Mul$plici$es and phenomenology

Transcription

1 Mul$plici$es and phenomenology Transversity 014, Chia (Cagliari) Andrea Signori In collabora<on with: A. Bacche6a M. Echevarria M. Radici G. Schnell 6/10/14 Andrea Signori - VU/Nikhef 1

2 Goals Inves<gate the 3D structure of hadrons in momentum space (access TMD distribu<ons) with a focus on its flavor structure and evolu<on 6/10/14 Andrea Signori - VU/Nikhef

3 The to- do list SIDIS fit with no evolu<on at all (Hermes) [done] Get hints on the non- perturba<ve parameters involved in evolu<on from e+e- annihila<ons, compa<ble with the previous fit [in progress] SIDIS fit with QCD evolu<on (Hermes + Compass) Global SIDIS + DY + e+e- fits TODAY: 1) SIDIS mul<plici<es ) e+e- mul<plici<es DOI: / JHEP 11(013)194 6/9/14 Andrea Signori - VU/Nikhef 3

4 SIDIS mul<plici<es 6/10/14 Andrea Signori - VU/Nikhef 4

5 TMDs in SIDIS Unpolarized! lepton SIDIS lepton hadron proton Parton model picture LO QED Zero- order QCD Leading twist (P ht ) X a f a 1 (x, k?) D a!h 1 (z,p?) 6/9/14 Andrea Signori - VU/Nikhef 5

6 Which transverse momenta? D1^a q! q 0 f1^a 6/9/14 Andrea Signori - VU/Nikhef 6

7 Flavor dependent Gaussians Different Gaussian of TMD parts f a 1 (x, k?)=f a 1 (x) 1 hk?,a i exp k? hk?,a i hk?,u v i6= hk?,d v i6= hk?,seai Simplified flavor dependence! /9/14 Andrea Signori - VU/Nikhef 7

8 Flavor dependent Gaussians Different Gaussian of TMD parts D1 a!h (z,p? )=D1 a!h 1 (z) hp?,a!h i exp P? hp?,a!h i different combina<ons out of u, d, s ±, K ± P?,u ~ + = P?, d~ + = P?,ū ~ = P?,d ~ P?,fav, P?,u ~ K+ = P?,ū ~ K P?,uK, P?, s ~ K+ = P?,s ~ K P?,sK, P?,all others P?,unf. 6/9/14 Andrea Signori - VU/Nikhef 8

9 Kinema<c dependence hk?,qi(x) =hk d?,qi (1 x) x (1 ˆx) ˆx Flavor independent Kinema<c dependence h d k?,qi = hk?,qi(ˆx =0.1) hp?,q!hi(z) =h \ P?,q!hi Flavor independent Kinema<c dependence (z + )(1 z) (ẑ + )(1 ẑ) h \ P?,q!hi = hp?,q!hi(ẑ =0.5) 6/11/14 Andrea Signori - VU/Nikhef 9

10 Flavor analysis 6/9/14 Andrea Signori - VU/Nikhef 10

11 Fijng procedure } Distributions 00 Monte Carlo fit of best-values 6/9/14 Andrea Signori - VU/Nikhef 11

12 Fijng procedure proton target global χ / d.o.f. = 1.63 ± 0.1 no flavor dep. 1.7 ± 0.11 mhx,z,p ht,q L, proton target π 1.80 ± ± p Xx\~0.15 XQ \~.9 GeV p <z< <z< <z< <z<0.80 π +.64 ± ± 0.3 K 0.78 ± ± K K + K ± ± P ht 6/9/14 Andrea Signori - VU/Nikhef 1 FIG. 3. Data points: Hermes multiplicities m h (x, z, P ; Q ) for pions and kaons o a proton target as functions of P for P ht

13 TMD FFs full analysis q π favored width < q K favored width point of no flavor dep. q π favored width < unfavored 6/9/14 Andrea Signori - VU/Nikhef 13

