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Sub Z0 Supersymmetry Precision Electroweak Physics Below the Z0 Pole M.J. Ramsey-Musolf J. Erler A. Kurylov S. Su Outline • Precision measurements & radiative corrections The Standard Model & SUSY • Charged Current Universality Is SUSY-breaking flavor neutral ? An evolving story: New Ke3 data & analyses; neutron b-decay • Neutral currents Is there SUSY dark matter ? • Some QCD Issues How well do we know the Standard Model predictions ? I. Radiative Corrections & Precision Measurements: SM & SUSY Why we love the Standard Model The Fermi theory of weak decays ee e H EFF e F n pee GFb 1 GF p n b F e e G G b L eL e HEFF p (gV gA 5 )n eL e 2 2 gV 1, gA 1.26 (1 5 ) The Fermi theory and QED corrections e e e e QED radiative corrections: finite 2 5 25 G m 1 F 2 1 3 192 2 4 The Fermi theory and higher order weak contributions e e e e e e e Weak radiative corrections: e infinite Can’t be absorbed through suitable re-definition of GF in HEFF e All radiative corrections can be incorporated in the Standard Model with a finite number of terms g W e e g g e W e Z0 e Re-define g e 0 Z e e W Finite e GF encodes the effects of all higher order weak radiative corrections g W e g e Z0 e W e e e W 2 GF g 1 Dr 2 2 8MW Drdepends on parameters of particles inside loops W e Comparing radiative corrections in different processes can probe particle spectrum Z e 0 g g e Z0 e Z0 e e Z0 e GFZ g2 2 1 DrZ 2 8MW Drdiffers from DrZ Z0 e Comparing radiative corrections in different processes can probe particle spectrum GFZ 1 DrZ Dr GF Z t 0 Z 0 W b W t t m DrZ ~ ln M 2 t 2 W mt2 Dr ~ 2 MW Comparing radiative corrections in different processes can probe particle spectrum Direct Measurements Radiative corrections • Precision measurements predicted a range for mt before top quark discovery • mt >> mb ! • mt is consistent with that range • It didn’t have to be that way Stunning SM Success J. Ellison, UCR Can we place analogous constraints on new physics using low-energy precision measurements ? This talk: SUSY Minimal Supersymmetric Standard Model (MSSM) LSM LSM + LSUSY e L,R , q L,R e˜ L,R , q˜ L,R sfermions W ,Z , , g ˜ , Z˜ , ˜ , g˜ W gauginos Hu , Hd ˜ ,H ˜ H u d Higgsinos 0 ˜ ˜ ˜ ˜ ˜ ˜ W, Z ,, Hu, d , tan b u d Charginos, neutralinos Minimal Supersymmetric Standard Model (MSSM) LSM LSM + LSUSY + Lsoft ˜ M M Lsoft ˜ M gives M contains 105 new parameters How is SUSY broken? The Fermi constant is too large 2 GF g 2 2 8MW g M 4 2 2 W 2 WEAK WEAK ~ 250 GeV GF ~ 10-5/MP2 NEW H0 H0 D 2 WEAK ~ M 2 SUSY protects GF from shrinking NEW H0 ˜ NEW H0 H0 H0 D 2 WEAK ~ M M log terms 2 2 ˜ =0 if SUSY is exact How is SUSY broken? Visible Sector: Hidden Sector: SUSY-breaking MSSM Flavor-blind mediation Gravity-Mediated (mSUGRA) W˜ , Z˜ ,˜ , g˜ H f˜ f˜ M1 / 2 M 2 0 Hu Hd f˜ A0 b0 How is SUSY broken? Visible Sector: Hidden Sector: SUSY-breaking MSSM Flavor-blind mediation Gauge-Mediated (GMSB) f˜ ˜ , Z˜ , ˜ , g˜ W M1 / 2 messengers a 4 W,Z,... a M Ca 4 2 0 2 