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Access to the Parton Model through Unpolarized Semi-Inclusive Pion Electroproduction

Access to the Parton Model through Unpolarized Semi-Inclusive Pion Electroproduction. E00-108 experiment in Hall C, 10 (!) days of beam time PAC-30 Proposal E12-06-104, approved for 40 days with A- per PAC-36 PAC-34 Proposal PR12-09-017, conditionally approved

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Access to the Parton Model through Unpolarized Semi-Inclusive Pion Electroproduction

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  1. Access to the Parton Model through Unpolarized Semi-Inclusive Pion Electroproduction E00-108 experiment in Hall C, 10 (!) days of beam time PAC-30 Proposal E12-06-104, approved for 40 days with A- per PAC-36 PAC-34 Proposal PR12-09-017, conditionally approved Rolf Ent, Hall C Summer Workshop, August 27, 2010 • Semi-Inclusive Deep Inelastic Scattering & the Parton Model • E00-108 Results: The Onset of the Parton Model • General Pion Electro-production Formalism • - Bridging the Formalism and the High-Energy “Factorized” Viewpoint • 12 GeV Examples: R in SIDIS & transverse momentum dependence

  2. SIDIS – Flavor Decomposition DIS probes only the sum of quarks and anti-quarks  requires assumptions on the role of sea quarks Solution: Detect a final state hadron in addition to scattered electron SIDIS  Can ‘tag’ the flavor of the struck quark by measuring the hadrons produced: ‘flavor tagging’ (M,0) (e,e’) Mx2 = W2 = M2 + Q2 (1/x – 1) (For Mm small, pm collinear with g, and Q2/n2 << 1) (e,e’m) Mx2 = W’2 = M2 + Q2 (1/x – 1)(1 - z) z z = Em/n Mx2 = W’2

  3. SIDIS – Flavor Decomposition DIS probes only the sum of quarks and anti-quarks  requires assumptions on the role of sea quarks Solution: Detect a final state hadron in addition to scattered electron SIDIS  Can ‘tag’ the flavor of the struck quark by measuring the hadrons produced: ‘flavor tagging’ Measure inclusive (e,e’) at same time as (e,e’h) • Leading-Order (LO) QCD • after integration over pT • and f • NLO: gluon radiation mixes • x and z dependences : parton distribution function : fragmentation function

  4. How Can We Verify Factorization? • Neglect sea quarks and assume no pt dependence to parton distribution functions • Fragmentation function dependence drops out in Leading Order [sp(p+) + sp(p-)]/[sd(p+) + sd(p-)] = [4u(x) + d(x)]/[5(u(x) + d(x))] ~ sp/sd independent of z and pt [sp(p+) - sp(p-)]/[sd(p+) - sd(p-)] = [4u(x) - d(x)]/[3(u(x) + d(x))] independent of z and pt, but more sensitive to assumptions

  5. E00-108: Onset of the Parton Model GRV & CTEQ, @ LO or NLO Good description for p and d targets for 0.4 < z < 0.65 (Note: z = 0.65 ~ Mx2 = 2.5 GeV2) Closed (open) symbols reflect data after (before) events from coherent r production are subtracted

  6. p quark E00-108: Onset of the Parton Model Collinear Fragmentation Seq2q(x) Dqp(z) (Deuterium data) factorization (Resonances cancel (in SU(6)) in D-/D+ ratio extracted from deuterium data)

  7. E00-108: Onset of the Parton Model Solid (open) symbols are after (before) subtraction of diffractive r events Solid curve is a naïve parton model calculation assuming CTEQ5M parton distribution functions at NLO and BKK fragmentation functions Overall, one finds good agreement, but there are detailed differences in the cross section measurements (also for the deuterium target) x = 0.4 x = 0.4

  8. E00-108: Onset of the Parton Model Solid (open) symbols are after (before) subtraction of diffractive r events. Blue symbols are old Cornell measurements. Solid curve is a naïve parton model calculation assuming CTEQ5M parton distribution functions at NLO and BKK fragmentation functions Agreement with the naïve parton model expectation is always far better for ratios, also for D/H, Al/D, or ratios versus z or Q2.

  9. SIDIS Formalism General formalism for (e,e’h) coincidence reaction w. polarized beam: [A. Bacchetta et al., JHEP 0702 (2007) 093] (Y = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction) If beam is unpolarized, and the (e,e’h) measurements are fully integrated over f, only the FUU,T and FUU,L responses, or the usual transverse (sT) and longitudinal (sL) cross section pieces, survive.

  10. R = sL/sTin DIS • RDIS is in the naïve parton model related to the parton’s • transverse momentum: R = 4(M2x2 + <kT2>)/(Q2 + 2<kT2>). • RDIS 0 at Q2  ∞ is a consequence of scattering • from free spin-½ constituents • Of course, beyond this, at finite Q2, RDIS sensitive to • gluon and higher-twist effects • No distinction made up to now between diffractive and • non-diffractive contributions in RDIS • RDISH = RDISD, to very good approximation (experimentally) • - from formal point of view they should differ! (u not equal to d at large x + evolution in Q2,H = spin-1/2 and D = spin-1, at low Q2)

  11. p quark R = sL/sTin (e,e’p) SIDIS Knowledge on R = sL/sT in SIDIS is essentially non-existing! • If integrated over z (and pT, f, hadrons), RSIDIS = RDIS • RSIDIS may vary with z • At large z, there are known contributions from exclusive • and diffractive channels: e.g., pions from D and r p+p- • RSIDIS may vary with transverse momentum pT • Is RSIDISp+ = RSIDISp- ? Is RSIDISH = RSIDISD ? • Is RSIDISK+ = RSIDISp+ ? Is RSIDISK+ = RSIDISK- ? We measure kaons too! (with about 10% of pion statistics) • RSIDIS = RDIS test of dominance of quark fragmentation “A skeleton in our closet” Seq2q(x) Dqp(z)

  12. R = sL/sT in SIDIS (ep  e’pX) Cornell data of 70’s Conclusion: “data both consistent with R = 0 and R = RDIS” RDIS Some hint of large R at large z in Cornell data? RDIS (Q2 = 2 GeV2)

  13. p quark So what about R = sL/sT for pion electroproduction? “Deep exclusive scattering” is the z  1 limit of this “semi-inclusive DIS” process “Semi-inclusive DIS” Seq2q(x) Dqp(z) Here, R = sL/sT ~ Q2(at fixed x) RSIDIS RDIS disappears with Q2! Planned scans in z at Q2 = 2.0 (x = 0.2) and 4.0 GeV2 (x = 0.4)  should settle the behavior of sL/sT for large z. Not including a comparable systematic uncertainty: ~1.6% Example of 12-GeV projected data assuming RSIDIS = RDIS Planned data cover range Q2 = 1.5 – 5.0 GeV2, with data for both H and D at Q2 = 2 GeV2 Have no idea at all how R will behave at large pT Planned data cover range in PT up to ~ 1 GeV. The coverage in f is excellent (o.k.) up to PT = 0.2 (0.4) GeV.

  14. Transverse Momentum Dependence of Semi-Inclusive Pion Production • Not much is known about the orbital motion of partons • Significant net orbital angular momentum of valence quarks implies significant transverse momentum of quarks Final transverse momentum of the detected pion Pt arises from convolution of the struck quark transverse momentum kt with the transverse momentum generated during the fragmentation pt. Pt= pt +zkt+ O(kt2/Q2) z = Ep/n pT ~ L < 0.5 GeV optimal for studies as theoretical framework for Semi-Inclusive Deep Inelastic Scattering has been well developed at small transverse momentum [A. Bacchetta et al., JHEP 0702 (2007) 093].

  15. m p X TMD Transverse momentum dependence of SIDIS Linked to framework of Transverse Momentum Dependent Parton Distributions s Unpolarized target Longitudinally pol. target TMDq(x,kT) Transversely pol. target Unpolarized kT-dependent SIDIS: in framework of Anselmino et al. described in terms of convolution of quark distributions q and (one or more) fragmentation functions D, each with own characteristic (Gaussian) width  Emerging new area of study I. Integrated over pT and f Hall C: PRL 98:022001 (2007) Hall B: arXiv:0809.1153 II. PT and f dependence Possibility to constrain kT dependence of up and down quarks separately by combination of p+ and p- final states, proton and deuteron targets Hall B: arXiv:0809.1153 Hall C: PL B665 (2008) 20 III. Transverse polarized target: E06-010 transversity experiment in Hall A

  16. Transverse momentum dependence of SIDIS General formalism for (e,e’h) coincidence reaction w. polarized beam: [A. Bacchetta et al., JHEP 0702 (2007) 093] (Y = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction) Azimuthal fh dependence crucial to separate out kinematic effects (Cahn effect) from twist-2 correlations and higher twist effects. data fit on EMC (1987) and Fermilab (1993) data assuming Cahn effect→ <m02> = 0.25 GeV2 (assuming m0,u =m0,d)