14 TMD PDFs full analysis replica 73 χ /dof = 1.70 replica 149 χ /dof = 1.87 sea width > (mostly) u v width replica 130 χ /dof = 1.77 replica 186 χ /dof = 1.38 point of no flavor dep. d v width < (mostly) u v width 6/9/14 Andrea Signori - VU/Nikhef 14

15 QCD evolu<on Looking towards SIDIS + DY + l + l - global fits Collins (011) EIS (01-013) Collinear OPE for small b T Intrinsic (large b) transverse momenta Perturba<ve transverse momenta and evolu<on (resummed logs) Som evolu<on 6/9/14 Andrea Signori - VU/Nikhef 15

16 e + e - mul<plici<es double goal: - pin down flavor dependence in TMD FFs - get info on the non- perturba<ve evolu<on 6/10/14 Andrea Signori - VU/Nikhef 16

17 Hadron produc<on e e + e + e! jets 6/10/14 Andrea Signori - VU/Nikhef 17

18 One hadron e e + e! hx P h zq T See A. Baccheoa s talk in QCD Evo 014 e + thrust axis d dzdq T 6 = dy Q A(y) z H(Q/µ) X q e q Z 1 0 db T b T J 0 (q T b T ) D q!h 1 (z,b T,µ) + Y (q T,Q ) 6/11/14 Andrea Signori - VU/Nikhef 18

19 One hadron e e + e! hx P h zq T See A. Baccheoa s talk in QCD Evo 014 thrust axis d dzdq T 6 = dy Q A(y) z H(Q/µ) X q e q Z 1 0 db T b T J 0 (q T b T ) D q!h 1 (z,b T,µ) + Y (q T,Q ) 6/10/14 Andrea Signori - VU/Nikhef 19

20 Two hadrons e e + e! h 1 h X P h P h1 zq T Boer, Jakob, Mulders, NPB504 (97) e + Z 1 d dz 1 dz dqt =6 dy Q A(y) z 1z H(Q/µ) X e q db T b T J 0 (q T b T ) q 0 apple D q!h 1 1 (z 1,b T,µ)D q!h 1 (z,b T,µ)+(q! q) + Y (qt,q ) 6/10/14 Andrea Signori - VU/Nikhef 0

21 e + e - mul<plici<es {e + e! h 1 h X} / {e + e! h 1 X} TMD collinear M(h 1,h )= d h dz 1 dz dydq T d 1h dz 1 dy The same structure as in the SIDIS case NB The experimental transverse momentum is P 1? = z 1 q T 6/9/14 Andrea Signori - VU/Nikhef 1

22 Evolved TMD FFs OPE of the perturba<ve part on the collinear distribu<on D a!h 1 (z,b T,Q,µ )= X i Perturba<ve evolu<on Intrinsic b T part Gaussians from Hermes! [C a/i D i/h ](z,b,µ b,µ b ) F NP FF (z,b T ) apple Z µ exp apple exp ds µ b s ln Q µ b FF ln Q s, S(s) D(b,µ b )+ g 4 b T b b T p 1+b T /b max b- star prescrip<on Som evolu<on Collins (011) EIS (01-013) 6/11/14 Andrea Signori - VU/Nikhef

23 Input from the Hermes fit P?,u ~ + = P?, d~ + = P?,ū ~ = P?,d ~ P?,fav, P?,u ~ K+ = P?,ū ~ K P?,uK, P?, s ~ K+ = P?,s ~ K P?,sK, P?,all others P?,unf. 00 VALUES Kinema<c dependence hp?,q!hi(z) =h \ P?,q!hi (z + )(1 z) (ẑ + )(1 ẑ) 6/10/14 Andrea Signori - VU/Nikhef 3

24 Effects of theore<cal accuracy M( +, ) Preliminary 0.0 NNLL Est. exp. error 0.10 LL 0.05 NLL band q T z 1 = z =0. 6/9/14 Andrea Signori - VU/Nikhef 4