A0 0 b0 0 Mass evolution 2 ˜f dM dt 3 ˜ a C M a ˜f a t 2 ln a1 ˜ M a gaugino mass ˜f a C 0 M ˜f increases as Mq˜ increases faster than Mq˜ M˜ group structure decreases M˜ q˜ 3 ˜ (C 0,C3 0) at the weak scale Sfermion Mixing M ˜2 ˜f L 2 ˆ M 2 M LR M 2 ˜ M f˜ R 2 LR m f ( t anb A f ) M m f ( cot b A f ) 2 LR f˜L , ˜f R f˜1 , ˜f2 Qf < 0 Qf > 0 MSSM and R Parity PR 1 3(BL) 1 2S Matter Parity: An exact symmetry of the SM SM Particles: Superpartners: PR 1 PR 1 MSSM and R Parity MSSM conserves PR vertices have even number of superpartners Consequences 0 ˜ Lightest SUSY particle is stable viable dark matter candidate Proton is stable Superpartners appear only in loops Precision Measurements: SUSY Sensitivity SUSY DO M SM ˜ O M Muon (g-2): SUSY 2 M=m ~ 2 x 10-9 Weak processes: M=MW exp ~ ~ 10-3 1 x 10-9 II. Charged Current Processes Is SUSY-breaking mediation flavor blind? Visible Sector: MSSM Hidden Sector: SUSY-breaking Charged Current (non) Universality 2 g M CC 2 (V A) (V A) 8MW Fermi Constants decay GF g2 2 2 8MW b decay GFb g2 2 Vud 2 8MW g 2 8MW2 is universal Universality obscured by 1 Dr 1 Dr b GbF GF Vud 1 Drb Dr Fermi Constants, Cont’d F b F 5 G (1.16639 0.00001)10 5 G (1.1312 0.0007) 10 GeV-2 0 0 GeV-2 Radiative Corrections Drb Dr ~ MW M˜ 2 ~ 0.2% ~ modulo log enhancements SM SUSY Fermi Constants, Cont’d F b F 5 G (1.16639 0.00001)10 5 G (1.1312 0.0007) 10 0 0 GeV-2 Status in early ‘04 CKM Unitarity 2 GeV-2 2 Vud Vus Vub 2 = 1 SM 0.9968 0.0014 Data + SM Require (Drb Dr ) SUSY 0 Drb Dr SUSY Radiative Corrections Drb Dr Universal e u W W e d e u W d e e W W e e W e SUSY Radiative Corrections Drb Dr Non-universal e u W ˜0 u e ˜ u˜ d W e d ˜ e e e ˜0 ˜ ˜ e ˜ e Vertex Corrections (Dominant) Non-universal u u W d ˜ 0 W ˜ ˜ 0 W ˜ d W ˜0 u˜ d˜ d u˜ u ˜ W ˜0 ˜ ˜ W Other Inputs 1. Muon (g-2): Size of error bar crucial 2. W Mass: M G 2MW2 MZ2 M 1 Dr 2 Z 2 W F 0.0091 Dr SUSY 3. Superpartner Masses: 0.0037 mt , MH Start analysis with collider lower bounds and vary later Model-independent Analysis Usual approaches: • Assume a model for SUSY-breaking mediation 105 parameters a few parameters (M1/2, M0, A0, …) • Assume most general SUSY-breaking sector 105 parameters random scan of parameter space This study: • Assume most general SUSY-breaking sector 105 parameters analytic exploration of parameter space Model Independent Analysis 1. Maximal L-R Mixing No solution 2. Increase M Changes sign of Drb- Drunless M˜2 M˜1 ,no solution 3. Increase M˜ , Mq˜ Alleviates (g-2)problem but shrinks allowed region 4. Reduce L-R Mixing Allowed solution but conflict with flavor-blind SUSY-breaking u d 5. Non-universal squarks LR LR Allowed solution, large gluino effects, but conflict with flavorblind SUSY-breaking 6. Heavy gluinos, Mg˜ 500 GeV muon g-2 CKM ‘04 W mass f˜ M˜f 2 Mf˜1 Model Independent Analysis Maximal L-R Mixing No solution 2. Increase M Changes sign of Drb- Drunless M˜2 M˜1 ,no solution 3. Increase M˜ , Mq˜ Alleviates (g-2)problem but shrinks allowed region 4. Reduce L-R