The transition from pqcd to npqcd

Transcription

1 The transition from pqcd to npqcd A. Fantoni (INFN - Frascati) First Workshop on Quark-Hadron Duality and the Transition to pqcd Laboratori Nazionali di Frascati, Italy June 6-8, 2005 Introduction Overview of Data Different approaches for duality and choice of the method Transition from pqcd to npqcd Studies of HT Conclusions & Outlook Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8, 2005

2 Introduction () High energy reaction: cross section factors into Long distance: measurable part Short distance: pert. calculable part /Λ QCD hadronic size Related to quarks and gluons distribution inside the nucleon: hadronic observables Low energy: confinement, npqcd /Q hadronic size Parton interaction negligible: asymptotically free quarks High energy: regime of perturbative QCD = Transition from soft to hard QCD Themechanismoftransformationofpartonintohadron(andviceversa)modifies the final state: partons get transformed but not the cross section Hadronic cross sections (averaged over appropriate energy range) Partonic cross sections (from perturbative quark-gluon theory) Σ hadrons = Σ quarks+gluons Complementarity between Parton and Hadron description of observables Relation to nature and transition from non-perturbative to pqcd Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

3 Introduction (2) Present in Nature in different aspects: e + -e hadrons q (e+ e q q) σ hadrons q ˆσ q ep ex dσ q dx q(x, Q 2 )dˆσ q ep ehx dσ q dx q(x, Q 2 )D h (z,q 2 )dˆσ q e p e X ea ex τ ν+ hadrons semi-leptonic decay of heavy quarks γp π + + n Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

4 Data () γp π + n ea ex ρ τ ν +hadrons M. Shifman, hep-th/ Aleph data Pert. theory Instanton model Resonance model s 7 dσ/dt 0 7 (nb/gev 2 )/GeV 4 L.Y. Zhu et al., PRL 9 (2003) , L.Y. Zhu et al., PRC 7 (2005) JLab old data 4 J. Arrington et al. (submitted) s, GeV s /2 (MeV) Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

5 Data (2) e + -e hadrons ep ex I. Niculescu et al., PRL 85 (2000) 82, I. Niculescu et al., PRL 85 (2000) Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

6 Data (3) e p e X A. Airapetian et al., PRL 90 (2003) e p e X e p e X Preliminary Eg data A.4.2 res A HERMES DIS A HERMES A DIS E43 R. Fatemi et al., PRL 9 (2003) DIS A SMC A DIS E SU(6) x <A res /A DIS >=. ± 0.6 ± 0.8 for Q 2 >.6 GeV 2 Strong violation of duality for Q 2 <. GeV 2 Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

7 Remarks and Questions Breakdown of Duality at sufficiently low Q 2 :. Which value of Q 2? 2. Same value for unpolarised and polarised structure functions? Duality expected to be isospin dependent:. p behavior 2. n behavior Close & Isgur, PL B509 (200) 8; Isgur et al., PRD 64 (200) Global duality = average over large W 2 range (whole resonance region) Local duality = average over small W 2 range (single resonances) Important: passage from qualitatively to quantitatively picture Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

8 Kinematical variables Ratio.3.2 x w /x (Q 2 =20 GeV 2 ) ξ/x (Q 2 =20 GeV 2 ) x /x (Q 2 =20 GeV 2 ) x =/ω ω =/x + M 2 /Q 2 B.G.. ξ =2x/( + ( + 4x 2 M 2 /Q 2 ) /2 ) x w = Q 2 + B/(Q 2 + W 2 M 2 + A) Jlab B.Y x w /x (Q 2 = 2 GeV 2 ) ξ/x (Q 2 = 2 GeV 2 ) x /x (Q 2 = 2 GeV 2 ) x x, ξ rescale S.F. to lower x with Q 2 dep. Rescaling larger at lower Q 2 Use of x to avoid ambiguities associated to usage other variables Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

9 3 approaches () a) Mellin moments: M n (Q 2 )= 0 dxx n 2 F 2 (x, Q 2 ) elastic contribution should be included elastic contribution dominant for Q 2 GeV 2 need of experimental values of SF outside resonance region b) Point by point comparison: SF vs Q 2 at specific x values elastic contribution excluded by kinematic ok for unpolarised SF because lot of data, NOT ok for polarised SF c) Comparison between SF integrals in RES & DIS regions, in the same x interval elastic contribution excluded by kinematic Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

