Isospin Violating Parton Distributions

1. Charge Symmetry for Parton Distributions Inclusion of CSV in phenomenological PDFs Theoretical Estimates of parton charge symmetry Experimental Constraints on parton CSV Implications of parton CSV NuTeV; PV expt’s Possible tests of parton charge symmetry Conclusions Isospin Violating Parton Distributions Tim Londergan Nuclear Theory Center, Indiana University Charge Symmetry Workshop ETC Trento June 17, 2005 Supported by NSF PHY- 0244822 In collaboration with Tony Thomas (Adelaide/JLab)

2. Charge Symmetry of Parton Distributions: Charge symmetry = 180o rotation about “2” axis in isospin space At the partonic level, charge symmetry operation (CS) corresponds to: (a similar relation holds for antiquarks) • Nuclear physics CS generally valid to fraction of % • Until 2003, all phenomenological PDFs assumed charge symmetry • (reduced # of PDFs by a factor of 2) • We know the origins of parton CSV: • quark mass difference: • Electromagnetic contributions: an important EM effect: n-p mass difference

3. Phenomenological Valence Parton CSV PDFs MRST Phenomenological PDFs include CSV for 1st time: Martin, Roberts, Stirling, Thorne (Eur Phys J C35, 235 (04)): Choose restricted form for parton CSV: [f(x): 0 integral; matches to valence at small, large x] Best fit: κ = -0.2 remarkably similar to quark model predictions -0.8 < κ < +0.65,90% confidence MRST (04) ADEL (94)

4. Phenomenological Sea Parton CSV PDFs MRST also included sea quark CSV term: Again chose restricted form: [momentum carried by sea ~ same for p, n] Best fit: δ = +0.08, surprisingly large! (corresponds to 8% CS violation in sea) • Minimum in χ2 substantially deeper than for valence • Increase in un sea better fit to NMC μ-D data • Much better fit to E605 Drell-Yan data Note: for simplicity, MRST neglect Q2 dependence of CSV terms  this will affect our estimates of CSV effects.

5. Models for CSV in Valence PDFs Violation of approximate symmetries:“window” non-perturbative physics Construct quark models that reproduce qualitative features of PDFs Examine their behavior under charge symmetry operations Quark models  predict sign, magnitude of valence parton charge symmetry violation Important to disentangle CSV effects from isospin violation, flavor symmetry effects  dedicated experiments

6. Quantitative Estimates, Valence Parton CSV Use quark-model wavefunctions for valence parton PDFs: Sather: study variation with nucleon, quark mass: analytic approximation (appears as derivatives of valence parton distribution) Note: Rodionov etal did not use Sather method; accounted for quark pT (neglected by Sather); yet, CSV PDFs agree to within 10%

7. “QED Splitting”: a New Source of Isospin Violation MRST, Eur.Phys.J. 39, 155 (05); Glueck, Jimenez-Delgado, Reya, hep-ph/0503103 (05) QED-generated evolution arising from photon radiation from quarks Evaluate at low Q2, evolve up to Q2 of interest (Q2 dependent effect!!) • qualitatively very similar to theoretical quark model CSV • δdv ~ -δuv; roughly same sign • adds to quark model CSV term increase ~ factor 2 • MRST incorporated QED splitting into latest PDFs

8. Experimental Limits on parton CSV • No Direct evidence for charge symmetry violation • Strongest limits  the “charge ratio” • Compare F2 structure functions from ν, EM DIS = F2 structure function for charged lepton DIS on isoscalar target = average F2 neutrino+ antineutrino CC DIS, isoscalar target (sometimes called the “5/18 rule”) Deviation of Rc from 1  evidence for CSV in PDFs

9. Experimental Measurements of Charge Ratio New experiments provide unprecedented precision • Best comparison: NMC mu-D DIS; CCFR nu-Fe CC DIS • Many corrections must be made in comparison CCFR/NMC (LO) analysis: Agreement for 0.1 < x < 0.4 Large errors for x > 0.4 (nuclear Fermi motion) Apparent disagreement x < 0.1  removed on re-analysis 1) ratio Rc ~1 to ~ 2-3 % • parton CSV determined to ~ 6-9 % level (includes valence, sea CSV)

