Jets: Theory

Ivan VitevHard Probes 2020, June 1 – June 5, 2020

Student Day Lecture

Outline of the lecture

n Inclusive hadron production era, energy loss in the QGP and jet quenching

n Jet production and jet modification, the discovery eran Modern effective theories of QCD, bridging the gap

between high energy and nuclear physics n Jet substructure

Use hard probes for jet tomography

More importantly – understand QCD in the many-body nuclear environment

The energy loss era

Stopping power of Cu for μ-

• Radiative energy loss - bremsstrahlung

Bethe, H. A. et al. (1934)

• Collisional energy loss - medium excitation

Bethe, H.A. (1930,1932)

n Understand the stopping power of matter for color-charged particles. Investigate implications

n Focus on radiative energy loss

M. Gyulassy et al. (1990)

Jet quenching – the suppression of leading hadron cross sections due to energy loss in the QGP

How to approach the problem

n Construct the reaction operator for a jet+mediuminduced gluon system

n Calculate a couple of orders to understand how the “Direct” and “Virtual” operators work. What is their color and kinematic structure in momentum space

n Identify the initial condition and solve the recursion relation (if possible)

nz

,n nq a,n nq a-

nznz

,n nq a ,n nq a

nz

,n nq a,n nq a-++ˆ = R

hadronsph

parton

E

The energy loss limit

The LPM effect

5

VirtualDirect

A Recursion Method is needed to go toward higher order correlations / orders in opacity

Example to first order in opacity

Boundary conditions and Reaction operator kernel diagrams

6

^

µaD » +

-

p aD » +

-

l µ

µ

(1) R s

3(1)

2

2g

g

2R s

2CE Log ... ,

4

Static medium

9 C 1E Log ... ,

4 A

(L)

dNdy (L

1+1D

)

L 2E

Bjo

L

2EL

L

rken

- transport coefficient- effective gluon rapidity

density

2 /µ l/gdN dy

Numerically slow dependence/E ED

M.Gyulassy et al., (2001)

Analytic formulas to first order in opacity

§ Path length dependence depends on the type of medium

• Radiation is moderately large angle (cancellation near the jet axis)

• Finite gluon number

7

Different E-loss approaches

M Djordjevic et al (2003, 2009)

n The work in the energy loss limit continues

X. Guo et al (2001)

DGLV

GLV

HT

BDMPS/Z R. Baier et al (2001)B. Zakharov et al (2001)

X. Feal et al (2018) Y. Mehtar-Tani et al (2019) C. Andres et al (2020)

AMY P. Arnold et al (2001)

8

M. Gyulassy et al., (2002)

Phenomenology§ We calculated single inclusive gluon spectrum§ We can include multiple gluon emission

1 1

0 0

( ) 1, ( ) EP d P dE

e e e e e D= =ò ò

P’xbP’

P

xaP

0p

0p

Pc

Pd

Pc / zc

Pd / zd

d

d

pdzò {

X

X

R. Baier et al., (2001)

12 2

/ /

0

(1 ),(1 )

1( , () ,1 1)

cc c c

med vach q h qP

zp p z

zD z Q d D Q

ee

e ee e

® - ®-

æ ö= ç ÷- -è øò

Effective fragmentation function modification

§ Starting point is factorization. Find the process dependent corrections

Jet tomography

IV et al (2002)

n Advantage of RAA : provides useful information for the hot/dense medium within a simple physics picture X. Wang et al (2003)

RAA(IAA...) =YieldAA /〈Nbinary 〉AA

Yieldpp=

1〈Nbinary 〉AuAu

dσAuAu /dpTdydσ pp /dpTdy

The jet eran Jets: collimated showers of energetic particles

that carry a large fraction of the energy available in the collisions.