Mixing Allowed solution but conflict with flavor-blind SUSY-breaking u d 5. Non-universal squarks LR LR Allowed solution, large gluino effects, but conflict with flavorblind SUSY-breaking 6. Heavy gluinos, Mg˜ 500 GeV Flavor-blind SUSY-breaking 1. CKM ‘04 M˜ L Mq˜ L Model Independent Analysis 1. Maximal L-R Mixing No solution 2. Increase M Changes sign of Drb- Drunless M˜2 M˜1 ,no solution 3. Increase M˜ , Mq˜ Alleviates (g-2)problem but shrinks allowed region 4. Reduce L-R Mixing Allowed solution but conflict with flavor-blind SUSY-breaking u d 5. Non-universal squarks LR LR Allowed solution, large gluino effects, but conflict with flavorblind SUSY-breaking 6. Heavy gluinos, Mg˜ 500 GeV muon g-2 W Mass CKM ‘04 Ad At Inconsistent with Higgs mass bounds, flavor-blind SUSYbreaking, color neutral vacuum CC (non) universality & the MSSM Data appeared to conflict with MSSM & models having flavor-blind SUSY-breaking mediation Possible resolutions: 1. MSUSY > TeV See end of talk LANSCE UCN SUSY irrelevant to low energy observables 2. Hadronic effects in SM predictions Better control of non-pQCD 3. Something is wrong with exp’t Exp’t: n bdecay, Ke3 decay 4. New models of SUSY-breaking ??? 5. Go beyond the MSSM Break R-parity But NuTeV Ke3 decays: recent developments Vus Vus f K 0 V. Cirigliano (0) Ke3 decays: current status O(p6) Vus f K 0 (0) G. Isidori, CKM 2005 Ke3 decays: current status Quenched LQCD Vus Large NC G. Isidori, CKM 2005 O(p6) CC (non) universality & the MSSM Data appeared to conflict with MSSM & models having flavor-blind SUSY-breaking mediation Possible resolutions: 1. MSUSY > TeV SUSY irrelevant to low energy observables 2. Hadronic effects in SM predictions 3. Something is wrong with exp’t Better control of nonpQCD Exp’t: n b decay, Ke3 decay 4. New models of SUSYbreaking 5. Go beyond the MSSM ??? Break R-parity III. Neutral Current Processes Is there SUSY dark matter? Weak Neutral Currents at Low Energies M NC GF NC J J ~ NC 2 2 gVf 2I3f 4Qf W sin2 J f g g f NC f V g Af 2I3f Parity-violating electron scattering LPV GF f Q 2 2 W Weak Charge e 5e f f f A 5 Weak Charges QWp = 1 - 4 sin2W ~ 0.1 QWe = -1 + 4 sin2W ~ -0.1 Need ~ few percent to probe SUSY Weak Mixing Angle: Scale Dependence Czarnecki, Marciano Erler. Kurylov, MR-M Atomic PV N deep inelastic sin2W e+e- LEP, SLD SLAC E158 (ee) JLab Q-Weak (ep) (GeV) QW and SUSY Radiative Corrections Tree Level Q g f W f V Flavor-dependent Radiative Corrections Q PV (2I 4Qf PV sin2 W ) f f W f 3 Normalization Scale-dependence of weak mixing Flavor-independent Universal corrections ˆ ˆ PV T VB SUSY PV muon decay cˆ 2 1 ˆ 2 2 T ˆ 2 2 2 S cˆ sˆ 4sˆ ( cˆ sˆ ) 2 2 ˆ ˆ cˆ Z (q ) Z (M Z ) 2 2 ˆs q MZ ˆ ' S,T, VV 2 ˆ ˆ ˆ ˆ (M ) c D Z 2 2 VB 2 cˆ sˆ ˆ M Z 2 gauge boson propagators Oblique Parameters SM fit only No SUSY effects Parameter Space Scan Comparing Qwe and QWp SUSY SUSY loopsloops QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. 