Color flow of quarks and gluons in high-energy collisions

1. Color flow of quarks and gluons in high-energy collisions Maarten Buffing (VUA) Track: theoretical physics Amsterdam master of physics symposium April 29, 2011

2. Content • Introduction to QCD and color • High-energy collisions • Theory: phases • Importance to experiments • Conclusion and outlook

3. QCD • Standard Model • Internal structure of proton • Focus on quarks and gluons Leptons: Quarks: Gauge bosons: Proton

4. QCD • Standard Model • Internal structure of proton • Focus on quarks and gluons Leptons: Quarks: Gauge bosons: Proton

5. Color • QCD has color charges (cc’s) forming a symmetry group • There exist 3 cc’s and 3 anti-cc’s • All observables are colorless Feynman diagram description: Quarks: Gluons:

6. Color • QCD has color charges (cc’s) forming a symmetry group • There exist 3 cc’s and 3 anti-cc’s • All observables are colorless Feynman diagram description: Quarks: Gluons:

7. Colorflow (1) • Quark-quark-gluon vertices give rise to multiple color flows • Singlet gluon contributions must be subtracted

8. Colorflow (2) • In Feynman diagrams, multiple color flows contribute • Consider qq-scattering with two gluons as an example

9. Colorflow (2) • In Feynman diagrams, multiple color flows contribute

10. Collisions (1) • Consider quark-quark scattering • Toy model: no color exchange

11. Collisions (2) • Implications for the cross-section of high energy collisions even in the case of no color exchange • Distribution functions • Fragmentation functions Δ

12. Collisions (2) • Implications for the cross-section of high energy collisions even in the case of no color exchange • Distribution functions • Fragmentation functions Δ

13. Collisions (2) • Implications for the cross-section of high energy collisions even in the case of no color exchange • Distribution functions • Fragmentation functions Δ

14. Collisions (3) • Additional leading gluons need to be considered, for instance: • They complicate color flow • Color entanglement T.C. Rogers, P.J. Mulders (2010)

15. Collisions (3) • Additional leading gluons need to be considered, for instance: • They complicate color flow • Color entanglement T.C. Rogers, P.J. Mulders (2010)

16. Theory: phases (1) • Color entanglement spoils factorization

17. Theory: phases (2) • Enormous amount of contributing Feynman diagrams: lots of mathematics • Example: a number of three gluon contributions

18. Importance to experiments • It turns out that summation of all diagrams with arbitrary number of gluons gives phases • The phases save color-gauge invariance • Non-trivial experimental effects in transverse plane for certain polarisations

19. Conclusion and outlook • Color flow is relevant for the understanding of high-energy collisions in specific observables • Inclusion of all possible diagrams assures color-gauge invariance and gives rise to novel features • M.G.A. Buffing, P.J. Mulders, “Gauge links for Transverse Momentum Dependent Correlators at tree-level” (will appear on the Archive soon)

20. Backup slides

21. Transverse momentum • Decomposition of quark momentum: Proton

22. Preventing double counting • Certain diagrams are identical, for example: