Scaling Study of the L-T Separated p(e,e’π+)n Cross Section at Large Q2 Tanja Horn Jefferson Lab APS/DNP meeting 2007 DNP07 October 2007.

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Scaling Study of the L-T Separated p(e,e’π+)n Cross Section at Large Q2 Tanja Horn Jefferson Lab APS/DNP meeting 2007 DNP07 October 2007

Partons and Factorization Deep Inelastic Scattering (DIS) can be factorized into short and long distance physics in the limit of large Q2 and at fixed values of xB Hard scattering can be calculated in perturbative QCD (pQCD) Soft physics is described by Parton Distribution Functions (PDFs) A similar factorization of scales is expected for hard exclusive processes – DVCS is simplest Generalized Parton Distributions (GPDs) are a generalization of PDFs, where initial and final quark-gluon momenta are not identical Unified concepts of quark parton density and elastic form factors Transverse spatial distribution of quarks Spin decomposition of the nucleon t x+ξ x-ξ “take out” “put back”

Hard-Soft Factorization To access physics contained in GPDs, one is limited to the kinematic regime where hard-soft factorization applies No single criterion for the applicability, but tests of necessary conditions can provide evidence that the Q2 scaling regime has been reached One of the most stringent tests of factorization is the Q2 dependence of the π electroproduction cross section σL scales to leading order as Q-6 σT scales as Q-8 As Q2 becomes large: σL >> σT Factorization Q2 ? Factorization theorems for meson electroproduction have been proven rigorously only for longitudinal photons

Q2 dependence of σL and σT Hall C data at 6 GeV: 3 different experiments The Q-6 QCD scaling law is consistent with the JLab σL data Limited Q2 coverage and large uncertainties make it difficult to draw a conclusion The two additional factorization predictions that σL>>σT and σT~Q-8 are not consistent with the data Testing the applicability of factorization requires larger kinematic coverage and improved precision Q2=2.7-3.9 GeV2 Q2=1.4-2.2 GeV2 σL σT Horn et al., arXiv:0707.1794 (2007)

Q2 Scaling of the Interference Terms Preliminary from Fpi1, Fpi2 Scaling prediction based on transverse content to the amplitude σLT ~ Q-7 σTT ~Q-8 Limited Q2 coverage complicates the interpretation Interference terms decrease in magnitude as Q2 increases Q2 range is small

Transverse Contributions Fpi2 L/T data at W=2.2 GeV VGL σL VGL σT Note: -tmin is different Even at Q2=2.45 GeV2, σT is not small But electroproduction is a multi-variable phase space At fixed W, tmin increases with Q2 and σL decreases more rapidly than σT Scaling tests need high precision separated cross sections at fixed xB and -t Horn et al., Phys. Rev. Lett. 97, 192001 (2006)

Fπ and Factorization Tests Fπ provides another test of the validity of QCD factorization If one replaces the GPD in the handbag mechanism by the Nπ vertex and the pion DA, one obtains Fπ The modified mechanism is also characterized by a single hard gluon exchange Naively expect a correlation between pQCD calculations of Fπ and experimental data where factorization applies Fπ scales to leading order as Q-2 Hard Scattering Hard Scattering

Fπ in 2007 T. Horn et al., Phys. Rev. Lett. 97 (2006) 192001. Q2>1 GeV2: Q2 dependence of Fπ is consistent with the power law behavior expected from the hard scattering mechanism (Q-2) But the monopole fit would provide an equally good description Fπ data still far from pQCD calculation Not in QCD factorization regime Or insufficient knowledge how to extend pQCD calculations to low Q2 AdS/CFT describes Q2-dependence, and provides a reasonable description of the magnitude Includes confinement and constituent quark counting rule behavior T. Horn et al., arXiv:0707.1794 (2007). A.P. Bakulev et al, Phys. Rev. D70 (2004)] H.J. Kwee and R.F. Lebed, arXiv:0708:4054 (2007) H.R.Grigoryan and A.V.Radyushkin, arXiv:0709.0500 (2007)

Scaling Test at 12 GeV Experiment approved for 42 days in Hall C SHMS E12-07-103 (T. Horn&G. Huber et al.) Measure the Q2 dependence of the p(e,e’π+)n cross section at fixed xB and –t to search for evidence of hard-soft factorization Separate the cross section components: L, T, LT, TT The highest Q2 for any L/T separation in π electroproduction Also determine the L/T ratio for π- production to test the possibility to determine σL without an explicit L/T separation SHMS HMS x Q2 (GeV2) W (GeV) -t (GeV/c)2 0.31 1.5-4.0 2.0-3.1 0.1 0.40 2.1-5.5 2.0-3.0 0.2 0.55 4.0-9.1 2.0-2.9 0.5

Projected Uncertainties for Q-n scaling QCD scaling predicts σL~Q-6 and σT~Q-8 Projected uncertainties for σL use an Fπ parameterization for L/T ratio Based on previous π+ L/T data Fit: 1/Qn xB dnL dnT dnLT dnTT 0.31 0.3 0.2 0.5 0.6 0.40 0.4 0.7 0.8 0.55 2.5 1.0 -

π- cross section – measure σL without explicit L/T? Fpi1 and Fpi2 saw σL/σT larger for π- than for π+ If σT is small, one may extract σL from the unseparated cross sections Scaling prediction for σT/σL is Q-2 Measure L/T from π- production to an absolute precision of 0.1-0.3 Uncertainties assume R= σL/σT for π+: π- is at least 1:2 (based on Fpi1 and Fpi2 results)

Fπ after the JLab Upgrade Experiment (E12-06-101) approved for 55 days in Hall C The 11 GeV electron beam and the SHMS in Hall C with θ=5.5º allows for Precision data up to Q2=6 GeV2 to study the transition to hard QCD

Summary The Q2-dependence of L/T separated π+ σL from Jefferson Lab is in relatively good agreement with the Q2-scaling prediction σT still significant at Q2=3.91 GeV2, and drops more slowly than the Q-8 scaling expectation The measured Q2-dependence of Fπ is also consistent with the Q2 scaling expected from the hard scattering mechanism, but pQCD calculations do not reproduce its magnitude L/T separated π+ cross sections will be essential for understanding the reaction mechanism at 12 GeV (E12-07-103) Relative contribution of σL and σT in π+ production - interpretation of asymmetry and ratios If transverse contributions are larger than anticipated, this may influence the accessible phase space for GPD studies π- data will check the possibility of measuring σL without explicit L/T separation

Regge Exchange Contribution Calculation by A.P. Szczepaniak et al. [arXiv:0707.1239v2] suggest significant scaling violations at small –t and independent of Q2 Expect Q2 behavior characteristic for hadronic Regge amplitudes σL,T ~ (Q-n) 2α(t)-1 x αL αT 0.31 0.46 ± 0.50 1.90 ± 0.36 0.45 0.92 ± 2.00 0.99 ± 0.51 HERMES π+ fit: α=0.31 ± 0.2 (0.26 < xB < 0.80), BUT not separated