PVDIS and nucleon structure

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1 Physics Beyond the SM and Precision Nucleon Structure with PVES ECT* Trento, August, 06 PVDIS and nucleon structure Wally Melnitchouk

2 PVDIS (~en! ex) is a valuable tool to study flavor and spin dependence of nucleon PDFs establish accurate baseline from which to eplore BSM physics s corrections (NLO) target mass corrections higher twists Outline PVDIS at lower Q and W (e.g. resonance region) provides vital input for estimates of Z interference corrections (e.g. for Qweak) Etraction of PDF information requires various subleading, finite-q corrections to be understood, L/ T C. Seng talk ratio P. Blunden, M. Gorshteyn talks

3 PVDIS at leading twist

4 Asymmetry between left- and right-handed inclusive electron-nucleon cross sections A PV = R L R + L for Q M Z numerator sensitive to Z interference only e (k) e (k ) γ (q ) Z (q ) N (p) N (p ) Q = (q + q ) denominator dominated by electromagnetic component

5 In terms of structure functions, A PV = GF Q 4 p g e F Z A Y F + g e V Y 3 F Z 3 F! Y,3 parameterize dependence on y = /E Y = +( y) y ( r /( + R Z )) ym/e +R Z +( y) y ( r /( + R )) ym/e +R ( y) r Y 3 = +( y) y ( r /( + R )) ym/e +R with r =+ Q =+4 M Q R ( Z) = ( Z) L ( Z) T = r F ( Z) F ( Z)

6 Leading twist electroweak structure functions (at leading order in ) s electromagnetic F =F () = X q e q q()+ q() V V interference F Z =F Z () = X q e q g q V q()+ q() V V F Z 3 = X q e q g q A q() q() V A g u V = 4 3 sin W ga u = = gd,s A g d,s V = + 3 sin W

7 Leading twist electroweak structure functions F p = 4 9 (u +ū)+ 9 (d + d + s + s)+ F n = 4 9 (d + d)+ (u +ū + s + s)+ 9 F Z,p = sin W (u +ū)+ 6 9 sin W (d + d + s + s)+ F Z,n = 9 (u +ū + d + d + s + s) sin W (d + d)+ 6 9 (d + d + u +ū + s + s)+ for sin W /4 9 sin W (u +ū + s + s)+ for sin W /4 strange quark sensitivity enhanced relative to e.m. case

8 Leading twist electroweak structure functions F p = 4 9 (u +ū)+ 9 (d + d + s + s)+ F n = 4 9 (d + d)+ (u +ū + s + s)+ 9 F Z,p = sin W (u +ū)+ 6 9 sin W (d + d + s + s)+ F Z,n = 9 (u +ū + d + d + s + s) sin W (d + d)+ 6 9 (d + d + u +ū + s + s)+ for sin W /4 9 sin W (u +ū + s + s)+ for sin W /4 F Z,p 3 = 3 (u ū)+ 3 (d d + s s)+ F Z,n 3 = 3 (d d)+ (u ū + s s)+ 3 sensitivity to strange-antistrange asymmetry

9 PV asymmetry in terms of PDFs A PV = GF Q 4 p (Y a + Y 3 a 3 ) (hadronic) vector term (hadronic) aial-vector term a = P q e qc q (q + q) P q e q(q + q) a 3 = P q e qc q (q P q e q(q + q) q) C q =g e A g q V C q =g e V g q A simplified y dependence Y! Y 3! ( y) +( y)

10 At large proton asymmetry sensitive to d/u ratio a = C u 6C d d/u 4+d/u a 3 = C u 6C d d/u 4+d/u d/u DIS only + BONuS + ` asym (& Z rap) + W asym CJ Accardi, Brady, WM, Owens, Sato PRD 93, 407 (06) ~% error on d/u epected in SoLID up to ~ 0.7 (note: different PDF uncertainty definitions in different analyses!!)

11 At large proton asymmetry sensitive to d/u ratio a = C u 6C d d/u 4+d/u a 3 = C u 6C d d/u 4+d/u d/u CJ5 DIS only + BONuS + ` asym (& Z rap) + W asym A` AW CJ5 CDF e DØ e DØ µ ` CJ5 CDF DØ y W error reduced by recent W asymmetry data - but rely on reconstruction from W! ` decays

12 At smaller, have order of magnitude greater sensitivity of F Z,p to strange-quark PDF than of e.m. F p ū/ū CJ Q = 0 GeV u/u CJ CJ5 90%CL CJ5 68%CL MMHT4 HERAPDF.5 NNPDF d/d CJ s/s CJ (s+s - )//d ū/ū 0.4 CJ CMS µ =.9 GeV, n f =3 ATLAS NuTeV/CCFR + NOMAD + CHORUS CHORUS + CMS + ATLAS Alekhin et al, PRD 9, (05) d/ d CJ Accardi et al, PRD 93, 407 (06) currently relatively large uncertainties on s() at intermediate - most information obtained from charm production in neutrino-nucleus DIS

13 Deuteron target - dependence on PDFs cancels at high Q a = 6 5 (C u C d ) a 3 = 6 5 (C u C d ) PV asymmetry independent of hadronic structure A PV = 3GF Q 0 p Y (C u C d)+y 3 (C u C d) sensitivity to electroweak couplings alternatively, could probe charge symmetry violation (CSV) in PDFs I. Cloet talk

14 Historically, PVDIS was first measured at SLAC (on deuterium) at Q ~ GeV and W ~ 3 GeV y Prescott et al, PLB 77, 347 (978) important for testing SM, but not for PDF determination

