Ivan Vitev

1. Ivan Vitev Effective theory of jet propagation in matter and applications to inclusive and tagged jet quenching at RHIC and the LHC • HPHD 2011 - EcolePolytechnique, Palaiseau, France • Thanks to my collaborators: Y. He, R.B. Neufeld, G. Ovanesyan, R. Sharma, S. Wicks, B.W. Zhang

2. Outline of the talk • Motivation: need for improvements in theory, recent experimental LHC and RHIC results, earlier work • An effective theory for jet propagation in matter SCETG , gauge invariance of jet broadening and energy loss results. Factorization of medium-induced radiative corrections • Medium-induced parton showers and their interactions in the QGP. Energy transfer and the death of the Mach cone • Fixed order perturbative QCD calculations: results in p+p collisions, generalization to reactions with heavy nuclei • Results for inclusive jets, Z0 tagged jets, inclusive Z0, and di-jets • Relation between leading particle quenching and jet quenching • Conclusions

3. I. Quenching of leading particles • Jet quenching: suppression of inclusive particle production relative to a binary scaled p+p result M. Gyulassy, et al. (1992) • Jet quenching in A+A collisions has been regarded as one of the most important discoveries at RHIC • Tested against alternative suggestions: CGC and hadronic transport models ✓ • Phenomenologically very successful ✓ • Difficulty in distinguishing between models and theories ✗ • New observables, physics reach extended at the LHC and also RHIC ✗ Adler, S. et al (2003) Adams, J. et al. (2003)

4. I. Toward jet physics results in A+A reactions at RHIC and LHC • Jet physics results have become available in nuclear collisions • Allow for new insights in the in-medium parton dynamics • Should be understood in conjunction with leading particle suppression ALICE, ATLAS, CMS, PHENIX, STAR (2008-2011)

5. I. Open questions in jet quenching theory In order of increasing importance • Improve upon the kinematics of the effective scattering centers in the medium, both light and heavy scattering centers • Calculate the large x=k+/p+ correction to the soft bremsstrahlung, i.e. improve the calculation of the medium-induced parton splitting • Construct a modern effective theory of jet interactions in matter • Prove the gauge invariance of the jet broadening and radiative energy loss results • Demonstrate the factorization of the final-state radiative corrections form the hard scattering Effective field theories have been with us for a while, e.g the 4-Fermi interaction A suitable framework is Soft Collinear Effective Theory

6. II. Examples of effective field theories [EFTs] • Simple but powerful idea to concentrate on the significant degrees of freedom [DOF]. Manifest power counting power counting DOF in FT DOF in EFT Q E Full Theory DOF in FT Q Effective Theory DOF in EFT G. Ovanesyan (2009) E

7. II. SCET formulation • Modes in SCET C. Bauer et al. (2001) D. Pirol et al. (2004) Soft quarks are eliminated through the equations of motion or integrated out in the QCD action • SCET Lagrangian to all orders in λ [Can expand to LO, NLO,…] • BPS transformation O. Cata et al. (2009) E

8. II. In more detail: the jet scattering kinematics • What is missing in the YM Lagrangian is the interaction between the jet and the medium G. Ovanesyan et al. (2011) • Kinematics and channels • t – jet broadening and energy loss • s– isotropisation • u – backward hard scattering • Fully dynamic medium recoil, cross section reduction (5% – 15%). Completely dominated by forward scattering

9. II. The Glauber gluon lagrangian • Glauber gluons (transverse) A. Idilbi et al. (2008) • Feynman rules for different sources and gauges G. Ovanesyan et al. (2011)

10. II. Main results: jet broadening • Jet broadening and its gauge invariance M. Gyulassy et al. (2001) Classes of diagrams (single Born, double Born). Reaction Operator • General result. Will evaluate the broadening (or lack off) of jets • In special cases such as constant density and the Gaussian approximation Starting with a collinear beam of quarks/gluons we recover M. Gyulassy et al. (2002)

