1. Transverse Momentum Dependence of Charged Pion Production
Rolf Ent, Hall C Physics Summer Meeting, Aug. 04, 2008
SIDIS: framework and general remarks
The Onset of the Quark Parton Model in SIDIS
Results from E00-108
R = sL/sT in SIDIS: E
Transverse Momentum Dependence of
Charged Pion Production: Results from E00-108
Transverse Momentum Dependence of Charged Pion Production at the

2. Flavor Decomposition quark polarization Dq(x)
DIS probes only the sum of quarks and anti-quarks  requires assumptions on the role of sea quarks
quark polarization Dq(x)
first 5-flavor separation
Du > 0
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’
Dd < 0
SIDIS
q parton distribution function
dsf elementary g*-q sub-process
Dfh fragmentation function

3. Semi-Inclusive DIS (SIDIS)}
Fragmentation Function p
quark
(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

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. LO and NLO Pdf expectations
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
open (solid): with (without) coherent r
No noticable pT-dependence in ratios
z = 0.55
x = 0.32
LO and NLO Pdf expectations
[sp(p+) + sp(p-)]/[sd(p+) + sd(p-)] [sp(p+) - sp(p-)]/[sd(p+) - sd(p-)]

6. some?
Factorization Studies give good faith in access to parton flavor decomposition at large x (x > 0.1) in SIDIS at 12 GeV
(semi-inclusive deep inelastic scattering)

7. General (e,e’h)/SIDIS framework
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).
Assumptions sometimes made in (e,e’h) analysis at higher energies:
1) assume full-f coverage  no effect of A and B
2) A and B are treated as constants (or even 0…)
3) sL/sT = RDIS

8. “A skeleton in our closet”
R = sL/sT in DIS and in (e,e’p) SIDIS
Knowledge on R = sL/sT in SIDIS is 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 (semi-)
exclusive channels: pions originating from r  p+p-
RSIDIS may vary with pT
Is RSIDISp+ = RSIDISp- ? Is RSIDISH = RSIDISD ?
RSIDIS = RDIS test of dominance of quark fragmentation
“A skeleton in our closet” p
quark

9. sL/sT and Fragmentation at lower energies: ep  e’hX
Cornell data of 70’s
Conclusion: “data both consistent with R = 0 and R = RDIS”
RDIS
Most precise data at Q2 = 1.2 GeV2 are from mid-z region. Hint of larger R
at large z?

10. For comparison, quality of approved 12 GeV data
Proposed data cover range Q2 = 1.5 – 5.0 GeV2, with data for both H and D at Q2 = 2 GeV2
RDIS
Scans in z are proposed at Q2 = 2.0 (x = 0.2) and 4.0 GeV2 (x = 0.4)  should settle the behavior of sL/sT for large z
RDIS (Q2 = 2 GeV2)

11. Measurements on both p+ and p- needed!
Flavor Decomposition:
For precise flavor decomposition, need to know RSIDISp+ and RSIDISp-
2. Behavior at large z may differ. Can constrain Rpo ~ (Rp+ + Rp-)/2.
3. In fact, also need knowledge on RSIDISK+ and RSIDISK- : we measure kaons too! (with about 10% of pion statistics)
4. Extract D-/D+ ratio separately for longitudinal and transverse fragmentation, e.g. using the deuterium data:
(Deuterium data)
Any Resonances cancel (in SU(6)) in the
D-/D+ ratio extracted from deuterium data

12. General (e,e’h)/SIDIS framework – cont.
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”:

13. kT-dependent SIDIS p┴ = PT – z k┴ + O(k┴2/Q2) Anselmino et al
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, …)

14. kT-dependent SIDIS pt = Pt – z kt + O(kt2/Q2) TMDu(x,kT)
Schematic diagram of semi-inclusive pion electroproduction with a factorized QCD quark parton model at lowest order in as. 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 – z kt + O(kt2/Q2)
Linked to framework of Transverse Momentum Dependent Parton Distributions
TMDu(x,kT)
f1,g1,f1T ,g1T
h1, h1T ,h1L ,h1 p m x
TMD

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

16. E (6 GeV): PT coverage
Can measure up to PT2 ~ 0.2 GeV2, but since f coverage not complete need to make assumptions on (PT,f) dependencies: assume ~ Cahn effect

17. 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):

18. 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! But … is the transverse momentum distribution of up quarks really far smaller than for down quarks??? Or, is there something very wrong in our simple model or the general SIDIS framework?

