1. Ivan Vitev HPHD 2011 - Ecole Polytechnique, Palaiseau, France Thanks to my collaborators: Y. He, R.B. Neufeld, G. Ovanesyan, R. Sharma, S. Wicks, B.W. Zhang

2.  Motivation: need for improvements in theory, recent experimental LHC and RHIC results, earlier work  An effective theory for jet propagation in matter SCET G, 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, Z 0 tagged jets, inclusive Z 0, and di-jets  Relation between leading particle quenching and jet quenching  Conclusions

3. 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 ✗ Adams, J. et al. (2003)Adler, S. et al (2003)  Jet quenching: suppression of inclusive particle production relative to a binary scaled p+p result M. Gyulassy, et al. (1992)

4. 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.  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 In order of increasing importance A suitable framework is Soft Collinear Effective Theory  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 Effective field theories have been with us for a while, e.g the 4-Fermi interaction

6. Chiral Perturbation Theory (ChPT) Λ QCD p/Λ QCD Heavy Quark Effective Theory (HQET) mbmb Λ QCD /m b Soft Collinear Effective Theory (SCET) Q p ⊥ /Q power countingDOF in FTDOF in EFT E E DOF in FT DOF in EFT Q Full Theory Effective Theory q, g ψ,A K,π hv,Ashv,As ξ n, A n, A s Q  Simple but powerful idea to concentrate on the significant degrees of freedom [DOF]. Manifest power counting G. Ovanesyan (2009)

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

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

9.  Glauber gluons (transverse) A. Idilbi et al. (2008)  Feynman rules for different sources and gauges G. Ovanesyan et al. (2011)

10.  Jet broadening and its gauge invariance M. Gyulassy et al. (2001)  General result. Will evaluate the broadening (or lack off) of jets Classes of diagrams (single Born, double Born). Reaction Operator  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.  Altarelli-Parisi splitting function  Note that a collinear Wilson line appears in the R ξ gauge G. Altarelli et al. (1978) Splitting functions factorize form the hard scattering cross section (spin-averaged for protons)  The case of medium-induced bremsstrahlung is more complicated  The single born diagrams Note the collinear Willson line

12.  Double Born diagrams G. Ovanesyan et al. (2011) Note the collinear Willson line  Result

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

14. M. Gyulassy et al. (2001)  First proof beyond the soft gluon approximation G. Ovanesyan et al. (2010)  In the soft limit we recover the GLV result 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

15.  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, …  Calculated diagrammatically from the divergence of the energy- momentum tensor (EMT)  Simple intuitive interpretation of the result R.B. Neufeld et al. (2011)  10-20 GeV from the shower energy can be transmitted to the QGP See next talk by Bryon Neufeld

16. Very few processes are known at NNLO. Final states such as the Higgs and Drell-Yan C. Anastasiou et al. (2009) LONLONNLO … LOαs2αs2 α s 2 α s med α s 2 α s 2 med … NLOαs3αs3 α s 3 α s med … NNLOαs4αs4 … …… medium vacuum Exact matrix elements: FO ✓ PS ✗ Precision: FO ✓ PS ✗ Hard region description: FO ✓ PS ✗ Soft region description: FO ✗ PS ✓ Large final states: FO ✗ PS ✓ We will present results consistently to O(α s 3 ), O(α s 2 α s ) J. Campbel (2009)

17.  Includes 2- and 3-parton final states S.D. Ellis et al. (1990)Z. Kunszt et al. (1992) I.Vitev et al. (2009) Excellent description of the cross sections at RHIC and the LHC Strong R dependence ~ ln( R/R 0 ) At one loop – jet size/algorithm dependence Y.He et al. (2011)

18. MechanismSignatureStatus Dissociative ~ Constant R AA jet =1 (No suppression) ✗ No calculation Radiative Continuous variation of R AA jet with R, w min ✔ Incl. jets at RHIC, LHC ✔ Di-jets at the LHC ✗ No γ-tagged jets Collisional ~ Constant R AA jet = R AA particle (Large suppression) ✗ Schematic application  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.  Jet cross sections with cold nuclear matter and final-state parton energy loss effect are calculated for different R I. Vitev et al (2008)  Calculate in real time  Obtain Fraction of the energy redistributed inside the jet The probability to lose energy due to multiple gluon emission

20.  Jet R AA with cold nuclear matter and final-state parton energy loss effect are calculated for different R I. Vitev et al (2009) R AA – CNM effects, QGP quenching and R dependence in p+p σ(R 1 )/σ(R 2 ) in A+A – QGP quenching and R dependence in p+p Y. Lai (2009) Y. He et al. (2011) K. Amadot et al. (2011)

21.  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 I. Vitev et al. (2008) 20 GeV 50 GeV 100 GeV 200 GeV

