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Transverse Momentum Dependence of Semi-Inclusive Pion Production

Transverse Momentum Dependence of Semi-Inclusive Pion Production. PAC-34 Proposal PR12-09-017 Spokespersons Peter Bosted, Rolf Ent, and Hamlet Mkrtchyan. Not much is known about the orbital motion of partons

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Transverse Momentum Dependence of Semi-Inclusive Pion Production

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  1. Transverse Momentum Dependence of Semi-Inclusive Pion Production PAC-34 Proposal PR12-09-017 Spokespersons Peter Bosted, Rolf Ent, and Hamlet Mkrtchyan • Not much is known about the orbital motion of partons • Significant net orbital angular momentum of valence quarks implies significant transverse momentum of quarks PR12-09-017: Map the pT dependence (pT ~ L < 0.5 GeV) of p+ and p- production off proton and deuteron targets to study the kT dependence of (unpolarized) up and down quarks. pT ~ L <0.5 GeV chosen 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].

  2. PR12-09-017 Collaboration

  3. Semi-Inclusive Deep-Inelastic Scattering Potentially rich physics arena for flavor decomposition, kT-dependent parton distribution functions, fragmentation, etc., but also many potential issues… Multi-hall approach seems best, combining the large acceptance potential of CLAS12: E12-06-112 Azimuthal distributions of final-state particles E12-06-109 Flavor decomposition at large-x (SIDIS part) E12-07-107 Spin-Orbit Correlations w. Long. Pol. Target E12-09-0xx 3 similar experiments emphasizing kaons and the precision of the Hall C magnetic-spectrometer setup: E12-06-104 Measurement of R = sL/sT in SIDIS (PAC-34) Precision p+/p- ratios in SIDIS: E12-09-002 I. Charge-Symmetry Violating PDFs E12-09-004 II. Flavor Dependence of the EMC Effect E12-09-017 Transverse Momentum Dependence of Semi-Inclusive Pion production (third advantage: reaching important corners of phase space, is not well enough established yet)

  4. 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

  5. E00-108: Applicability of 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) PR12-09-017: 2.9 < Mx2 < 7.8 GeV2 Closed (open) symbols reflect data after (before) events from coherent r production are subtracted

  6. m p x TMD SIDIS – kT Dependence 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. TMDu(x,kT) f1,g1,f1T ,g1T h1, h1T ,h1L ,h1 Pt= pt +zkt+ O(kt2/Q2) Linked to framework of Transverse Momentum Dependent Parton Distributions

  7. 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) 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.

  8. 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)

  9. Transverse momentum dependence of SIDIS Constrain kT dependence of up and down quarks separately 1) Probe p+ and p- final states 2) Use both proton and neutron (deuteron) targets 3) Combination allows, in principle, separation of quark width from fragmentation widths (if sea quark contributions small) Spectrometers a must for such %-type (!) measurements: acceptance is a common factor to all measurements (and can use identical H and D cells) First example from JLab at 6 GeV on next slide (E00-108 experiment in Hall C, H. Mkrtchyan, P. Bosted et al., Phys. Lett. B665 (2008) 20)

  10. 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

  11. Transverse momentum dependence of SIDIS 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.)  (m+)2 ~ width of D+(z,pt), (m-)2 ~ width of D-(z,pt), (mu)2 ~ width of u(x,kt), (md)2 ~ width of d(x,kt) Many authors believe these widths to be of order 0.25 GeV2 these numbers are close! Many authors believe these widths to be of order 0.25 GeV2 these numbers are close! But … is (mu)2 < (md)2?? Expected from diquark models… Or, is there something wrong in our simple model or the used SIDIS framework?

  12. 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)

  13. Choice of E12-09-017 Kinematics 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

  14. Choice of Kinematics – cont. Map of pT dependence in x and z, in Q2 to check (pT/Q) and (pT2/Q2) behavior Kinematics I, II, III, and IV are identical to those where this collaboration also plans to map R (= sL/sT) in SIDIS in E12-06-104. This saves a total of five days, as follows: 1) three days of data taking 2) one day of dedicated checkout 3) one day for pass/kinematics changes and beam energy meas.

  15. 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)

  16. Choice of Kinematics – cont. • Keep HMS momentum (~E’) constant for all kinematics • Dedicated measurements (within requested beam time) will be added with E’ increased by 25% and possibly • 50% for radiative correction modeling. • (HMS goes to 7.3 GeV momentum  need to swap HMS-SHMS roles for 50%) • E12-06-104 includes beam time at E = 6.6 GeV. • We plan to dedicate part of that time also for • radiative correction modeling.

