1. Peter Bosted (Jefferson Lab)
SIDIS and TMDs (Semi-Inclusive Deep Inelastic Scattering and Transverse Momentum-Dependent Distribtuionsat Jefferson Lab)
Clermont-Ferrand, May 2009
Peter Bosted (Jefferson Lab)
kT-effects with unpolarized protons and neutrons
kT-effects with longitudinally polarized targets
PT-dependence of A1
Transversely polarized quarks and SSA
Conclusions

2. Main ideas
Hit a quark hard (high Q2, n, W) and it flies away from target remanents and fragments into pions. “Current fragmentation”. Controlled by PDFs (u(x), d(x), du(x), dd(x)…)
Leading (highest z) pion will tend to select out which quark was hit (p+ from u, p- from d). Controlled by fragmentation functions (FF) D+(z) (favored) and D-(z) (unfavored)
Real life: Q2 dependence (QCD evolution, higher twist sensitive to correlations), and both PDFs and FFs likely depend on pt.

3. pion MX SIDIS kinematic plane and relevant variables
Pt is transverse momentum relative to virtual photon
W2=M2+Q2(1/x-1) is invariant mass of total hadronic final state

4. Start with spin-averaged Cross Sections with 6 GeV electrons

5. SIDIS – Flavor Decomposition
Leading-order
picture: hit one
quark: how big
should Mx be?
(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

6. Z-Dependence of cross sections at Pt=0
Good agreement with prediction using CTEQ5M PDFs and Binnewies fragmentation functions, except for z>0.7, or Mx>1.4 GeV.
D or D+,D-
Jlab Hall C
X=0.3, Q2=2.5 GeV2, W=2.5 GeV

7. Is SIDIS framework OK at low Mx?
Neglect sea quarks and assume no pt dependence to parton distribution functions
[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

8. Yes, These two ratios make sense more or less
Even though only a few pions being produced
GRV & CTEQ,
@ LO or NLO
“Works” better
(recall, z = 0.65 ~
Mx2 = 2.5 GeV2)
“Works” worse
Closed (open) symbols reflect data after (before) events from coherent r production are subtracted

9. And, the Q2-dependence seems flat and in agrreement with LO model too, for Q2>2 GeV2

10. More 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).
Note: typical assumption is that that sL/sT = RDIS
Determination of the pT and f dependencies are interesting for their potential to determine the transverse momentum distributions of quarks.

11. 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

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

13. 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)

14. kT-dependent SIDIS p┴ = PT – z k┴ + O(k┴2/Q2) Anselmino et al
(see presentation on PR by H. Avagyan)
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

15. Transverse momentum dependence of SIDIS
(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)
Find reasonable
fragmentation widths
but small u quark width
Diquark model
tends to agree
but not Gaussian

16. Can also look at some
very preliminary data from CLAS detector at JLab with 6 GeV electrons: wider kinematic coverage than spectrometers we have been looking at up until now, but only ratios of deuteron over proton can be measured well.

17. Very preliminary d/p ratios versus Pt in 4 z bins

18. Very preliminary d/p ratios versus Q2 in 4 z bins

19. Very preliminary d/p ratios versus f in 4 Pt bins
0.1
0.2
0.3
0.4 p+ p- p0

20. While most d/p ratios for pi0 and pi+ seem in reasonable agreement with LO SIDIS model, there seems to be a puzzle for pi-: generally higher than predicated, and possibly has large f and Q2 dependence.
12-GeV upgrade at JLab will allow to go to much higher Q2 and Mx, where higher twist and resonance effects may be much smaller.

21. CLAS12: Kinematical coverage
epX
Track resolution:
dp (GeV/c) p p2
dq (mr) < 1
df (mr) < 3
SIDIS kinematics
Q2>1
W2>4
y<0.85
MX>2
Large Q2 and MX accessible with CLAS12 are important for separation of HT contributions

22. sL/sT in SIDIS: ep  e’hX
Cornell data of 70’s (only available data until 12 GeV)
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?

