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

PR Collaboration

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

Solution: Detect a final state hadron in addition to scattered electron  Can ‘tag’ the flavor of the struck quark by measuring the hadrons produced: ‘flavor tagging’ DIS probes only the sum of quarks and anti-quarks  requires assumptions on the role of sea quarks Measure inclusive (e,e’) at same time as (e,e’h) SIDIS SIDIS – Flavor Decomposition Leading-Order (LO) QCD after integration over p T and  NLO: gluon radiation mixes x and z dependences : parton distribution function : fragmentation function

Closed (open) symbols reflect data after (before) events from coherent  production are subtracted GRV & LO or NLO (Note: z = 0.65 ~ M x 2 = 2.5 GeV 2 ) E00-108: Applicability of Parton Model Good description for p and d targets for 0.4 < z < 0.65 PR : 2.9 < M x 2 < 7.8 GeV 2

P t = p t + z k t + O(k t 2 /Q 2 ) p m x TMD TMD u (x,k T ) f 1,g 1,f 1T,g 1T h 1, h 1T,h 1L,h 1 Final transverse momentum of the detected pion P t arises from convolution of the struck quark transverse momentum k t with the transverse momentum generated during the fragmentation p t. Linked to framework of Transverse Momentum Dependent Parton Distributions SIDIS – k T Dependence

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

Transverse momentum dependence of SIDIS General formalism for (e,e’h) coincidence reaction w. polarized beam: (  = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction) Azimuthal  h 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 → = 0.25 GeV 2 (assuming  0,u =  0,d ) [A. Bacchetta et al., JHEP 0702 (2007) 093]

Transverse momentum dependence of SIDIS Constrain k T dependence of up and down quarks separately 1) Probe  + and  - 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 (E experiment in Hall C, H. Mkrtchyan, P. Bosted et al., Phys. Lett. B665 (2008) 20)

Transverse momentum dependence of SIDIS P t dependence very similar for proton and deuterium targets, but deuterium slopes systematically smaller? E P t dependence very similar for proton and deuterium targets

Many authors believe these widths to be of order 0.25 GeV 2  these numbers are close! 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.)  (  + ) 2 ~ width of D + (z,p t ), (   ) 2 ~ width of D - (z,p t ), (  u ) 2 ~ width of u(x,k t ), (  d ) 2 ~ width of d(x,k t ) Many authors believe these widths to be of order 0.25 GeV 2  these numbers are close! But … is (  u ) 2 < (  d ) 2 ?? Expected from diquark models… Or, is there something wrong in our simple model or the used SIDIS framework?

Transverse Momentum Dependence: E Summary E results can only be considered suggestive at best: limited kinematic coverage - assume (P T,  ) dependency ~ Cahn effect very simple model assumptions but P T dependence off D seems shallower than H and intriguing explanation in terms of flavor/k T deconvolution Many limitations could be removed with 12 GeV: wider range in Q 2 improved/full coverage in  (at low p T ) larger range in P T 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 - D u  + = D d  - - Higher-twist contributions - consistency of various kinematics (global fit vs. single-point fits)

HMS + SHMS Accessible Phase Space for Deep Exclusive Scattering For semi-inclusive, less Q 2 phase space at fixed x due to: i) M X 2 > 2.5 GeV 2 ; and ii) need to measure at both sides of   Choice of E Kinematics 6 GeV phase space 11 GeV phase space E PR Scan in (x,z,p T ) + scan in Q 2 at fixed x

Choice of Kinematics – cont. KinxQ 2 (GeV 2 ) zP  (GeV)   (deg) I – – 23.0 II – – 25.5 III – – 25.5 IV – – 28.0 V – – 30.5 VI – – 20.5 Kinematics I, II, III, and IV are identical to those where this collaboration also plans to map R (=  L /  T ) in SIDIS in E 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. Map of p T dependence in x and z, in Q 2 to check (p T /Q) and (p T 2 /Q 2 ) behavior

PR : P T coverage Excellent  coverage up to p T = 0.2 GeV Sufficient  coverage up to p T = 0.4 GeV (compared to the E case below, now also good coverage at  ~ 0 o ) Limited  coverage up to p T = 0.5 GeV P T ~ 0.5 GeV: use  dependencies measured in CLAS12 experiments (E , LOI )  = 0 o  = 90 o  = 180 o  = 270 o p T = 0.4 p T = 0.6 Can do meaningful measurements at low p T (down to 0.05 GeV) due to excellent momentum and angle resolutions! E

Choice of Kinematics – cont. KinE (GeV) E’ (GeV)  e’ (deg) W 2 (GeV 2 )   (deg) q  (GeV) I II III IV V VI 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%) E includes beam time at E = 6.6 GeV. We plan to dedicate part of that time also for radiative correction modeling.

