ivan vitev

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

Ivan Vitev

Quark Matter 2011 - Annecy, France

Thanks to my collaborators: Y. He, R.B. Neufeld, G. Ovanesyan, R. Sharma, S. Wicks, B.W. Zhang

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

Outline of the talk

I. Quenching of leading particles

RAA (IAA ...) =YieldAA /⟨Nbinary⟩AA

Yieldpp

=1

⟨Nbinary⟩AuAu

dσAuAu/dpTdydσ pp /dpTdy

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 resultM. Gyulassy, et al. (1992)

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

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

Soft Collinear Effective Theory (SCET) Q p⊥/Q ψ,A ξn, An, As

EDOF in FTDOF in EFT

Q

Full TheoryEffective 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

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)

LO NLO NNLO …LO αs

2 αs2αs

med αs2αs

2

med…

NLO αs3 αs

3αsmed …

NNLO αs4 …

… …

mediumva

cuum

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(αs

3), O(αs

2αs)

J. Campbel (2009)

Includes 2- and 3-parton final states S.D. Ellis et al. (1990)

Z. Kunszt et al. (1992)

II. Inclusive jet cross sections at NLO and p+p results

I.Vitev et al. (2009)

Excellent description of the cross sections at RHIC and the LHC

Strong R dependence ~ ln( R/R0)

• At one loop – jet size/algorithm dependence

Y.He et al. (2011)

III. Exploting the jet variables in heavy-ion collisions

Mechanism

Signature Status

Dissociative ~ Constant RAAjet=1

(No suppression) ✗ No calculation

Radiative Continuous variation of RAA

jet with R, wmin

✔ Incl. jets at RHIC, LHC✔ Di-jets at the LHC✗ No γ-tagged jets

Collisional~ Constant RAA

jet= RAA

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

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

I. Vitev et al (2008)

Calculate in real time

Calculate

Fraction of the energy redistributed inside the jet

The probability to lose energy due to multiple gluon emission

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

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. Lai (2009)

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

I. Vitev et al. (2008)

20 GeV

50 GeV

100 GeV

200 GeV

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, …

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 poster by Bryon Neufeld

III. The ambiguity of jet/background separation

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 pT

min

Can easily wipe out the R dependence of jet observables (also for di-jets)

Constrain NP corrections in p+p

III. 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

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

T. Awes et al. (2003)

B. Neufeld et al. (2010)

• Mean pT and standard deviation for Z0-tagged jets at the LHC

III. Quenching of Z0/γ*- tagged jets at the LHC, inclusive Z0

Quenched Z0-tagged jet cross section

S.Chatrchyan et al. (2011)

Strong redistribution of the energy and enhanced IAA below the trigger pT

Inclusive Z0 production has also been evaluated


Isospin +3%, CNM energy loss -6%

Associated with the part of phase space of quickly increasing with pT cross section

III. NLO results for di-jets in p+p collisions at the LHC

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 ET1, ET2

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

III. Calculating the di-jet suppression

Y. He et al. (2011)

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

III. Results for enhanced di-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

Still LO, predicted 2002 2006 – growing RAA at high pT

Include the quenched parton and the radiative gluon fragmentation

I. Vitev (2006)I. Vitev et al. (2002)

VI. Soft Collinear Effective Theory

A. Majumder et al. (2009)

Galuber gluons (transverse to the jet direction )

G. Ovanesyan et al. (2011)

Complete Feynman rules in the soft, collinear and hybrid gauges

Many more …

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

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

See poster by G. Ovanesyan

Summary of references for presented work

Subject ArXiv JournalThe 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


Phys.Rev.Lett. 104 (2010) 132001

NLO calculation of Z0 tagged jets, inclusive Z0 at the LHC


Phys.Rev. C83 (2011) 034902

NLO calculation of inclusive jets and di-jets at the LHC, di-jet asymmetry


-See Poster

SCET theory of jet propagation in matter, gauge invariance, factorization, large x


JHEP sub. (2011)

Parton showers a sources of energy momentum deposition in the QGP


PLB sub. (2011)See Poster

Inclusive particle production, gluon “feedback”, still LO

hep-ph/0603010

Phys.Lett. B639 (2006) 38-45

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

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)

Conclusions

Experimental results for discussion


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)

IV. Soft Collinear Effective Theory

Chiral Perturbation Theory (ChPT) ΛQCD p/ΛQCD

Heavy Quark Effective Theory (HQET) mb ΛQCD/mb

Soft Collinear Effective Theory (SCET) Q p⊥/Q

power countingDOF in FTDOF in EFT

EDOF in FT

DOF in EFTQ

Full TheoryEffective Theory

q, g

ψ,A

ψ,A

K,π

hv,As

ξn, An, As

Q

IV. Examples of effective field theories [EFTs]

Simple but powerful idea to concentrate on the significant degrees of freedom [DOF]. Manifest power counting

G. Ovanesyan (2009)

IV. SCET formulation

SCET Lagrangian to all orders in λ [Can expand to LO, NLO,…]

D. Pirol et al. (2004)


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, antiquarksCollinear gluons, soft gluons

ξn , ξn

An , As

( + LYM )

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

J. Collins et al. (1985) V. Ahrens et al.

(2009)

N3LL

IV. Factorization in SCET and angularities

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)


IV. Applications to nuclear collisions 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

q̂ = q⊥2 / lg

I. RHIC results on jet production in p+p collisions

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)

I. RHIC results on open heavy flavor quenching

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)

1≥R AA(B) > R AA(D) > R AA(p,K)≥0.2 π0

RadiativeRadiative+collisional

Jet tomography

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

I.V., M. Gyulassy (2002)

