1. Factorization and Transverse Momentum in SIDIS at JLab P. Bosted, H. Avakian (JLab)  Semi-inclusive processes  Factorization as a test of quark-hadron duality  Factorization tests in unpolarized SIDIS  Facorization tests in polarized SIDIS  Tranverse momentum in fragmentation Trento, Italy, May 2007

2. 2 Semi-inclusive DIS  orbital motion of quarks (p t,  dependence)  parton distributions (separate valence, sea) X.Ji  Where region I/II boundary?  Can useful information come from Region II? Main focus of SIDIS studies: MXMX pion

3. 3 SIDIS kinematic plane and relevant variables P t is transverse momentum relative to virtual photon W 2 =M 2 +Q 2 (1/x-1) is invariant mass of total hadronic final state pion MXMX

4. 4 Factorzation in SIDIS Basic idea: hit a single quark in nucleon which then hadronizes into a jet with negligible interaction with remenant quarks.  (x,z,p t ) =? PDF(x,k t ) x Frag.Fun.(z,p t )   (x,z,p h ) =? u(x,k t ) x D + (z,p t ) When integrated over transverse momenta of quarks and hadrons Example, SIDIS  + from u quark in proton

5. 5 Missing mass of pions in ep->e’  X with 6 GeV electrons Duality question: will factorization work if M x <2 GeV, even though  (1232) reonance visible? For  -, guess need M x >1.4 GeV. -- 00 ++ n 00  ++

6. 6 EXPERIMENT E00-108 at JLAB Halll C  Unpolarized electrons E=6 GeV  Scattered electrons E’=1.6 GeV, 25 to 40 deg. Average Q 2 2.5 GeV 2.  W about 2.5 GeV, but M x <2 GeV.  Detected positive and negative pions near 12 degrees  Proton and deuteron targets  Made scans in x, z. p t <0.2 GeV

7. 7 Z-Dependence of cross sections Good agreement with prediction using CTEQ5M PDFs and Binnewies fragmentation functions, except for z>0.7, or Mx>1.4 GeV. X=0.3, Q 2 =2.5 GeV 2, W=2.5 GeV  or D +,D -

8. 8 In more detail, form super-ratios Simple LO picture in valence region:  p (  + ) = 4u(x,p t )D + (z,p t ) + d(x,p t )D - (z,p t )  p (  - ) = 4u(x,p t )D - (z,p t ) + d(x,p t )D + (z,p t )  d (  + ) = [u(x,p t )+d(x,p t )] [4D + (z,p t ) + D - (z,p t )]  d (  - ) = [u(x,p t )+d(x,p t )] [4D - (z,p t ) + D + (z,p t )] R pd+ = [  p (  + ) +  p (  - )] / [  d (  + ) +  d (  - )] = [4u(x,p t ) + d(x,p t )] / 5[u(x,p t )+d(x,p t )] =  p (x)/  d (x) for any z, x, p t (if d and u have same p t depdendence)!

9. 9 In more detail, form super-ratios Simple LO picture in valence region:  p (  + ) = 4u(x,p t )D + (z,p t ) + d(x,p t )D - (z,p t )  p (  - ) = 4u(x,p t )D - (z,p t ) + d(x,p t )D + (z,p t )  d (  + ) = [u(x,p t )+d(x,p t )] [4D + (z,p t ) + D - (z,p t )]  d (  - ) = [u(x,p t )+d(x,p t )] [4D - (z,p t ) + D + (z,p t )] R pd- = [  p (  + ) -  p (  - )] / [  d (  + ) -  d (  - )] = [4u v (x,p t ) - d v (x,p t )] / 3[u v (x,p t )+d v (x,p t )] for any z, x!

10. 10 R pd+ R pd- Both ratios agree PDF models for z 1.4 GeV)

11. 11 Both ratios agree PDF models 0.2<x<0.5 for z=0.55 (possible complications x>0.5) R pd+ R pd-

12. 12 Another test: D - /D + from Deuteron  + to  - ratio Results agree HERMES (higher W, Mx>2 GeV) up to z=0.7 (Mx>1.4 at pt=0), after rho correction  d (  + ) = [u+d] [4D + +D - ]  d (  - ) = [u+d] [4D - +D + ]

13. 13 Results agree HERMES and EMC for z=0.55 and x>0.35. Maybe some x depdendence x<0.35 (sea quark correction?) Another test: D - /D + from Deuteron  + to  - ratio