  17. Systematic Uncertainties in p+/p- Ratios Anticipated systematic uncertainties in ratios of transverse momentum dependences. The combined use of the CLAS12 experiments is assumed to fully constrain the (pT,f) dependency. (*) HMS is kept at constant momentum of 5.67 GeV, at forward scattering angles (<22 degrees, hence viewing a 3.7 cm effective target length), at singles rates < 100 kHz, and at p/e ratios < 13. (**) The main uncertainties are due to spectrometer polarity changes. The SHMS total rate is kept <700 kHz to constrain the tracking eff. (***) Assuming dedicated measurements to constrain the required radiative correction model input.

  18. 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!

  19. 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.

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

  21. 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

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

  23. 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 PR12-09-017: Map the pT dependence (pT ~ L < 0.5 GeV) of p+ and p- production off proton and deuteron targets to measure the kT dependence of up and down quarks Can only be done using spectrometer setup capable of %-type measurements (an essential ingredient of the global SIDIS program!) Beam time request: 32 days of beam time in Hall C Spin-off: Radiative correction modeling for (e,e’p) Single-spin asymmetries at low pT (< 0.2 GeV) Low-energy (x,z) factorization for kaons

  24. Appendix

  25. PR12-09-017: Beam Time Request • Map yields as function of z and pT at x = 0.2 and Q2 = 2.0 GeV2 • 4.5 Days (incl. overhead) • Map yields as function of z and pT at x = 0.3 and Q2 = 3.0 GeV2 • 5.8 Days • Map yields as function of z and pT at x = 0.4 and Q2 = 4.0 GeV2 • 5.3 Days • Map yields as function of z and pT at x = 0.5 and Q2 = 5.0 GeV2 • 5.3 Days • Map yields as function of z and pT at x = 0.3 and Q2 = 1.8 GeV2 • 6.9 Days • Map yields as function of z and pT at x = 0.3 and Q2 = 4.5 GeV2 • 4.0 Days • Total: 32 Days(incl. overhead) * Overhead consists of spectrometer polarity, momentum, and angle, and target changes

  26. 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

  27. 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

  28. Choice of PR12-09-017 Kinematics • W2 = 5.08 GeV2 and larger (up to 11.38 GeV2) • Use SHMS angle down to 5.5 degrees (for p detection) • HMS angle down to 10.5 degrees (e- detection) • separation HMS-SHMS > 17.5 degrees • MX2 = Mp2 + Q2(1/x – 1)(1 – z) > 2.9 GeV2(up to 7.8 GeV2) • Choice to keep Q2/x fixed  qg ~ constant • exception are data scanning Q2 at fixed x • All kinematics both for p+ (and K+) and p- (and K-), both for LH2 and LD2 (and Al dummy) • Choose z > 0.3 (pp > 1.7 GeV) to be able to neglect • differences in s(p+N) and s(p-N) • not possible for x = 0.3, Q2 = 1.80: pp > 1.1 GeV

  29. Experimental Details Experimental Details and Spin-Off • Beam current is varied to keep the total SHMS rate below 700 kHz • 10-80 mA beam currents (with 10 cm LH2/LD2) • rate limitation to guarantee precision p+/p- ratios • Anticipated syst. uncertainty in ratio 0.9% • Real : Accidental ratio typically ~ 2 : 1 • Syst. uncertainty has four roughly equal ingredients: spectrometer • acceptance, tracking + detector efficiencies, radiative corrections • to model latter, include dedicated runs at lower E and E’ • Collaboration did similar (published) modeling efforts on • JLab inclusive 1H(e,e’) and 2H(e,e’) scattering results • While this measurement is not ideally suited to measurement of Single-Spin Asymmetries (lack of full f coverage), we expect to map such SSA’s well up to pT ~ 0.2 GeV (with errors of typ. 0.003-0.008), further facilitating kT-dependence model checking • Hence, we request 80% long. polarized beam • Kaon identification would be facilitated by the addition of an • aerogel detector to the SHMS base detector package • study the low-energy (x,z) factorization for charged kaons • Collaboration built HMS aerogel detector (NIM A548, 364)

  30. PR12-09-017 TAC Report • The proposal assumes that the experiment will be scheduled so that its run plan can be combined with E12-06-104. Therefore, the time request does not include time for checkout, pass changes and beam energy measurements. • This is correct. Including this time would require an additional five (three DAQ and two overhead) days. In the proposal we stated eight days, which is incorrect: E12-06-104 required higher statistics runs. • In the early years of 12 GeV operation, the practical limit on beam current for 11 GeV running will be 75 mA. • In about half of the kinematics beam currents of 75 mA or less are used to limit the hadron singles rates in SHMS to less than 700 kHz. The impact from Table IX is then ((80-75)/75*260) = 17.5 hours. • Comments on measurements of SIDIS observables: • The adequate f coverage at small (!) pT is shown in the proposal. This experiment only addresses the pT dependence of p+ and p- off LH2 and LD2. Pions from diffractively produced r mesons are simulated taking into account HERMES input and checked vs. CLAS data. • 4. Comments on measurements involving kaons/strange quarks: • PR12-09-017 kaon measurements affect factorization tests only.