10 3 approaches (2) a) Mellin moments b) Point by point comparison S. Liuti et. al, PRL 89 (2002) 6200 I n, M n 0 - M n I n 0-2 F 2 p(x,q 2 ) Q 2 (GeV 2 ) Q 2 (GeV 2 ) Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

11 3approches(3) c) Comparison between SF integrals in RES & DIS regions, in the same x interval I res (Q 2 )= I DIS (Q 2 )= xm x m xm x m F Res 2 (x, Q 2 ) dx F DIS 2 (x, Q 2 ) dx Γ res (Q 2 )= Γ DIS (Q 2 )= xm x m xm x m g = A (x M x m ) W 2 m W 2 M 4GeV2 Q 2 g Res (x, Q 2 ) dx g DIS (x, Q 2 ) dx F 2 2x(+R) R = I Res /I DIS = = Duality fulfilled = R = Γ Res / Γ DIS = Resonance region can be described in terms of quark degrees of freedom Distinction between resonance & DIS region is somehow artificial = Duality provides access to large x where DIS data suffer for low statistic Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8, 2005

12 Transition from pqcd to npqcd Problem of continuation of the pqcd curve into the resonance region Theoretically based on the idea that partonic d.o.f are dominant in the RES region Starting point: NLO PDF for the unpolarised structure function F 2 Practically - even under this assumption - corrections to the NLO analysis arise from: Target Mass Corrections (TMC) O(/Q 2 ) Large x Resummation effects (LxR) Leading Twist NNLO Leading Twist Dynamical Higher Twist (HT) O(/Q 2 ) For the neutron: nuclear effects Leading Twist Anything else beyond twist expansion Corrections have to be applied consistently to ALL observables to guarantee universality Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

13 F DIS 2 from PDF (LO & NLO) / I LT LT res R = I unpol LT ~ R = Γ res / Γ ~ LT pol 0 - PDF uncertainty 0 - PDF uncertainty Exp. uncertainty Exp. uncertainty 0 Q 2 [GeV 2 ] 0 Q 2 [GeV 2 ] PDFs: MRST99, CTEQ5, GRV94 (LO & NLO), GRV98 (LO & NLO) Quark-Hadron Duality NOT fulfilled by PDFs at LO or NLO NLO PDF unable to reproduce large x region Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

14 F DIS 2 from Phenomenological Parameterisations / I DIS DIS res R = I unpol DIS ~ R = Γ res / Γ ~ DIS pol 0 - Phen. Param. uncertainty 0 - Phen. Param. uncertainty Experimental uncertainty Experimental uncertainty 0 Q 2 [GeV 2 ] 0 Q 2 [GeV 2 ] Phen. Parameterisations: ALLM97, NMC95, BY (GRV94mod) Obtained by fitting DIS data even at low Q 2 = implicitely include non-perturbative effects Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

15 Non-perturbative Contributions Starting point: NLO PDF at Q 2 = Q 2 0 Evaluation of Target Mass Correction Evaluation of Large x Resummation Quantitative analysis: Disentangle Non Perturbative Contributions Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

16 Target Mass Corrections (TMC) F 2 (x, Q 2 )=F LT 2 (x, Q 2 )+ H(x,Q2 ) Q 2 + O(/Q 4 ) F LT,TMC 2 (x, Q 2 )= x2 F ξ 2 γ 3 2 (ξ,q 2 )+6 x3 M 2 Q 2 γ 4 ξ dξ ξ 2F 2 (ξ,q 2 ) F 2 =F 2 without TMC Limit of validity: x 2 M 2 /Q 2 < Applied in a similar way to g = A F 2 2x(+R) Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

17 Large x Resummation () First observed by Brodsky and Lepage, SLAC-REP224 (979) Recently reconsidered by:. R.G. Roberts Eur. Phys. Journal C 0 (999) S. Liuti et al. PRL 89 (2002) N. Bianchi, AF, S. Liuti PRD 69 (2004) Scattering from off-shell quark: k 2 μ = x [ M 2 k2 +M 2 X x k2 x ] m 2 Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

