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Search for Gravitinos in R-Parity violating Supersymmetry at HERA

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### Search for Gravitinos in R-Parity violating Supersymmetry at HERA

SLAC experimental seminar

Claus Horn (DESY / Univ. Hamburg)

Introduction

HERA & ZEUS

SUSY processes at HERA

Analysis

Summary & Outlook

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 accelerator

e± p collider, in Hamburg

Protons: 920 GeV

Leptons: 27.5 GeV

CMS-Energy: 320 GeV

Length: 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

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

e±

ZEUS detectorCalorimeter: Uranium Scintillator

- 3° < q< 178°
- EMC DE/E = 18%/(E/GeV) 1%
- HAC DE/E = 35%/(E/GeV)1%

Central Tracking Detector:Drift Chamber

- 15° < q< 164°
- 1.4 T magnetic field

Weight: 3500T, Size: 12m ×10m ×19m

In MSSM SUSY breaking is introduced “by hand“

via soft terms. over 100 free parameters!

SupersymmetryPostulate superpartner for each SM particle with

same QNs but spin different by ½.

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

No superpartners with same masses are observed.

SUSY is a broken symmetry.

MSSM: Minimal number of sparticles and couplings.

LSP is always gravitino.

Typically very light:

Candidate for dark matter (even in RPV models).

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

Distinct event signature: photon/tau + missing energy.

Gauge Mediated SUSY Breaking ModelSuper trace theorem: SUSY breaking not possible in visible sector. ->Hidden Sector Models

Example for generation

of sfermion masses:

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

R-Parity

+1 for SM particles

-1 for sparticles

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

RPC: sparticles pair-produced, LSP stable

Most general Lagrangian contains additional trilinear terms

in superpotential which violate RP:

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

Former analyses looked for resonant squark production.

squarks are heavy.

SUSY Classification Scheme

Motivation: Check all possible SUSY channels at HERA

before start of LHC.

Systematic approach:

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

Particles are producedon-shell (same for all SUSY models).

Decay depends on sparticle spectra of SUSY model.

Sparticle creation at HERA:

}

HERA topologies

Abstract notation

SUSY-flow graphs

Fundamental vertices

Abstract diagrams

HERA Topologies

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

SUSY-flow Graphs

Choose RPV vertices

Mark sparticle lines with a „~“.

In the case of RPC: C-like loops result.

Example

F, RPC:

Number of SUSY propagators

Number of SUSY particles

discarded

Abstract Notation & Fundamental Vertices

Physics description on an abstract level to reduce complexity.

All vertices of the MSSM !

(neglecting pure bosonic SM vertices and Higgs)

Only SM propagators.

All l‘ couplings can be investigated.

Signature e.g. in GMSB: l+G

~

~

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

ResultsAfter all cuts: 55 abstract diagrams of sparticle production.

Additionally consider dominant sparticle decays:

Complete list of SUSY signatures at HERA.

Characteristic signatures for different

SUSY models / scenarios.

Example of new found diagram:

(now investigated by new PhD student)

Analysis

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

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)

First ZEUS thesis with complete data set!

Signal Processes

Gaugino production

via slepton exchange:

Gravitino channel

R-parity violating decay channels

Electron channel

e±+ multiple jets

Neutrino channel

Signature:

n + multiple jets

jet + g + missing energy

Signal Topologies

Simulated events (SUSYGEN+Geant detector simulation)

RPV decay

GMSB decay

p

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

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

Event Selection – Gravitino Channel

Loos selection to maximize signal efficiency!

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

- PT miss > 22 GeV
- Df(jet,g) < 3.0
- Background rejection

Data/MC : 4751/4787 e70%-77% -> good agreement.

Gravitino Channel – Final Selection

Additional cuts:

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

Data/MC : 1254/1275 e61%-68% -> good agreement.

Signal to Background Optimization

One dimensional cuts do not maximize S/B (for a given

signal efficiency) if correlations between variables exist.

Discriminant:

Only select events in signal

dominated areas!

Disadvantage: A lot of MC needed.

Advantages compared to:

Likelihood ratios

- Take into account all correlations.

Neural Networks

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

Dynamic Discriminant Method

Box size needs to be fixed before

counting starts, however counting

several too small boxes is faster

than counting one too big box.

1-dim factor for which N Nmin.

# events /box ~ (box_size)dim

464000

Advantages of variable bin size method:

Less parameters have to be set by hand.

More events get classified.

Faster calculation.

More accurate results.

Gravitino Channel – Discriminant Vars

Selection of best set of

discriminant variables:

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

Purity and efficiency after

different discriminant cuts.

RPV Electron Channel

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

RPV Neutrino Channel

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

SUSY Parameters

Process Parameters

Parameter DependenceProblem factorizes:

Effects of model parameters sometimes interchangeable,

or have only small effect.

Set limits on process parameters.

Slepton mass treated as free parameter.

Results

~

~

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

For l‘111=1 sparticle

masses of up to

m(e) < 360 GeV and

m(c) < 190 GeV can

be excluded at 95%CL.

~

~

Best existing limits

in RPV GMSB!

Limits calculated for different strengths of l‘ coupling.

GMSB Phenomenology

Dominating decay channels:

~

~

~

~

BR(c->gG)+BR(c->eqq)+BR(c->nqq) 100%.

RPV decays get important:

- Toward high sqrt(F);
- for stronger RPV couplings.

Contribution from different gauginos:

Low sqrt(F): Lightest neutralino dominates.

High sqrt(F): Partly contribution from lightest chargino.

NLSP:

Neutralino is NLSP for low N and high tanb.

