ProbingProbing SupersymmetrySupersymmetry with with NeutralNeutral CurrentCurrent ScatteringScattering ExperimentsExperiments

ShufangShufang SuSu •• U.U. ofof ArizonaArizona Sub-ZSub-Z precisionprecision measurementsmeasurements

• scattering • heavy quark • CP violation, EDM • Rare K -decay, CKM unitarity • g-2 • lepton flavor violation …

• polarized ee scattering (SLAC E158) • polarized ep scattering (JLab Qweak) • -nucleus scattering (NuTeV)

A. Kurylov, M. Ramsey-Musolf, SS

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 2 OutlineOutline

• motivation • -violating scattering experiments

• radiative corrections to weak charge QW

• analysis of SUSY contributions to QW – MSSM contributions – RPV analysis – distinguish various new physics / SUSY • NuTeV experiment – MSSM contributions – RPV analysis • conclusion

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 3 MotivationMotivation

• high precision low energy experiment available

ααα πππ 2 size of loop effects from new physics: ( / )(M/M new ) new -9 exp -9 - muon g-2: M=m µµµ , δδδ ∼∼∼ 2x10 , δδδ < 10 βββ πππ δδδnew ∼∼∼ -3 δδδexp ∼∼∼ -3 – -decay, -decay: M= mW , 10 , 10 δδδnew ∼∼∼ -3 – parity -violating : M= mW , 10 ,

e,p ∼∼∼ 2θθθ ∼∼∼ Q W 1-4 sin W 0.1

e,p ≈  1/Q W 10 more sensitive to new physics  need δexp ∼ 10 -2 “easier” experiment • probe new physics off the Z -resonance - sensitive to new physics not mix with Z • indirect+direct: complementary information – consistency test of theory at loop level

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 4 22θθ TestTest ofof sinsin WW runningrunning

2θθθ 2θθθ 2 • sin W(0) - sin W(m Z ) = +0.007 Cs 2 – Q w: agree Q =0 - – NuTeV : +3 σσσ Q2=20 (GeV) 2

• parity -violating electron scattering (PVES) e ee Moller scattering (SLAC) Q W p ep elastic scattering (J -lab) Q W

- δδδ 2θθθ ∼∼∼ - 2 2 sin W 0.0007 at Q =0.03 (GeV)  clean environment: Hydrogen target  theoretically clean: small hadronic uncertainties  tree level ∼∼∼ 0.1 ⇒⇒⇒ sensitive to new physics

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 5 GoalGoal

Develop consistency checks for theories of new physics using the low energy precision measurements

• minimal Supersymmetric extension of SM (MSSM) SUSY: most promising candidate for new physics – solution to – gauge coupling unification – provide a natural electroweak symmetry breaking – candidate ? (PVES)  with R -parity : loop corrections  without R -parity: tree -level contribution

• low -energy precision measurements - e p Cs ννν(ννν) – PVES: weak charge Q W , Q W , ( Q W ) - NuTeV : R

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 6 WeakWeak chargecharge QQ WW

A N -N ≡≡≡ + - ∝∝∝ f ALR Q W N++N - V e e g A = I 3

f f f 2 weak charge Q W = 2g V = 2 I 3 -4Q fs

p e ep Qweak exp Q W ee Moller exp Q W e,p 2 2 Q W tree 1-4s -(1 -4s ) e,p Q W loop 0.0721 -0.0449 exp precision 4% 8% δδδ 2θθθ sin W 0.0007 0.0009 SM running 10 σσσ 8 σσσ

Cs δδδ 2θθθ δδδ 2θθθ Q W : sin W = 0.0021 NuTeV : sin W = 0.0016

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 7 ff GeneralGeneral structurestructure ofof radiativeradiative corrections corrections toto QQ WW

Including radiative corrections:

f ρρρρ f κκκκ 2 λλλλ Q W = (2 I 3 - 4 Qf s ) + f ρρρ κκκ λλλ , : universal, f: depend on species ρρρρ δρδρδρδρ SM δρδρδρδρ SUSY κκκκ δκδκδκδκ SM δκδκδκδκ SUSY λλλλ λλλλ SM λλλλ SUSY = 1+ + , = 1+ + , f= f + f

ρρρρ

correction to muon life time

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 8 RadiativeRadiative contributions contributions

f ρρρρ f κκκκ 2 λλλλ Q W = (2 I 3 - 4 Qf s ) + f

κκκκ

α ⇒ 2 correction to , G µ and m Z s

λλλλ f

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 9 MSSMMSSM particleparticle contentscontents

SM particle Spin differ by 1/2 superpartner

mass parameter ∼∼∼∼ ∼∼∼∼ ∼∼∼∼ 2 2 2 mqL , mqR , mqLR ∼∼∼∼ ∼∼∼∼ ∼∼∼∼ 2 2 2 mlL , mlR , mlLR µ µ ββββ , tan =v u/vd

M3 M2 M1

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 10 SUSYSUSY interactionsinteractions

replace two SM particles into SUSY partners

⇒⇒⇒⇒ ∝∝∝∝ gauge coupling

⇒⇒⇒⇒ ∝∝∝∝ gauge coupling

⇒⇒⇒⇒ ∝∝∝∝ Yukawa coupling

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 11 OneOne looploop SUSYSUSY contributionscontributions toto PVESPVES

• self -energies

• external leg corrections • vertex corrections

• box diagrams

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 12 NumericalNumerical analysisanalysis

Model -independent analysis

• MSSM parameter range: random scan ~ ~ µ 50 GeV < mq, m l, M 1,2 , < 1000 GeV 1.4 < tan βββ < 60

∗ hard to impose bounds on certain MSSM parameter ∗ show the possible range of MSSM corrections