22.  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  The level of suppression – yes  The E T independence – yes  Centrality dependence – yes  Complete lack of R dependence - no ATLAS (2011) R.B.Neufeld et al. (2011)

23.  There is no first-principles understanding of heavy ion dynamics at all scales and consequently jet/medium separation Y. He et al. (2011)  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 p T min Can easily wipe out the R dependence of jet observables (also for di-jets)

24. 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 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 Z 0 -tagged and photon-tagged jets T. Awes et al. (2003) B. Neufeld et al. (2010) Mean p T and standard deviation for Z 0 -tagged jets at the LHC

25.  Quenched Z 0 -tagged jet cross section S.Chatrchyan et al. (2011) Strong redistribution of the energy and enhanced I AA below the trigger p T  Inclusive Z 0 production has also been evaluated R.B. Neufeld et al. (2010) Isospin +3%, CNM energy loss -6%  Associated with the part of phase space of quickly increasing with p T cross section

26. Y.He et al. (2011)  We have adapted the NLO EKS code to calculate the di-jet cross section  The most important feature is how broad it is in E T1, E T2  Limits the amount of additional asymmetry that can be generated by the QGP The di-jet assymetry is a derivative observable Excellent description in p+p collisions

27. Y. He et al. (2011)  The suppressed di-jet cross section is calculated as follows (differentially over the collisions geometry, L 1 L 2, Real time P(ε) )  Generalized multi-jet suppression  Characteristic features: broad flat suppression and transition to strong enhancement

28. Y. He et al. (2011)  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  A peak at finite A J is not compatible with NLO calculations due to the broad E1 E2 distribution  The AJ more sensitive than R AA

29.  Still LO, predicted 2002 2006 – growing R AA at high p T Inc l ude the quenched parton and the radiative gluon fragmentation I. Vitev (2006) I. Vitev et al. (2002)

30.  There is tension between ALICE and CMS R AA at high p T baseline? Centrality dependence?

31. SubjectArXivJournal The original paper on theory of jets in A+A, cross sections and shapes (LO) arXiv:0810.2807 [hep-ph] JHEP 0811 (2008) 093 NLO calculation of inclusive jets at RHIC, separating IS, FS effects arXiv:0910.1090 [hep-ph] Phys.Rev.Lett. 104 (2010) 132001 NLO calculation of Z 0 tagged jets, inclusive Z 0 at the LHC arXiv:1006.2389 [hep-ph] Phys.Rev. C83 (2011) 034902 NLO calculation of inclusive jets and di- jets at the LHC, di-jet asymmetry arXiv:1105.2566 [hep-ph] - See Poster SCET theory of jet propagation in matter, gauge invariance, factorization, large x arXiv:1103.1074 [hep-ph] JHEP sub. (2011) Parton showers a sources of energy momentum deposition in the QGP arXiv:1105.2067 [hep-ph] PLB sub. (2011) See Poster Inclusive particle production, gluon “feedback”, still LO hep-ph/0603010Phys.Lett. B639 (2006) 38-45

32.  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, Z 0 - 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 R AA dependence and ~50% of the di-jet asymmetry can be explained

33.  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. R.B. Neufeld et al. (2011)

39.  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 N g =4 (quark) and N g =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. Chiral Perturbation Theory (ChPT) Λ QCD p/Λ QCD Heavy Quark Effective Theory (HQET) mbmb Λ QCD /m b Soft Collinear Effective Theory (SCET) Q p ⊥ /Q power countingDOF in FTDOF in EFT E E DOF in FT DOF in EFT Q Full Theory Effective Theory q, g ψ,A K,π hv,Ashv,As ξ n, A n, A s Q  Simple but powerful idea to concentrate on the significant degrees of freedom [DOF]. Manifest power counting G. Ovanesyan (2009)

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

43.  SCET is very effective in resumming in large infrared logarithms using Renormalization group equations  It can improve upon traditional techniques, such as CCS J. Collins et al. (1985) V. Ahrens et al. (2009) N 3 LL

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

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

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

47. 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) PHENIX Collab. (2007) Radiative Resonances Dissociation Unexpectedly large heavy quark energy loss via the suppression of single non-photonic electrons Y. Dokshitzer et al. (2001) π0π0 Radiative Radiative+collisional

48.  Advantage of R AA : providing useful information for the hot/dense medium within a simple physics picture I.V., M. Gyulassy (2002)

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

50.  At tree level (not realistic) you can get at P(ε) N g  Beyond tree level - significantly different result R.B. Neufeld et al. (2010) Strong redistribution of the energy and strongly enhanced I AA below the trigger p T

51.  Effectively recovers the behavior of more inclusive processes Typically ~ 5 GeV gluons at the LHC R.B. Neufeld et al. (2010)