Systematic Uncertainties in  + /  - Ratios Project SourceHMS (*) SHMS Spectrometer Acceptance (**) 0.1%0.4% Tracking Efficiency (**) 0.1%0.4% Detection Efficiency (**) 0.1%0.4% Pion Absorption Correction0.1% Radiative Corrections (***) 0.5% Added in Quadrature0.9% Anticipated systematic uncertainties in ratios of transverse momentum dependences. The combined use of the CLAS12 experiments is assumed to fully constrain the (p T,  ) 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  /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.

Radiation contributions, including from exclusive Contributions from  Non-trivial contributions to (e,e’  ) Cross Section Further data from CLAS12 (  ) and Hall C (F  -12,  CT-12) will constrain!

Non-trivial contributions to (e,e’  ) Cross Section Radiative Corrections - Typical corrections are <10% for z < Checked with SIMC and POLRAD Good agreement between both methods. Exclusive Pions - Interpolated low-W 2, low-Q 2 of MAID with high-W 2, high-Q 2 of Brauel/Bebek. - Introduces large uncertainty at low z, but contributions there are small. - Tail agreed to 10-15% with “HARPRAD”. - Further constraints with F  -12 and  CT-12. Pions from Diffractive  - Used PYTHIA with modifications as implemented by HERMES (Liebing,Tytgat). - Used this to guide  cross section in SIMC. - simulated results agree to 10-15% with CLAS data (Harut Avagian). - In all cases, quote results with/without diffractive  subtraction.

PR Projected Results - I III II I IV VI V

Kaon Identification Particle identification in SHMS: 0) TOF at low momentum (~1.5 GeV) 1)Heavy (C4F8O) Gas Cherenkov to select  + (> 3 GeV) 2)60 cm of empty space could be used for two aerogel detectors: - n = to select  + (> 1 GeV) select K + (> 3 GeV) - n = to select K + (>1.5 GeV) Heavy Gas Cherenkov and 60 cm of empty space

PR Projected Results - Kaons III II I IV VI V

Transverse Momentum Dependence of Semi-Inclusive Pion Production PR : Map the p T dependence (p T ~  < 0.5 GeV) of  + and  - production off proton and deuteron targets to measure the k T dependence of up and down quarks Not much is known about the orbital motion of partons Significant net orbital angular momentum of valence quarks implies significant transverse momentum of 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’  ) Single-spin asymmetries at low p T (< 0.2 GeV) Low-energy (x,z) factorization for kaons

Appendix

PR : Beam Time Request Map yields as function of z and p T at x = 0.2 and Q 2 = 2.0 GeV Days (incl. overhead) Map yields as function of z and p T at x = 0.3 and Q 2 = 3.0 GeV Days Map yields as function of z and p T at x = 0.4 and Q 2 = 4.0 GeV Days Map yields as function of z and p T at x = 0.5 and Q 2 = 5.0 GeV Days Map yields as function of z and p T at x = 0.3 and Q 2 = 1.8 GeV Days Map yields as function of z and p T at x = 0.3 and Q 2 = 4.5 GeV Days Total: 32 Days (incl. overhead) * Overhead consists of spectrometer polarity, momentum, and angle, and target changes

PR Projected Results - II Simulated data use (  u ) 2 = (  d ) 2 = 0.2, and then fit using statistical errors. Step 1: Kinematics I-VI fitted separately, (p T,  ) 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

Step 1: Kinematics I-VI fitted separately, (p T,  ) dependency ~ Cahn (if all six fitted together, diameter < 0.01 GeV 2 ) 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 GeV 2 ) 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 GeV 2 ) PR Projected Results - II Step 1: Kinematics I-VI fitted separately, (p T,  ) 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 Simulated data use (  u ) 2 = (  d ) 2 = 0.2, and then fit using statistical errors.

Choice of PR Kinematics W 2 = 5.08 GeV 2 and larger (up to GeV 2 ) Use SHMS angle down to 5.5 degrees (for  detection) HMS angle down to 10.5 degrees (e - detection) separation HMS-SHMS > 17.5 degrees M X 2 = M p 2 + Q 2 (1/x – 1)(1 – z) > 2.9 GeV 2 (up to 7.8 GeV 2 ) Choice to keep Q 2 /x fixed  q  ~ constant exception are data scanning Q 2 at fixed x All kinematics both for  + (and K + ) and  - (and K - ), both for LH2 and LD2 (and Al dummy) Choose z > 0.3 (p  > 1.7 GeV) to be able to neglect differences in  (  + N) and  (  - N) not possible for x = 0.3, Q 2 = 1.80: p  > 1.1 GeV

Experimental Details Beam current is varied to keep the total SHMS rate below 700 kHz  A beam currents (with 10 cm LH2/LD2) rate limitation to guarantee precision  + /  - ratios Anticipated syst. uncertainty in ratio 0.9% Real : Accidental ratio typically ~ 2 : 1 Experimental Details and Spin-Off 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 1 H(e,e’) and 2 H(e,e’) scattering results While this measurement is not ideally suited to measurement of Single-Spin Asymmetries (lack of full  coverage), we expect to map such SSA’s well up to p T ~ 0.2 GeV (with errors of typ ), further facilitating k T -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)