– impose exp search limit on SUSY particles – impose S -T 95% CL constraints – impose g -2 constraints (2nd slepton LR mixing)

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 13 CorrectionCorrection toto weakweak chargecharge

f ρρρ f κκκ 2 λλλ Q W = (2 T 3 - 4Q f s ) + f

e p  Q W and Q W correlated

dominant : δκδκδκ (<0) ⇒⇒⇒ 2θθθ negative shift in sin W

δδδ p p δδδ e e (Q W)SUSY / (Q W)SM < 4%, (Q W)SUSY / (Q W)SM < 8%

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 14 DominantDominant contributionscontributions

f ρρρρ f κκκκ 2 λλλλ Q W = (2 T 3 - 4Q f s ) + f

• non -universal corrections – vertex + wavefunction : cancel – box diagrams numerically suppressed • δρδρδρδρ contribution suppressed by (1 -4 s 2) • dominant contribution from δκδκδκδκ

δκδκδκ ⇒⇒⇒ 2θθθ (<0) negative shift in sin W

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 15 VariousVarious contributionscontributions toto δκδκ

S

• within δκδκδκδκ – various terms have T comparable importance

– oblique approximation gives a poor description

δκδκδκδκ δδδ e,p e,p • <0 ( (Q W)SUSY / (Q W)SM >0 ) ⇒⇒⇒⇒ 2θθθθ reduction in effective sin W

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 16 R-parityR-parity

• General MSSM, including B,L -violating operators

λλλλ ijk ∆∆∆ L = - 1

λλλλ ’ijk

• dangerous ⇒⇒⇒⇒ introduce decay • R-parity SM particle: even superparticle : odd – stable LSP as dark matter candidate • RPV: only look at L -violating operator

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 17 R-parityR-parity violatingviolating (RPV)(RPV)

e,p • RPV operators contribute to Q W at tree level

Exp constraints

βββ RPVδδδ MSSM±±± δδδδQp • decay: RPV|Vud | = -0.00145 0.0007 Q W δδδ Cs ±±±loop • APV(Cs): 95%Q WCL = -0.0040 0.0066 δδδ ±±± • Re/ µµµ : Re/ µµµ = -0.0042 0.0033 • Gµµµ: δδδ Gµµµ = 0.00025 ±±± 0.00188 No SUSY dark matter I) Obtain 95% CL allowed region in RPV coefficients δδδ e δδδ p Gµµµ II) Evaluate QW and QW

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 18 pp ee CorrelationCorrelation betweenbetween QQ WW and and QQ WW

 SUSY correction to heavy nuclei QW δδδ δδδ u δδδ d • QW (Z,N)=(2Z+N) Q W +(2N+Z) Q W δδδ u Q W >0 ⇒⇒⇒⇒ δδδ δδδ d QW(Z,N) / QW(Z,N) < 0.2 % for Cs Q W <0

 Distinguish new physics δδδδ p δδδδ e δδδδ Cs Q W Q W Q W • MSSM: small • extra Z ’: sizable • leptoquark : • RPV SUSY

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 19 AdditionalAdditional PVPV electronelectron scatteringscattering ideasideas

Czarnecki, Marciano  Erler et al.

ννν N deep inelastic Linear Collider e -e-

DIS -Parity, JLab 2θ sin W DIS -Parity, SLAC

APV e+e- LEP, SLD SLAC E158 JLab Q -Weak (ee) JLab Moller (ep ) (ee )

µ (GeV)

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 20 NuTeVNuTeV experiment experiment

NC CC

σσσ ννν →→→ ννν ννν ννν- ( N X) Rννν(ννν) ≡≡≡ MSSM σσσ((ννν-)N →→→ l-(+) X)

δδδδRννν=-0.0033 ±±±± 0.0015 - δδδδRννν=-0.0019 ±±±± 0.0026

wrong -sign contribution! Davidson et. al., JHEP 02, 037, 2002

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 21 GluinoGluino contribution contribution

negative gluino contribution CC data constraints Kurylov, Ramsey-Musolf,PRL88,071804,2002  large LR -mixing both up/down sector

 inconsistent with current CC data

 constraints relaxed if first row CKM unitarity confirmed

 could partially account for 2θθθ deviation in sin W unitarity deviation decrease by 1/3 σσσ

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 22 22θθ DeviationDeviation ofof sinsin WW

• extracted using Paschos -Wolfenstein relation

• in practice, modified version

ξξξξ different from r 1C 0C ⇒⇒⇒⇒ mass m constrained free uncertainties c ξξξ 0.249 0.453 • gluino contributions δδδsin 2θθθ -1.6x10 -3 -1x10 -4 ∝∝∝∝ ξξξ - r W

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 23 R-parityR-parity violatingviolating (RPV)(RPV)

- • RPV operators contribute to R ννν(ννν) at tree level

either wrong sign or too small hard to explain NuTeV deviation

NC

CC

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 24 ConclusionConclusion

• Parity -violating ee and ep scattering – could be used to test SM and probe new physics e p ≈≈≈ σσσ – MSSM contribution to Q W and Q W is 8% and 4% 1 exp need higher exp precision to constrain SUSY e p – correlation between Q W and Q W • distinguish various new physics • distinguish various SUSY scenario whether dark matter is SUSY particle ? • SUSY contribution to NuTeV result SUSY– MSSM is withnot Rresponsible-parity: wrong for sign the /small NuTeV deviation – negative– gluinoother contribution:new physics ? – size constrained by other considerations – hard to –explainhadronic NuTeVeffectsin RPV ?

S. Su LoopFest III Probing SUSY with Neutral Current Scattering experiments 25