  17. Transverse momentum dependence of SIDIS General formalism for (e,e’h) coincidence reaction: Factorized formalism for SIDIS (e,e’h): In general, A and B are functions of (x,Q2,z,pT,f). e.g., “Cahn effect”:

  18. PR12-09-017: PT coverage Can do meaningful measurements at low pT (down to 0.05 GeV) due to excellent momentum and angle resolutions! f= 90o • Excellent f coverage • up to pT = 0.2 GeV • Sufficient f coverage • up to pT = 0.4 GeV • (compared to the E00-108 • case below, now also good • coverage at f ~ 0o) • Limited f coverage • up to pT = 0.5 GeV pT = 0.6 pT = 0.4 f= 0o f= 180o E00-108 f= 270o PT ~ 0.5 GeV: use f dependencies measured in CLAS12 experiments (E12-06-112, LOI12-09-005)

  19. Model PT dependence of SIDIS Gaussian distributions for PT dependence, no sea quarks, and leading order in (kT/q) Inverse of total width for each combination of quark flavor and fragmentation function given by: And take Cahn effect into account, with e.g. (similar for c2, c3, and c4):

  20. Unpolarized SIDIS – JLab data (cont.) Constrain kT dependence of up and down quarks separately 1) Probe p+ and p- final states 2) Use both proton and neutron (d) targets 3) Combination allows, in principle, separation of quark width from fragmentation widths (if sea quark contributions small) Example 1st example: Hall C, PL B665 (2008) 20 Simple model, host of assumptions (factorization valid, fragmentation functions do not depend on quark flavor, transverse momentum widths of quark and fragmentation functions are gaussian and can be added in quadrature, sea quarks are negligible, assume Cahn effect, etc.) 

  21. Unpolarized SIDIS – JLab data (cont.) Constrain kT dependence of up and down quarks separately 1) Probe p+ and p- final states 2) Use both proton and neutron (d) targets 3) Combination allows, in principle, separation of quark width from fragmentation widths (if sea quark contributions small) Example 1st example: Hall C, PL B665 (2008) 20 x = 0.32 z = 0.55 Numbers are close to expectations! But, far too early to claim success: simple model only, not a complete f coverage, uncertainties in exclusive event & diffractive r contributions, SIDIS partonic framework valid? Example <pt2> (favored) <kt2> (up)

  22. PR12-09-017 Projected Results - I III IV II VI I V

  23. Kaon Identification • Particle identification in SHMS: • 0) TOF at low momentum (~1.5 GeV) • Heavy (C4F8O) Gas Cherenkov • to select p+ (> 3 GeV) • 60 cm of empty space could be • used for two aerogel detectors: • - n = 1.015 to select p+ (> 1 GeV) • select K+ (> 3 GeV) • - n = 1.055 to select K+ (>1.5 GeV) Heavy Gas Cherenkov and 60 cm of empty space

  24. Spin-off: study x-z Factorization for kaons P.J. Mulders, hep-ph/0010199 (EPIC Workshop, MIT, 2000) At large z-values easier to separate current and target fragmentation region  for fast hadrons factorization (Berger Criterion) “works” at lower energies If same arguments as validated for p apply to K: At W = 2.5 GeV: z > 0.6 (but, z < 0.65 limit may not apply for kaons!)

  25. PR12-09-017 Projected Results - Kaons III IV II VI I V

  26. Summary • Access to the parton model through semi-inclusive DIS data was established with 6-GeV data • Still many questions about the exact interpretation of SIDIS experiments and the validity of such access in cross section measurements • In ratios (or similar, asymmetries) life seems to become simpler, and access seems verified • Many outstanding questions remain: • Is R in SIDIS the same as R in DIS, as anticipated from the high-energy factorized Ansatz? • To what extent is factorization truly valid? (especially at high pT, at small pT it should be valid at tree-level) • Experimentally, where does it work for kaons? • Does fragmentation depend on quark flavor? • What are the transverse momentum distributions of the various quark and fragmentation functions?

