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PV DIS: NP and Higher Twist

PV DIS: NP and Higher Twist. M.J. Ramsey-Musolf Wisconsin-Madison. NPAC. Theoretical Nuclear, Particle, Astrophysics & Cosmology. http://www.physics.wisc.edu/groups/particle-theory/. PVDIS Workshop, June 2009. S. Mantry & M. Glatzmaier Madison G. Sacco JPL G. Paz IAS. Outline.

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PV DIS: NP and Higher Twist

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  1. PV DIS: NP and Higher Twist M.J. Ramsey-Musolf Wisconsin-Madison NPAC Theoretical Nuclear, Particle, Astrophysics & Cosmology http://www.physics.wisc.edu/groups/particle-theory/ PVDIS Workshop, June 2009 S. Mantry & M. Glatzmaier Madison G. Sacco JPL G. Paz IAS

  2. Outline PV DIS & new physicsModel independent analysis SUSY effects PV DIS & Higher twist Puzzles from JLab data The twist expansion What does QCD predict? Q2-dependence, operator matrix elements, Sacco thesis General remarks

  3. I. PV DIS & New physics

  4. Model Independent Constraints Low energy effective PV eq interaction PV DIS eD asymmetry: leading twist

  5. Model Independent Constraints P. Reimer, X. Zheng

  6. Like QWp,e ~ 1 - 4 sin2qW Flavor-dependent Normalization Scale-dependent effective weak mixing Constrained by Z-pole precision observables Flavor-independent Ciq and Radiative Corrections Tree Level Radiative Corrections

  7. New atomic th’y JLab Future SLAC Moller Z0 pole tension Parity-violating electron scattering Scale-dependence of Weak Mixing Weak Mixing in the Standard Model Derevianko et al

  8. Vertex & External leg SUSY Radiative Corrections Propagator Box

  9. “Superpotential” : a convenient way to derive supersymmetric interactions by taking derivatives w.r.t. scalar fields Li, Qi SU(2)L doublets Ei, Ui, Di SU(2)L singlets R-Parity Violation (RPV) L=1 WRPV = ijk LiLjEk + ijk LiQjDk +/i LiHu + ijkUiDjDk B=1 proton decay: Set ijk =0 RPV: no  DM

  10. 12k 1j1 12k 1j1 L=1 L=1 Four-fermion Operators

  11. 1j1 1j1 SUSY RPV Effects

  12. e RPV Loops p Comparing AdDIS and Qwp,e

  13. 0nbb sensitivity l111/ ~ 0.06 for mSUSY ~ 1 TeV m->eg m->e LFV Probes of RPV: LFV Probes of RPV: l12k ~ 0.3 for mSUSY ~ 1 TeV & dQWe/ QWe ~ 5% lk31 ~ 0.03 for mSUSY ~ 1 TeV lk31 ~ 0.15 for mSUSY ~ 1 TeV Probing SUSY with PV eN Interactions

  14. 0nbb signal equivalent to degenerate hierarchy Loop contribution to mn of inverted hierarchy scale Lepton Flavor & Number Violation

  15. II. PV DIS & Higher Twist

  16. ~ 50% fluctuations about leading twist Alekhin NNLO MRST NNLO MRST NNLO with Barbieri Target Mass Corrections • Smooth transition from DIS (solid squares) to resonance region • Resonances oscillate about perturbative curves (quark-hadron duality in transverse channel) - all Q2 • Target mass corrections large and important Probing Higher Twist: Beyond the Parton Model 2xF1 Experimental Status Data from JLab E94-110 (nucl-ex/0410027, submitted to PRL) Courtesy C Keppel

  17. Where are theqq and qqg correlations ? n = 2 Cornwall-Norton Moments F2 F2, F1 in excellent agreement with NNLO + TM above Q2 = 2 GeV2 No (or canceling) higher twists Yet, dominated by large x and resonance region Remove known HT (a bit novel), the elastic, and there is no more down to Q2 = 0.5 GeV2 The case looks different for FL (data or curve?) 2xF1 FL

