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
Ivan Vitev. 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. - PowerPoint PPT Presentation
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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
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
R.B. Neufeld et al. (2010)
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
arXiv:0910.1090 [hep-ph]
Phys.Rev.Lett. 104 (2010) 132001
NLO calculation of Z0 tagged jets, inclusive Z0 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/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
R.B. Neufeld et al. (2011)
Experimental results for discussion
Experimental results for discussion
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)
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
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