

p


Event Selection – Gravitino Channel

• trigger selection• Q²JB > 700 GeV• 1 jet with pT>6 GeV and –1.5 < < 2.5

• PT miss > 22 GeV• (jet,) < 3.0• Background rejection

Loos selection to maximize signal efficiency!

Data/MC : 4751/4787 70%-77% good agreement.

1.step


Gravitino Channel – Final Selection

• photon candidate, with E > 4 GeV, –2.8 < < 2.8• DCA > 30 cm (track cut)

Additional cuts:

Data/MC : 1254/1275 61%-68% good agreement.

2.step


Signal to Background OptimizationOne dimensional cuts do not maximize S/B (for a givensignal efficiency) if correlations between variables exist.

DS

S B

Only select events in signal dominated areas!

Advantages compared to:

Neural Networks

Likelihood ratios

• No training needed.• No interpolation into empty phase space.

• Take into account all correlations.

Discriminant:

Disadvantage: A lot of MC needed.


Dynamic Discriminant Method

Advantages of variable bin size method:

Less parameters have to be set by hand.More events get classified.Faster calculation.More accurate results.

# events /box ~ (box_size)dim

Box size needs to be fixed beforecounting starts, however counting several too small boxes is fasterthan counting one too big box.

1-dim factor for which N Nmin.

464000


Gravitino Channel – Discriminant VarsSelection of best set of discriminant variables:

Purity and efficiency afterdifferent discriminant cuts.

• Chose characteristic variables.• Calculate discriminants for all possible combinations.


Gravitino Channel Discriminant

No excess observed in signal region!

ZEUS data 1996-2005


RPV Electron Channel

• e±trigger selection• ET > 60 GeV• 2 jet with –0.5 < < 2.7 pT>25 GeV (first jet) pT>12 GeV (second jet)• electron candidate with E>10 GeV, –1.2 < < 2.8, pT>15 GeV (3°<<17°) pT>6 GeV (17°<<115°)


RPV Neutrino Channel

• trigger selection• ET > 50 GeV • PT>20 GeV• 1 jet with –0.5 < < 2.7 pT>10 GeV • reject electron with pT>6 GeV, < 180


RPV DiscriminantsElectron channel Neutrino channel

No excess observed in signal region!


Parameter DependenceProblem factorizes:

Set limits on process parameters.

Effects of model parameters sometimes interchangeable,or have only small effect.

Slepton mass treated as free parameter.

Observables Process ParametersSUSY Parameters


ResultsLimit set in mass plane of process particles m(e)-m().

Limits calculated for different strengths of ‘ coupling.

For ‘111=1 sparticlemasses of up to m(e) < 360 GeV andm() < 190 GeV canbe excluded at 95%CL.

~

~

~ ~

Best existing limits in RPV GMSB!


GMSB Phenomenology

Dominating decay channels:

Contribution from different gauginos:

NLSP:

BR(G)+BR(eqq)+BR(qq) 100%.

RPV decays get important:• Toward high sqrt(F); • for stronger RPV couplings.

Low sqrt(F): Lightest neutralino dominates.High sqrt(F): Partly contribution from lightest chargino.

