Supersymmetry at HERA Motivation for SUSY Basic SUSY facts Different SUSY models Current limits Sparticle creation at HERA SUSY analyses at ZEUS Future

Supersymmetry at HERA

Motivation for SUSYBasic SUSY factsDifferent SUSY modelsCurrent limitsSparticle creation at HERASUSY analyses at ZEUSFuture prospects

DESY Student Seminar, 14.Nov.2005

Claus Horn

SUSY at HERA, 14.Nov.2005 Claus Horn

Shortcomings of the Standard Model

SM is only low energy approximation,In a fundamental theory all interactions should be unifiedGUT + gravity

What is the origin of mass,Introduction of Higgs boson runs into problems.

Cosmological problems

21 parameters – too many!Why three generations ?Why |Qel| = |Qp| ?...


Motivation for Supersymmetry

• Coleman-Mandula theorem • Unification of the forces • Solution of the Hierarchy problem • Candidates for dark matter • Necessary for quantum-gravity


Coleman-Mandula Theorem

„In a theory with non-trivial scattering in more than 1+1 dimensions, the only possible conserved quantities that transform as tensors under the Lorentz group are the generators of the Poincare group and scalar quantum numbers.“

SUSY is the only possibel extension of the Poincare group.

Our last chance to discover a fundamental space-time symmetry!

Tensors fulfill comutation relationsAdd anti-commutators

Graded Lie-algebras„super algebra“

P: Energy-momentum operatorQ: Supercharge


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!


Solution of the Hierarchy ProblemCorrections to the Higgs mass:

Contributions of particles arecanceled by contribution of theirsuperpartners.

SM:

MSSM:

Cancelation requires fine tuning to 17 orders of magnitude!


For unbroken SUSY: No quantum correction to the Higgs mass (mH=0).

Broken SUSY: “running” Higgs mass

superpartners have to be lighter than 1 TeV

SUSY exact

Q²SUSY particles

No SUSY

mH

mh

SUSY Higgs sectorvery restricted:

mh < 150 GeV Q2


Basic Facts about SUSY

Symmetry between fermions and bosons

Q|boson> = |fermion> Q+|fermion> = |boson>

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

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

Hidden sector models


Supermultiplets

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

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


Sparticles of the MSSM

Neutral gauginos mix to form four neutralinos.

Charged gauginos mix to form two charginos.

M depends on M2, tan() and . BRs of 0 and


Parameters of the MSSM

• mA : pseudoscalar Higgs boson mass

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

• : Higgs mixing parameter

• M1, M2, M3 : gaugino mass terms

• All sfermion masses

• Ai: all mixing parameters of squark and slepton sector


SUSY BreakingMSSM does not explain origin of SUSY breakingsoft breaking terms are introduced „by hand“

more than 100 free parametersHidden sector models: mSUGRA, GMSB

Flavour problem solved in GMSB model.


minimal SUperGRavity (mSUGRA)

Parameter: m0, m1/2, A0, tan(), sign()

• Unified masses at the GUT scale m0: common scalar mass m1/2: common gaugino mass

• Unified trilinear couplings = A0

• Radiative EW symmetry breaking

Constraints:

M(G~) 1 TeV (in AMSB 10 TeV)


Gauge Mediated SUSY Breaking (GMSB)

Possible NLSPs: neutralino, stau

LSP (in not-yet excluded parameter space) is always gravitino

Distinct event signature: photon/tau + missing energy

Gravitino might be candidate for dark mattereven in RPV models.

Gravitino can be very light:

Parameter: , sqrt(F), Mmess, N, tan(), sign()

Very predictive mass spectrum, easy to distinguish from SUGRA.


Typical Mass Spectra

Neutralino1 is light(est)Next: right-handed slepton (stau) & chargino1

Squarks are relatively heavy


R-parity

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:

HERA is the ideal place to look for ‘ !

(Proton decay only if ‘ and ‘‘ are 0 at the same time.)

RPC: sparticles pair-produced, LSP stable


Overview of current best Limits

• Neutralinos / Charginos RPC and RPV • Sleptons RPC and RPV• Squarks RPC and RPV

Huge multidimensional parameter spaces

Comparison between different analysis difficult.

Results only valid under restricted conditions.


Current best Limits

Neutralinos / CharginosParameter region:

LEP m(> 92GeV RPC MSSM m(> 103GeV tan()=2, =-200

D0 m() > 84 GeV RPV mSUGRA m() > 160 GeV tan()=1.5

LEP m(> 40GeV RPV MSSM m(> 103GeV tan()=1.5


Current best Limits - sleptons

selectronR > 100 GeVsmuonR > 95 GeVstauR > 86 GeV

LEP: RPC MSSM= -200 tan() = 1.5

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

selectronR > 100 GeVsmuonR > 98 GeVstauR > 97 GeV

LEP: RPV MSSM = -200 tan() = 1.5


Current best Limits - squarks

D0: m(g~) > 232 GeV

D0: m(q~) > 320 GeV

RPC

mSUGRA m0 = 25 GeV

mSUGRA m0 = 500 GeV


Current best Limits - squarksRPV

CDF m(t~) > 155 GeV ‘3330HERA m(t~) > 275 GeV ‘1j1=0.3


Sparticle Creation at HERA

Systematic approach needed to filter all interesting channels.

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

Approach:


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

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

F, RPC:


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

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


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 expicetly• 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


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: beeing analysed at the moment !

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:


ResultsDiagrams with squarks are neglected.

Characteristic signatures for different models!


Results

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


Interesting SUSY Diagram D1

Highest expected cross section for:• = • Low Q2 (PhP)

Calculated cross section: 20 pb for m=me~=120 GeV (no warrenty!)

• Only SM propagators • Production of two sparticles with m100 GeV each

Signature:RPC MSSM: E + e-

RPC GMSB: e-+2(+G~)


Interesting SUSY Diagram F4-2

Highest expected cross section for: resolved PhP

Cross section: to be determined

Signature:RPV MSSM: 2jets / 2jets+2lRPV GMSB: l+G~ / l++G~

• Only SM propagators• Only one sparticle • Slepton production (first time at HERA)


Current Analyses at ZEUS

Decay in MSSM:Gaugino analysis

Decay in GMSB:Gravitino analysis

'

Production via C5

NC-like channel

CC-like channel

Signature:

e- + jets

+ jets

jet + + missing energy


Gravitino Analysis


Discriminant Method

Box size

All events get classified.Less statistics needed.Faster calculation.More accurate results.Generally better S/B seperation.

Improvement: variable box size

Multidimensional cuts generallyresult in a better S/B ratio, than one dimensional cuts.

DS

S B

# events /box ~ (box_size)d


Gravitino Analysis

No events in signal region


Limits – Gravitino Analysis


Limits – Gaugino Analysis

Extended LEP limits in M2 - plane:


Future: LHC and ILC


Future Prospects - LHC

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

Discovery is no problem. (reonstruct Meff)

SUSY signal and SM bkg. for tt- decay (m0=1TeV, m1/2=500 GeV)


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


Summary

• SUSY is a very interesting and promising theory.

• It is challenging, but there are SUSY channels were HERA is favoured compared to LEP and the Tevatron.

• If we do not find it before, then the LHC will give the final answer: Be prepared to discover a new world !

Documents

Supersymmetry at HERA Motivation for SUSY Basic SUSY facts Different SUSY models Current limits Sparticle creation at HERA SUSY analyses at ZEUS Future