3000 randomly chosen SUSY parameters but effects are correlated Effects in sin2W dominate Negligible SUSY loop impact on cesium weak charge Correlated Radiative Corrections total QWf PV (2I3f 4Qf PV sin2 W ) f Correlated Radiative Corrections susy T Z VB S e- anapole R-Parity Violation (RPV) DL=1 WRPV = ijk LiLjEk + ijk LiQjDk +/i LiHu + ijkUiDjDk DB=1 proton decay: Set ijk =0 Li, Qi SU(2)L doublets Ei, Ui, Di SU(2)L singlets Four-fermion Operators e e 12k e˜ Rk q˜ Lj 1j1 12k e d 1j1 e d DL=1 DL=1 D 12 k 12 k 2 2 ˜eRk 4 2GF M D / 1j 1 / 2 ij i 4 2GF Mq2˜ j L Corrections to Weak Charges DQWp 2 k / k / j ˜ ˜ ˜ p 2 2 sˆ D 12k (e R ) 2D 11k (dR ) D1 j1 (q L ) QW 1 4 sˆ DQ 4 k ˜ 2 sˆ D12 k (eR ) Q 1 4 sˆ e W e W sˆ 2 (1 sˆ 2 ) sˆ 2 ˆ 1 2s shift in sin2 W Other Constraints 1. CKM unitarity 2. l2 decays 3. -GF-MZ-MW relation 4. Cesium atomic PV Other constraints, cont’d. MW CKM Unitarity APV l2 Comparing Qwe and QWp SUSY dark matter SUSY loops -> QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. e+e is Majorana RPV 95% CL Comparing Qwe and QWp QWP = 0.0716 0.0029 QWe = 0.0449 0.0040 Experiment SUSY Loops E6 Z/ boson RPV SUSY Leptoquarks SM SM Erler, Kurylov, R-M Additional PV electron scattering ideas Czarnecki, Marciano Erler et al. DIS-Parity, JLab Atomic PV Linear Collider e-e- N deep inelastic DIS-Parity, SLAC sin2W e+e- LEP, SLD SLAC E158 (ee) JLab Q-Weak (ep) Moller, JLab (GeV) Comparing AdDIS and Qwp,e e RPV p Loops Comparing Qwe and QWp “DIS Parity” Kurylov, R-M, Su SUSY loops SUSY dark matter E158 &QWeak QWp,SUSYQuickTime™ QWp,SM and a TIFF (Uncompressed) decompressor are needed to see this picture. Linear collider JLab Moller RPV 95% CL QWe,SUSY QWe, SM Weak Mixing Angle: Scale Dependence Czarnecki, Marciano Erler, Kurylov, MR-M Atomic PV N deep inelastic Increase Vus for CKM unitarity (BNL E865, Ke3) sin2W e+e- LEP, SLD SLAC E158 (ee) JLab Q-Weak (ep) (GeV) Weak Neutral Currents at Low Energies M NC GF NC J J ~ NC 2 2 gVf 2I3f 4Qf W sin2 J f g g f NC f V f A 5 g Af 2I3f -Nucleus Deep Inelastic Scattering 5 q NC Lq,NC G F q 2L PL 2RPR (1 ) 2 Lq,CC GF 2 CC q (1 5 ) u (1 5 )d q q + h.c. -Nucleus DIS, Cont’d. Cross section ratios R g rg NC N CC N 2 L 2 R g 1 2 R R g r g NC N CC N 2 L 2 L,R r NC N CC N CC N 2 ( Lq ,R )2 q CC N Radiative corrections I Qq q L 3 L Qq q L W q L sin2 W sin2 q R NC,CC L,R NuTeV-SM Discrepancy R R 0.0033 0.0007 exp SM R R 0.0019 0.0016 exp SM Paschos-Wolfenstein Relation R rR 2 R (1 2sin W ) /2 1r -Nucleus DIS: SUSY Loop Corrections wrong sign RPV Effects k ˜ D12 k (eR ) NC N k / k ˜ ˜ D12 k (eR ) D21k (d R ) CC N 1 k / k ˜ ˜ sˆ D12k (eR ) D21k (d R ) 3 1 d k / k ˜ ˜ R sˆ D12k (eR ) D2k1(d L ) 3 2 u u k ˜ L R ˆs D12 k ( eR ) 3 d L unconstrained elsewhere -Nucleus DIS: RPV Effects -Nucleus DIS: RPV Effects Neutral Currents: Summary • Comparison of weak charges may allow one to distinguish between SUSY with or without R parity conservation Test for viability of SUSY dark matter, solution to the charged current problem, and Majorana character of the neutrino • SUSY presently cannot account for