25 Sensi<vity to evolu<on parameters {0.5 GeV 1, 0.68} {1.0 GeV 1, 0.41} {1.5 GeV 1, 0.18} M( +, ) Preliminary Est. exp. error z 1 = z = {b max, g } q T 6/10/14 Andrea Signori - VU/Nikhef 5

26 Sensi<vity to evolu<on parameters {b max, g } Preliminary Est. exp. error {0.5 GeV 1, 0.68} {1.0 GeV 1, 0.41} {1.5 GeV 1, 0.18} q T 6/10/14 Andrea Signori - VU/Nikhef 6 z 1 = z =0.7 M( +, )

27 Intrinsic parameters: z- dependence M(K +,K ) z= z= Est. exp. error Preliminary z= q T 6/9/14 Andrea Signori - VU/Nikhef 7

28 Intrinsic parameters: flavor M( +, ) Preliminary Est. exp. error z 1 = z = M(K +,K ) q T {b max =1.5 GeV 1,g =0.18} 6/10/14 Andrea Signori - VU/Nikhef 8

29 Intrinsic parameters: flavor M( +, ) M(K +,K ) z 1 = z =0. Preliminary Est. exp. error q T {b max =1.5 GeV 1,g =0.18} 6/10/14 Andrea Signori - VU/Nikhef 9

30 Intrinsic parameters: flavor M( +, ) M(K +,K ) z 1 = z =0. Preliminary Est. exp. error q T {b max =1.5 GeV 1,g =0.18} 6/10/14 Andrea Signori - VU/Nikhef 30

31 Conclusions SIDIS mul$plici$es There is a lot of room for flavor dependence : clear indica<on in TMD FFs that q π favored width < unfavored & q K favored TMD PDFs: hints that d v width < u v width < sea width flavor- independent fit is not ruled out an<correla<on: many intrinsic {k,p } give same P ht 6/9/14 Andrea Signori - VU/Nikhef 31

32 Conclusions e+e- mul$plici$es Electron- positron data at 100 GeV can be extremely valuable to pin down evolu6on parameters They are useful to constrain flavor dependence of the TMD fragmenta<on func<ons They are needed to determine the nonperturba6ve parameters of TMD fragmenta<on func<ons Indirectly, the knowledge of TMD fragmenta<on func<ons will help constraining TMD distribu<on func<ons 6/10/14 Andrea Signori - VU/Nikhef 3

33 Backup slides 6/9/14 Andrea Signori - VU/Nikhef 33

34 Flavor in transverse space Since the flavor dependence In the collinear case is strong why not looking for it in!! k dependence!! of TMDs?! 6/11/14 Andrea Signori - VU/Nikhef 34

35 Flavor in transverse space ü Lajce QCD calcula<ons Musch et al., PRD 83 (11) [ ] ü Model calcula<ons Chiral quark soliton model [ Scweitzer et al., JHEP 1301 (913) 163 ] Diquark spectator model [ Baccheoa et al., PRD 78 (08) ] Sta<s<cal approach [ Bourrely et al., PRD 83 (11) ] NJL- jet model [ Matevosyan et al., PRD 85 (1) ] [ ] ü Previous fits JLab Hall C [ Asaturyan et al., (E00-108), PRC 85 (1) 0150 ] 6/11/14 Andrea Signori - VU/Nikhef 35

36 Flavor in transverse space With flavor dependence we can account for different cross sec<ons for different target/final state hadron combina<ons. 6/11/14 Andrea Signori - VU/Nikhef 36

37 Hermes e ± + P/D! e ± + { ± /K ± } + X 6 bins in x, 8 bins in z, 7 bins in P ht, targets, 4 final- state hadrons 688 points Our selec<on Remove the first bin x- Q (Q >1.4 GeV ) 0.1 < z < 0.8 P ht < Q / analyzed points limited Q range safely neglect evolu<on everywhere 6/11/14 Andrea Signori - VU/Nikhef 37

