1. NuTeV – charged, neutral currents induced by neutrinos New measurement of Weinberg angle Possible “New Physics” Beyond Standard Model? Normal (“QCD”) Explanations of NuTeV Anomaly? radiative corrections parton Charge Symmetry Violation strange quark momentum asymmetry nuclear, shadowing corrections Implications of NuTeV Standard Model Test Beyond the Standard Model?? “QCD Effects”?? Tim Londergan Nuclear Theory Center, Indiana University PAVI06 Milos, Greece May 16-20, 2006 Supported by NSF PHY- 0244822 In collaboration with Tony Thomas (Adelaide/JLab)

2. The NuTeV Experiment: charged, neutral currents from neutrino DIS 800 GeV p at FNAL produce pi, K from interactions in BeO target; Decay of charged pi, K produces neutrinos, antineutrinos; Almost pure muon neutrinos; (small ν e contamination from K e3 decay) Only neutrinos penetrate shielding Dipoles select sign of charged meson: Determine nu/nubar type NuTeV: Rochester/Columbia/FNAL/Cincinnati/Kansas State/Northwestern/ Oregon/Pittsburgh neutrino collaboration G. Zeller etal, PRL 88, 091802 (02); PR D65, 111103 (02)

3. Separate Neutral, Charged-Current Events Charged current: Track through several plates Large visible energy deposit Neutral current: Short visible track Large missing energy NuTeV event selection: Large E in calorimeter event vertex in fiducial volume NuTeV Events: 1.62 million 351,000 NuTeV Detector: 18 m long, 690-ton steel scintillator; Steel plates interspersed with liq scintillator, drift chambers

4. The Paschos-Wolfenstein Ratio: Neutrino Total Cross Sections on Isoscalar Target: Paschos & Wolfenstein ( PR D7, 91 (73)): Independent measurement of Weinberg angle, using ratio of total X-sections for neutrinos, antineutrinos on isoscalar target: PW ratio  minimizes sensitivity to PDFs, higher-order corrections

5. The Paschos-Wolfenstein Ratio: PW Ratio depends on the following assumptions: Isoscalar target (N=Z) include only light (u, d) quarks neglect heavy quark masses assume isospin symmetry for PDFs no nuclear effects (parton shadowing, EMC, ….) no contributions outside Standard Model

6. NuTeV Determination of Weinberg Angle: Construct ratios Individual ratios less dependent on overall normalization Very precise charged/neutral current ratios: Different cuts, acceptance: don’t construct PW ratio directly : depends strongly on Weinberg angle : weak dependence on Weinberg angle These ratios lead to a NuTeV value for the Weinberg angle: The NuTeV result is ~ 3 σ above very precise value (from EW processes at LEP) 3σ below SM agree with SM

7. NuTeV work at LO in QCD (with improvements) and find s 2 w (NuTeV)=0.2276 ±0.0013 stat ±0.0006 syst ±0.0006 th -0.00003( M t /GeV-175 )+0.00032 ln M H /100GeV where s 2 w =1-M 2 w /M 2 z (on-shell) Global fit: s 2 w = 0.2229 ±0.0004 ~2.8σ discrepancy Nuclear effects and ν oscillation explanations very unlikely NuTeV Result: 3σ Discrepancy from LEP value Corresponds to 1.2% decrease in g L 2 ; This is large compared to precision of EW measurements! SM

8. Low Q 2 (~10 -4 GeV 2 ) atomic PV exp’t in Cs [PRL 82, 2484 (99)] Moller scatt exp’t (E158) at SLAC; Q 2 ~ 0.026 GeV 2 [PRL 95, 081601 (05)] NuTeV exp’t, Q 2 ~ 20 GeV 2 [PRL 88, 091802 (02)] LEP, e + e - at Z pole, Q 2 = M Z 2 Q weak, pol e-p at JLab (proposed), “Running” of Weinberg Angle Effective Weinberg angle depends on Q 2 Warning: gauge and process dependent parameter Q weak E158: Q dependence of Weinberg angle confirmed at 6σ level NuTeV: discrepancy of ~3σ with SM prediction [Czarnecki-Marciano, PRD53, 1066 (96)]

9. “New Physics” explanation for NuTeV? The problem: extremely precise EW data confirms SM! Mass, width of Z, W X-sections, branching ratios at Z peak [LEP, SLD] LR and FB asymmetries in e + e - scattering new particles must satisfy all these constraints EW constraints ~ 0.1% level [NuTeV ~ 1.2%] new particles have heavy masses  Q 2 dependence must be slow “new physics” hard to satisfy EW constraints! NuTeV

10. “Designer Particles” I: delicately adjust to fit all existing data oblique corrections [high mass scale, couples only to vector bosons]: parameters constrained by EW data – can’t fit NuTeV extra Z’ (unmixed) – possible; runs into trouble with latest muon g-2

