1. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 1 Correlations in double parton distributions at small x MTA KFKI RMKI, Budapest, Hungary Dept. of Astronomy and Theoretical Physics, Lund University, Sweden András Ster

2. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 2 Content Introduction Double Parton Scattering & Double Parton Distributions The Lund Dipole Cascade Model Application to Double Parton Distributions Results Summary

3. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 3 Introduction - Motivation Multiple hard parton (q,g) collisions are common in high energy pp collisions For example: 4 jets in 63 AGeV events @ CERN ISR (AFS) 4 jets and 3 jets +  in 1.8 TeV events @ Tevatron (CDF, D0) ? @ LHC Larger probability found than expected for uncorrelated hard subcollisions

4. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 4 Literature Connection between correlations in momentum and impact parameter (b) space have not yet been studied

5. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 5 Correlation studies Our solution: detailed dynamical model for parton evolution (Lund Dipole Cascade Model) Earlier Sjöstrand and van Zilj assumed that the dependence of double-parton density on kinematic variables (x, Q 2 ) and on the separation in impact parameter space (b) factorizes. Implemented in PYTHYA and HERWIG event generators Problem: how to extrapolate to higher energies (LHC)

6. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 6 Correlation studies Lund Dipole Cascade Model Based on BFKL and Müller’s dipole cascade model Correlation sources in the model: 1) from fluctuations (event by event) 2) “hot spots” makes the profile narrower

7. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 7 Double Parton Scattering & Double Parton Distributions - Experimental results Measure of correlation is defined by  eff according to  D (A,B) is the cross-section of the two hard processes  S A and  S B are the single inclusive cross-sections If hard interactions were uncorrelated,  eff would be equal to the total non-diffractive corss-section

8. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 8 Experimental results CERN ISR (AFS) results:  eff  15 mb Tevatron (CDF, D0) results:  eff  5 mb

9. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 9 The formalism: Stirling and Gaunt: Essential formulae

10. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 10 The Lund Dipole Cascade Model We define: With the constraint:

11. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 11 The Lund Dipole Cascade Model Dipole cascades:

12. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 12 The Lund Dipole Cascade Model We define: With the constraint:

13. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 13 Results

14. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 14 Results

15. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 15 Results

16. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 16 Results

17. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 17 Results

18. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 18 Results

19. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 19 Results

20. ZIMANYI-SCHOOL11, Budapest, 01/12/2011 A. Ster, RMKI, Hungary 20 Summary In our analysis we have found that the two-parton correlation function F(b) in a non-trivial way on all kinematic variables x 1,x 2,Q 2 1,Q 2 2 Lund Dipole Cascade Model offers unique possibility to study gluon evolution inside hadrons at small x Our results show a non-flat energy dependence within errors compatible with experiments in their energy range.