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 = 180 o rotation about “2” axis in isospin space At the partonic level, charge symmetry operation (CS) corresponds to: We know the origins of parton CSV: o quark mass difference: o Electromagnetic contributions: an important EM effect: n-p mass difference (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)

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

4. Phenomenological Sea Parton CSV PDFs MRST also included sea quark CSV term: Again chose restricted form: Best fit: δ = +0.08, surprisingly large! (corresponds to 8% CS violation in sea) [momentum carried by sea ~ same for p, n] Minimum in χ 2 substantially deeper than for valence Increase in u n sea  better fit to NMC μ-D data Much better fit to E605 Drell-Yan data Note: for simplicity, MRST neglect Q 2 dependence of CSV terms  this will affect our estimates of CSV effects.

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

6. Sather: study variation with nucleon, quark mass: analytic approximation (appears as derivatives of valence parton distribution) Quantitative Estimates, Valence Parton CSV Use quark-model wavefunctions for valence parton PDFs: Note: Rodionov etal did not use Sather method; accounted for quark p T (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 Q 2, evolve up to Q 2 of interest (Q 2 dependent effect!!) qualitatively very similar to theoretical quark model CSV δd v ~ -δu v ; 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 F 2 structure functions from ν, EM DIS = F 2 structure function for charged lepton DIS on isoscalar target = average F 2 neutrino+ antineutrino CC DIS, isoscalar target (sometimes called the “5/18 rule” ) Deviation of R c from 1  evidence for CSV in PDFs

9. Experimental Measurements of Charge Ratio New experiments provide unprecedented precision 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 Best comparison: NMC mu-D DIS; CCFR nu-Fe CC DIS Many corrections must be made in comparison 1) ratio R c ~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 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 from SM agree with SM

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 Q 2  Both numerator, denominator involve 2 nd moment of valence dist’ns  numerator, denominator evolve identically with Q 2  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) Valence-valence terms cancel completely Contributions to R from sea quarks + CSV + strange (typical Q 2 ~ 25 GeV 2 ) DY X-sections cancel to within ~ 10% in R (normalize to J/ψ production) Measure pi PDFs in this pi DY experiment Look at valence region, large  (this relation is observed in earlier DY expt’s) Form the ratio

15. 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, Q 2 = 25 GeV 2 ) used pion PDFs from [Sutton etal, PR D45, 2349 (92)] Charge Symmetry Test: Pion Drell-Yan Compare X-sections in pi-D DY

16. Charge Asymmetry in Semi-Inclusive Leptoprod’n 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 R D vs. x for fixed z could measure at HERMES, J Lab possible at future e-Collider (BNL, JLab) X-section contains product of PDF with fragmentation function

17. Charge Asymmetry SIDIS e-prod’n 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 e+ D  π ± + X

18. Theoretical models suggest magnitude, sign of valence parton CSV “Charge ratio”  few % limits on magnitude of CSV “QED splitting”  new I-spin violating (Q 2 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) Conclusions: suggested experiments to measure CS violation require excellent precision, dedicated experiments New experiments  new precision for partonic quantities (charge symmetry, strange quarks, sea)