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### Next-to-leading order analysis of inclusive jet, tagged jet and di-jet production in Pb+Pb collisions at the LHC

- Quark Matter 2011 - Annecy, France
- Thanks to my collaborators: Y. He, R.B. Neufeld, G. Ovanesyan, R. Sharma, S. Wicks, B.W. Zhang

Outline of the talk

- I. Motivation: need for improvements in theory, recent experimental LHC and RHIC results, earlier work
- II. Fixed order perturbative QCD calculations: results in p+p collisions, generalization to reactions with heavy nuclei
- III. Results for inclusive jets at RHIC and the LHC, parton showers as sources of energy-momentum deposition
- IV. Results for Z0 tagged jets at the LHC, inclusive Z0 production and cold nuclear matter effects
- V. Results for di-jet production, importance of the NLO theory, di-jet asymmetry, jet/background separation
- VI. Relation between leading particle quenching and jet quenching, future plans and SCETG
- Conclusions

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)

I. Toward jet physics results in A+A reactions at RHIC and LHC

- Jet physics results are becoming 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)

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

E

Full

Theory

A suitable framework is Soft Collinear Effective Theory

DOF in FT

Q

Effective Theory

DOF in EFT

C. Bauer et al. (2001)

II. 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)

II. 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)

III. 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

III. 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)

- Calculate

III. 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)

III. 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)

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, …

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
- See poster by Bryon Neufeld

III. The ambiguity of jet/background separation QGP

- 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)

Constrain NP corrections in p+p

Y. He et al. (2011)

III. Tagged QGPjet 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)

III. Quenching of Z QGP0/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%

III. NLO results for QGPdi-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)

III. Calculating the QGPdi-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)

III. Results for enhanced QGPdi-jet asymmetry at the LHC

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

- A peak at finite AJ is not compatible with NLO calculations due to the broad E1 E2 distribution

VI. Relation between jet and leading particle quenching QGP

- 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)

VI. Soft Collinear Effective Theory QGP

- Galuber gluons (transverse to the jet direction )

A. Majumder et al. (2009)

G. Ovanesyan et al. (2011)

- CompleteFeynman rules in the soft, collinear and hybrid gauges

- First proof of gauge invariance of the broadening/radiative energy loss results

Many more …

- Showed factorization of the final-state process-dependent radiative corrections and the hard scattering cross section, calculated large-x

- See poster by G. Ovanesyan

Conclusions QGP

- 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
- 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
- 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

Conclusions QGP

- Developed an effective theory of jet propagation in matter. 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.
- Predictions for leading particle suppression in agreement with data. Gluon “feedback” is very important at the LHC. With the present baseline uncertainty it is not clear if different jet-medium coupling is necessary. Even if it is, the differences with RHIC will be small
- In the future we will expand the NLO calculations to leading particles. We will evaluate all necessary splitting processes in SCETG . We will improve the accuracy of energy loss/jet quenching calculations and investigate in detail the suppression of leading particles (NLO)

Experimental results for discussion QGP

R.B. Neufeld et al. (2011)

III. Why are Mach cones initiated by jets unlikely QGP

- 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)

IV. Examples of effective field theories [ QGPEFTs]

- 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

IV. SCET formulation QGP

- 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

IV. QGPResummation, 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)

IV. Factorization in SCET and QGP 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)

IV. Applications to QGPnuclear 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)

I. RHIC results on jet production in QGPp+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

I. RHIC results on open heavy flavor quenching QGP

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

Jet QGP tomography

- Advantage of RAA : providing useful information for the hot/dense medium within a simple physics picture

I.V., M. Gyulassy(2002)

Limitations QGPof 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

Quenching of tagged jets – LO QGPvs 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)

Integrating over the Z QGP0(large rapidity and pT acceptance)

- Effectively recovers the behavior of more inclusive processes

- Typically ~ 5 GeV gluons at the LHC

R.B. Neufeld et al. (2010)

Geometry of the heavy ion collisions QGP

Jet binary collision density

Medium density ~ participant density

- Jets – binary collisions density, Medium – participant density, full numerical evaluation, integrals cut off naturally

Tagged QGP jet cross sections

- Tree level cross sections – example of Z0+jet+X

K. Kajantie et al (1978)

- At tree level the vector boson and the jet are exactly back-to back

B. Neufeld et al. (2010)

J. Campbell, R.K. Ellis et al (1992, 1996)

Intra-jet QGPenergy flow - jet shape and generalizations

- Global jet observables

- Differential and integral jet shapes

- Sphericity, spherocity, Fox-Wolfram moments, thrust, angularities

- Differential and integral jet shapes
- Generalization of angularities to single jets

Leading order (LO) results QGPand Sudakovresummation

- Jet shapes induced by a quark and a gluon are:

Seymour, M. (1998)

The collinear divergence

requires Sudakov resummation

- First take the small r/R limit

- Soft gluon emission exponentiates

Power QGP correction (PC) and initial-state radiation (IS)

- Power correction: include running coupling inside the z integration and integrate over the Landau pole.

non-perturbative scale Q0.