  18. twist 2 twist 4 Jaffe ‘97 Twist Expansion: OPE I Light cone expansion: x2 ~ 0 Momentum sum rules Twist = d(n) - j Power corr:

  19. twist 2 twist 4 Twist Expansion: OPE II Light cone expansion: x2 ~ 0 Momentum sum rules Twist = d(n) - j Power corr:

  20. Factorization Hard: S(k) Soft: (k) Taylor expand S(k) about k = xp 2. Insert 1 = 3. Power count in g: associate deriv in lower-order graph with gluon in next order graph 4. Write in co-ord space using 5. Convert to light cone transformation using Soft functions: Twist Expansion: EFP I Ellis, Furmanski, Petronzio

  21. Twist Expansion: EFP II 6. Apply gauge invariance (Ward identities) to get factorization formula 4 quark (double hand bag) not included here

  22. OPE & EFP Expand in powers of n& take moments: recover OPE expressions for moments in terms of forward matrix elements of local operators Expand Aetc in powers of p, n A0() pis LT term; all others are HT

  23. Sacco Thesis I Structure Functions: 2 quark contributions Analogous formulae for F EM-NC

  24. Sacco Thesis II Structure Functions: 4 quark contributions

  25. Sacco Thesis III Computation of Tj(x,y) and Uj(x,y,z) in MIT bag model: Compute moments & use inverse Mellin Transform LT: pdf

  26. Non singlet Singlet Singlet Twist Expansion: Q2 Evolution Twist two Singlet moments: 2 x 2 mixing only Twist four: correlations Operator mixing: basis size grows with n (for nth moment)

  27. DGLAP splitting function No known analog for twist four Need RGE & anom dim computation Anomalous dimension Twist Expansion : Q2 Evolution Equivalence to parton model: twist two

  28. Non singlet Singlet + … Singlet + … + … + … Flavor: isosinglet mixing + … Twist Expansion : Q2 Evolution Twist two Singlet moments: 2 x 2 mixing only Twist four: correlations Operator mixing: basis size grows with n (for nth moment)

  29. Looking beyond the parton description PV Deep Ineslastic eD (J Lab 12 GeV) Theoretical Challenges pQCD evolution of twist four moments Lattice QCD for t =4 matrix elements Organizing the program: what kinematics, complementarity with PC F1,2 , … ~0.4% Different PDF fits E=11 GeV q=12.50 Sacco, R-M preliminary Probing Higher Twist with PV

  30. Bjorken ‘78 Isospin decomposition: V = isovector S = isoscalar y-independent term: C1q Differences in VV and SS: C1q terms are “contaminated” only by 4q, double handbag = 4 effects

  31. ~ 50% fluctuations about leading twist Alekhin NNLO MRST NNLO MRST NNLO with Barbieri Target Mass Corrections • Smooth transition from DIS (solid squares) to resonance region • Resonances oscillate about perturbative curves (quark-hadron duality in transverse channel) - all Q2 • Target mass corrections large and important Probing Higher Twist: Beyond the Parton Model 2xF1 Experimental Status Data from JLab E94-110 (nucl-ex/0410027, submitted to PRL) Courtesy C Keppel

  32. Are twist 4 matrix elements suppressed or canceling? • Need C(Q2) to unpack matrix elements from data • Complementary probes (PV DIS) could provide new insight >> 10 % ?? Where are theqq and qqg correlations ? n = 2 Cornwall-Norton Moments F2 F2, F1 in excellent agreement with NNLO + TM above Q2 = 2 GeV2 No (or canceling) higher twists Yet, dominated by large x and resonance region Remove known HT (a bit novel), the elastic, and there is no more down to Q2 = 0.5 GeV2 The case looks different for FL (data or curve?) 2xF1 FL

  33. III. General remarks • PV DIS provides a comprehensive probe of QCD beyond the parton model & possible deviations from the SM EW sector • Looking beyond the parton model is a natural continuation of the JLab strange quark searches • Rich set of challenges for theory & experiment: higher twist, CSB in pdfs, d/u… • Important complement to 12 GeV Moller that would be a focused and powerful probe of EW SM & possible new physics

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