  27. Choice of Kinematics (here for PR12-09-017) HMS + SHMS Accessible Phase Space for Deep Exclusive Scattering 11 GeV phase space 6 GeV phase space E00-108 PR12-09-017 Scan in (x,z,pT) + scan in Q2 at fixed x For semi-inclusive, less Q2 phase space at fixed x due to: i) MX2 > 2.5 GeV2; and ii) need to measure at both sides of Qg

  28. Seq2q(x) Dqp(z) Kinematic Factorization (after integration over pT and f) Both Current and Target Fragmentation Processes Possible. At Leading Order: Berger Criterion Dh > 2 Rapidity gap for factorization Separates Current and Target Fragmentation Region in Rapidity

  29. Low-Energy x-z Factorization Seq2q(x) Dqp(z) (after integration over pT and f) P.J. Mulders, hep-ph/0010199 (EPIC Workshop, MIT, 2000) At large z-values easier to separate current and target fragmentation region  for fast hadrons factorization (Berger Criterion) “works” at lower energies p At W = 2.5 GeV: z > 0.4 At W = 5 GeV: z > 0.2 (Typical JLab-6 GeV) (Typical HERMES)

  30. Non-trivial contributions to (e,e’p) Cross Section Radiation contributions, including from exclusive Contributions from r Further data from CLAS12 (r) and Hall C (Fp-12, pCT-12) will constrain!

  31. Estimate of Contribution of r to R = sL/sT High e Low e • Conclusion: If r contribution is as simulated and • known to 10%  5% relative error in R (worst case) • (CLAS12 data important to constrain r contributions!) • Above uncertainty assumed RSIDIS = RDIS (small!) • Essentially same uncertainty at Q2 = 2.0 and 4.0 GeV2

  32. SIDIS Formalism General formalism for (e,e’h) coincidence reaction w. polarized beam: [A. Bacchetta et al., JHEP 0702 (2007) 093] (Y = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction) Unpolarized kT-dependent SIDIS: in framework of Anselmino et al. described in terms of convolution of quark distributions fq and (one or more) fragmentation functions Dqh, each with own characteristic (Gaussian) width.

  33. Transverse momentum dependence of SIDIS E00-108 Pt dependence very similar for proton and deuterium targets, but deuterium slopes systematically smaller? Pt dependence very similar for proton and deuterium targets

  34. Transverse Momentum Dependence: E00-108 Summary • E00-108 results can only be considered suggestive at best: • limited kinematic coverage • - assume (PT,f) dependency ~ Cahn effect • very simple model assumptions • but PT dependence off D seems shallower than H • and intriguing explanation in terms of flavor/kT deconvolution • Many limitations could be removed with 12 GeV: • wider range in Q2 • improved/full coverage in f (at low pT) • larger range in PT • wider range in x and z (to separate quark from fragmentation widths) • possibility to check various model assumptions • Power of (1-z) for D-/D+ • quantitative contribution of Cahn term • Dup+ = Ddp- • Higher-twist contributions • consistency of various kinematics (global fit vs. single-point fits)

  35. PR12-09-017 Projected Results - II Simulated data use (mu)2 = (md)2 = 0.2, and then fit using statistical errors. Step 1: Kinematics I-VI fitted separately, (pT,f) dependency ~ Cahn Step 2: Add eight parameters to mimic possible HT, but assume Cahn  uncertainties grow with about factor of two Step 3: Simulate with and without Cahn term  results remain similar as in step 2

  36. PR12-09-017 Projected Results - II Simulated data use (mu)2 = (md)2 = 0.2, and then fit using statistical errors. Step 1: Kinematics I-VI fitted separately, (pT,f) dependency ~ Cahn (if all six fitted together, diameter < 0.01 GeV2) Step 2: Add eight parameters to mimic possible HT, but assume Cahn  uncertainties grow with about factor of two (if all six fitted together, diameter remains < 0.01 GeV2) Step 3: Simulate with and without Cahn term  results remain similar as in step 2 (if all six fitted together, diameter grows to < 0.02 GeV2) Step 1: Kinematics I-VI fitted separately, (pT,f) dependency ~ Cahn Step 2: Add eight parameters to mimic possible HT, but assume Cahn  uncertainties grow with about factor of two Step 3: Simulate with and without Cahn term  results remain similar as in step 2

  37. Non-trivial contributions to (e,e’p) Cross Section Radiative Corrections - Typical corrections are <10% for z < 0.7. - Checked with SIMC and POLRAD 2.0. - Good agreement between both methods. Exclusive Pions - Interpolated low-W2, low-Q2 of MAID with high-W2, high-Q2 of Brauel/Bebek. - Introduces large uncertainty at low z, but contributions there are small. - Tail agreed to 10-15% with “HARPRAD”. - Further constraints with Fp-12 and pCT-12. Pions from Diffractive r - Used PYTHIA with modifications as implemented by HERMES (Liebing,Tytgat). - Used this to guide r cross section in SIMC. - simulated results agree to 10-15% with CLAS data (Harut Avagian). - In all cases, quote results with/without diffractive r subtraction.

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