Webber, B. et al. (1998)

- Initial-state radiation should be included. The leading order result is:

Theory QGPversus Tevatron data

Acosta et al. (2005)

- Total contribution to the
jet shape in the vacuum:

Note the subtraction to avoid double counting in the collinear regime

This theoretical model describes CDF II data fairly well after including all relevant contributions

I.V., S. Wicks, B.W. Zhang. (2008)

LPM QGP effect and the medium-induced shower

- The medium induced parton splitting is the double differential bremsstrahlung distribution

I.V. (2005)

X.N.Wang et al. (2005)

- Coherence and interference effects guarantee broad angular spectrum

S. Wicks (2008)

Bremsstrahlung QGP distributions

- 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 GeVparton at the LHC

R QGPAAjet vs Rmax and

- RAA for the jet cross section evolves continuously with the cone size
- Rmax and the acceptance cut .
- Contrast: single result for leading particles.
- Limits: small Rmaxand large approximate single particle suppression.

II. Parton Energy Loss QGP(Early Work)

- 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

Challenges (2 of them)

“Medium induced” part

Number of scatterings

Coherence phases

(LPM effect)

Color current propagators

An operator approach to multiple scattering in QCD- Very general algebraic approach

M. Gyulassy et al., NPB (2001)

Leading Particle Quenching QGP

- Nuclear modification factor

- Predictions of this formalism tested vs
- particle momentum, C.M. energy, centrality

IV, (2005)

Jet Cross Section and Jet Shapes QGP

Phenomenological approaches focus exclusively on 1 point

- Direct access to the characteristics of the in-medium parton interactions

IV, S. Wicks, B.-W. Zhang, JHEP (2008)

I. First LHC jet physics results QGP

- Excellent jet physics capabilities. Motivated by Higgs and new physics searches

J. Kirk [ATLAS] (2010)

M. Vouitilainen [CMS] (2010)

- LHC will have an active heavy ion program. ATLAS and CMS are optimized for jet studies. Recently the ALICE collaboration has added calorimetric capabilities

R QGP

II. Jet definitions and jet finding algorithms- Jets: collimated showers of energetic particles that carry a large fraction of the energy available in the collisions

G. Sterman, S. Weinberg (1977)

- Jet finding algorithms [have to satisfy collinear and infrared safety]:
1) Successive recombination algorithms

a) ktalgorithm

b) anti-kt algorithm

2) Iterative cone algorithms:

a) cone algorithm with “seed”: CDF, D0

b) “seedless” cone algorithm

c) midpoint cone algorithm

S. Ellis et al. (1993)

G. Salam et al. (2007)

II. Jet reconstruction in nuclear collisions QGP

- Enormous underlying event in heavy ion collisions complicates jet reconstruction

G.Soyez (2010)

- One can define areas by inserting “ghost” particles in jet algorithms to identify soft background particle insertion

III. Fixed order QGP

pQCD calculations

II. The status of higher-order QGP calculations in p+p

- 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 - pT leading, pT trailing, mll, Φll

C. Anastasiou et al. (2009)

- For example, for inclusive jets in p+p the coefficient A4 is not known

E. Laenen (2004)

III. Fixed order calculations and QGPparton showers

- “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 ✓

J. Campbel (2009)

III. Combining NLO effects with effects of the nuclear medium

- Not tractable in the standard LO, NLO, … pQCD prescription

medium

- Process-dependent contributions
- Model dependence in the implementation of nuclear effects
- Model dependence in the evaluation of nuclear effects, e.g. energy loss model

vacuum

- One aims to calculate the separate pieces of the problem and combine them in a probabilistic fashion
- We will present results consistently to O(αs3), O(αs2αs)
- Lack of relevant O(αs2αs2), O(αs2αs3), … calculations constrains analytic models and MC to independent medium-induced gluon emission

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