19. Transverse Momentum Dependence: E00-108 Summary
E results can only be considered suggestive at best:
limited kinematic coverage
very simple model assumptions
but PT dependence off D seems shallower than H
and tempting to think about flavor/kT deconvolution
Many limitations could be removed with 12 GeV:
wider range in Q2
full coverage in f
large range in PT
wider range in z (to separate quark from fragmentation widths)
possibly include p0 final state (add’l consistency check, particularly
on the assumption that only two
fragmentation functions are needed)

20. 12 GeV w.r.t. 6 GeV Kinematics
For illustration: Hall C HMS + SHMS Combination
11 GeV phase space
6 GeV phase space
E00-108
For semi-inclusive, less Q2 phase space at fixed x (MX2 > 2.5 GeV2)

21. Example of 12 GeV KinematicsQ2
W’2 z
0.20
8.8
2.7
6.3
0.35
6.6
3.0
3.7
4.1
4.7
11.0
5.5
6.0
0.50
3.5
2.6
5.2
7.0
4.4
0.60
8.0
3.6
Use SANE setup at constant angle: Qe constant at 25o
Three settings in SHMS momentum to cover z-range
Seven settings in SHMS angle with 2.5 degree steps to cover pT-range
Grid of 21 settings per beam energy (6.6, 8.8 and 11 GeV)
for each target (LH2, LD2)
and polarity (p+ and p-)

22. (if certain angles are fixed, like Qg,min or Qe’)
Q2-x Phase Space at 12 GeV
Can obtain largest range in Q2 including <11 GeV beam energies (8.8 GeV and in limited cases 6.6 GeV)
(if certain angles are fixed, like Qg,min or Qe’)
E = 11 GeV
E = 8.8 GeV Q2 x x

23. Example of coverage at 8.8 GeV
Vary SHMS momentum to cover range in z (0.3 – 0.6 desired):
 3 SHMS settings.
Reasonable coverage in PT (and, will measure f dependencies separately in CLAS12 experiments (H approved, D to be proposed)

24. Outstanding issue(s?) Use SHMS to access forward angles (down to 5.5o)
to measure precision p+/p- ratios
Use SANE-SHMS or HMS-SHMS Setup?
SANE setup at 25 degrees:
p/e ratio may be large, need Cherenkov for PId
How large is (e,e’p) rate vs (e,pp) concidence rate?
May limit beam current to 1 mA only (want 10 mA), in which case HMS-SHMS setup competitive

25. Summary
Onset of quark-hadron duality in pion electroproduction seems unambiguously verified by E experiment.
Factorization 6 GeV work well for 0.4 < z < 0.7, pT < 1 GeV, even for W’ < 2 GeV (another evidence of quark-hadron duality).
PT dependence seems consistent with data from higher-energy experiments (HERMES), but somewhat shallower PT dependence found for pions produced from deuterium target.
Still a lot of work to do to further quantify (and understand!) low-energy factorization in semi-inclusive reactions …
… and then to convert this into a precision tool to learn about flavor decomposition and the transverse momentum dependence of such quark flavors.

27. Flavor Decomposition through semi-inclusive DIS
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
 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)

28. Duality in Pion Electroproduction
quark
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

29. Example of 12-GeV projected data assuming RSIDIS = RDIS
PR : Choice of Kinematics
Map RHSIDIS and RDSIDIS as a function of z
at x = 0.2 and Q2 = 2.0 GeV2
- Need to experimentally verify RHSIDIS = RDSIDIS, just as RHDIS = RDDIS!
Map RHSIDIS as a function of z at x = 0.4 and Q2 = 4.0 GeV2
- Test dominance of quark fragmentation
- Study the inclusive-exclusive connection (soft vs. hard gluon exchange?)
Map RHSIDIS as a function of pT2 at x = 0.3 and Q2 = 3.0 GeV2
- extend understanding of fragmentation process to high pT
- no guidance from factorization theorems here yet
Add kinematics to map RHSIDIS for Q2 = GeV2
- Does RSIDIS behave like RDIS as function of Q2?
Not clear what R will behave like at large pT
Example of 12-GeV projected data assuming RSIDIS = RDIS

30. Semi-Inclusive Deep-Inelastic Scattering
Potentially rich physics arena for flavor decomposition, kT-dependent parton distribution functions, fragmentation, etc., but also many potential issues…
SIDIS Working Group at JLab (Theory, Halls A, B, and C) believes multi-hall approach is best, combining the large acceptance potential of CLAS12:
PR Azimuthal distributions of final-state particles
PR Flavor decomposition at large-x (SIDIS part)
LOI Transverse Polarization Effects
LOI Single- and Double-Spin azimuthal asymmetries
and the precision of the Hall C magnetic-spectrometer setup:
PR Measurement of R = sL/sT in SIDIS
PR Precision differences of p+ and p- multiplicities
(Flavor decomposition of light-quark sea)
PR12-xx-xxx Precision measurement of p+/- PT-dependencies

31. Flavor Decomposition HERMES quark polarization Dq(x)
first 5-flavor separation
Flavor decomposition within reach at 12-GeV JLab
HERMES
D region
Solid lines: simple Parton Model prescription assuming factorization

32. No Noticable pT-Dependence Found in Ratios