Neutralino is NLSP for low N and high tan.

~~~ ~


Gaugino Composition

MSSM GMSB

High cross section requires: 1. Small higgsino component (for large ee coupling)2. Large photino component (for GMSB decay into photon)

= ( H0, Z0, ~ ~ ~ ~Gauginos are superposition:

~~

= (W, H~ ~ ~


Limit VariationsVariation of M and sign(): Variation of N:

Similar limits are valid in large part of GMSB parameter space!

Different RPV couplings:

Typical GMSBscenario

mSUGRA-likescenario

Dependence on sqrt(F):


Outlook


SUSY Discovery at LHC

SUSY gauge couplings are the same as in SM.Cross sections only surpressed by mass terms.At high energies SUSY production rates are similar to SM!

Measure SUSY spectrum:• Masses• QNs• Lifetimes• Decay modes


Summary

• SUSY is a promising candidate for physics BSM. • New methods: Classification scheme for SUSY processes There are still open SUSY discovery channels at HERA Dynamic discriminant method • Best existing limits in RPV GMSB:

• LHC will give the final answer: Be prepared to discover a new world !


Backup slides


Solution of the Hierarchy ProblemCorrections to the Higgs mass:

Contributions of SM particles and their superpartnerscompensate each other.

SM:

MSSM:

Cancelation requires fine tuning to 17 orders of magnitude!


Unification of the Forces

Renormalisation Group Equations describe running of the coupling constants due to screening / antiscreening.

SM MSSM

Example:

Slope depends on number and masses of particlesin the model.

Miracle!


Status of SUSY SearchesExamples of best current limits:Neutralinos/Charginos:

Sleptons:

Squarks:

LEP: m( > 45 GeV (RPV) m( > 103 GeVselectronR > 100 GeV

smuonR > 95 GeVstauR > 86 GeV

D0: sneutrinoR > 460 GeV (132=0.05 & ‘311=0.16)

LEP:

D0: squark > 320 GeV gluino > 232 GeV

HERA: squark > 275 GeV (‘1j1=0.3)


MSSM Parameters• mA : pseudoscalar Higgs boson mass

• tan() : ratio of VEV of two Higgs doublets

• : Higgsino mixing parameter

• M1, M2, M3 : gaugino mass terms

• All sfermion masses

• Ai: all mixing parameters of squark and slepton sector


Broken Supersymmetry

Spontaneous SUSY breaking in SM sector not possiblesupertrace theorem sum rules between particle andsparticle masses, e.g.: excluded!

Hidden sector models

mSUGRA, GMSBAMSB, gMSB, ...~

Explain origin of SUSY breaking!


Data Set


Investigated Production Processes


Radiative EW Symmetry Breaking


Slepton mass splitting

where the al are positively correlated with tan.


Example: Application to type C DiagramsRPC:

RPV:SUSY-flow graphs:


C3: disfavoured due to high limits on squark massesC7: - “ –C6: lepto-quark search / contact interactionC5: gaugino production analysis !

Possible abstract diagrams:


Sparticle Decays Neutralino:

RPC MSSM RPV MSSM GMSB

Chargino:

stable LSP

missing energy

RPC RPV


Sparticle DecaysSleptons:

Squarks decay in the same way.

RPC MSSM: missing E, e / / RPV MSSM: 2 jets / 2 l / 2jets+2l GMSB: l + + G~

RPC: RPV:


Results

Diagrams with squarks are neglected.

Characteristic signatures for different models!

55 abstract diagrams.


Results

With two outgoing lines: C5With three outgoing lines and one sparticle: F4-2With three outgoing lines and two sparticles: D1


Restrictions

• diagrams with > 3 on-shell produced (s)particles are neglected• diagrams with outgoing , g, Z0 are not discussed• diagrams with initial g/ and 3 outgoing particles are discarded• u-channel diagrams are not stated explicitly• diagrams with > 1 sparticle propagator are discarded• interactions of Higgs bosons are not considered• vertices with only SM bosons are neglected• diagrams with three RPV vertices are discarded


GMSB Parameter Space


HERA Kinematicsep collision:

Mandelstam variables: Bjorken variables:


Gravitino Channel Kinematics

Gravitino reconstruction: (E-pz)G + (E-Pz)DET =55 GeV E²=pT²+pz²Neutralino mass: m()² = (p+pG)²

