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Simona Malace University of South Carolina

Applications of quark- hadron duality in F 2 structure function: constraints for p QCD fits at large x?. Simona Malace University of South Carolina. Overview. Standard pQCD fits and their limitations (example => CTEQ6).

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Simona Malace University of South Carolina

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  1. Applications of quark-hadron duality in F2 structure function: constraints for pQCD fits at large x? Simona Malace University of South Carolina

  2. Overview • Standard pQCD fits and their limitations (example => CTEQ6) • Another kind of QCD fits: extension of fits at larger x in the nonperturbative region • (example => Alekhin) • Can we go even further? • Quark-hadron duality: • => experimental observation & working hypothesis for PDFs extension at large x • => recent results from Jlab on quark-hadron duality in the F2p,d structure function • => Quark-hadron duality in F2n • Plans for future

  3. leading-twist The quark and gluon structure of the Proton in QCD Operator Product Expansion in pQCD: higher-twist Naive picture Complete picture (or closer to …) + + = ? perturbative ln(Q2) corrections nonperturbative corrections

  4. How does it compare to data? • Very good, where only the leading twist is expected to contribute • Most cases, parton distribution functions (PDFs) are extracted from data from “safe kinematic regions”, only (no nonperturbative effects) • What is the price to pay? • A: Unconstrained PDFs outside the “safe kinematic regions” Let’s see why….

  5. PDFs Extraction in pQCD • Two basic ideas of QCD: Factorization: separate the long-distance from short-distance dependence perturbative nonperturbative input (PDF) Evolution:knowledge of implies knowledge of ……………at all Q2 > (<) Q20, where a perturbative expansion is still appropriate => DGLAP equations splitting functions

  6. PDFs Extraction in pQCD: Recap • Three basic quantities needed for pQCD calculation of F2 : • To constrain the x dependence is evolved to all Q2 where data exist in the “safe kinematic regions” Computed perturbatively as power series in as Q2 evolution of PDF calculated via DGLAP equations • Examples of parameterizations for nonperturbative input: • Only requirements: flexible enough to accommodate small/large x behavior + obey the sum rules x dependence of PDF assumed and constrained by data CTEQ6: MSTW: Alekhin:

  7. Standard pQCD fits: PDFs from CTEQ6 JHEP 0207:012, 2002 • CTEQ6: pQCD fit to hard scattering and DIS data with • Q2 > 4 GeV2 and W2 > 12.25 GeV2; the x dependence of PDFs parameterized at Q2 = 1.3 GeV2; evolution up to NLO x < 0.7 Constraints from data W2 > 12.25 no constraints Q2 > 4

  8. CTEQ6: Comparison to Data c2 c2 /ndf = 1.1 /ndf = 1.52 • Good fit to data in the “safe kinematic regions” but beyond …

  9. CTEQ6: Large Uncertainties at Large x • Large uncertainties where there are no constraints from data • Large x region important for (see Alberto’s talk): • - study the mechanism of spin-flavor symmetry breaking in valence …..quark distributions • - determining high-energy cross sections at collider energies • - quantification of quark-hadron duality, etc. but what’s involved in extending PDFs validity to larger x?

  10. PDFs at Large x and low Q2 • Corrections beyond leading twist Higher-Twists: kinematic and dynamical Complete picture Kinematic HT – associated to twist-2 operator => no additional information on the quark dynamics Dynamical HT – contains information about the valence quarks dynamics (confinament) 2) Large-x resummation 3) Nuclear Corrections – for the neutron 4) … • Messy but needs to be done to achieve exhaustive knowledge of the dynamic of the nucleon!

  11. Example: PDFs from ALEKHIN Phys. Rev. D 68, 014002 (2003); JETP Lett. 82, 628 (2005) • Extension of PDF fits to larger x: kinematic cuts (W2,Q2,x,) are relaxed to provide more constraints from data ALEKHIN • Stepping out of the • “safe kinematic region” => inclusion of nonperturbative effects (TMC, HT) • (and nuclear effects for nuclear targets) CTEQ6 x < 0.75 Constraints from data W2 > 3.2 no constraints Q2 > 2.5 • The x dependence of PDFs parameterized at Q2 = 9 GeV2; evolution up to NNLO

  12. Uncertainties: Alekhin vs CTEQ6 • Result: smaller uncertainties at large x Reduction by ~ 10 of d uncertainty at large x Reduction by ~ 4 of u uncertainty at large x Relative experimental uncertainties of PDFs at a Q2 of 9 GeV2: full = Alekhin;dotted = CTEQ6 Phys. Rev. D 68, 014002 (2003)

  13. Dynamical Higher Twist • Interplay of Higher-Order QCD corrections and dynamical Higher Twists • Decrease of magnitude of HT with increase of pQCD order but HT don’t vanish in NNLO • From extrapolation: HT not expected to vanish in NNNLO either • HT contribution to F2: at most ~10% of Leading Twist (maximal at x~0.6 and Q2 = 5 GeV2) Phys. Rev. D 68, 014002 (2003)