14. 14 Now look at transverse momentum dependence  Previous plots all for pion transverse momentum P t  <0.1 GeV  Looks like factorization works for 0.3<z<0.7, 0.2<x<0.5, Q 2 =2.5 GeV 2.  Pulsihed in Phys. Rev. Lett. 98, 022001 (2007)  Now look at P t  dependence: found need some Q 2 -dependence to model to get good overlap of spectrometer settings.  P t  probes combination of quark intrinsitc momentum k t and favored and unfavored fragmentation widths p t (not necessarily same)

15. 15 Cross sections drop exponentially to P t  0.4: slopes for all four cases are similar and about 4.5 GeV -2 (vaires from about 4 to 5 GeV -2 depending on Q 2 correction) Cross sections at x=0.3, z=0.55 versus P t   - from p  + from p  + from d  - from d

16. 16 R pd+ R pd- Both ratios independent of p t (to 0.3 GeV) for z=0.55 Super-ratios versus transverse momentum

17. 17 Ratio of fragmentation functions appears independent of hadron transverse momentum at these kinematics (x=0.3, Q 2 =2.5, z=0.55) Another test: D - /D + from Deuteron  + to  - ratio

18. 18 Again, ratios appear constant at these kinematics (x=0.3, Q 2 =2.5, z=0.55), although bit higher than Lund MC predictions Another test: d/p ratios for  +,  - ++ --

19. 19 VERY preliminary d/p ratios from CLAS - ++ -- 00 For z=0.55 and x=0.3, CLAS results consistent with Hall C, but when average over wider kinematic range 0.3<z<0.7 and 0.15<x<0.45, find: d/p increases with p t  for  + d/p decreases with p t  for  - (for first bin, ratio 1.3, off plot!) d/p flat with p t  for  0 WHY? (acceptance, kinematic effect, nuclear effects, pr real physics?) Possible explanation: unfavored D - Wider in pt than favored D + for z<0.5

20. 20 Scattering of 5.7 GeV polarized electrons off polarized NH 3, ND 3  ~8M  + in SIDIS kinematics x x Now to polarized SIDIS at JLAB using CLAS

21. 21 Target polarization about 0.7 (0.3) for NH 3 (ND 3 ) Longitudinal beam polarization P B about 0.7 Dilution factor f varies from 0.1 to 0.3: used Lund model for n/p ratio (agrees with Hall C data) and preliminary Hall B data for A-dependence Depolarization factor D LL (y) evaluated assuming R=  L /  T same as for inclusive. Assumed A perp =0 (not measured) “  + ” and “  - ” include some K +, K - for P>1.5 GeV  0 events cleanly identified with two photons Determination of g 1 /F 1 (approximately A 1 )

22. 22 x-depenence of SIDIS proton g 1 /F 1 Good agreement with HERMES  + data at higher W. x-dependence follows PEPSI (Lund) Monte Carlo using GRSV polarized PDFs (LO) Magnitude also in good agreement with simulation W>2 GeV, Q 2 >1.1 GeV 2, 0.4<z<0.7

23. 23 Simple picture in valence region:  p (  + ) = 4u(x)D + (z) + d(x)D - (z)  p (  - ) = 4u(x)D - (z) + d(x)D + (z)  p (  + ) = 4  u(x)D + (z) +  d(x)D - (z)  p (  - ) = 4  u(x)D - (z) +  d(x)D + (z) (g 1 /F 1 ) +- =[  p (  + )+  p (  - )]/[  p (  + )+  p (  - )] = [4  u(x) +  d(x)] / [4u(x) + d(x)] = (g 1 /F 1 ) inclusive Similarly for  0 (g 1 /F 1 ) 0 = (g 1 /F 1 ) inclusive Polarized SIDIS: factorization tests Proton (g 1 /F 1 ) +- and (g 1 /F 1 ) 0 should be independent of z and p t, and equal to inclusive (g 1 /F 1 )

24. 24 Polarized SIDIS factorization test g 1 /F 1 for inclusive, for the sum of     , and for   are fairly consistent with each other in the range 0.4<z<0.7, as expected in LO if factorization works. Cuts used: Mx>1.4 GeV, Q 2 >1.1 GeV 2, W>2 GeV GRVS Significant ?

