1. 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)

2. Introduction

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

4. 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.

5. Jet shape: intra-jet energy flow
Jets: collimated showers of energetic particles that carry a large fraction of the energy available
in the collisions. R
Introducing acceptance cuts needed in heavy-ion collisions: pT>pT min or E>Emin .

6. Jet shapes in vacuum: the p+p baseline
An analytical approach with the generalization to incorporate acceptance cuts.

7. Leading order An analytic approach to the energy distribution of jet
Seymour, M. (1998)
QCD splitting kernel
In the calculation we will follow the analytic approach outlined by Seymour, and generalize it to include finite acceptance cut.
Jet shape at LO with the acceptance cut

8. Sudakov resummation Jet shapes for a quark and a gluon are:
Collinear divergence
Requires Sudakov resummation
Sudakov form factors:

9. 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.

10. 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)

11. 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

12. Medium-induced jet shape
hadrons ph
parton E

13. An analytic approach GLV formalism provides an analytic approach 2
Gyulassy-Levai-Vitev
GLV formalism provides an analytic approach 2 x
+2Re
I. Vitev (2005)
It is proven to all order in opacity expansion.

14. Energy loss distribution
Energy ratio goes down with larger b.
Energy ratio becomes smaller with smaller R and larger

15. in heavy-ion collisions
Tomography of jets
in heavy-ion collisions
Jets at LHC

16. Jet cross section@HIC and RAA
Higher energy needed due to energy loss
Only a fraction of lost energy falls inside
the cone and above the acceptance cut.
Define nuclear modification
factor for jet cross section:
Centrality dependence of RAA for
jet cross section is similar to that for single hadron production

17. 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

18. 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.

19. 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.

20. Conclusions Heavy meson suppression Talk by R. Sharma
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.
Heavy meson suppression
Talk by R. Sharma
From light to heavy

21. Backup

22. Outline Introduction Jet shapes in vacuum Medium-induced jet shapes
Jet shapes & jet cross sections in heavy-ion collision
Conclusions

23. Jets cross section in p+p
10% 160GeV inclusive jets
5%-30% 100GeV jet shapes

24. 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.

25. Jet shape in vacuum VS Rsep and Q0

26. Jet shape in vacuum VS Rsep and Q0

27. 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.

28. LPM effect and medium-induced Jet shape
An intuitive approach to medium-induced jet shapes
Gyulass-Levai-Vitev

29. Double differential medium-induced jet shape
We study double
differential jet shape:
0.01
0.03
0.1
0.3
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.