1. NON COMMUTATIVITY and LORENTZ VIOLATION in RELATIVISTIC HEAVY ION COLLISIONS PAOLO CASTORINA Università and INFN-Catania-Italy Martina Franca June.2010 – QCD @ Work - Beppe Nardulli memorial workshop

3. 1. QCD at finite temperature and density 2. Topological field configurations 3. Space-time non-commutativity and Lorentz violation (Kharzeev et. al. NPA 803(2008)227) P.Castorina,A.Iorio,D.Zappalà 1004.2454 FUNDAMENTAL ASPECTS IN RELATIVISTIC HEAVY ION COLLISIONS See also N. Paver– this workshop

4. Where ? When? Theoretical motivations Phenomenology ScheduleLHC RHIC ? Why? NON COMMUTATIVITY AND LORENTZ VIOLATION How?Formulations

5. Why? First paper - Snyder : Phys. Rev. 71 (1947) 38 Non commutativity in Lowest Landau level Quantum gravity Localization at Planck scalerequires momenta Gravitational effects of this localized energy ! String theory NON COMMUTATIVITY AND LORENTZ VIOLATION R.Jackiw hep-th/0305027; G.Dunne and R.Jackiw NPB33C(1993)114 R.J.Szabo, Phys. Rep. 378(2003)207 See For example S.Doplicher et al. Comm. Math. Phys.172(1995)187

6. System localization is meaningless for distances CANONICAL FORM (spatial coordinates) surface NON CANONICAL FORM NON COMMUTATIVITY AND LORENTZ VIOLATION HOW ? M.R.Douglas and N.A.Nekrasov, Rev. Mod. Phys. 73(2001)977 See For example S.Doplicher et al. Comm. Math. Phys.172(1995)187

7. NON COMMUTATIVITY AND LORENTZ VIOLATION HOW ? PLANE WAVES DEFORMATION OF THE MASS SHELL RELATION Example: Quantum gravity inspired phenomenology G.Amelino-Camelia, gr-qc/0402009,T.Jacobson et al., Springer. Proc. Phys. 98(2005)83; Nature 424(2003)1019

8. NON COMMUTATIVITY AND LORENTZ VIOLATION NON COMMUTATIVE ALGEBRAIC STRUCTURE MOYAL PRODUCT DEFORMED PRODUCT HOW ? standard product

9. NON COMMUTATIVE FIELD THEORY Non commutative NON COMMUTATIVE ELECTRODYNAMICS

10. SEIBERG- WITTEN MAP ? NON LINEAR RELATION NON COMMUTATIVE ELECTRODYNAMICS ≈ NON LINEAR ELECTRODYNAMICS

11. NON COMMUTATIVE ELECTRODYNAMICS Solution of field equations in background magnetic field B PLANE WAVES Transverse to R.Jackiw et al. Phys. Lett. B 517(2001)450

12. NON COMMUTATIVE PHOTONS Deformed mass-shell relation spectrum out of plane radiation Modification of synchrotron radiation in vacuum ! Modification of Cherenkov radiation Modification of kinematical thresholds pair production by free photon P.C,A.Iorio,D.Zappalà: PRD 69(2004)065008,EuroPhys. Lett. 69(2005)912, 64(2003)641,Nucl.Phys.Proc.Sup 136(2004)333.

13. NON COMMUTATIVE ELECTRODYNAMICS Synchrotron radiation Cherenkov effect High energy gamma rays O() NO DETECTABLE EFFECTS FOR TERRESTRIAL MAGNETIC FIELD NO DETECTABLE EFFECTS FOR GALACTIC/EXTRAGALACTIC MAGNETIC FIELDS WHERE ? S.Carroll et al. PRL 87(2001)141601

14. MAGNETIC FIELD IN NON CENTRAL RELATIVISTIC HEAVY ION COLLISIONS Order of magnitude estimate: ions move on straight line trajectories with impact parameter b and Lorentz factor γ in the collider system, G.Baur et al. Phys. Rep. 453(2007)1 RHIC LHC CALCULATIONS Microscopic transport model (Skokov et al.,0907.1396) Magnetic field generated by the spectators and partecipants using classical calculation which included the effect of baryon stopping in the partecipants region (Kharzeev et. al. NPA 803(2008)227)

15. Gold-Gold 100 Gev/A increases with b B orthogonal to the reaction plane

16. Terrestrial Lab magnetic field 1 – 10 Tesla Galactic/extragalactic magnetic field Relativistic heavy ion collisions BUTBUT…

17. Non Commutative free photon T = transverse to k

18. IF

19. Non Commutative photons Enhancement of low invariant mass lepton pairs BACKGROUND Drell-Yan production Resonance decays Large invariant mass Quasi real photons

20. ISOLATION CUTS Ratio between the yelds of low invariant mass lepton pairs in nuclues-nucleus and proton-proton collisions 1 Produced B is orthogonal to the reaction plane, y=0, B || y 2

21. TRANSVERSE TO k If the photon is IN the reaction plane If the photon is OUT the reaction plane Maximizes non-commutative effects Reduces non-commutative effects 2 IN/OUT reduction of low invariant mass e+e- pairs, on event by event basis Large transverse energy (photon) lepton pair IN the reaction plane 3

22. ** NC * + +

23. * * ….. STANDARD MODEL BACKGROUND

24. LOW INVARIANT MASS AND LARGE TRANSVERSE MOMENTUM Aurenche et al. Phy.Lett.B 209(1988)375, hep-ph 0311131 Photon Physics in HIC at the LHC

25. , 1.15 ≈0.014- A.Bedall E.P.J.C54(2008)365

26. Pair-Pair Correlations 4 This correlators is different from zero if the up-down symmetry ( with respect to the reaction plane) is violated - S.Voloshin- nucl-ex 1003.1127 =Angle of the reaction plane in the lab. frame Average over all events

27. 5 Time modulations Defined in the Lab. ROTATING frame NON ROTATING frame = rotation axis of the Earth = celestial equatorials coordinates

28. Conclusions In HIC huge magnetic fields at the early stage of the collision Magnetic field amplifies non commutative and Lorentz violating effects Free non commutative photons decay in (very) low invariant mass e+e- 1 2 5 The yield of low invariant mass e+e- “grid”: (0) Very high pT IN The reaction plane,very low invariant mass pairs AB/pp IN/OUT of reaction plane Correlations Time modulations UNIQUE? Signature of new fundamental space-time properties – LHC heavy ion program Ciao beppe 4 3 10% effect - Threshold effect in impact parameter DIFFICULT BUT NOT IMPOSSIBLE

30. Kharzeev et al