ET = ET , i

iÎjetå

h = hiET , iiÎjetå / ET

f = fiET , iiÎjetå / ET

R { , , }i Ti i iEa h f= n Jet finding algorithms:1) KT algorithm: collinear and

infrared safe2) Iterative cone algorithms:a) cone algorithm with “seed”: CDF, D0 b) “seedless” algorithmc) midpoint cone algorithm

R = (h -h jet )2 + (f - f jet )

2 G. Salam et al. (2007)

G. Sterman et al (1977)

n Includes 2- and 3-particle final states

Inclusive jets at NLO

S.D. Ellis et al (1990)

n Rsep can account for jet algorithm dependence

n Phase space for jets and finding algorithms

Z. Kunszt et al (1992)

n Includes Z + 1 or 2 jets

Tagged jets at NLO

J. Campbell, S.D. Ellis et al (1992, 1996)

n MCFM (Monte Carlo for Femtobarn Processes) – many processes at NLO

For jet production at small-x lecture by R. Boussarie, plenary talk by M. Sievert

Energy loss distribution

n In-medium parton shower distribution inside and outside of the jet cone

n Only a fraction of lost energy falls inside the cone

n Initially larger energy

IV et al (2008)

n Jet substructure

Intra-jet energy flow

n Differential and integral jet shapesn Generalization of angularities to single

jetsn Jet fragmentation functions

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

n Global jet observables

Jet shapes vs centrality & energy

n Big difference between the medium-induced jet shape and the vacuum jet shape

n Jet shapes in the medium and in vacuum are narrower at higher energy

A superposition

Vacuum and medium contributions shown separately above

RAAjet and shape modification

n RAA for the jet cross section evolves continuously with the cone size Depends on radiative and collisional energy losses

n Jet suppression and jets substructure modification are closely relatedn Important to understand and develop theory if possible before the

measurements

First jet measurementsn Not of inclusive jets – the were dijets and tagged jets

C. Young et al. (2011)

Y. Quin et al. (2011)

n Around this time Monte Carlo models to incorporated elements of in-medium QCD for phenomenology were developed

See plenary talk by K. Kauder

Inclusive jets and substructure n Observed – radius

dependence of jet quenching

n Related modification of jet shapes

n Photon/Z0 tagged jet asymmetries

See lecture by O. Evdokimov

sNN ! 2.76 TeV

! Η ! # 2, 0$10%

50 100 150 2000.8

1.0

1.2

1.4

1.6

1.8

2.0

pT

RRCP

R0.2CP

g ! 2.0 "&0.1#

R ! 0.3

R ! 0.4

R ! 0.5

S. Milov et al. (2012)

G. Aad et al. (2012)

CMS

sNN ! 2.76 TeVR ! 0.3, 0.3"! Η !"2

pT $ 100 GeVcentrality 0%10&

0.00 0.05 0.10 0.15 0.20 0.25 0.300.4

0.6

0.8

1.0

1.2

1.4

1.6

r

Ρ "r#PbPb

Ρ "r#pp

All effects

CNM(RAA

CNM only

S. Chatrchyan et al. (2013)

Beyond energy loss and modern EFTs

§ Traditional energy loss approach, phenomenologically successfulbut cannot be systematically improved, higher orders and resummation

§ In HEP significant effort has been devoted to understanding the parton shower. This parton shower technology can be applied to heavy ion reactions, NLO, NLL, etc

§ The same techniques should be applied to hard probes: particles, jets, and heavy flavor

Initial-state radiation

Final-state parton shower

ALICE Collab. (2015)

SCET and SCETG¡ Jet physics presents a multiscale problem, EFT treatment

¡ Factorization, with modified J, B, S

Ovanesyan et al. (2011)

D. Pirol et al. (2004)

C. Bauer et al. (2001)SCET (Soft Collinear Effective Theory)

~ EJ

~ k⊥,q⊥

~ ΛQCD

~ T,gT,...

q = (�2,�2,�)Q A. Idilbi et al. (2008)

Glauber gluons to mediate physical interactions with the QCD medium

§ Implemented in DGLAP evolution equations

G. Ovanesyan et al. (2012)

N.B. x→1− x

�

dN(tot.)dxd2k⊥

=dN(vac.)dxd2k⊥

+dN(med.)dxd2k⊥

�

A,...D,Ω1...Ω5 − functions(x,k⊥,q⊥ )

¡ Soft gluon emission – the only well defined energy loss limit

1. Incoming hadron (gray bubbles)

➡ Parton distribution function

2. Hard part of the process

➡ Matrix element calculation at LO, NLO, ... level

3. Radiation (red graphs)

➡ Parton shower calculation

➡ Matching to the hard part

4. Underlying event (blue graphs)

➡ Models based on multiple interaction

5. Hardonization (green bubbles)

➡ Universal models

The description of an event is a bit tricky...