  14. How about extending PDFs to even large x? Q2 = 2 GeV2 Q2 = 5 GeV2 • Extending to larger x at finite Q2 => encounter the resonance region • Resonances are basically “made” of higher twists • The contribution of higher-twist terms in the resonance region would be expected to be large… Or is it? 2nd resonance region at Q2 = 2 GeV2 2nd resonance region at Q2 = 5 GeV2

  15. Yes, but not on average Bloom-Gilman Duality • The resonance region data: • - oscillate around the scaling curve • - are on average equivalent to the scaling curve. • - “slide” along the deep inelastic curve with increasing Q2 “… resonances are not a separate entity but are an intrinsic part of the scaling behavior of nW2 …” • Quantitatively: comparing the lhs to the rhs, relative difference 10% for Q2=1 GeV2 to <2% for Q2=2 GeV2. Phys. Rev. Lett. 25, 1140 (1970)

  16. Duality in QCD • De Rujula, Georgi, Politzer: • “The most intriguing aspects of SLAC data on inclusive electroproduction are precocious scaling and local duality ” Q2 = 1 GeV2 nW2 Phys. Lett. B 64, 428 (1976) Operator product expansion: twist-2 Q2 = 3 GeV2 nW2 pQCD calculation of nW2 Q2 = 5 GeV2 data • On average, the resonance region data mimic the twist-2 pQCD calculation Mellin transform of twist-2 nW2 pQCD • Duality = higher-twists are either small or cancel on average (on average, the interactions between the valence quarks are suppressed)

  17. Quark-Hadron Duality in F2: Recent Experiments at JLab Jefferson Lab Electron-beam accelerator As of now, beam energies up to 6 GeV As of now, three experimental halls: A, B, C Two spectrometers: HMS & SOS

  18. Inclusive Resonance Region Measurements in Hall C Among other, three experiments: JLab-96, E94-110, E00-116 • 1996 JLab-96 (I. Niculescu): duality dedicated experiment; measures H(e,e’) & D(e,e’) cross sections • 1998 E94-110 (Y. Liang): performs Rosenbluth separation (measures R = sL/sT); measures H(e,e’) cross sections • 2003 E00-116 (S. Malace): duality dedicated experiment, push to larger x and Q2; measures H(e,e’) & D(e,e’) cross sections JLab-96 E94-110 E00-116 CTEQ6 ALEKHIN Kinematics covered: x between ~0.3 and 0.9, Q2 up to 7 GeV2, in the resonance region (mainly)

  19. Procedure for F2 extraction • Differential one-photon exchange (Born) cross section x, Q2, W2 Experimental natural variables: momentum and angle of scattered electron + energy of incoming electron crap • F2 extraction requires the knowledge of cross section and R crap crap E94-110: measured R JLab-96: used R from E94-110 E00-116: used R from R1998 (R < 0.2 @ E00-116 kinematics)

  20. Physics Results from JLab-96 • Verifying quark-hadron duality “a la Bloom-Gilman” NMC fit to DIS data at the same x but higher W2, Q2 than RES data • The new precision data display the signature oscillation around the DIS curve (the agreement, on average, better than 10%) • JLab-96 conclusively verifies the observations of Bloom and Gilman

  21. Physics Results from JLab-96 • Verifying quark-hadron duality in a pQCD framework: analysis in fixed W2 bins Averaged RES data pQCD(NLO) pQCD(NLO)+TMC large-x resummation: brings pQCD calculation in better agreement with data • TMC significant effect: pQCD calculation in better agreement with data • LxR: resummation on ln(1-z) in x space => Q2 scale replaced by Q2(1-z)/z • HT: in RES region similar to those for W2> 10, with exception of D

  22. Physics Results from E94-110 • More precise data from JLab: the resonances average to pQCD+TMC calculations from CTEQ and MRST • The resonance data slide with increasing Q2 to higher x always following the pQCD curves inegrals over entire RES region • The ratio of F2 integrals data to pQCD better than 5% at Q2 = 0.5 GeV2 but ~ 18% at Q2 = 3.5 GeV2 ?!? • Violation of duality, unconstrained PDFs at large x, something else ?

  23. Physics Results from E00-116 • Verify quark-hadron duality at higher Q2 DIS Large discrepancies in the description of F2 at large x 4th 3rd 2st 2nd 2st 1st Define: Calculate: Compare: Data from E00-116, E94-110, JLab-96 and SLAC; parametrizations from CTEQ6, MRST, ALEKHIN

  24. Physics Results from E00-116 Comparison: data [H(e,e’)] to CTEQ6M (NLO) + TM • I ~ 1 at Q2 ~ 1.5 GeV2 then rises with increasing Q2 and reaches a plateau at ~ 4 GeV2; above this value Q2 dependence saturates • This behavior displayed when integrating globally and locally except for first resonance. Not a failure of pQCD in describing the Q2 evolution but a paucity in the strength of PDFs at large x • I becomes constant at different value for each RES region Related to growing uncertainty of PDFs strength at large x Phys. Rev. C 80, 035207 2009

