Electroweak Physics at an Electron-Ion Collider M.J. Ramsey-Musolf Wisconsin-Madison NPAC Theoretical Nuclear, Particle, Astrophysics & Cosmology ECT* Trento, July 2008

Outline Brief Context: Precision and Energy Frontiers Neutral Current Processes: PV DIS & PV Moller Charged Current Processes: e - +A K E T + j Lepton flavor violation: e - +A K  - + A Disclaimer: some ideas worked out in detail; others need more research

Low-Energy: What we have learned Weak interactions violate P  QCD is tiny Q W P ~ 0.1 Q W n ~ -1 S-quarks: impt for spin, not for  N Sin 2  W runs TeV scale technicolor unlikely Nuclei have large anapole moments

What we would like to know Does the “new SM” violate CP? Can it explain the abundance of matter? Are there new TeV scale interactions? If so, what are their symmetries? How does QCD make a proton? Are lepton number and charged lepton flavor conserved ?

Precision Probes of New Symmetries Beyond the SMSM symmetry (broken) Electroweak symmetry breaking: Higgs ? New Symmetries 1.Origin of Matter 2.Unification & gravity 3.Weak scale stability 4.Neutrinos ? LHC: energy frontier Low-energy: precision frontier EIC: Post LHC Era

Precision & Energy Frontiers Radiative corrections Direct Measurements Stunning SM Success J. Ellison, UCI Precision measurements predicted a range for m t before top quark discovery m t >> m b ! m t is consistent with that range It didn’t have to be that way Probing Fundamental Symmetries beyond the SM: Use precision low- energy measurements to probe virtual effects of new symmetries & compare with collider results Precision Frontier: Precision ~ Mass scale Look for pattern from a variety of measurements Identify complementarity with collider searches Special role: SM suppressed processes

Nuclei & Charged Leptons PV Electron Scattering Weak Decays n decay correlations nuclear  decay pion decays muon decays Q-Weak 12 GeV Moller PV DIS Muons g  -2  A->eA EIC: More PV New CC ?  LFV ?

Neutral Current Probes: PV Basics of PV electron scattering Standard Model: What we know New physics ? SUSY as illustration Probing QCD

PV Electron Scattering Parity-Violating electron scattering “Weak Charge” ~ 0.1 in SM Enhanced transparency to new physics Small QCD uncertainties (Marciano & Sirlin; Erler & R-M) QCD effects (s-quarks): measured (MIT-Bates, Mainz, JLab)

Nuclei & Charged Leptons: Theory PV Electron Scattering Q-Weak 12 GeV Moller PV DIS Muons g  -2  A->eA Essential Role for Theory Precise SM predictions (QCD) Sensitivity to new physics & complementarity w/ LHC Substantially reduced QCD uncertainty in sin 2  W running QCD uncertainties in ep box graphs quantified Comprehensive analysis of new physics effects Weak Decays n decay correlations nuclear  decay pion decays muon decays

Effective PV e-q interaction & Q W Low energy effective PV eq interaction Weak Charge: N u C 1u + N d C 1d Proton: Q W P = 2 C 1u + C 1d = 1-4 sin 2  W ~ 0.1 Electron: Q W e = C 1e = -1+4 sin 2  W ~ - 0.1

Q W and Radiative Corrections Tree Level Radiative Corrections sin 2 Flavor-independent Normalization Scale-dependent effective weak mixing Flavor-dependent Constrained by Z-pole precision observables Large logs in  Sum to all orders with running sin 2  W & RGE

Weak Charge & Weak Mixing SU(2) L U(1) Y Weak mixing depends on scale

Weak Mixing in the Standard Model Scale-dependence of Weak Mixing SLAC Moller Parity-violating electron scattering Z 0 pole tension

Z Pole Tension ⇒ m H = GeV ⇒ S = ± 0.10 A LR A FB (Z→ bb) sin 2 θ w = (3) ↓ m H = GeV S= ± 17 sin 2 θ w = (3) ↓ m H = GeV S= ± 17 Rules out the SM! Rules out SUSY! Favors Technicolor! Rules out Technicolor! Favors SUSY! (also APV in Cs) (also E158) W. Marciano The Average: sin 2 θ w = (17) 3σ apart Precision sin 2  W measurements at colliders very challenging Neutrino scattering cannot compete statistically No resolution of this issue in next decade K. Kumar

Weak Mixing in the Standard Model Scale-dependence of Weak Mixing JLab Future SLAC Moller Parity-violating electron scattering Z 0 pole tension

Effective PV e-q interaction & PVDIS Low energy effective PV eq interaction PV DIS eD asymmetry: leading twist Weak Charge: N u C 1u + N d C 1d Proton: Q W P = 2 C 1u + C 1d = 1-4 sin 2  W ~ 0.1 Electron: Q W e = C 1e = -1+4 sin 2  W ~ - 0.1

Model Independent Constraints P. Reimer, X. Zheng

C 2q and Radiative Corrections Tree Level Radiative Corrections Flavor-dependent Flavor-independent Normalization Scale-dependent effective weak mixing Constrained by Z-pole precision observables Like Q W p,e ~ sin 2  W

New Physics: Comparing PV Observables Q W P = Q W e = Experiment SUSY Loops E 6 Z / boson RPV SUSY Leptoquarks SM

SUSY Radiative Corrections Propagator Box Vertex & External leg  Kurylov, RM, Su

SUSY: R Parity-Violation 12k  1j1  L=1 No SUSY DM: LSP unstable Neutrinos are Majorana

PVES & APV Probes of SUSY  Q W P, SUSY / Q W P, SM RPV: No SUSY DM Majorana s SUSY Loops  Q W e, SUSY / Q W e, SM g  -2  12 GeV  6 GeV E158 Q-Weak (ep)Moller (ee)  Kurylov, RM, Su Hyrodgen APV or isotope ratios Global fit: M W, APV, CKM,  l 2,…

Comparing A d DIS and Q w p,e e p RPV Loops

Deep Inelastic PV: Beyond the Parton Model & SM e-e- N X e-e- Z*Z* ** d(x)/u(x): large x Electroweak test: e-q couplings & sin 2  W Higher Twist: qq and qqg correlations Charge sym in pdfs

PVDIS & QCD Low energy effective PV eq interaction PV DIS eD asymmetry: leading twist Higher Twist (J Lab) CSV (J Lab, EIC) d/u (J Lab, EIC) +

PVDIS & CSV Direct observation of parton-level CSV would be very exciting! Important implications for high energy collider pdfs Could explain significant portion of the NuTeV anomaly Londergan & Murdock Few percent  A/A Adapted from K. Kumar

PVDIS & d(x)/u(x): xK1 Adapted from K. Kumar SU(6):d/u~1/2 Valence Quark:d/u~0 Perturbative QCD:d/u~1/5 PV-DIS off the proton (hydrogen target) Very sensitive to d(x)/u(x)  A/A ~ 0.01

PVES at an EIC Scale-dependence of Weak Mixing JLab Future SLAC Moller Parity-violating electron scattering EIC PVDIS ? Z 0 pole tension EIC Moller ?

Charged Current Processes The NuTeV Puzzle HERA Studies W Production at an EIC ? CC/NC ratios ?

Weak Mixing in the Standard Model Scale-dependence of Weak Mixing JLab Future SLAC Moller  nucleus deep inelasticscattering Z 0 pole tension

The NuTeV Puzzle Paschos-Wolfenstein SUSY Loops RPV SUSY Wrong sign

Other New CC Physics? Low-Energy Probes Nuclear & neutron  decay Pion leptonic decay Polarized  -decay  O / O SM ~  O / O SM ~  O / O SM ~ HERA W production  O / O SM ~ A. Schoning (H1, Zeus)

Lepton Number & Flavor Violation LNV & Neutrino Mass  Mechanism Problem LFV as a Probe  K e Conversion at EIC ?