H

As in vacuum, a total of 4 splitting functionsG. Altarelli et al. (1977)

In-medium splitting functions

L. Apolinario et al. (2015)

The evolution equations are given by standard Altarelli-Parisi equations:

dDq

(z,Q)

d lnQ=

↵s

(Q2)

⇡

Z

1

z

dz0

z0

n

Pq!qg

(z0, Q)Dq

⇣ z

z0, Q

⌘

+ Pq!gq

(z0, Q)Dg

⇣ z

z0, Q

⌘o

, (45)

dDq̄

(z,Q)

d lnQ=

↵s

(Q2)

⇡

Z

1

z

dz0

z0

n

Pq!qg

(z0, Q)Dq̄

⇣ z

z0, Q

⌘

+ Pq!gq

(z0, Q)Dg

⇣ z

z0, Q

⌘o

, (46)

dDg

(z,Q)

d lnQ=

↵s

(Q2)

⇡

Z

1

z

dz0

z0

(

Pg!gg

(z0, Q)Dg

⇣ z

z0, Q

⌘

+Pg!qq̄

(z0, Q)⇣

Dq

⇣ z

z0, Q

⌘

+ fq̄

⇣ z

z0, Q

⌘⌘

)

. (47)

The complete medium-induced splitting functions look like:

P(1)

i

(z,Q) = P vac

i

(z) [1 + gi

(x,Q,L, µ)] , (48)

where the individual terms with all the plus prescriptions and virtual pieces are summarized insections 2, 3. These evolution equations have to be solved with initial conditions for parton densitiesfor quarks, anti-quarks and gluons to equal �(1� z) at some infrared scale ⇠ fewGeV. The resultingso-called PDF’s at the hard scattering scale Q = p

T

look like fi/j

(z, pT

), and have an intuitiveinterpretation: probability of the parton i to be found in the parton j at the momentum transferscale Q = p

T

. For example fg/q

(z, pT

) is the solution for the gluon density from the evolutionequations with the initial conditions f

q

(z, µIR

) = �(1� z), fq̄

(z, µIR

) = fg

(z, µIR

) = 0, and so forth.As a result of solving the A-P evolution equations we get the full LL series resummed by:

�(i)(pT

) =X

j=q,q̄,g

Z

1

0

dz �(j)

⇣pT

z

⌘

fi/j

(z, pT

), (49)

where i = q, q̄, g. It is straightforward to check, that by plugging in the lowest order solutions ofthe evolution equations, into the equations above, we reproduce Eq. (42), a nice sanity check. Inaddition, the equation above when combined properly with the evolution equations contains all theleading order logarithms resummed. This should be more relevant for the LHC phenomenology wherethe energies are higher than RHIC.

TODO: Check if there are additional factors from reversing A-P equations and thecross section formulas from initial state to the final state.

The soft gluon approximation

The coupled Altarelli-Parisi evolution equations Eq. (45)-Eq. (47) simplify tremendously for x ⌘1� z ! 0. In this small x approximation the equations decouple and reduce to describe the e↵ect ofleading patrons that shower soft gluons.

To see this we present the small x approximation of medium-induced splitting functions:

Pq!qg

=2C

F

x+

+

✓

2CF

xg[x,Q,L, µ]

◆

+

, (50)

7

Evolution of the fragmentation functions

¡ Large phase space still yields logarithmic enhancement to be resumed

¡ We work in LLA or MLLA

Implement medium –induced splittings as corrections to vacuum evolution

Better theoretical control. Opens directions to higher accuracy

+ q term

Y.T-Chien et al. (2015)

Jet quenching from QCD evolution¡ There is a connection between the

energy loss and the evolution approach, it is in the soft gluon limit

¡ We solve the DGLAP evolution equations analytically

The evolution equations are given by standard Altarelli-Parisi equations:

dDq

(z,Q)

d lnQ=

↵s

(Q2)

⇡

Z

1

z

dz0

z0

n

Pq!qg

(z0, Q)Dq

⇣ z

z0, Q

⌘

+ Pq!gq

(z0, Q)Dg

⇣ z

z0, Q

⌘o

, (45)

dDq̄

(z,Q)

d lnQ=

↵s

(Q2)