38 Flavor in transverse space valence picture of proton, #u / #d = Less up at larger transverse momentum..! Lajce QCD Musch et al., P.R. D83 (11) /9/14 Andrea Signori - VU/Nikhef 38

39 Flavor in transverse space valence Chiral quark soliton model (Schweitzer, Strikman, Weiss) JHEP 1301 (913) 163 sea And other models Diquark spectator (Baccheoa, Courtoy, Radici PRD 78 (08) ) Sta<s<cal approach (Bourrely, Buccella, Soffer - PRD 83 (11) /9/14 Andrea Signori - VU/Nikhef 39

40 Flavor in transverse space TMD FFs - NJL- jet model Matevosyan et al., P. R. D85 (1) /9/14 Andrea Signori - VU/Nikhef 40

41 Flavor in transverse space Asaturyan et al. (E00-108), P. R. C85 (1) 0150 up is wider than down favored wider than unfavored 6/9/14 Andrea Signori - VU/Nikhef 41

42 Flavor independent Gaussianity Gaussian of TMD parts f a 1 (x, k?)=f a 1 (x) 1 hk? i exp k? hk? i hk?,ui = hk?,di = The same variance for all the flavors! /9/14 Andrea Signori - VU/Nikhef 4

43 Flavor independent Gaussianity Gaussian of TMD parts D a!h 1 (z,p?)=d a!h 1 (z) 1 hp? i exp P? hp? i hp?,u! + i = hp?,u! i = hp?,u!k + i = The same variance for all the fragmenta<on processes /9/14 Andrea Signori - VU/Nikhef 43

44 TMD PDFs full analysis 68% confidence intervals of best- fit parameters for TMD PDFs in the different scenarios Parameters for TMD PDFs Default Q > 1.6 GeV Pions only Flavor-indep. ˆk?,dv [GeV ] 0.30 ± ± ± ± 0.10 ˆk?,uv [GeV ] 0.36 ± ± ± ± 0.10 ˆk?,sea [GeV ] 0.41 ± ± ± ± 0.10 (random) 0.95 ± ± ± ± 0.64 (random) 0.10 ± ± ± ± 0.1 6/11/14 Andrea Signori - VU/Nikhef 44

45 TMD FFs full analysis 68% confidence intervals of best- fit parameters for TMD FFs in the different scenarios Parameters for TMD FFs Default Q > 1.6 GeV Pions only Flavor-indep. ˆP?,fav [GeV ] 0.15 ± ± ± ± 0.03 ˆP?,unf [GeV ] 0.19 ± ± ± ± 0.03 ˆP?,sK [GeV ] 0.19 ± ± ± 0.03 ˆP?,uK [GeV ] 0.18 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± /11/14 Andrea Signori - VU/Nikhef 45

46 Results Tension in the collinear case 6/9/14 Andrea Signori - VU/Nikhef 46

47 TMD PDFs without Kaons sea width < (mostly) u v width Strange quarks are relevant! point of no flavor dep. d v width ~ (mostly) u v width 6/9/14 Andrea Signori - VU/Nikhef 47

48 TMD lib & plooer TMD lib : a library of parametriza<ons of TMDs and updfs on the same foo<ng of LHAPDF F. Hautmann, H. Jung T. Rogers, P. Mulders, AS 6/9/14 Andrea Signori - VU/Nikhef 48

49 Fijng procedure Sample of original data 6/10/14 Andrea Signori - VU/Nikhef 49

50 Fijng procedure Replica of the original data with Gaussian noise 6/10/14 Andrea Signori - VU/Nikhef 50

51 Fijng procedure We fit the replicated data 6/10/14 Andrea Signori - VU/Nikhef 51

52 Fijng procedure repea<ng the fit over the 00 replicas 6/10/14 Andrea Signori - VU/Nikhef 5

53 Fijng procedure Plot of the 68% CL bands 6/10/14 Andrea Signori - VU/Nikhef 53