Jet shape & jet cross section: from hadrons to nuclei

Ben-Wei Zhang

T-2, Los Alamos National Laboratory

Ivan Vitev, Simon Wicks, Ben-Wei Zhang

JHEP 0811,093 (2008)

Introduction

Jet quenching at RHIC

pp

AuAubinaryAuAuAA Yield

NYieldR

/

Finding of the jet quenching effect in A+A collisions has been regarded as one of the most important discoveries made at RHIC.

Jets: new opportunity at LHC

RAA for single hadron or IAA for dihadron only measure the leading fragments of a jet.

LHC will open an entirely new frontier: to study the internal structure of a whole jet.

Jet shape and jet cross section.

Jet shape: intra-jet energy flow

Jets: collimated showers of energetic particles that carry a large fraction of the energy available

in the collisions.

ET ET , i

ijet

iET , iijet / ET

iET , iijet / ET

R { , , }i Ti i iE

R ( jet )2 ( jet )

2

Introducing acceptance cuts needed in heavy-ion collisions: pT>pT min or E>Emin .

Jet shapes in vacuum: the p+p baseline

An analytical approach with the generalization to incorporate acceptance cuts.

Leading orderAn analytic approach to the

energy distribution of jet

Seymour, M. (1998)

QCD splitting kernel2

22( )

2s

a bca

ddzP

dzdP

Jet shape at LO with the acceptance cut

Sudakov resummationJet shapes for a quark and a gluon are:

Collinear divergenceRequires Sudakov

resummation

Sudakov form factors:

Power correc. & Initial-state radia.

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

non-perturbative scale Q0.

Initial-state radiation should be included, which gives:

Sudakov resummation & power correction for ISR can be given in same way as those for FSR.

Theory VS Tevatron Data Total contribution to jet shape in vacuum:

Theoretical model describes CDF II data fairly well after including all kinds of contributions

CDF collaboration Acosta et al (2005)

Predictions for Jet shape at LHC

Jet shapes at LHC are very similar to those at Tevatron:

- As a function of the jet opening angle jet shapes are self-similar.

- First study of finite detector acceptance effect is carried out: the effect is observable with 10-20% energy cut.

- Jet shapes change dramatically with ET

20GeV

100GeV

500GeV

Medium-induced jet shape

hadrons

ph

parton

E

An analytic approach GLV formalism provides

an analytic approach

2 *2 Resin *

...gmed

a b c

dNM M M

d d d

0

2 2

2

2

2

2

0

2

2

2

0

2

( s

2 1

sin * ( )

1 cos2

cos

coin * 2 sin * )

( sin * 2 sin * )

s

cos

Lgmed R s el

g elz

dN C d z ddq q

d d d z d

q q

q

q

d

q z

2

x+2Re

It is proven to all order in opacity expansion.

I. Vitev (2005)

Gyulassy-Levai-Vitev

Energy loss distribution

Energy ratio goes down with larger b.

Energy ratio becomes smaller with smaller R and larger .

Tomography of jets in heavy-ion collisions

Jets at LHC

Jet cross section@HIC and RAA

Only a fraction of lost energy falls inside the cone and above the acceptance cut.

Higher energy needed due to energy loss

Define nuclear modification factor for jet cross section:

Centrality dependence of RAA for

jet cross section is similar to that for single hadron production

RAA vs Rmax and ωmin

RAA for jet cross section evolves continuously by varying cone size and acceptance cut.

Contrast: single result for leading particle Limits: RAA approaches to single hadron suppression with very

Rmax and large ωmin

Total jet shape in medium (I)

Surprisingly, there is no big difference between jet shape in vacuum and total jet shape in medium. Broadening effect is offset by steeper jet shape in vacuum due to energy loss.

The medium is “gray” instead of “black”: only a fraction of energy of leading parton lost in the QGP.

Total jet shape in medium (II)

The ratio of total jet shape in medium to jet shape in vacuum is smaller than 1 at 0.25<r/R<0.5, and larger than 1 when r/R>0.5.

Big difference is manifest at the peripheral of the cone, and with smaller cone radius: the ratio is about 1.7 when r/R~1 and R=0.4.

Conclusions The theory of jet shape in vacuum was generalized to

include finite detector acceptance effect. Medium-induced jet shapes were computed and shown

to be quite different with jet shape in vacuum. A variable quenching of RAA for jet cross section at LHC

was demonstrated, which is contrary to single result of RAA for leading particle.

Total jet shapes in Pb+Pb collisions at LHC were given: small broadening at mean relative jet radii; up to 70% deviation relative to vacuum jet shape was shown at the “tails” r/R>0.5 with smaller jet cone radii.

From light to heavy

Heavy meson suppression

Talk by R. Sharma

Backup

Outline

Introduction Jet shapes in vacuum Medium-induced jet shapes Jet shapes & jet cross

sections in heavy-ion collision Conclusions

Jets cross section in p+p

10% statistical @ 160GeV inclusive jets 5%-30% statistical @ 100GeV jet shapes

Cone algorithm with seed

1) Define cell size δ0Xδ0 in ηXΦ space in a calorimeter.

2) Every cell with energy above E0 is consider as a “seed cell”.

3) A jet is defined by summing all cells within an angle R of the seed cell.

4) If the jet direction does not coincide with the seed cell, redo step 3) again with current jet direction as the seed cell.

5) “Infrared safe” requires a parameter “Rsep” in theory, whereby if two partons are within Rsep R of each other, they are merged into one jet.

Jet shape in vacuum VS Rsep and Q0

Jet shape in vacuum VS Rsep and Q0

Jet Shapes vs centrality & Energy

Big difference between medium-induced jet shape and vacuum jet shape, especially with smaller cone radius.

Medium-induced jet shape becomes flatter at peripheral collisions. Jet shapes in medium and in vacuum are steeper with higher energy.

LPM effect and medium-induced Jet shape An intuitive approach to medium-induced jet shapes

Gyulass-Levai-Vitev

Double differential medium-induced jet shape

We study doubledifferential jet shape:

At small z medium-induced jet shape is dominated by gluon radiation at large opening angle.

With z increasing, the jet shape profile becomes narrow, and the peak shifts to smaller open angle.

0.01 0.03 0.1 0.3