⇡

Z

1

z

dz0

z0

n

Pq!qg

(z0, Q)Dq̄

⇣ z

z0, Q

⌘

+ Pq!gq

(z0, Q)Dg

⇣ z

z0, Q

⌘o

, (46)

dDg

(z,Q)

d lnQ=

↵s

(Q2)

⇡

Z

1

z

dz0

z0

(

Pg!gg

(z0, Q)Dg

⇣ z

z0, Q

⌘

+Pg!qq̄

(z0, Q)⇣

Dq

⇣ z

z0, Q

⌘

+ fq̄

⇣ z

z0, Q

⌘⌘

)

. (47)

The complete medium-induced splitting functions look like:

P(1)

i

(z,Q) = P vac

i

(z) [1 + gi

(x,Q,L, µ)] , (48)

where the individual terms with all the plus prescriptions and virtual pieces are summarized insections 2, 3. These evolution equations have to be solved with initial conditions for parton densitiesfor quarks, anti-quarks and gluons to equal �(1� z) at some infrared scale ⇠ fewGeV. The resultingso-called PDF’s at the hard scattering scale Q = p

T

look like fi/j

(z, pT

), and have an intuitiveinterpretation: probability of the parton i to be found in the parton j at the momentum transferscale Q = p

T

. For example fg/q

(z, pT

) is the solution for the gluon density from the evolutionequations with the initial conditions f

q

(z, µIR

) = �(1� z), fq̄

(z, µIR

) = fg

(z, µIR

) = 0, and so forth.As a result of solving the A-P evolution equations we get the full LL series resummed by:

�(i)(pT

) =X

j=q,q̄,g

Z

1

0

dz �(j)

⇣pT

z

⌘

fi/j

(z, pT

), (49)

where i = q, q̄, g. It is straightforward to check, that by plugging in the lowest order solutions ofthe evolution equations, into the equations above, we reproduce Eq. (42), a nice sanity check. Inaddition, the equation above when combined properly with the evolution equations contains all theleading order logarithms resummed. This should be more relevant for the LHC phenomenology wherethe energies are higher than RHIC.

TODO: Check if there are additional factors from reversing A-P equations and thecross section formulas from initial state to the final state.

The soft gluon approximation

The coupled Altarelli-Parisi evolution equations Eq. (45)-Eq. (47) simplify tremendously for x ⌘1� z ! 0. In this small x approximation the equations decouple and reduce to describe the e↵ect ofleading patrons that shower soft gluons.

To see this we present the small x approximation of medium-induced splitting functions:

Pq!qg

=2C

F

x+

+

✓

2CF

xg[x,Q,L, µ]

◆

+

, (50)

7Pg!gg

=2C

A

x+

+

✓

2CA

xg[x,Q,L, µ]

◆

+

, (51)

Pg!qq̄

= 0, (52)

Pq!gq

= 0, (53)

where the function g equals to:

g(x,Q ⌘ k;↵) =

Z

d�z

�g

(�z)d2q?

1

�el

d�medium

el

d2q?

2k? ·q?(k? � q?)2

1� cos(k? � q?)2

xp+0

�z

�

. (54)

From this it is clear that the A-P equations uncouple for di↵erent partons. In the following sectionwe solve approximately the small-x evolution equations and show connections to the energy lossapproach.

ALTERNATIVEFlavor conservation is implicit in the small x approximation we focus on momentum conservation

Pq!qg

= 2CF

⇢

1

x+

+ �(x) +

1

xg(x,Q;↵)

�

+

+A(Q;↵)�(x)

�

, (55)

Pg!gg

= 2CA

⇢

1

x+

+ �(x) +

1

xg(x,Q;↵)

�

+

+A(Q;↵)�(x)

�

, (56)

Pg!qq̄

= 0, (57)

Pq!gq

= 0, (58)

where, in terms the function g, we have:

A(Q;↵) =

Z

1

0

dx g(x,Q ⌘ k;↵) ⌘ ⇡2

CR

↵s

Z

1

0

dxQ2

dN

dxd2Q(x,Q;↵) (59)

3.3 From QCD evolution to energy loss

In this section we show that in the soft gluon small-x limit the approximate solution to the decoupledevolution equations for the fragmentation functions is intimately connected with the energy-lossapproach. In the small x approximation the evolution equation for the fragmentation function lookslike:

dDh/c

(z,Q)

d lnQ=

↵s

⇡

Z

1

z

dz0

z0⇥

Pc!cg

(z0, Q)⇤

+

Dh/c

(z/z0, Q). (60)