11. “Designer Particles” II: More Attempts to fit NuTeV minimal SUSY loops – No – most have wrong sign; others violate existing constraints Leptoquarks (bosons that couple to leptons & quarks): models with very carefully tuned mass splittings still possible – could be tested at Tevatron, LHC [Davidson, Gambino etal, J High E Phys 2, 37 (2002) ] MSSM, light sleptinos, gauginos Leptoquark (solid); extra gauge bosons (red)

12. EM radiative corrections, process specific to NuTeV, are large –Bremsstrahlung from final state lepton in CC  significant correction. Not present in NC (promotes CC events to higher y so they pass energy cut)  R,  R ,  sin 2  W } ≈ {+.0074,+.0109,-.0030} –New calculation of this effect (Diener, Dittmaier, Hollik PR D69, 073005 (04) ) not yet implemented in analysis Corrections likely larger than NuTeV estimate EW Radiative Corrections D. Yu. Bardin and V. A. Dokuchaeva, JINR-E2-86-260, (1986)

13. Isospin Violating Corrections to PW Ratio: Changes in PW ratio from isospin violating PDFs: PW Correction  valence parton charge symmetry violation (CSV) parton charge symmetry: CS: (rotation of 180 o about “2” axis in isospin space) We know the origins of parton CSV: o quark mass difference: o Electromagnetic contributions: most important EM effect: n-p mass difference

14. CSV Contribution to NuTeV Result: Sather: Analytic Quark Model Approximation for Valence Parton CSV. PW Ratio CSV Corr’n using Sather: Rodionov: Sather: CTEQ4LQ: 40% decrease in anomaly! NuTeV: Don’t evaluate PW Ratio! CSV Contrib’n to NuTeV result:  Calculate parton CSV at low (quark model) momentum scale  Evolve up to Q 2 of NuTeV exp’t (20 GeV 2 )  Evaluate with NuTeV functional 30% decrease in anomaly Leads to analytic results (model-dependent)

15. Phenomenological Parton CSV PDFs MRST PDFs from global fits include CSV for 1 st time: Martin, Roberts, Stirling, Thorne [Eur Phys J C35, 325 (04)]: Choose restricted form for parton CSV: Best fit: κ = -0.2, large uncertainty ! Best fit remarkably similar to quark model CSV calculations MRST (2004) ADEL (1994) [f(x): 0 integral; matches to valence PDFs at small, large x] 90% conf limit (κ)

16. “QED Splitting”: a New Source of Isospin Violation MRST, Eur.Phys.J. 39, 155 (05); Glueck, Jimenez-Delgado, Reya, PRL95, 022002 (05) “QED evolution”, quark radiates photon Evolve in Q 2 qualitatively similar to quark model CSV QED varied while quarks “frozen” contributes even if m u = m d and M n = M p add to quark model CSV term  increase CSV ~ factor 2 MRST incorporate QED splitting with PDFs in global fit to high energy data

17. Phenomenology: MRST global fit  limits valence CSV -0.8 ≤ κ ≤ +0.65 κ = -0.6  remove NuTeV anomaly! κ = +0.6  anomaly twice as large! Theoretical estimates:  quark model remove ~1/3 anomaly  “QED splitting” remove ~1/3  at current limits, CSV could produce observable effects (~ 5-6%) in certain reactions Summary, CSV Effects on Weinberg angle MRST global fit to valence CSV 90% confidence limits:

18. Strange Quark Contributions to PW Ratio: Contribution from strange quarks: Strange quark normalization: constrained (no net strangeness in nucleon) If s quarks carry more momentum than sbardecrease anomaly Determination of s, sbar quark PDFs: Opposite sign dimuons from neutrinos CCFR: charge of faster muon determines neutrino or antineutrino; most precise way to determine s, sbar PDFs  CCFR, NuTeV s-sbar momentum asymmetry

19. Analyses of s quark momentum asymmetry NuTeV: analyzed s, sbar for small x: Best fit: Do not enforce normalization condition NLO treatment of dimuon prod’n But, from normalization: If s sbar for large x CTEQ: [Kretzer etal, PRL 93, 041802 (04), Olness etal, Eur Phys J C40, 145 (05)] Global analysis of parton PDFs  CTEQ6 Includes CCFR, NuTeV dimuon data (includes expt’l cuts on dimuons) Extract “best fit” for s, sbar dist’ns [enforce s normalization cond’n] Catani et al. hep-ph/0404240; 0406338 in NNLO, can generate nonzero momentum asymmetry find small mom asymmetry < 0 from 3-loop contrib’ns

20. positive [S - ] Results: CTEQ Global fit vs. Bjorken x CTEQ: S - > 0, strange asymmetry decreases NuTeV anomaly; dimuon data: most sensitive for s PDFs CTEQ: s contrib’n removes 0  25% of anomaly μ ± other -.001 < [S - ] < +.004

21. NuTeV Analysis of s, sbar Quark Dist’n: Re-analyzed dimuon data:  preliminary analysis [S - ] ~ 0  appears negative  strangeness not conserved?  NLO treatment of dimuon prod’n NuTeV group:  now using CTEQ PDFs (u,d)  very similar analysis method  acceptance corrections?  fragmentation functions?  charm mass (CTEQ uses HERA data) ? Qualitative disagreement between NuTeV/CTEQ, using same data, techniques to extract s, sbar ??