18 Consequence: Large x Resummation (2) 0 2 Phase space for the parton s k T limited by kt 2 (MAX) = Q2 ( z)/z instead of kt 2 (MAX) Q2 k T 2 MAX (GeV 2 ) z LxR terms arise from terms containing power of ln(-z) termsinc NS (z) F2 NS (x, Q 2 )= α s 2π q x dz C NS(z) q NS (x/z, Q 2 ) - z longitudinal variable in evolution equations; C(z) Wilson coefficient functions - only valence quark distributions relevant in this kinematic F NS 2 x C NS Q 2 Q 2 ( z)/z and α S (Q 2 ) α S (Q 2 ( z)/z) Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

19 Size of Non-perturbative Contributions R LT unpol = I res / I LT R LT pol = Γ res / Γ LT 0 - Data/NLO Data/NLO+TMC Data/NLO+TMC+LxR 0 - Data/NLO Data/NLO+TMC Data/NLO+TMC+LxR 0 Q 2 [GeV 2 ] 0 Q 2 [GeV 2 ] Effects of Target Mass Correction (TMC) and Large x Resummation (LxR) Duality seems satisfied within 0% for Q 2.5 GeV 2 Investigation of this 0% effect Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

20 Polarised case and data from Jlab LT ~ R = Γ res / Γ ~ LT pol LT ~ R = Γ res / Γ ~ LT pol 0 - Data/NLO Data/NLO+TMC Data/NLO+TMC+LxR 0 - HERMES, SLAC Fatemi 03 R from Jlab 0 Q 2 [GeV 2 ] 0 Q 2 [GeV 2 ] R. Fatemi et al., PRL 9 (2003) E940-data supplied by V. Tvaskis Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

21 x dependence of HT R LT unpol = I res / I LT NLO NLO+TMC NLO+TMC+LxR Alekhin (TMC) R pol LT = Γ ~ res / Γ ~ LT NLO NLO+TMC NLO+TMC+LxR x x NLO + TMC + LxR analysis very small HT in whole x region Extracted values consistent with different method & more precise Different behaviour for HT at low Q 2 Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

22 HT contributions H(x, Q 2 ) = Q 2 (F res 2 (x, Q 2 ) F LT 2 ); C HT = H(x,Q2 ) F pqcd 2 Q 2 F res 2 (x,q 2 ) F2 LT F LT 2 I res / I LT Fixed W 2 analysis Botje (no TMC) BCDMS (no TMC) Alekhin (TMC) R pol LT = Γ ~ res / Γ ~ LT Unpolarised Polarised NLO NLO+TMC+LxR Comparison of HT from RES and from DIS (old analyses) at same x values x Low Q 2 :HT pol large and negative x Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

23 HT contribution C(x) 2 BFL (2004) W 2 < 4 GeV 2 H(x) MRST (2004) DIS 0.2 BFL (2004) W 2 < 4 GeV 2 LSS (2003) DIS ) LT +HT F2 = F2 LT (+ CQ 2 high x: C res (x) C DIS (x) x LT +HT F2 = F2 LT + H Q 2 high x: fewh res (x), noh DIS (x) C(x) =H(x)/F LT 2 No Q 2 dependence in C(x) and H(x) Different behavior for unpolarised and polarised HT x Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

24 Conclusions Quantitative analysis of Unpolarised and Polarised data compared with: - pqcd analyses using global PDF (GRV94, GRV98, CTEQ5, MRST99) - phenomenological fits with non-perturbative contributions (ALLM97, NMC95, BY (GRV94mod)) Non perturbative contributions, TMC and LxR disentangled Duality seems satisfied within 0% Extraction of HT:. Polarised Unpolarised 2. RES DIS Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

25 Open questions: Outlook. Are we unraveling new degrees of freedom more pertinent to the scale of the hadronization phase? 2. Do we understand the Q 2 dependence in terms of a standard pqcd based scheme? 3. Are we witnessing a breakdown on factorization? 4. How are the smooth curves compared to the data? What are the best statistical estimators to be used? Many data from different reactions on proton, neutron, GDH, nuclei, semiinclusive, photoproduction... are available More e + e, τ decays...to be explored Many new results and approaches seen in this workshop Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,

26 LT ~ R = Γ res / Γ ~ LT pol 0 - g GRSV (2000) g BB (2002) PDF uncertainty Exp. uncertainty 0 Q 2 [GeV 2 ] Alessandra Fantoni Frascati, First Workshop on Quark-Hadron Duality and the Transition to pqcd, June 6-8,