PR TAC Report 1.The proposal assumes that the experiment will be scheduled so that its run plan can be combined with E 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: E required higher statistics runs. 2.In the early years of 12 GeV operation, the practical limit on beam current for 11 GeV running will be 75  A. In about half of the kinematics beam currents of 75  A 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. 3.Comments on measurements of SIDIS observables: The adequate  coverage at small (!) p T is shown in the proposal. This experiment only addresses the p T dependence of  + and  - off LH2 and LD2. Pions from diffractively produced  mesons are simulated taking into account HERMES input and checked vs. CLAS data. 4. Comments on measurements involving kaons/strange quarks: PR kaon measurements affect factorization tests only.

Backup Slides (not printed)

Total point-to-point systematic uncertainty for E is 1.6%. Compare with SLAC E140X (DIS) 1 x % 1 x % 0.1 mr0.3%0.3%0.2%0.3%0.1%0.2%0.5%1.0% 1.3% Systematic Uncertainties – the (e,e’) Case

Projected Systematic Uncertainty Source Pt-Pt ε-random t-random ε- uncorrelated common to all t-bins Scale ε-global t-global Spectrometer Acceptance0.4% 1.0% Target Thickness0.2%0.8% Beam Charge-0.2%0.5% HMS+SHMS Tracking0.1%0.4%1.5% Coincidence Blocking0.2% PID0.4% Pion Decay Correction0.03%-0.5% Pion Absorption Correction-0.1%1.5% MC Model Dependence0.2%1.0%0.5% Radiative Corrections0.1%0.4%2.0% Kinematic Offsets0.4%1.0%- Added in quadrature: 1.8% Systematic Uncertainties – the z  1 Limit From: G. Huber’s presentation on PR “Measurement of the Charged Pion Form Factor to High Q 2 ”

SHMS Tracking Efficiency Considerations Several approved experiments (E , E , E ) 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 1 MHz probable (but lot of work)

So what about R =  L /  T for pion electroproduction?  quark “Semi-inclusive DIS” R SIDIS  R DIS disappears with Q 2 ! “Deep exclusive scattering” is the z  1 limit of this “semi-inclusive DIS” process Here, R =  L /  T ~ Q 2 Not clear what R will behave like at large p T Example of 12-GeV projected data assuming R SIDIS = R DIS

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

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

E (6 GeV): P T coverage E measured up to P T 2 ~ 0.2 GeV 2, but  coverage was not complete  needed to make assumptions on (P T,  ) dependencies: ~ Cahn effect

General formalism for (e,e’h) coincidence reaction: Factorized formalism for SIDIS (e,e’h): In general, A and B are functions of (x,Q 2,z,p T,  ). e.g., “Cahn effect”: Transverse momentum dependence of SIDIS

Model P T dependence of SIDIS Gaussian distributions for P T dependence, no sea quarks, and leading order in (k T /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 c 2, c 3, and c 4 ):

Duality in Meson Electroproduction hadronic descriptionquark-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 Q 2,W 2  3 GeV 2 (Close and Isgur, Phys. Lett. B509, 81 (2001))

p ┴ = P T – z k ┴ + O(k ┴ 2 /Q 2 ) k T -dependent SIDIS data fit assuming Cahn effect → = 0.25 GeV 2 EMC (1987) and Fermilab (1993) data (assuming  0 u =  0 d ) Anselmino et al Factorization of k T -dependent PDFs proven at low P T of hadrons (Ji et al) Universality of k T -dependent distribution and fragmentation functions proven (Collins,Metz, …)

Transverse Momentum Dependence of Semi-Inclusive Pion Production Outline: SIDIS: framework and general remarks Results from E Low-energy (x,z) factorization for charged pions - Transverse momentum dependence of charged pions PR 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 PR Beam Time Request and Projected Results PAC-34 Proposal PR

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

Low-Energy x-z Factorization P.J. Mulders, hep-ph/ (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 At W = 2.5 GeV: z > 0.4At W = 5 GeV: z > 0.2 (Typical JLab-6 GeV) (Typical HERMES)  (after integration over p T and  )

Final transverse momentum of the detected pion P t arises from convolution of the struck quark transverse momentum k t with the transverse momentum generated during the fragmentation p t. SIDIS – k T Dependence PR : Map the p T dependence (p T ~  < 0.5 GeV) of  + and  - production off proton and deuteron targets to study the k T dependence of (unpolarized) up and down quarks P t = p t + z k t + O(k t 2 /Q 2 )

Spin-off: study x-z Factorization for kaons P.J. Mulders, hep-ph/ (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 At W = 2.5 GeV: z > 0.6 If same arguments as validated for  apply to K: (but, z < 0.65 limit may not apply for kaons!)