11. II. Main results: in-medium splitting / parton energy loss • Altarelli-Parisi splitting function Splitting functions factorize form the hard scattering cross section (spin-averaged for protons) G. Altarelli et al. (1978) • Note that a collinearWilson line appears in the Rξ gauge • The case of medium-induced bremsstrahlung is more complicated • The single born diagrams Note the collinear Willson line

12. II. Main results: in-medium splitting / parton energy loss • Double Born diagrams Note the collinear Willson line G. Ovanesyan et al. (2011) • Result

13. II. The lightcone gauge • Treatment of the pole • Prescription dependence in the standard treatment • Appearance of a T Wilson line A. Idilbi et al. (2010) A. Majumder et al. (2009) • New Feynman rule – gauge invariance G. Ovanesyan et al. (2010)

14. II. Factorization of medum-induced radiative corrections • First proof beyond the soft gluon approximation G. Ovanesyan et al. (2010) Final-state medium-induced radiative corrections factorize form the hard scattering cross section in QCD One is left with an integral convolution over the parton splitting / energy loss probability • In the soft limit we recover the GLV result M. Gyulassy et al. (2001)

15. III. Parton showers as sources of energy deposition in the QGP • The first theory calculation to describe a splitting parton system as a source term, including quantum color interference effects • Think of it schematically as the energy transferred to the QGP through collisional interactions at scales ~ T, gT, … See next talk by Bryon Neufeld R.B. Neufeld et al. (2011) • Calculated diagrammatically from the divergence of the energy-momentum tensor (EMT) • Simple intuitive interpretation of the result • 10-20 GeV from the shower energy can be transmitted to the QGP

16. IV. The status of higher-order calculations in p+p • Very few processes are known at NNLO. Final states such as the Higgs and Drell-Yan C. Anastasiou et al. (2009) Exact matrix elements: FO ✓PS ✗ Precision: FO✓PS✗ Hard region description: FO✓PS✗ Soft region description: FO✗PS✓ Large final states: FO✗PS ✓ medium vacuum J. Campbel (2009) We will present results consistently to O(αs3), O(αs2αs)

17. IV. Inclusive jet cross sections at NLO and p+p results • Includes 2- and 3-parton final states S.D. Ellis et al. (1990) Z. Kunszt et al. (1992) • At one loop – jet size/algorithm dependence • Excellent description of the cross sections at RHIC and the LHC • Strong R dependence ~ ln( R/R0) I.Vitev et al. (2009) Y.He et al. (2011)

18. V. Exploting the jet variables in heavy-ion collisions • One can leverage the differences between the vacuum parton showers, the medium-induced showers and the medium response to jets to experimental signatures of parton interaction in matter I.Vitev et al. (2008) • Calculations at NLO

19. V. Inclusive jet cross sections in A+A reactions • Jet cross sections with cold nuclear matter and final-state parton energy loss effect are calculated for different R • Calculate in real time Fraction of the energy redistributed inside the jet The probability to lose energy due to multiple gluon emission I. Vitev et al (2008) • Obtain

20. V. Jet cross sections in A+A reactions at RHIC and LHC • Jet RAA with cold nuclear matter and final-state parton energy loss effect are calculated for different R Y. Lai (2009) I. Vitev et al (2009) RAA – CNM effects, QGP quenching and R dependence in p+p σ(R1)/σ(R2) in A+A – QGP quenching and R dependence in p+p Y. He et al. (2011) K. Amadot et al. (2011)

21. V. QGP – modified jet shapes • Surprisingly, there is no big difference between the jet shape in vacuum and the total jet shape in the medium • Take a ratio of the differential jet shapes 20 GeV 50 GeV 100 GeV 200 GeV I. Vitev et al. (2008)

22. V. Experimental results for inclusive jets • The level of suppression –yes • The ET independence – yes • Centrality dependence – yes • Complete lack of R dependence - no • One has to investigate the implications of the medium excitation by the parton shower and the energy carried away from the cone by this excitation ATLAS (2011) R.B.Neufeld et al. (2011)