22. Nuclear Effects ?? NuTeV: All data neutrino DIS on iron Nuclear modification of PDFs: Shadowing EMC Effect Fermi motion …. Miller/Thomas Int J Mod Phys A20, 95 (05) : Shadowing effect for NuTeV?? charged leptons: Vector meson dominance CC events: NC events: Miller/Thomas:  shadowing very different from  Z o : very small coupling to    NC shadowing ~ 0 Different shadowing for  account for anomaly?? NuTeV: NO !  Shadowing low Q 2, data much higher Q 2  value very close to SM value (should be quite different in MT scenario) Nuclear effects in  reactions: Hirai, Kumano, Nagai, PR D71, 113007 (05) Shadowing: increase NuTeV anomaly??

23. Nuclear Effects (part II) Brodsky, Schmidt, Yang (PR D70, 116003 (04)) Shadowing/Antishadowing ν-A processes include Pomeron, Odderon, Reggeon effects obtain both shadowing, antishadowing effects both constructive, destructive interference processes modified in different ways Predict greater effect on Remove ~ 20% of Weinberg angle anomaly Partial contribution along with CSV, s quarks ?? than

24. Conclusions: NuTeV: Measured CC, NC X-sections for on Fe Large (~ 3σ), surprising discrepancy for “New Physics” – difficult to fit LEP results, NuTeV “designer particles” unlikely  very delicate “QCD Corrections” to NuTeV measurement?? radiative corr’ns  new calc’n, not in analyses parton CSV  ~ could remove effect [MRST] strange quark asymmetry ~ 1-2 σ [CTEQ] nuclear effects ~ 20%, Brodsky etal NuTeV: no!! CSV, strangeness at present, most plausible explanations for NuTeV anomaly small additive contrib’ns from CSV, strangeness, nuclear effects ?? (model dependence)

25. NuTeV – charged, neutral currents induced by neutrinos New measurement of Weinberg angle Possible “New Physics” Beyond Standard Model? Normal (“QCD”) Explanations of NuTeV Anomaly? radiative corrections parton Charge Symmetry Violation strange quark momentum asymmetry nuclear, shadowing corrections Implications of NuTeV Standard Model Test Beyond the Standard Model?? “QCD Effects”?? Tim Londergan Nuclear Theory Center, Indiana University PAVI06 Milos, Greece May 16-20, 2006 Supported by NSF PHY- 0244822 In collaboration with Tony Thomas (Adelaide/JLab)

26. NuTeV/LEP/ PV MØller/ Q weak E158 at SLAC first measurement of PV in M Ø ller sc. huge luminosity high polarization (~80%) Suppressed sensitive to sin 2 θ w Large radiative corrections, ≈-40% Czarnecki-Marciano,Denner-Pozzorini,Petriello,Ferroglia et al Very low Q 2 atomic PV exp’t in Cs JLab: Q weak e-p PV exp’t Warning: gauge and process dependent parameter At tree level, A PV ≈280 10 -9 Q weak !!

27. “QCD Corrections” to the NuTeV Result: ( “Something Old”) Isoscalar Effect (N ≠Z for Fe) Depends only on 2 nd moment of light quark valence PDFs (momentum carried by up, down valence quarks) Isoscalar corrrection to PW ratio: NuTeV Isoscalar correction: NuTeV exp’t doesn’t evaluate PW ratio Isoscalar correction from Monte Carlo simulation of exp’t Although NuTeV significant difference from PW corr’n, under control

28. At low Q 2, generate from quark models: residual (ud) diquark Under CSV n  p, residual (ud) diquark [only n-p mass difference] Qualitative Features of Parton Distributions [True for all intermediate states!] “Majority” valence quark:“Minority” valence quark residual (uu) diquark residual (dd) diquark [diquark mass difference]

29. Calculating CSV Corrections to PW Ratio: o Construct models for valence parton distributions o Test how these models behave under CSV transformation: o Predict sign, magnitude of CSV effects in NuTeV exp’t CSV Corrections to PW Ratio:  CSV correction to PW ratio independent of Q 2  Both numerator, denominator involve 2 nd moment of valence dist’ns  numerator, denominator evolve identically with Q 2 under LO evolution,  Evaluate valence PDFs at low Q 2 o Dominated by configurations with 3 valence quarks o Easy to calculate, study behavior

30. Quantitative Estimates of Parton CSV Quark-model formula for parton PDFs: Large x: dominated by X=diquark states Sather: study variation with nucleon, quark mass: analytic expression small shift in PDFs, due to quark, nucleon mass. For large x, Sather predicts d > u in both cases. (From normalization, d < u at small x) X = qq; 3q+qbar; 4q+2 qbar. …. [work at low Q 2 where 3-quark states dominate]