Limitations of leading particle observables

Disadvantage: cannot distinguish between competing models of parton energy loss and theoretical approximations

1000 ≤dNg

dy≤2000

(Probability >10%) 10%)ty (Probabili

/fmGeV 24ˆ6 2

>

≤≤ q

If we present results for the same quantity dNg/dy the problem becomes apparent

A. Adare et al. (2008)

Quenching of tagged jets – LO vs NLO

At tree level (not realistic) you can get at P(ε) Ng

Beyond tree level -significantly different result


Strong redistribution of the energy and strongly enhanced IAA below the trigger pT

Integrating over the Z0 (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)

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

Geometry of the heavy ion collisions

Jet binary collision density Medium density ~ participant density

Tagged jet cross sections

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 Z0+jet+X K. Kajantie et al

(1978)

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

Differential and integral jet shapes

Intra-jet energy flow - jet shape and generalizations

r ⊂(0, R =0.7)

Differential and integral jet shapes Generalization of angularities to

single jets

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

Global jet observables

Leading order (LO) results and Sudakov resummation

Jet shapes induced by a quark and a gluon are:

The collinear divergencerequires Sudakov

resummation• First take the small r/R limit

1= y(r)dr= y (r')dr'+ y (r')dr'r

R

∫0

r

∫0

1

∫

P(r<)=1− y(r')dr'r

R

∫ + ...

Soft gluon emission exponentiates

Seymour, M. (1998)

Power 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:

C =CA

2≈CF

Theory versus Tevatron data

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)

LPM effect and the medium-induced shower

The medium induced parton splitting is the double differential bremsstrahlung distribution

Coherence and interference effects guarantee broad angular spectrum

dI g

dwdr

I.V. (2005)

S. Wicks (2008)

X.N.Wang et al. (2005)

Bremsstrahlung 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 GeV parton at the LHC

RAAjet vs Rmax and ωmin

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 Rmax and large approximate single particle

suppression.

minω

minω

Focused on soft multiplicities and the incoherent regime

II. Parton Energy Loss (Early Work)

DErad =c2EL

ωdN g

dωd 2k⊥=

CRaσ

p 2

q⊥2

k⊥2 (k⊥ −q⊥ )

2

G. Bertsch et al, PRD (1982)

Essential physics is the transverse dynamics of the gluon and the color excitation of the quark

M 0 + M1

2=M0

2+ ReM1

*M0 + 2 M1

2

“Medium induced” part

Challenges (2 of them)

An operator approach to multiple scattering in QCD

Coherence phases(LPM effect)

Color current propagators

( ) ( )( ) ( )( ) ( )( )( )

1

... ...2 1

2 222 2 2

1 1

1... 1... ...

10

1

- cos c

( )( )

2 s

1

o

njj i el

n ng g R s

n n

L zi

g ii i

e

n m n

i

m

m mk kk n

n

n

l

mn

i

kk k

d zz

d dd q q

N dN Ck k

dk d k dk d k d q

B z zC

σδ

σ

ω ω

απ λ

= +∞ ∞

+ ++ +

= =

=

=⊥ ⊥

=

Δ

=

−

+

⎛ ⎞−⎜ ⎟

⎝ ⎠

⎡ ⎤= = ⎢ ⎥

⎢ ⎥⎣

Δ

Δ∑

⎦⎡ ⎤× ⋅⎢ Δ⎣

−⎦

∫∑ ∑

∑ ∑

∫∏

∑ ⎥

Number of scatteringsMomentum transfers( )

1

1...1

1 1

1 1

1 1

1 1

......2

......

....

†

.

†

.

ˆ

n

ni in

n

n

n

n

ng i i

i i

i ii i

i ii i

D D V V

dNk Tr A A

dk d k

A A

A AR

−

−

−

−

++

⊥∝

= +

=

+

∑

∞ ∞∞

21 ( )2 el qσ d ⊥− 21 ( )

2 el qσ d ⊥−2eld

d qσ

⊥

M. Gyulassy et al., NPB (2001)

Very general algebraic approach

52

• Predictions of this formalism tested vsparticle momentum, C.M. energy, centrality

• Nuclear modification factor

TNN

TAA

collTAA dpdd

dpddN

pRησηση

//1

),( 2

2

⋅><

=

Leading Particle Quenching

IV, (2005)

Jet Cross Section and Jet Shapes 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)

I. First LHC jet physics results

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

II. Definitions and jet finders

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

R = (η η jet )2 + ( jet )

2

ET = ET , i

ijet

η = ηiET , iijet / ET

= iET , iijet / ET

R { , , }i Ti i iEa η =

Jet finding algorithms [have to satisfy collinear and infrared safety]:

1) Successive recombination algorithms

a) kt algorithm b) anti-kt 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)

II. Jet reconstruction in nuclear collisions

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)

R = SignalBackground ≤1

III. Fixed order pQCD calculations

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

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 - pT leading, pT

trailing, mll, Φll C. Anastasiou et al. (2009)

III. Fixed order calculations and parton showers

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 ✓

61

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(αs

3), O(αs2αs)

Lack of relevant O(αs2αs

2), O(αs2αs

3), … calculations constrains analytic models and MC to independent medium-induced gluon emission

LO NLO NNLO …LO αs

2 αs2αs

med αs2αs

2

med…

NLO αs3 αs

3αsmed …

NNLO αs4 …

… …

III. Combining NLO effects with effects of the nuclear 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

medium

vacu

um

ivan vitev

Documents

jet quenching theory

jet anddijet production

lhc jet physics results

jet broadening

jet asymmetry

rhic results

p p collisions

inclusive jet cross