23. V. The ambiguity of jet/background separation • There is no first-principles understanding of heavy ion dynamics at all scales and consequently jet/medium separation • Background fluctuations may affect jet observabled • Part of the jet energy may be misinterpreted as background • It may also diffuse outside R through collisional processes M. Cacciari et al. (2011) In our approach we can simulate these scenarios with the cut pTmin • Caneasily wipe out the R dependence of jet observables (also for di-jets) Y. He et al. (2011)

24. V. Tagged jet at NLO with strong momentum constraints • Goal: precisely constrain the energy of the leading recoil jet [e.g. through lepton pair decays] to pinpoint parton energy loss. Exact result at LO T. Awes et al. (2003) • At NLO Z-strahlung and parton splitting compromise the tagging power of electroweak bosons • Induce +/- 25% uncertainty • At least NLO accuracy is necessary to study Z0-tagged and photon-tagged jets • Mean pT and standard deviation for Z0-tagged jets at the LHC B. Neufeld et al. (2010)

25. V. Quenching of Z0/γ*- tagged jets at the LHC, inclusive Z0 • Quenched Z0-tagged jet cross section • Inclusive Z0 production has also been evaluated Strong redistribution of the energy andenhanced IAAbelow the trigger pT R.B. Neufeld et al. (2010) S.Chatrchyan et al. (2011) • Associated with the part of phase space of quickly increasing with pT cross section Isospin +3%, CNM energy loss -6%

26. V. NLO results for di-jets in p+p collisions at the LHC • We have adapted the NLO EKS code to calculate the di-jet cross section • The most important feature is how broad it is in ET1, ET2 • Limits the amount of additional asymmetry that can be generated by the QGP • The di-jet assymetry is a derivativeobservable • Excellent description in p+p collisions Y.He et al. (2011)

27. V. Calculating the di-jet suppression • The suppressed di-jet cross section is calculated as follows (differentially over the collisions geometry, L1 L2, Real time P(ε) ) • Generalized multi-jet suppression • Characteristic features: broad flat suppression and transition to strong enhancement Y. He et al. (2011)

28. V. Results for enhanced di-jet asymmetry at the LHC Y. He et al. (2011) • A peak at finite AJ is not compatible with NLO calculations due to the broad E1 E2 distribution • Only about 30%-50% of the additional asymmetry can be explained by the radiative processes • The remainder may be related to the jet/background ambigutiy, fluctuation or thermalization of the parton shower - simulated • The AJ more sensitive than RAA

29. V. Relation between jet and leading particle quenching • Include the quenched parton and the radiative gluon fragmentation • Still LO, predicted 2002 2006 – growing RAA at high pT I. Vitev et al. (2002) I. Vitev (2006)

30. V. Current experimental results for particle RAA • There is tension between ALICE and CMS RAA at high pT baseline? Centrality dependence?

31. Summary of references for presented work

32. Conclusions • New theoretical developments are needed to address the physics of jets in heavy ion collisions as opposed to the physics of leading particles • Developed an effective theory of jet propagation in matter with complete set of Feynman rules in different sources and gauges. Proved gauge invariance of the jet broadening and energy loss results. Showed factorization of the medium-induced radiative corrections for the hard scattering, accurate results beyond the soft gluon approximation • Derived the differential energy and momentum transfer between a splitting parton system and the QGP(or the source term). Found that a significant part of the shower energy may be thermalized. Showed that in-medium parton showers are unlikely sources of well-defined conical signatures • Presented NLO results for inclusive jet production at RHIC and the LHC, Z0-tagged jets and di-jets at the LHC. Showed that this level of accuracy is critical for the new jet observables. We also found that from radiative energy loss calculations there is residual RAA dependence and ~50% of the di-jet asymmetry can be explained