In the equation above the splitting function Pc!cg

contains both vacuum or medium terms, and isgiven by expressions in Eq. (55) and Eq. (56). Let is first focus only on the vacuum contributionfor large z, motivated by the fact that high p

T

hadron production is dominated by large values of z,especially close to the kinematic limit. Furthermore, since D(z/z0, Q) is a steeply falling function ofz/z0, we expect that the region z0 ⇡ 1 will be the most important:

dDh/c

(z,Q)

d lnQ= 2C

R

↵s

⇡

⇢

Z

1

z

dz01

1� z0

1

z0D

h/c

(z/z0, Q)�Dh/c

(z,Q)

�

+Dh/c

(z,Q) ln(1� z)

�

. (61)

8

The equation above can be easily solved exactly

Dh/c

(z,Q) = e�2CR

↵s⇡

h

ln

QQ0

i

{[n(z)�1](1�z)�1�ln(1�z)}D

h/c

(z,Q0

). (71)

—–Using the same technique and approximations it is straightforward to generalize to the case

when Pc!cg

(z0, Q) contains both vacuum [· · · ]vac.

and medium-induced parts. Note that our runningQ ⌘ k?, for example dN/dz0d2Q = dN(z0 ⌘ x,k? ⌘ Q)/dxd2k?. Without writing explicitly thevacuum evolution part above, we find

dDmed.

h/c

(z,Q)

d lnQ= [· · · ]

vac.

+↵s

⇡

⇢

Z

1

z

dz02⇡2

↵s

Q2

dN

dz0d2Q(1� z0, Q)

1

z0Dmed.

h/c

(z/z0, Q)�Dmed.

h/c

(z,Q)

�

�Z

z

0

dz02⇡2

↵s

Q2

dN

dz0d2Q(1� z0, Q)Dmed.

h/c

(z,Q)

�

. (72)

Chaging variables z0 ! 1 � z0 in the medium-induced part to make contact with the energy lossapproach, Eq. (77) becomes

d lnDmed.

h/c

(z,Q)

d lnQ= [· · · ]

vac.

� [n(z)� 1]

⇢

Z

1�z

0

dz0 z0QdN

dz0dQ(z0, Q)

�

�Z

1

1�z

dz0QdN

dz0dQ(z0, Q) . (73)

Eq. (78) integrates as follows

Dmed.

h/c

(z,Q) = e�2CR

↵s⇡

h

ln

QQ0

i

{[n(z)�1](1�z)�ln(1�z)}D

h/c

(z,Q0

)

⇥e�[n(z)�1]

n

R 1�z0 dz

0z

0 RQQ0

dQ

0 dNdz0dQ0 (z

0,Q

0)

o

�R 11�z dz

0 RQQ0

dQ

0 dNdz0dQ0 (z

0,Q

0)

= Dh/c

(z,Q)e�[n(z)�1]

˜h�EE i

z� ˜hNgiz . (74)

Here, we have chosen Q0

and Q cover all relevant phase space for medium-induced gluon emissionand defined

˜⌧

�E

E

�

z

=

Z

1�z

0

dz0 z0Z

Q

Q0

dQ0 dN

dz0dQ0 (z0, Q0) =

Z

1�z

0

dz0 z0dN

dz0(z0) !

z!0

⌧

�E

E

�

, (75)

˜hNgiz

=

Z

1

1�z

dz0Z

Q

Q0

dQ0 dN

dz0dQ0 (z0, Q0) =

Z

1

1�z

dz0dN

dz0(z0) !

z!1

hNgi . (76)

Note that it is in opposite limits that Eqs. (75) and (76) reduce to the mean fractional energy loss andthe mean gluon emission number. It should be noted that for final state interactions in the coherentLPM limit both hNgi and h�E/Ei are dominated by small z gluon emission for very energeticjets. This, most of the time the modification is primarily driven by the full fractional energy loss.However, at the kinematic bound the energy loss component vanishes and the suppression is givenby the probability not to radiate gluons, exp(�hN

g

i).ALTERNATIVE

Using the same technique and approximations it is straightforward to generalize to the case whenPc!cg