  31. Backup Slides (not printed)

  32. Systematic Uncertainties – the (e,e’) Case Compare with SLAC E140X (DIS) 1 x 10-3 0.3% 1 x 10-3 0.2% 0.1 mr 0.3% 0.3% 0.3% 0.2% 0.2% 0.3% 0.3% 0.1% 0.1% 0.2% 0.2% 0.5% 0.5% 1.0% 1.0% 1.3% Total point-to-point systematic uncertainty for E94-110 is 1.6%.

  33. Systematic Uncertainties – the z  1 Limit From: G. Huber’s presentation on PR12-06-101 “Measurement of the Charged Pion Form Factor to High Q2” Added in quadrature: 1.8%

  34. SHMS Tracking Efficiency Considerations Several approved experiments (E12-06-101, E12-06-104, E12-07-105) require good tracking efficiency knowledge at ~1 MHz rate. HMS tracking efficiency is robust, but we typically still restrict rates to < 0.5 MHz: • Rate dependence well understood on basis of Poisson statistics: • DC TDC’s have wider window than hodoscope TDC’s (difference fit with 77 ns) • varying width of DC TDC window  find same corrected yield! • 2 electron tracks  tracking efficiency 70 +/- 3% (can’t find track for two electrons close-by): agrees well with number found from TDC window study • Important to have device with well-defined rates and aperture SHMS Design incorporates well-shielded detector hut, well-defined apertures, 3X and 3Y measurements per chamber, and multi-hit TDCs  Good knowledge @ 1 MHz probable (but lot of work)

  35. 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” Here, R = sL/sT ~ Q2 RSIDIS RDIS disappears with Q2! Example of 12-GeV projected data assuming RSIDIS = RDIS Not clear what R will behave like at large pT

  36. 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

  37. p quark E00-108: Leading-Order x-z factorization Collinear Fragmentation factorization (Deuterium data) D region Should not depend on x But should depend on z (Resonances cancel (in SU(6)) in D-/D+ ratio extracted from deuterium data) Solid lines: simple Quark Parton Model prescription assuming factorization

  38. E00-108 (6 GeV): PT coverage E00-108 measured up to PT2 ~ 0.2 GeV2, but f coverage was not complete  needed to make assumptions on (PT,f) dependencies: ~ Cahn effect

  39. 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”:

  40. 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):

  41. Duality in Meson Electroproduction hadronic description quark-gluon description Transition Form Factor Decay Amplitude Fragmentation Function Requires non-trivial cancellations of decay angular distributions If duality is not observed, factorization is questionable Duality and factorization possible for Q2,W2  3 GeV2 (Close and Isgur, Phys. Lett. B509, 81 (2001))

  42. kT-dependent SIDIS Anselmino et al p┴= PT– zk┴+ O(k┴2/Q2) data fit assuming Cahn effect→ <m02> = 0.25 GeV2 EMC (1987) and Fermilab (1993) data (assuming m0u=m0d) • Factorization of kT-dependent PDFs proven at low PT of hadrons (Ji et al) • Universality of kT-dependent distribution and fragmentation functions proven (Collins,Metz, …)

  43. Transverse Momentum Dependence of Semi-Inclusive Pion Production PAC-34 Proposal PR12-09-017 • Outline: • SIDIS: framework and general remarks • Results from E00-108 • - Low-energy (x,z) factorization for charged pions • - Transverse momentum dependence of charged pions • PR12-09-017 • Choice of kinematics • Experimental details • Spin-off relevant for the general SIDIS program • Radiative correction modeling: linking to z = 1 • Single-spin asymmetries • Low-energy (x,z) factorization for charged kaons • PR12-09-07 Beam Time Request and Projected Results

  44. 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 = Em/n

  45. Low-Energy x-z Factorization (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)

  46. SIDIS – kT Dependence 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) PR12-09-017: Map the pT dependence (pT ~ L < 0.5 GeV) of p+ and p- production off proton and deuteron targets to study the kT dependence of (unpolarized) up and down quarks

  47. 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!)

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