Published on October 15, 2007
Experimental moments of the nucleon structure function F2: Experimental moments of the nucleon structure function F2 M. Osipenko, July 3, QCD 06, Montpellier , France CLAS Collaboration in collaboration with S. Simula, W. Melnitchouk and S. Kulagin Moments: Moments *Present technique of Lattice QCD can handle Non-Singlet operators only (noisy disconnected diagrams are cancelled there) necessary to measure moments of both the proton and neutron. QCD Structure Function Moments OPE evolution static Perturbative QCD Lattice QCD - anomalous dimension (NNLO) - coefficient functions (NNLO) n – operator spin - operator twist =dimension-spin - arbitrary scale R. Horsley, hep-lat/0412007 r0=0.5 fm observable calculable Twists: Twists Leading twist Higher twists suppressed in DIS by 1/Q Twist separation through Q2-evolution study of the moments in a large Q2 interval X. Ji and Unrau, PRD52 Higher Twists Leading Twist Higher Twists represent virtual photon scattering off interacting (correlated) partons: e.g. diquarks, entire nucleon etc. lower Q2 larger distance between currents * and are known only in few cases: LO Coefficient function Operator matrix element E.Shuryak and A.Vainstein, NPB201 H.Kawamura, MPLA12 asymptotic freedom Q2 Nobel prize 2004! Future Nobel prize? + F2 Experimental Data: F2 Experimental Data Continuous two-dimensional kinematics Wide x-coverage at each fixed Q2 Very detailed large-x region is taken from recent Hall-C experiment: C. Keppel E94-110 CLAS 2.5 GeV + 5.8 GeV JLab Hall C World CLAS 1.5 GeV + 2.5 GeV + 4 GeV proton deuteron F2 Deuteron vs. Proton: F2 Deuteron vs. Proton The measurement of the deuteron structure function was performed in the same bins as for proton F2. Resonance peaks seem to be smaller in the deuteron also at low Q2. But, mostly it is the effect of the Fermi motion. CLAS proton CLAS deuteron CLAS proton CLAS deuteron Q2=1.025 GeV2 Q2=3.025 GeV2 Extraction of moments: Extraction of moments CLAS data cover most significant region for higher moments (n>2) For deuteron we also measured quasi-elastic peak at each Q2 value Extraction method is essentially independent of x-behavior of the structure function Reliable evaluation of the Q2-evolution of structure function moments. proton deuteron In interpolation regions the function is locally normalized to the data. JLab Q2=0.825 GeV2 Moment Integrand Moments: Moments Leading Twist Q2-evolution is the same for the proton and deuteron Deuteron is weakly bound nucleus, the scale change is expected to be small Higher Twist contribution in the deuteron contains additional nuclear HT terms Proton and deuteron moments have similar Q2-behavior suggesting a small contribution of nuclear Higher Twists. proton proton deuteron deuteron D p JLab JLab (Gev/c)2 (Gev/c)2 Twist Expansion: Twist Expansion Leading and Higher Twists were separated by a fit to the data with the following expression: Leading Twist is determined by one free parameter Higher Twists contribution is described by four free parameters Only one HT term in M2 Need more than one HT term Fit Leading Twist Higher Twists Uncertainties: Uncertainties Modifying the number of Higher Twist terms: the total Higher Twist contribution does not depend on the arbitrary number of Higher Twist terms in the expansion. Changing pQCD order of the Leading Twist: Fixed pQCD order calculations are saturated (NLONNLO), but for high moments (n=8) Sudakov logarithms become important. Resummation techniques are crucial. 2 HT terms 3 HT terms 4 HT terms LO NLO NNLO Sudakov NLL Sln1/(1-x) *Our leading twist is calculated at NLO including soft gluon resummation (NLL). Sudakov LL Neutron Moments: Neutron Moments In the moment space, exploiting properties of Mellin transformation, one obtain: We based on the Impulse Approximation treating all effects beyond it as (small?) corrections: Nuclear structure function moments: Direct access to neutron moments: *Using Leading Twist moments and we remove bulk of effects beyond IA (e.g. FSI) before applying nuclear corrections. fD(z) Moments: Argon v18 fD(z) Moments Instant Form formalism (W. Melnitchouk) Relativistic wave function Bonn CD Paris Nijmegen RSC93 Gross Van Orden Light Cone formalism (S. Simula) Non-relativistic wave function We applied momentum cutoff: Moments were then rescaled to satisfy: nucleon 4-momentum Leading Twist u/d Ratio: Leading Twist u/d Ratio Extracted Higher Moments of the neutron can shed light on u/d ratio in the nucleon at x->1 at Leading Twist. Q2=100 GeV2 Gross w.f. Melnitchouk offshell. 1/4 3/7 2/3 CTEQ6 PDFs 1/4 3/7 Isospin dependence of HT: Isospin dependence of HT Assuming that nuclear effects beyond IA are small we can estimate isospin dependence of the Higher Twist contribution suggesting two possible scenarios: SU(2) flavor independent parton correlations Dominance of ud-correlations p p D/2 D/2 corrected for Fermi motion corrected for Fermi motion Lattice QCD: Lattice QCD At the scale Q2=4 GeV2 in MS renormalization scheme and NLO accuracy Non-singlet combination of moments can be related to lattice QCD simulations: Chiral loops in the expansion to physical pion mass are important for the first two moments (W. Detmold et al., PRL87) Role of chiral loops is expected to decrease at large n values (large-x region) Deviation of linearly extrapolated moments from the data is 3.3 s at n=2 but only 1.6 s at n=4 linear extrapolation chiral extrapolation Summary: Summary Proton and deuteron structure functions F2 were measured in continuous two-dimensional kinematical range of x and Q2; These data combined with all previous measurements were used to obtain experimental moments; Extracted moments were analyzed in terms of OPE; Combining two Leading Twist moments of the proton and deuteron and applying nuclear corrections we extracted neutron structure function moments; The ratio of the neutron to proton moments was studied and estimates of u/d ratio at x->1 were obtained; Higher Twist contributions to the proton and deuteron moments were compared and isospin independence of the multi-parton correlation was observed; Non-singlet moments were compared to Lattice QCD confirming quantitatively the disagreement with linearly extrapolated simulations.