~

~

~

~

~

~

c = (W, H)

c0 = ( H0, Z0, g )

Gaugino CompositionGauginos are superposition:

High cross section requires:

1. Small higgsino component (for large eec coupling)

2. Large photino component (for GMSB decay into photon)

~

~

MSSM

GMSB

Limit Variations

Variation of M and sign(m):

Different RPV couplings:

Variation of N:

Dependence on sqrt(F):

mSUGRA-like

scenario

Typical

GMSB

scenario

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

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

- 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 !

Solution of the Hierarchy Problem

Corrections to the Higgs mass:

SM:

Cancelation requires fine tuning

to 17 orders of magnitude!

MSSM:

Contributions of SM particles

and their superpartners

compensate each other.

MSSM

Unification of the ForcesRenormalisation Group Equations describe running of

the coupling constants due to screening / antiscreening.

Example:

Slope depends on number and masses of particles

in the model.

Miracle!

Status of SUSY Searches

Examples of best current limits:

Neutralinos/Charginos:

LEP: m(c0) > 45GeV (RPV)

m(c±) > 103GeV

Sleptons:

selectronR > 100 GeV

smuonR > 95 GeV

stauR > 86 GeV

LEP:

D0: sneutrinoR > 460 GeV

(l132=0.05 & l‘311=0.16)

Squarks:

D0: squark > 320 GeV

gluino > 232 GeV

HERA: squark > 275 GeV (l‘1j1=0.3)

MSSM Parameters

- mA : pseudoscalar Higgs boson mass
- tan(b) : ratio of VEV of two Higgs doublets
- m: Higgsino mixing parameter
- M1, M2, M3 : gaugino mass terms
- All sfermion masses
- Ai: all mixing parameters of squark and slepton sector

Broken Supersymmetry

Explain origin of SUSY breaking!

Spontaneous SUSY breaking in SM sector not possible

supertrace theorem-> sum rules between particle and

sparticle masses, e.g.: excluded!

Hidden sector models

mSUGRA, GMSB

AMSB, gMSB, ...

~

Slepton mass splitting

where the al are positively correlated with tanb.

C3: disfavoured due to high limits on squark masses

C7: - “ –

C6: lepto-quark search / contact interaction

C5: -> gaugino production analysis !

Sparticle Decays

Sleptons:

RPV:

RPC:

RPC MSSM: missing E, e / m / t

RPV MSSM: 2 jets / 2 l / 2jets+2l

GMSB: l + g + G~

Squarks decay in the same way.

Results

55 abstract diagrams.

Diagrams with squarks are neglected.

Characteristic signatures for different models!

Results

With two outgoing lines: C5

With three outgoing lines and one sparticle: F4-2

With three outgoing lines and two sparticles: D1

Restrictions

- diagrams with > 3 on-shell produced (s)particles are neglected
- diagrams with outgoing g, g, Z0 are not discussed
- diagrams with initial g/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

Gravitino Channel Kinematics

Gamma not too forward (small dependence on m(c)),

PT Jacobian peak ~ m(c) smeared out by LT.

Gravitino reconstruction: (E-pz)G + (E-Pz)DET =55 GeV

E²=pT²+pz²

Neutralino mass: m(c)² = (pg+pG)²

Selectron: Qe² = (pe-pc)²

~

Signal Cross Sections & BRs

For low sqrt(F):

Number of Expected Events

Different RPV couplings

pick different quarks from p,

dependent on e-/e+.

Data 96-00

(HERA I)

Example for x-section ratios:

Data 96-05

(HERA I &

HERA II)

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

Electron Control Sample

ZEUS data 96-00:

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

Electron selection works fine.

Contribution from different Gauginos

GMSB decays

at low sqrt(F):

Contribution from lightest neutralino dominates.

RPV decays

at high sqrt(F):

Partly contribution from lightest chargino.

Different NLSPs in the GMSB Model

Gaugino masses:

Scalar masses:

For high values of N stau NLSP is favoured.

Stau is NLSP for small M and high tanb:

Contribution from different Decay Channels

In region where lightest neutralino is NLSP:

BR(c->gG)+BR(c->eqq)+BR(c->nqq) 100%.

Importance of GMSB-decay/RPV-decay depend on sqrt(F)

and strength of l‘ coupling.

Monte Carlo Simulation

Signal MC

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

(At least twice the data lumi.)

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)

Systematic Uncertainties

CC SUSY

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%

Scale uncertainty: -- 10%

Signal efficiency: -- 2.5%

|zVtx| < 40 cm ±10 cm 1.9% 2%

Q²jb > 700 GeV² ±100 GeV² 1.9% 0.4%

Pt > 20 GeV ± 4 GeV 5.6% 2.5%

Yjb > 0.1 ± 0.02 2.3% 0.1%

Df(jet,g) > 3.0 rad ± 0.033 rad (2°) 0.5% 1.4%

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

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

Straightforward approch:

Generate events for each parameter point.

Costly!

Better: Seperate event generation and parameter scan!

Use slim or Nlim as interface.

For m produced particles decaying into n different decay channels.

Difficult to handle!

Solution:

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

Advantages:

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

Limit Calculation

1. Straightforward method

- Disadvantage:
- Different events have to be
- generated for each parameter point.

2. Seperate event generation

and parameter scan.

If different prod. Particles and different decay channels contribute:

Difficult to handle!

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

LHC 5s discovery curves

But:

Complicated decay channels: g~ -> q~q -> cqq -> l~lqq -> cllqq

Problem is to seperate different SUSY channels.

Future Prospects - ILC

Higher luminosity at similar energy

Precision measurements of SUSY parameters!

LHC:

ILC:

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