Selectron: Qe² = (pe-p)²

Gamma not too forward (small dependence on m()), PT Jacobian peak ~ m() smeared out by LT.

~


Signal Cross Sections & BRs

For low sqrt(F):


Number of Expected EventsData 96-00(HERA I)

Data 96-05(HERA I & HERA II)

Different RPV couplingspick different quarks from p,dependent on e-/e+.

Example for x-section ratios:

Ordering depends on L(e-)/L(e+).


Electron Control Sample

• NC trigger selection• |zvtx| < 40 cm• 45 < E-pz < 62 • Q²DA > 400 GeV• 1 jet with pT>6 GeV and –1.5 < < 2.5• electron candidate with pT>15 GeV and –1.2 < < 2.8

Electron selection works fine.

ZEUS data 96-00:


Gravitino Control Plots - HERA II


Contribution from different GauginosGMSB decaysat low sqrt(F):

RPV decaysat high sqrt(F):

Contribution from lightest neutralino dominates.

Partly contribution from lightest chargino.


Different NLSPs in the GMSB Model

For high values of N stau NLSP is favoured.

Stau is NLSP for small M and high tan:

Gaugino masses: Scalar masses:


Contribution from different Decay ChannelsIn region where lightest neutralino is NLSP: BR(G)+BR(eqq)+BR(qq) 100%.

Importance of GMSB-decay/RPV-decay depend on sqrt(F) and strength of ‘ coupling.


Circularity

Circularity0 Circularity1


• SUSYGEN - sqrt(F)=233, 3300; - m()=50 GeV .. 210 GeV; - various m(e)• CompHEP (for systematics) 3 ×25K events

Monte Carlo SimulationSignal MC

Background MC• NC DIS Ariadne (MEPS) Q² > 25 GeV, .. ,Q² > 50K GeV• CC DIS Ariadne (MEPS) Q² > 10 GeV, .., Q² > 20K GeV• PhP Herwig (direct/resolved)

(At least twice the data lumi.)


Systematic Uncertainties

Energy scale of CAL cells: 2.5% 0.6%(fhac & bhac: ±2%, rhac: ±3%, emc: ±1.5%)Luminosity measurement: 2.25% 2.25%Ariadne => MEPS: 1.7% (less) --PDF uncertainty: 7% 7%

Q²jb > 700 GeV² ±100 GeV² 1.9% 0.4%

|zVtx| < 40 cm ±10 cm 1.9% 2%

Pt > 20 GeV ± 4 GeV 5.6% 2.5% Yjb > 0.1 ± 0.02 2.3% 0.1% (jet,) > 3.0 rad ± 0.033 rad (2°) 0.5% 1.4%

Scale uncertainty: -- 10%

CC SUSY

Signal efficiency: -- 2.5%

10.4% 13.2%


Confidence Limit Calculation Modified frequentist method by Thomas Junk.Likelihood Ratio for multi-channel analysis.Estimator function needed:

CL = 1 – P(s+b) / P(b)

Sytematic Uncertainties: Average over systematic variations on s and b in all channels, assuming Gaussian distribution with lower cutoff at zero.


Supermultiplets

Chiral supermultiplets: (fermion,sfermion) = (spin ½, spin 0)

Vectorial supermultiplet: (gauge boson, gauginos) = (spin 1, spin ½)


Limit Calculation

• Amount of events to be generated highly reduced.• Limits can be produced for an arbitrary large parameter space.

For m produced particles decaying into n different decay channels.

Advantages:

Straightforward approch:Generate events for each parameter point. Costly!

Better: Seperate event generation and parameter scan!Use lim or Nlim as interface.

Difficult to handle!

• Calculate discriminants (efficiency and shape!) for different masses and interpolate.• Seperate discriminants for each channel.

Solution:

Use discriminant bins for S, B and data for limit calculation.


Limit Calculation

Difficult to handle!

1. Straightforward methodDisadvantage:• Different events have to be generated for each parameter point.

If different prod. Particles and different decay channels contribute:

2. Seperate event generation and parameter scan.


Limit Calculation

• Important: 1. Discriminant height (eff.) 2. Discriminant shape. (depends on prod. particle and decay channel.)• Seperate event generation and parameter scan.


SUSY at LHC

Complicated decay channels: g~ -> q~q -> qq -> l~lqq -> llqq

Problem is to seperate different SUSY channels.

But:

LHC 5 discovery curves


Future Prospects - ILCHigher luminosity at similar energy

Precision measurements of SUSY parameters!

LHC:

ILC:


Future


Analysis Framework

Documents

Search for Gravitinos in R-Parity violating Supersymmetry at HERA