23. For comparison, quality of projected 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)

24. Now lets look at what can be learned with polarized targets and electron beam Structure function g1, in the parton model, measures difference in probability for quarks to be aligned or anti-aligned with nucleon spin

25. W>2 GeV, Q2>1.1 GeV2, 0.4<z<0.7 Good agreement with
x-depenence of SIDIS proton A1 = g1/F1
W>2 GeV, Q2>1.1 GeV2, 0.4<z<0.7
Good agreement with
HERMES p+ data at
higher W.
x-dependence follows PEPSI (Lund) Monte Carlo using GRSV polarized PDFs (LO)
Magnitude also in good
agreement with simulation 25

26. z-depenence of SIDIS proton g1/F1
No significant z-dependence seen for p0 and p++ p- for 0.3<z<0.7, as expected if factorization holds
Good agreement with PEPSI predictions including dropoff at high z for p-, due to increasing importance of dd(x), in turn due to increase of D+/D- with increasing z
CLAS 5.7 GeV
PRELIMINARY

27. ALL = g1/F1 -PT-dependence
Assume different Gaussian widths for quarks aligned or not with proton spin
Even more possibilities are opened by the polarized Cahn effect studies. As discussed by Mauro the observable is sensitive to the k_T width of polarized and unpolarized quark distributions and high precision studies will provide info on those widths, which are also related to the distributions in the transverse plain.
PT-dependence of double spin asymmetries provide access to difference in kT-distributions of quarks with spin orientations along and opposite to the proton spin.

28. CLAS data for pi+ seem to suggest indeed a spin
hep-ph/
m02=0.25GeV2
mD2=0.2GeV2
CLAS data for pi+ seem to suggest indeed a spin
dependent width. What going on with pi- though?
Even more possibilities are opened by the polarized Cahn effect studies. As discussed by Mauro the observable is sensitive to the k_T width of polarized and unpolarized quark distributions and high precision studies will provide info on those widths, which are also related to the distributions in the transverse plain.

29. A1-PT-dependence on cos(f)
Quark width enters directly in this case
Even more possibilities are opened by the polarized Cahn effect studies. As discussed by Mauro the observable is sensitive to the k_T width of polarized and unpolarized quark distributions and high precision studies will provide info on those widths, which are also related to the distributions in the transverse plain.

30. Again, CLAS pi+ data suggest a smaller width
Even more possibilities are opened by the polarized Cahn effect studies. As discussed by Mauro the observable is sensitive to the k_T width of polarized and unpolarized quark distributions and high precision studies will provide info on those widths, which are also related to the distributions in the transverse plain.
Again, CLAS pi+ data suggest a smaller width
for g1 than F1

31. Collins fragmentation: Longitudinally polarized target
(sTkT)(pSL)↔ h1L
Kotzinian-Mulders Asymmetry y PT sT fC
sUL ~ KM fh
fS=fh
fS’
sin(fC) =sin(2fh)
curves, cQSM from Efremov et al
Measure the twist-2 Mulders TMD (real part of interference of L=0 and L=1 wave functions)
Study the Collins asymmetry with longitudinally polarized target will provide independent information on the Collins function.

32. PROSPECTS
Current CLAS run (eg1-dvcs) 15x (40x) more data for charged (neutral) pions with 6 GeV electrons.
CLAS-12 with 11 GeV electrons will go to higher Q2, W, Mx with about 5x again more data
Study of Pt dependence in many bins in x, z; etc to provide a much more detailed picture.

33. EXPERIMENTAL CHALLENGES
Radiative corrections (need complete map of exclusive and semi-inclusive meson production
Particle identification (pi, K especially)
Subtraction of pions from decays of diffractive vector mesons.

34. THEORETICAL CHALLENGES
Need more than two fragmentation functions?
Higher twist contributions.
Higher order QCD corrections.
Better understanding of fragmentation.
Role of intermediate resonances
etc

35. Summary DIS has given us longitudinal distributions
EXCITING TIMES AHEAD. SIDIS can provide flavor and spin dependence of the transverse momentum distributions of quards in the nucleon.
Hints of interesting results already.

36. support slides…

37. CLAS12: Mulders TMD projections
sUL ~ KM
Simultaneous measurement of, exclusive r,r+,w with a longitudinally polarized target important to control the background.

38. Azimuthal moments in SIDIS (1/Q2)

39. initial quark
A1-PT-dependence
hep-ph/
m02=0.25GeV2
mD2=0.2GeV2
scattered quark
Even more possibilities are opened by the polarized Cahn effect studies. As discussed by Mauro the observable is sensitive to the k_T width of polarized and unpolarized quark distributions and high precision studies will provide info on those widths, which are also related to the distributions in the transverse plain.
PT-dependence of double spin asymmetries provide access to difference in kT-distributions of quarks with spin orientations along and opposite to the proton spin.