10. CSV and the Paschos-Wolfenstein Ratio: Neutrino Total Cross Sections on Isoscalar Target: Paschos/Wolfenstein: Independent measurement of Weinberg angle PW ratio minimizes sensitivity to PDFs, higher-order corrections • NuTeV: different cuts, acceptances for • can’t simply construct PW ratio: Monte Carlo procedure (errors differ from PW estimates!)

11. NuTeV Determination of Weinberg Angle: • Construct ratios • Individual ratios less dependent on overall normalization • Very precise charged/neutral current ratios: • : depends strongly on Weinberg angle • : weak dependence on Weinberg angle 3σ from SM agree with SM 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)

12. Isospin Violating Corrections to PW Ratio: Changes in PW ratio from isospin violating PDFs: PW Correction  valence parton charge symmetry violation (CSV) • CSV correction to PW ratio independent of Q2 • Both numerator, denominator involve 2nd moment of valence dist’ns • numerator, denominator evolve identically with Q2 • quark models: remove 1σ of NuTeV effect • “QED splitting”: also remove 1σ of NuTeV effect • Phenomenology (MRST): can remove 100% of NuTeV effect  CSV sufficiently large to remove NuTeV anomaly would produce observable effects in certain reactions

13. New Expt’s to Search for Charge Symmetry Violation?? • pi-D Drell-Yan Reactions • SIDIS e-production of pions • PV scattering (K Kumar, next talk)

14. Valence CSV Test:Pion Drell-Yan Compare X-sections in pi-D DY processes (e.g, FNAL) Look at valence region, large  (this relation is observed in earlier DY expt’s) Form the ratio • Valence-valence terms cancel completely • Contributions to R from sea quarks + CSV + strange • (typical Q2 ~ 25 GeV2) • DY X-sections cancel to within ~ 10% in R • (normalize to J/ψ production) • Measure pi PDFs in this pi DY experiment

15. Charge Symmetry Test:Pion Drell-Yan Compare X-sections in pi-D DY • Plot vs. x for constant • CSV terms dominate for x > 0.3 • differences, limits of MRST CSV ~ 50% or more • (90% conf limit of MRST valence CSV) • (LO calculation, Q2 = 25 GeV2) • used pion PDFs from [Sutton etal, PR D45, 2349 (92)]

16. Charge Asymmetry in Semi-Inclusive Leptoprod’n X-section contains product of PDF with fragmentation function • Ratio of yields: • first term depends only on z; constant in x • CSV term depends only on x; relatively large for large x • remaining (sea) term decreases rapidly with x • to find CSV, plot RD vs. xfor fixed z • could measure at HERMES, J Lab • possible at future e-Collider (BNL, JLab)

17. Charge Asymmetry SIDIS e-prod’n e+ D  π± + X • Various terms in ratio • dashed term: nonstrange sea; dot-dashed, strange z=0.4 • CSV, MRST, κ = -0.8; κ = +0.65 • CSV significant for x ≥ 0.4 • precise measurement of individual yields is critical • essential that X-sections factorize

18. Conclusions: • Theoretical models suggest magnitude, sign of valence parton CSV • “Charge ratio” few % limits on magnitude of CSV • “QED splitting” new I-spin violating (Q2 dependent) effect • First phenomenological CSV PDFs (MRST 03): valence CSV – weak evidence, remarkable agreement w/models sea CSV – roughly 8% effect; improved fit, NMC, E605 data • “I-spin Corrections” to NuTeV measurement of (most likely single explanation of NuTeV anomaly) • suggested experiments to measure CS violation • require excellent precision, dedicated experiments • New experiments  new precision for partonic quantities (charge symmetry, strange quarks, sea)