52.  Jets – binary collisions density, Medium – participant density, full numerical evaluation, integrals cut off naturally Jet binary collision densityMedium density ~ participant density

53. At tree level the vector boson and the jet are exactly back-to back B. Neufeld et al. (2010)  Tree level cross sections – example of Z 0 +jet+X K. Kajantie et al (1978) J. Campbell, R.K. Ellis et al (1992, 1996)

54.  Differential and integral jet shapes Differential and integral jet shapes Generalization of angularities to single jets Sphericity, spherocity, Fox-Wolfram moments, thrust, angularities Global jet observables

55.  Jet shapes induced by a quark and a gluon are: The collinear divergence requires Sudakov resummation First take the small r/R limit Soft gluon emission exponentiates Seymour, M. (1998)

56.  Power correction: include running coupling inside the z integration and integrate over the Landau pole. non-perturbative scale Q 0. Webber, B. et al. (1998) Initial-state radiation should be included. The leading order result is:

57.  Total contribution to the jet shape in the vacuum: This theoretical model describes CDF II data fairly well after including all relevant contributions Acosta et al. (2005) Note the subtraction to avoid double counting in the collinear regime I.V., S. Wicks, B.W. Zhang. (2008)

58.  The medium induced parton splitting is the double differential bremsstrahlung distribution Coherence and interference effects guarantee broad angular spectrum I.V. (2005) S. Wicks (2008) X.N.Wang et al. (2005)

59.  The medium induced energy loss can be evaluated for any phase space for the jet particles  The same has to be true for bremsstrahlung from hard scattering For a 100 GeV parton at the LHC

60. R AA for the jet cross section evolves continuously with the cone size R max and the acceptance cut. Contrast: single result for leading particles. Limits: small R max and large approximate single particle suppression.

61. Focused on soft multiplicities and the incoherent regime G. Bertsch et al, PRD (1982) Essential physics is the transverse dynamics of the gluon and the color excitation of the quark “Medium induced” part Challenges (2 of them)

62. Coherence phases (LPM effect) Color current propagators Number of scatterings Momentum transfers M. Gyulassy et al., NPB (2001) Very general algebraic approach

63. 63 Predictions of this formalism tested vs particle momentum, C.M. energy, centrality Nuclear modification factor IV, (2005)

64. Direct access to the characteristics of the in-medium parton interactions Phenomenological approaches focus exclusively on 1 point IV, S. Wicks, B.-W. Zhang, JHEP (2008)

65.  LHC will have an active heavy ion program. ATLAS and CMS are optimized for jet studies. Recently the ALICE collaboration has added calorimetric capabilities M. Vouitilainen [CMS] (2010) J. Kirk [ATLAS] (2010)  Excellent jet physics capabilities. Motivated by Higgs and new physics searches

66. II. Definitions and jet finders

67.  Jets: collimated showers of energetic particles that carry a large fraction of the energy available in the collisions R Jet finding algorithms [have to satisfy collinear and infrared safety]: 1) Successive recombination algorithms a) k t algorithm b) anti-k t algorithm 2) Iterative cone algorithms: a) cone algorithm with “seed”: CDF, D0 b) “seedless” cone algorithm c) midpoint cone algorithm G. Salam et al. (2007) G. Sterman, S. Weinberg (1977) S. Ellis et al. (1993)

68.  Enormous underlying event in heavy ion collisions complicates jet reconstruction One can define areas by inserting “ghost” particles in jet algorithms to identify soft background particle insertion G. Soyez (2010)

69. III. Fixed order pQCD calculations

70. For example, for inclusive jets in p+p the coefficient A4 is not known E. Laenen (2004) Very few processes are known at NNLO. Final states such as the Higgs and Drell-Yan Artificial Neural Network builds a variable from kinematic distributions - p T leading, p T trailing, m ll, Φ ll C. Anastasiou et al. (2009)

71. J. Campbel (2009) “Good” and “bad” features Exact matrix elements: FO ✓ PS ✗ Precision: FO ✓ PS ✗ Hard region description: FO ✓ PS ✗ Soft region description: FO ✗ PS ✓ Large final states: FO ✗ PS ✓

72. 72  Not tractable in the standard LO, NLO, … pQCD prescription  One aims to calculate the separate pieces of the problem and combine them in a probabilistic fashion  We will present results consistently to O(α s 3 ), O(α s 2 α s )  Lack of relevant O(α s 2 α s 2 ), O(α s 2 α s 3 ), … calculations constrains analytic models and MC to independent medium-induced gluon emission LONLONNLO … LOαs2αs2 α s 2 α s med α s 2 α s 2 med … NLOαs3αs3 α s 3 α s med … NNLOαs4αs4 … …… - Process-dependent contributions - Model dependence in the implementation of nuclear effects - Model dependence in the evaluation of nuclear effects, e.g. energy loss model medium vacuum