15 More recently, PVDIS measured more precisely at Jefferson Lab E08-0 at lower W (GeV A pv (ppm) / Q ) Data I Data II Data III Data IV E b =4.867GeV Theory A Theory B Theory C DIS(CJ) E b =6.067GeV W(GeV) Wang et al, PRL, 0850 (03) indication of quark-hadron duality in in the nucleon resonance region Z structure functions

16 Z structure functions measured at HERA at very high Q & W γz F H Collaboration Transformed to Q = 500 GeV H HPDF 0 γz F H Collaboration Transformed to Q = 500 GeV H HPDF HERA II H Collaboration, JHEP 09 (0) 6 HERA I+II essentially no proton PVDIS data at lower Q

17 Finite-Q corrections

18 Contribution from aial-vector term R Z = R 0.8 Y ± 0% Y,3 0.6 Y 3 R =0,r = 0.4 Q =5GeV full Hobbs, WM, PRD 77, 403 (008) Bjorken limit hadronic aial-vector term relatively more important at finite Q

19 Sensitivity to R = L / T and R Z = Z L / Z T * * Q =5GeV relative change to Bjorken limit asymmetry uncertainty due to R smaller than d/u error* at high need estimate for R Z to determine impact on asymmetry uncertainty * assuming d/u! 0 or 0. at = ; uncertainty smaller with new W asymmetry data

20 What could break R Z = R? higher order pqcd corrections R ( Z) =0 at leading order (perturbatively); at NLO different /Z couplings induce R 6= R Z target mass corrections ( kinematical /Q corrections) since TMCs for F L and F T are different, differences in ratios will be different with & without TMC (depend on treatment of struck parton - off-shell, collinear,...) dynamical higher twist /Q corrections from multi-parton correlations nuclear effects in deuteron

21 Target mass corrections operator product epansion (Georgi, Politzer) PRD 4, 89 (976) standard approach, uses inverse Mellin transform; threshold problem at = collinear factorization (Ellis, Furmanski, Petronzio) diagrammatic approach, impose < by definition; include parton virtuality & k T ; to O(/Q ) only NP B, 9 (983) collinear factorization (Accardi, Qiu) similar to EFP, but include only -leg (cf. 4-leg) diagrams; allow for jet-mass corrections, NLO effects JHEP 07, 090 (008) -scaling (Aivazis et al., Kretzer-Reno) similar to AQ, but at leading order PRD 69, (004)

22 Target mass corrections F γ / F γ (0).6. OPE EFP ξ-s AQ Q =GeV F γ / F γ OPE EFP ξ-s AQ effects large at high (and low Q ) up to ~0% model dependence in structure functions

23 Target mass corrections R γz / R γ no TMC OPE EFP ξ-s AQ proton Q = GeV Q = 0 GeV less than ~ 4% TMC and NLO effects cf. R reduced to ~ % at Q =0 GeV

24 Target mass corrections R γz / R γ Q = GeV deuteron no TMC OPE EFP ξ-s AQ R d γz / RN γz no TMC OPE EFP ξ-s AQ differences between R & R Z small at high significant nuclear effect in R Z ratio - reduced with inclusion of TMCs

25 QCD /Q Dynamical higher twists corrections from multi-parton correlations for deuterium, only one twist-4 (four-quark) operator ū(z) µ u(z) d(0) d(0) + (u $ d) MIT bag model estimate of matri elements etension to dependence Bjorken, PRD 8, 339 (978) Wolfenstein, NP B46, 477 (978) Castorina, Mulders, PRD 3, 760 (985) Mantry, Ramsey-Musolf, Sacco, PRC 8, (00) estimate using multi-parton light-cone wavefunctions Belitsky, Manashov, Schaefer, PRD 84, 0400 (0) matri elements sensitive to OAM in initial state C.-Y. Seng talk Seng, Ramsey-Musolf, PRC 88, 050 (03) Alternatively, estimate HT contribution phenomenologically

26 Dynamical higher twists In global QCD analyses parametrize structure function as F (, Q )=F (LT) (, Q ) + C HT() Q CHT (GeV ) Accardi et al. PRD 93, 407 (06) AV8 CD-Bonn WJC WJC LO NLO C HT = h 0 h ( + h ) cannot accommodate Q dependence of data without power corrections crucial for etracting correct PDFs at high can do the same with PVDIS data, especially with sufficient Q coverage - isolate isospin dependence of higher twists vs.!

27 Polarized PVDIS

28 PVDIS from a polarized target 3 LOI to JLab PAC44 for PVDIS from polarized He Just as with sensitivity to s in F Z, the spin-dependent structure function has enhanced sensitivity to s g Z,p = g Z X e q g q V ( q + q) 9 ( u + ū + d + d + s + s)+ q g Z,n significant uncertainty eists for s(), even in sign! most PDF analyses assume flavor SU(3) symmetry for hyperon decay constants JAM5 JAM3 DSSV09 NNPDF4 BB0 AAC09 LSS d u s + g polarized PVDIS would be first ever test of SU(3) in DIS Nobuo Sato et al, PRD 93, (06) Jefferson Lab Angular Momentum (JAM) Collaboration

29 Summary PVDIS offers unique window on nucleon structure, with unambiguous flavor separation (u, d and s) Corrections to leading-twist PVDIS from finite Q effects identified and quantified PVDIS data (unpolarized and polarized) can be included in global QCD analyses (CJ, JAM) that are continuously being improved and developed