 -Decay: LNV? Mass Term? Dirac Majorana  -decay Long baseline ? ? Theory Challenge: matrix elements+ mechanism m EFF & neutrino spectrum NormalInverted

 -Decay: LNV? Mass Term? Dirac Majorana  -decay Long baseline ? ? Theory Challenge: matrix elements+ mechanism m EFF & neutrino spectrum NormalInverted See-saw mechanism Leptogenesis L L R HH Lepton Asym ! Baryon Asym GERDACUORE EXOMajorana

 -Decay: Mechanism Dirac Majorana Theory Challenge: matrix elements+ mechanism Mechanism: does light M exchange dominate ? How to calc effects reliably ? How to disentangle H & L ? O(1) for  ~ TeV Does operator power counting suffice? Prezeau, R-M, Vogel: EFT

 -Decay: Interpretation  signal equivalent to degenerate hierarchy Loop contribution to m of inverted hierarchy scale

Lepton Flavor & Number Violation Present universeEarly universe Weak scalePlanck scale MEG:   ~ 5 x  2e: B  ->e ~ 5 x ?? R = B  ->e B  ->e  Also PRIME

Lepton Flavor & Number Violation MEG: B  ->e  ~ 5 x  2e: B  ->e ~ 5 x Logarithmic enhancements of R Low scale LFV: R ~ O(1) GUT scale LFV: R ~ O  0  decay Light M exchange ? Heavy particle exchange ? Raidal, Santamaria; Cirigliano, Kurylov, R- M, Vogel k11 / ~ 0.09 for m SUSY ~ 1 TeV  ->e  LFV Probes of RPV: k11 / ~ for m SUSY ~ 1 TeV  ->e LFV Probes of RPV: m  “naturalness”:  :

Lepton Flavor & Number Violation Exp: B  ->e  ~ 1.1 x EIC:  ~ 10 3 | A 1  e | 2 fb Raidal, Santamaria; Cirigliano, Kurylov, R- M, Vogel Logarithmic enhancements of R |A 2  e | 2 < EIC:  ~ fb If |A 1  e | 2 ~ |A 2  e | 2 Log enhancement: |A 1  e | 2 / |A 2  e | 2 ~ | ln m e / 1 TeV | 2 ~ 100 B  Ke   48    |A 2  e | 2 Need ~ 1000 fb

LFV with  leptons: HERA Veelken (H1, Zeus) (2007) Leptoquark Exchange  qq eff op  lq | 2 < (M LQ / 100 GeV) 2 Induce  Ke  at one loop?

LFV with  leptons: recent theory Kanemura et al (2005)  qq eff op SUSY Higgs Exchange  lq | 2 < 2 x (M LQ / 100 GeV) 2  lq | 2 < (M LQ / 100 GeV) 2 HERA

Summary Precision studies and symmetry tests are poised to discovery key ingredients of the new Standard Model during the next decade There may be a role for an EIC in the post-LHC era Promising: PV Moller & PV DIS for neutral currents Homework: Charged Current probes -- can they complement LHC & low-energy studies? Intriguing: LFV with eK  conversion:

Thank you ! Precision studies and symmetry tests with neutrons are poised to discovery key ingredients of the new Standard Model during the next decade Physics “reach” complements and can even exceed that of colliders: d n ~ e-cm ;  O/O SM ~ Substantial experimental and theoretical progress has set the foundation for this era of discovery The precision frontier is richly interdisciplinary: nuclear, particle, hadronic, atomic, cosmology To the organizers, ECT* staff, and participants for a lively and stimulating workshop

Back Matter Precision studies and symmetry tests with neutrons are poised to discovery key ingredients of the new Standard Model during the next decade Physics “reach” complements and can even exceed that of colliders: d n ~ e-cm ;  O/O SM ~ Substantial experimental and theoretical progress has set the foundation for this era of discovery The precision frontier is richly interdisciplinary: nuclear, particle, hadronic, atomic, cosmology