25. 25 z-depenence of SIDIS proton g 1 /F 1 CLAS 5.7 GeV PRELIMINARY No significant z- dependence seen for  0 and  + +  - for 0.3<z<0.7, as expected if factorization holds Good agreement with PEPSI predictions including dropoff at high z for  -, due to increasing importance of  d(x), in turn due to increase of D + /D - with increasing z

26. 26 p t -depenence of SIDIS proton g 1 /F 1 First, need to account for LARGE p t -depenence of dilution factor (ratio of counts from ptons to counts from all materials in polarized target, mainly nitrogen). Used CLAS measurements of C/d averaged over our kinematics for SIDIS  +. Assumed N/d same as C/d and  - and  0 same as  +. Results on next page assume NO p t -depenence to d/p ratio needed to obtain final dilution factor. CLAS Preliminary

27. 27 Signicant decrease of  + A 1 with increasing p t ! Can be explained in terms of broder kt distributions for anti-aligned quarks compared to quarks aligned with proton spin (blue curves). p t -depenence of SIDIS proton A 1 CLAS Preliminary

28. 28 IF we used very preliminary pt dependence of d/p to correct dilution factor as shown on slide 19,  + lies almost on top of blue curve, and the strange rise in the  - becomes less significant. Essential to understand p t -dependence of deuteron/proton for precision measurements using polairzed NH3 target. p t -depenence of SIDIS proton A 1 CLAS Preliminary

29. 29 p t -depenence of SIDIS proton g 1 /F 1 Another explanation for opposite slopes for  + and  - is that D - /D + increases with p t (I.e. unfavored fragmentation has a wider transverse momentum dependence), as can be seen from above. This effect magnified in g 1 compared to F 1 due to  d negative while  u positive  p (  + ) = 4  u(x,p t )D + (z,p t ) +  d(x,p t )D - (z,p t )  p (  - ) = 4  u(x,p t )D - (z,p t ) +  d(x,p t )D + (z,p t )

30. 30 In region where factorization tests hold, analyze  depdendence of A LL, A LU, and A UL to learn about orbital motion of quarks, polarized fragmentation, and higher twist contributions. CLAS 5.7 GeV PRELIMINARY

31. 31 Significant phi-dependence seen for proton  + CLAS 5.7 GeV PRELIMINARY cos(  ) in A LL sin(  ) and sin(2  ) in A UL sin(  ) in A LU sin(2  ) in A UL of particular interest: leading twsit function Sensitive to L=0 and L=1 interference

32. 32 Significant SSA measured for pions with longitudinally polarized target Complete azimuthal coverage crucial separation of sin  sin2  moments SSA measurements at CLAS p 1 sin  +p 2 sin2  0.12<x<0.48 Q 2 >1.1 GeV 2 P T <1 GeV ep→e’  X W 2 >4 GeV 2 0.4<z<0.7 M X >1.4 GeV y<0.85 CLAS PRELIMINARY p 1 = 0.059±0.010 p 2 =-0.041±0.010 p 1 =-0.042±0.015 p 2 =-0.052±0.016 p 1 =0.082±0.018 p 2 =0.012±0.019

33. 33 SSA: x-dependence PRELIMINARY 5.7 GeV Twist-2 Higher Twist Data in rough agreement with Efremov et al. predictions, except for  0 sin(  ) term (evidence for terms not involving Collins fragmentation?)

34. 34 For Collins fragmentation function use HERMES data Systematic error only from unknown ratio of favored and unfavored Collins functions (R= H 1 d→  /H 1 u→  ), band correspond to -2.5<R<0 CLAS-5.7GeV First glimpse of Twist-2 TMD h 1L ┴ PRELIMINARY More data required with  - &  0 Exclusive 2 pion background may be important: analysis in progress. Distribution functions from  QSM from Efremov et al

35. 35 sin  SSA  + increases with PT and is consistent with HERMES measurement. A UL SSA: P T -dependence HT –SSA significant for  + and  0 CLAS PRELIMINARY

36. 36 Future Full NLO, higher twist anlayses 20x more  +,  -, 40x more  0 for g 1 /F 1 at 6 GeV on proton (using CLAS) 3x more  + and  - g 1 /F 1 data on deuteron (Hall C) Jlab upgrade to 11 GeV electrons combined with major upgrade to CLAS will allow huge increase in kinematic coverage and statstical accuracy in SIDIS!

37. 37 Summary Factorization in SIDIS pion production seems to work for 0.3 2 GeV, Mx>1.4 GeV, 0.2 1 GeV 2. Opens opportunity for studies of transverse momentum in PDF, fragmentation Jlab upgrade will allow definitive measurements for x>0.1 Puzzling results for negative pions in both spin-average d/p, and proton g1/F1 versus pt. Could both be due to p t width of favored and unfavored fragmentation differing?

38. 38 In region where factorization tests hold, can use data to constrain polarized PDFs in NLO analysis(separate out polarized up, down valence and sea quark parton distributions). CLAS 5.7 GeV PRELIMINARY