(z0, Q) contains both vacuum [· · · ]vac.

and medium-induced parts. Note that our running Q ⌘

10

¡ E-loss in initial conditions and then evolution

The equation above can be easily solved exactly

Dh/c

(z,Q) = e�2CR

↵s⇡

h

ln

QQ0

i

{[n(z)�1](1�z)�1�ln(1�z)}D

h/c

(z,Q0

). (71)

—–Using the same technique and approximations it is straightforward to generalize to the case

when Pc!cg

(z0, Q) contains both vacuum [· · · ]vac.

and medium-induced parts. Note that our runningQ ⌘ k?, for example dN/dz0d2Q = dN(z0 ⌘ x,k? ⌘ Q)/dxd2k?. Without writing explicitly thevacuum evolution part above, we find

dDmed.

h/c

(z,Q)

d lnQ= [· · · ]

vac.

+↵s

⇡

⇢

Z

1

z

dz02⇡2

↵s

Q2

dN

dz0d2Q(1� z0, Q)

1

z0Dmed.

h/c

(z/z0, Q)�Dmed.

h/c

(z,Q)

�

�Z

z

0

dz02⇡2

↵s

Q2

dN

dz0d2Q(1� z0, Q)Dmed.

h/c

(z,Q)

�

. (72)

Chaging variables z0 ! 1 � z0 in the medium-induced part to make contact with the energy lossapproach, Eq. (77) becomes

d lnDmed.

h/c

(z,Q)

d lnQ= [· · · ]

vac.

� [n(z)� 1]

⇢

Z

1�z

0

dz0 z0QdN

dz0dQ(z0, Q)

�

�Z

1

1�z

dz0QdN

dz0dQ(z0, Q) . (73)

Eq. (78) integrates as follows

Dmed.

h/c

(z,Q) = e�2CR

↵s⇡

h

ln

QQ0

i

{[n(z)�1](1�z)�ln(1�z)}D

h/c

(z,Q0

)

⇥e�[n(z)�1]

n

R 1�z0 dz

0z

0 RQQ0

dQ

0 dNdz0dQ0 (z

0,Q

0)

o

�R 11�z dz

0 RQQ0

dQ

0 dNdz0dQ0 (z

0,Q

0)

= Dh/c

(z,Q)e�[n(z)�1]

˜h�EE i

z� ˜hNgiz . (74)

Here, we have chosen Q0

and Q cover all relevant phase space for medium-induced gluon emissionand defined

˜⌧

�E

E

�

z

=

Z

1�z

0

dz0 z0Z

Q

Q0

dQ0 dN

dz0dQ0 (z0, Q0) =

Z

1�z

0

dz0 z0dN

dz0(z0) !

z!0

⌧

�E

E

�

, (75)

˜hNgiz

=

Z

1

1�z

dz0Z

Q

Q0

dQ0 dN

dz0dQ0 (z0, Q0) =

Z

1

1�z

dz0dN

dz0(z0) !

z!1

hNgi . (76)

Note that it is in opposite limits that Eqs. (75) and (76) reduce to the mean fractional energy loss andthe mean gluon emission number. It should be noted that for final state interactions in the coherentLPM limit both hNgi and h�E/Ei are dominated by small z gluon emission for very energeticjets. This, most of the time the modification is primarily driven by the full fractional energy loss.However, at the kinematic bound the energy loss component vanishes and the suppression is givenby the probability not to radiate gluons, exp(�hN

g

i).ALTERNATIVE

Using the same technique and approximations it is straightforward to generalize to the case whenPc!cg

(z0, Q) contains both vacuum [· · · ]vac.

and medium-induced parts. Note that our running Q ⌘

10

N. Chang et al. (2014)

See lecture by B. Surrow

0 5 10 15 20

pT [GeV]

0

0.2

0.4

0.6

0.8

1

RA

A(p

T)

PHENIX π0, 0-10%

Full evolution numerics, g=2.3

Soft gluon energy loss, g=2.3

Soft gluon analytic evolution, g=2.3

Soft gluon evolution numerics, g=2.3

Central Au+Au, s1/2

=200 GeV

Z. Kang et al. (2014)

Calculating jet cross section in SCET

The approach can also be extended to hadron fragmentation inside jets

§ Jet production with semi-inclusive jet functions§ Can be conveniently formulated in SCET