  25. Physics Results from E00-116 Comparison: data [H(e,e’)] to MRST04 (NNLO) + TM • The observed Q2 dependence of I yields similar conclusions as drawn from the CTEQ6 Differences: Not surprising: the extraction procedure (and kinematic cuts) of PDFs similar for MRST04 and CTEQ6 Possibly results from the difference in modeling the x dependence of PDFs (?) • MRST04 undershoots the data by an even larger amount and I saturates at a larger value of Q2 • than for CTEQ6 Phys. Rev. C 80, 035207 2009

  26. Physics Results from E00-116 Comparison: data [H(e,e’)] to ALEKHIN (NNLO) + HT + TM • Due to cuts employed for data selection, Alekhin’s fits far better constrained at large x • For the 4thRESregion and DIS, • I very close to 1 for entire Q2 range analyzed • Good agreement for 3rdand 2ndRESregions: I deviates from 1 by about 5% HT in RES region, on average, differ by at most 5% from those extracted by Alekhin • 1st resonance in disagreement with Alekhin’s fit: the validity of the fit questionable at these kinematics Phys. Rev. C 80, 035207 2009 • Averaged RES data could be used to constrain PDF fits

  27. Physics Results from E00-116 ALEKHIN • Good description at Q2= 3,5 GeV2 (except for largest x regime: 1st RES) • Q2= 7 GeV2 : probing the largest x regime (ALEKHIN least constrained) => growing discrepancy • Q2= 1 GeV2 : discrepancy as x grows  reached limits of applicability CTEQ6 • Fails to describe x dependence of data • Better data description by ALEKHIN than CTEQ6

  28. Physics Results from E00-116 Comparison: data [D(e,e’)] to CTEQ6 and ALEKHIN • F2d(ALEKHIN,CTEQ6) = F2p(ALEKHIN,CTEQ6) * d/p (from empirical fit) • The Q2 dependence of I: similar characteristics as in the study of H(e,e’) • ALEKHIN offers better description of averaged RES data than CTEQ6

  29. Is Quark-Hadron Duality Verified in the Proton? • Duality is an experimental observation and could be a working hypothesis for extending PDFs at large x => needs to be verified and quantified • It has been observed to work better 5% down to a Q2 as low as 1 GeV2 when compared to pQCD fits from MRST: E94-110 • Surprisingly, it has been observed that the violation of duality becomes more pronounced as x and Q2 increase • Our studies indicate that this increasing violation of duality with Q2is very likely only APPARENT: duality studies involve extrapolations of pQCD fits (unconstrained at large x) • The unconstrained PDFs at large x pose problems for quantifying how well duality holds in this kinematic regime • (and that’s not good)

  30. Extraction of the Neutron Structure Function F2n New method of extracting neutron SF from inclusive SFs of nuclei: employs iterative procedure of solving integral convolution equations (Phys. Rev. C 79, 035205 2009) • Impulse Approximation (IA) – virtual photon scatters incoherently from individual nucleons • Can write the nuclear structure functions as convolutions of nucleon structure functions smearing functions (can be calculated from nuclear wave function) • Beyond IA: nuclear shadowing, MEC, FSI, relativistic effects, off-shell corrections (most not addressed in present analysis) Present analysis does not attempt to provide a complete description of nuclear SFs (yet)

  31. Extraction of F2n • In the Weak Bound Approximation (WKA): the deuteron SF is sum of smeared proton and neutron SF and an additive term to account for modifications of SF off-shell • The effective smeared neutron SF: • Need to solve equation: Method assumed - Parameterize the nuclear corrections by an additive term D - F2n extracted using an iterative procedure which gives after first iteration • Study sensitivity of extraction to: number of iterations, first guess for neutron SF etc.

  32. Results from E00-116: Extraction of F2n Application of method to data (Phys. Rev. Lett., xx, to be submitted) • The resonances are obvious in the extracted F2n • After only two iterations F2d reconstructed from F2p data and extracted neutron F2n agrees well with the F2d data • The extracted F2n yields similar results after two iterations when different inputs are used [F2n(0) = F2p & F2n(0) = F2p/2] • Both F2p and F2n average to the QCD fit from Alekhin suggesting the onset of duality How well?

  33. Quark-Hadron Duality in F2n Compare integrals of neutron “data” to integrals of Alekhin’s newest fit (arXiv:0908.2766, August 2009) • Without HT: agreement at the level of 10-15% for Q2 < 3 GeV2 (except for D) • D covers the highest x regime (the fit least constrained) • The discrepancy increases with increasing Q2 (unconstrained PDFs at larger x?, …) … sounds familiar? • With HT: good agreement; deviation less than 10% in most cases

  34. Neutron/Proton vs Q2 & x • Good agreement between data and pQCD fits, except for D region which is somehow underestimated • The agreement slightly worsens as we go to larger Q2 and x

  35. Need more data at large x and “low” Q2? We can help … To be proposed at the next PAC in January 2010: Measurements at 11 GeV @ JLab • Extend RES region and low W2 DIS region measurements at even higher x and Q2 at JLab • Systematic study of quark-hadron duality; extraction of dynamical HT (interesting in their own right); additional constraints for PDFs at large x; extract the neutron SF at even larger x (and maybe constrain the d quarks distribution better) … CTEQ6 ALEKHIN

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