TMDs and simulations for EIC

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1 POETIC 2012, August 19 22, Indiana University Jefferson Lab TMDs and simulations for EIC F E

2 Nucleon landscape Nucleon is a many body dynamical system of quarks and gluons Changing x we probe different aspects of nucleon wave function How partons move and how they are distributed in space is one of the future directions of development of nuclear physics Technically such information is encoded into Generalised Parton Distributions and Transverse Momentum Dependent distributions See talks by Christian Weiss, Jianwei Qiu, Marc Schlegel,... Plot courtesy of Christian Weiss These distributions are also referred to as 3D (three-dimensional) distributions 2

3 Wigner distribution Tansverse Momentum Dependent distributions Generalized Parton Distributions Parton Distribution Functions Form Factors 3

4 Transverse Momentum Dependent distributions SIDIS If produced hadron has low transverse momentum it will be sensitive to quark transverse momentum TMD factorization proven in QCD Ji, Ma, Yuan (2002) Collins (2011) 4

5 Transverse Momentum Dependent distributions SIDIS in IMF: St r uc k Gauge link qu ar k Ensures gauge invariance of the distribution, cannot be canceled by gauge choice 5

6 TMDs 8 functions in total (at leading Twist) Each represents different aspects of partonic structure Each function is to be studied Kotzinian (1995), Mulders, Tangerman (1995), Boer, Mulders (1998) 6

7 Correlation of transverse quark motion and the nucleon spin Sivers function This function gives access to 3D imaging Spin-orbit correlation Physics of gauge links is represented Requires Orbital Angular Momentum No polarisation: Polarisation: EIC report, Boer, Diehl, Milner, Venugopalan,Vogelsang et al, 2011; Duke workshop report: Anselmino et al Eur.Phys.J.A47:35,2011 EIC Whitepaper

8 What do we know about TMDs Sivers n o i t c n u f 8

9 HERMES, COMPASS, RHIC, BELLE, BABAR and JLab are sources of experimental information for TMD physics Hundreds of experimental points on Sivers function There exists a number of extractions Anselmino et al 2009 HERMES 02 COMPASS 04 JLAB 11 Vogelsang, Yuan 05 Collins et al 06 Anselmino et al Bacchetta, Radici 11 9

10 Extractions compare well with each other Anselmino et al 2006 Collins et al

11 Extractions compare well with models MIT bag model Quark-diquark model LCWF Quark-diquark model MIT bag model Yuan 03 Gamberg, Goldstein, Schlegel 08 Yuan, Pasquini 10 Bacchetta et al 10 Avakian et al 10 etc Anselmino et al 09 Bacchetta et al 10 11

12 Steady growth of interest 100 Title Sivers in the literature < 2005 < 2008 <

13 Estimate of current uncertainty Based on Anselmino et al 09 Up quark Down quark 13

14 Estimate of current uncertainty Based on Anselmino et al 09 Up quark Down quark Current uncertainty in low x region 14

15 Estimate of current uncertainty Based on Anselmino et al 09 Up quark Down quark Region of x covered by existing data 15

16 Estimate of current uncertainty Based on Anselmino et al 09 Up quark Down quark EIC can reach here 16

17 Estimate of current uncertainty Based on Anselmino et al 09 Estimate of uncertainty is based on Monte Carlo method 17

18 Estimate of current uncertainty Based on Anselmino et al 09 Estimate of uncertainty is based on Monte Carlo method Value of parameter corresponds to the minimum of 18

19 Estimate of current uncertainty Based on Anselmino et al 09 Estimate of uncertainty is based on Monte Carlo method Error of parameter corresponds to 19

20 Estimate of current uncertainty Based on Anselmino et al 09 Estimate of uncertainty is based on Monte Carlo method We use Monte Carlo to populate Robust in case of non symmetric errors 20

21 Estimate of current uncertainty Based on Anselmino et al 09 Estimate of uncertainty is based on Monte Carlo method Choice of is important 21

22 Estimate of current uncertainty Based on Anselmino et al 09 Estimate of uncertainty is based on Monte Carlo method Choice of is important Anselmino et al 09 22

23 What do we expect from EIC? 23

24 Kinematics Kinematics JLab 12 and future Electron Ion Collider are complimentary 24

25 Kinematics and existing data 25

26 Kinematics and existing data W E N R E I T N O R F 26

27 What do we expect at EIC? Prediction for EIC 5x100 kinematics based on Anselmino et al 09 27

28 What do we expect at EIC? HERMES data, se t a t a e d n onl y h t t of a ti o P a r o n str dem EIC Estimates of experimental error for EIC at 10/fb 28

29 What do we expect at EIC?, se t a t a e d n onl y h t t of a ti o P a r o n str dem Very small error in low-x region Estimates of experimental error for EIC at 10/fb 29

30 Generate pseudo-data, se t a t a e d n onl y h t t of a ti o P a r o n str dem Generate pseudodata around our predictions Estimates of experimental error for EIC at 10/fb 30

31 Generate pseudo-data ta, l y a d u al i o n o n t c a at N o t o n str dem Generate pseudodata 1- around our predictions Based on Anselmino et al 09 31

32 Fit the pseudo-data ta, l y a d u al i o n o n t c a at N o t o n str dem Fit the pseudodata and estimate the error Based on Anselmino et al 09 32

33 Generate pseudo-data ta, l y a d u al i o n o n t c a at N o t o n str dem Compare the error to the existing one Based on Anselmino et al 09 33

34 Tomographic scan of the nucleon 34

35 Results 35

36 Current knowledge Expected at EIC 36

37 Results 37

38 Results 38

39 Drawbacks The estimate is pure statistical No control over systematical theoretical error, such as dependence on functional form, higher twist contributions, evolution etc Note that generated pseuododata does not have estimate on systematical errors either No error propagation due to the use of existing PDFs and FFs (those have substantial uncertainty) Given all this one should comment results carefully 39

40 Advantages s n o i s u l c Con The estimate of the error uses the same method as the estimate of current error Thus the comparison of existing uncertainty and the projected one at EIC is trustworthy Some of theoretical uncertainties such as evolution can be controlled There is no doubt that EIC precision in TMD measurements is going to be great! 40

41 Thanks to Xin Qian (CALTECH) Tom Burton (BNL) Min Huang (JLab) for their contribution to the analysis 41