the NuTeV anomaly Hadronic physics in the SM or more exotic new physics scenario responsible IV. Interpretation issues Do we have QCD under sufficient control? Interpretation of precision measurements How well do we now the SM predictions? Some QCD issues Proton Weak Charge GFQ p p 2 ALR QW F (Q , ) 4 2 2 Weak charge Form factors: MIT, JLab, Mainz Q2=0.03 (GeV/c)2 Q2>0.1 (GeV/c)2 Interpretation of precision measurements How well do we now the SM predictions? Some QCD issues Proton Weak Charge GFQ2 p p 2 ALR QW F (Q , ) 4 2 FP(Q2, -> 0) ~ Q2 Use PT to extrapolate in small Q2 domain and current PV experiments to determine LEC’s QCD Effects in QWP Box graphs e W Z Z W Z p QW ~ 26% e p QW ~ 3% kloop ~ MW : pQCD e p QW ~ 6% QCD < kloop < MW : non-perturbative Box graphs, cont’d. Protected by symmetry W W 2 ˆ GF (M s W ) MWW 2 2 5 1 2 2 4sˆ Short-distance correction: OPE QWp(QCD) ~ -0.7% QWp(QCD) ~ -0.08% WW ZZ pQCD Corrections OPE: s corrections Integrand b e(K)[k k g k i b 5 ](1 5 )e(K)T (k) Hadronic tensor T (k) d x e 4 ikx p T J (0)J (x) p Contract with k k T (k) i d x e (x0 ) p [J (0), J (x)] p 4 ikx Equal time commutator: protected by SU(2)L symmetry 0 Soft terms Box graphs, cont’d. Z + Z Long-distance physics: not calculable [ ˆ GF 5 2 ˆ MZ 1 4s 2 2 2 ln ] 2 M Z C () 2 Z Fortuitous suppression factor: box + crossed ~ b kJ JbZ ~ A gv e = (-1+4 sin2W) Neutron b-decay e p W MW e G F ˆ 2 2 [ ln ] 2 M Z C () 2 W n |CW| < 2 to avoid exacerbating CKM non-unitarity |CZ| < 2 QWp < 1.5% Higher Twist “Pollution” ~0.4% Different PDF fits ALR Q2 y E=11 GeV 0 =12.5 Sacco, R-M preliminary Higher Twist “Pollution” Sacco & R-M preliminary FLD, HT Castorina & Mulders Open issues F2D, HT • QCD evolution • Double handbag • Moment inversion Interpretation & QCD Issues • QCD effects in electroweak radiative corrections not problematic for QWp, l2-decays, but more of concern for neutron b-decay, (g-2) Future study of CW, CZ on the lattice • Form factors in Ke3 decays (Vus) PT at O(p6) • N Deep inelastic scattering PDF’s: isospin, shadowing… • Deep inelastic scattering Higher twist Conclusions • Precision electroweak measurements below the Z-pole can provide important clues about the structure of the “new” Standard Model Comparison of a variety of measurements is essential • Charged current processes provide a window on the mechanism of SUSY-breaking mediation at very high energy scales b-decay, l2-decays, -decay, Ke3-decay • Neutral current measurements may allow one to test the viability of SUSY dark matter PV ep, ee, eA scattering, N deep inelastic scattering • Theoretical control of QCD uncertainties is crucial Future QCD-electroweak theory “synergy” References A. Kurylov, MR-M, & S. Su, Phys. Rev. D68: 035008 (2003) A. Kurylov, J. Erler, & MR-M, Phys. Rev. D68: 016006 (2003) A. Kurylov, MR-M, & S. Su, Nucl. Phys. B667, 321 (2003) A. Kurylov, MR-M, & S. Su, Phys. Lett. B582, 222 (2003) A. Kurylov & MR-M, Phys. Rev. Lett. 88: 071804 (2002) MR-M, Phys. Rev. D 62: 056009 (2000)