33. Conclusions • Jet measurements at RHIC and the LHC are strongly suggestive of the quenching scenario. However, a consistent picture has not emerged yet. There are difficulties is separating the jets from the QGP background. Only part of the features of the di-jet asymmetry may be understood in the jet quenching picture. A suite of measurements is necessary to form a solid physics understanding of the jet processes in QCD matter at high energies and densities • On the way to deriving all splitting functions in the medium, implementing more consistently the parton shower interaction in the medium and improving the application to jets in heavy ion reactions

34. Experimental results for discussion R.B. Neufeld et al. (2011)

35. Experimental results for discussion

36. Experimental results for discussion

37. Experimental results for discussion

38. Experimental results for discussion

39. III. Why are Mach cones initiated by jets unlikely • An individual parton (or a collinear system) can produce a Mach cone on an event by event basis. Multiple events will reduce the observable effect • Typical medium-induced shower multiplicities are Ng=4 (quark) and Ng=8 (gluon) and emitted at large angles ~ 0.7 (much larger than in the vcuum) • Each parton quickly becomes an individual source of excitation and these multiple sources wipe out any conical signature I. Vitev (2005)

40. IV. Soft Collinear Effective Theory

41. IV. Examples of effective field theories [EFTs] • Simple but powerful idea to concentrate on the significant degrees of freedom [DOF]. Manifest power counting power counting DOF in FT DOF in EFT Q E Full Theory DOF in FT Q Effective Theory DOF in EFT G. Ovanesyan (2009) E

42. IV. SCET formulation • Modes in SCET C. Bauer et al. (2001) D. Pirol et al. (2004) Soft quarks are eliminated through the equations of motion or integrated out in the QCD action • SCET Lagrangian to all orders in λ [Can expand to LO, NLO,…] • Especially suited for jet physics • Different SCET for formulations are possible • - equivalent O. Cata et al. (2009) E

43. IV. Resummation, RG equations and Higgs production at the LHC • SCET is very effective in resumming in large infrared logarithms using Renormalization group equations • It can improve upon traditional techniques, such as CCS N3LL J. Collins et al. (1985) V. Ahrens et al. (2009)

44. IV. Factorization in SCET and angularities • Factorization theorems have been proven in SCET for a number of observables: event shapes [e+e-], Higgs [pp], top [e+e-] … • Angularity observables: generalization of traditional event shapes C. Berger et al. (2003) • Factorized in hard function, jet functions and soft function C. Bauer et al. (2008) A. Hornig et al. (2010)

45. IV. Applications to nuclear collisions • Final state parton broadening in semi-inclusive DIS. A. Idilbi et al. (2008) • Have argued to recover the general QCD result in the Gaussian broadening region J. Qiu et al. (2003) • Formulation of a transport coefficient as a Wilson line • Not gauge-invariant. Proof needed F. D’Eramo et al. (2010)

46. I. RHIC results on jet production in p+p collisions STAR Collab. (2010) Y. Lai (2009) • Jet have been measured in p+p collisions at RHIC since 2006. • Experimental results are in good agreement with NLO perturbative QCD calculations

47. I. RHIC results on open heavy flavor quenching PHENIXCollab. (2007) • Unexpectedly large heavy quark energy loss via the suppression of single non-photonic electrons Radiative Radiative+collisional π0 Y. Dokshitzer et al. (2001) • Direct open heavy flavor measurements are necessary. FVTX [PHENIX], HFT [STAR] • Observables that can differentiate between models of heavy flavor quenching [jets in heavy ion collisions] STAR Collab. (2010) Radiative Resonances Dissociation

48. Jet tomography • Advantage of RAA : providing useful information for the hot/dense medium within a simple physics picture I.V., M. Gyulassy(2002)

49. Limitations of leading particle observables • Disadvantage: cannot distinguish between competing models of parton energy loss and theoretical approximations A. Adare et al. (2008) • If we present results for the same quantity dNg/dy the problem becomes apparent

50. Quenching of tagged jets – LO vs NLO • Beyond tree level -significantly different result • At tree level (not realistic) you can get at P(ε) Ng Strong redistribution of the energy and strongly enhanced IAAbelow the trigger pT R.B. Neufeld et al. (2010)