Z. Kang et al. (2016)

(A) (B) (C) (E)(D)

LONLO

10−3

10−2

10−1

100

101

102

103

104

105

0.1 1

R = 0.4, anti-kT , |η| < 1.6

pp → (jeth±)X,√s = 2.76 TeV

[60, 80]

[160, 210]× 102

F(z

h,pT)

zh

NLO+NLLR

ATLAS

Good description but can still benefit from improvements at low z

Standard DGLAP can be used to resumlogs of the jet radius

Corrections in A+A collisions

The short-distance hard part remains the same

Encodes the effects of the jet evolving in the QCD medium

CNM effects

The jet function receives medium contributions from collisional energy loss and in-medium branching processes

Medium induced corrections to the LO jet function

Medium induced corrections to the NLO jet function

Vacuum jet function:

Medium corrections:

H. Li et al. (2018)

Examples of phenomenology – heavy flavor jets

§ Heavy flavor and the dead cone effect

The mass can have rather significant effect on jet substructure

See lecture by R. Rapp, M. Calderon

D. Kharzeev et al (2001)

H. Li et al (2018)

M. Sievert et al (2019)

Mass effect (dead cone effect) is different for the different splitting functions

Vacuum splitting functions, similarly in the medium

Note that the results are preliminary

M. Taylor et al . / CMS (2019)

Examples of phenomenology –inclusive jets

SCET gives good description of the data

Challenges medium recoil models, AdS CFT based models Lecture by S. Grozdanov

Jet substructureJet substructure – collectively describes the intra jet particle and energy flow.

See plenary talk by Y.T. Chien

A. Larkoski et al 2014

rg = ΔR12

pT1

pT2

zg =

Jet shapes, jet fragmentation functions, jet momentum sharing distributions, jet charge …

To LO this is directly proportional to the splitting functions N. Chang et al (2017)

In-medium modificationH. Li et al . (2017)

Sudakovresumamtion can affect angular distributions

Jet splitting functions give direct information for the in-medium splittings

0.1 0.2 0.3 0.4 0.5

gz

0.4

0.6

0.8

1

1.2

1.4

1.6

PbPb/pp

0±g = 2.0 < 250 GeVT,jet

200 < p0.1 0.2 0.3 0.4 0.5

gz

0.4

0.6

0.8

1

1.2

1.4

1.6

PbPb/pp

= 5.02 TeVNNs Centrality: 0-10%

< 160 GeVT,jet

140 < p

Data

0.1 0.2 0.3 0.4 0.5

gz

0.4

0.6

0.8

1

1.2

1.4

1.6

PbPb/pp

< 300 GeVT,jet

250 < p0.1 0.2 0.3 0.4 0.5

gz

0.4

0.6

0.8

1

1.2

1.4

1.6

PbPb/pp

|<1.3jetη R=0.4 |Tanti-k

< 180 GeVT,jet

160 < p

LO

0.1 0.2 0.3 0.4 0.5

gz

0.4

0.6

0.8

1

1.2

1.4

1.6

PbPb/pp

< 500 GeVT,jet

300 < p0.1 0.2 0.3 0.4 0.5

gz

0.4

0.6

0.8

1

1.2

1.4

1.6

PbPb/pp

>0.112R∆=0.1, cut

=0, zβSoft Drop

< 200 GeVT,jet

180 < p

MLL

Y.T. Chien et al . (2018)

Jet flavor separation

QGPHadron gas¡ Medium modification

depends on the flavor of the jet (color charge)

¡ First indications from photon-tagged vs inclusive jets (photon tagging isolates the inverse Compton scattering process in QCD)

R. Field et al. (1978) D. Krohn et al. (2013)

M. Aaboud et al . (2019)

¡ Jet charge – proxy for the charge of the parton. Will hear more in the conference

What we learned todayn The energy loss of partons in nuclear matter and the

QGP. The basics of jet quenching phenomenology and various E-loss approaches

n The differences between the suppression of inclusive hadrons and reconstructed jets. The connection between inclusive and tagged jet modifications and intra jet observables

n Modern effective theories of QCD – in the vacuum and in matter, higher order calculations and resummation. How to go beyond energy loss and improve theoreticalaccuracy

n Jet substructure, and more differential flavor-dependent jet modification. How to have consistent picture based on QCD