Jet Quenching Liliana Apolinrio 26th February 2019 COST THOR - - PowerPoint PPT Presentation

26th February 2019 COST THOR School, Lund, Sweden

Jet Quenching

Liliana Apolinário

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ pp collision: a “simple” (few particles) system

2

Proton-Proton Collision

➡ Hard scattering: ➡ Process evolution can be

described with Quantum Field Theory first principles

See talk “Jets” (S. Prestel) Monday

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ PbPb collision: a complex multi-particle system

3

Heavy-Ions Collision

➡ Hard scattering ➡ Hot and dense medium (QGP)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ PbPb collision: a complex multi-particle system

3

Heavy-Ions Collision

➡ Hard scattering ➡ Particles modified w.r.t pp: Jet

Quenching effects

➡ Hot and dense medium (QGP) ➡ Fluid with collectivity phenomena ➡ Also QCD system, but strongly

interacting!

➡ How collectivity emerge from a

QFT?

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ PbPb collision: a complex multi-particle system

3

Heavy-Ions Collision

See talk “Flow” (C. Plumberg) today

➡ Hard scattering ➡ Particles modified w.r.t pp: Jet

Quenching effects

➡ Hot and dense medium (QGP) ➡ Fluid with collectivity phenomena ➡ Also QCD system, but strongly

interacting!

➡ How collectivity emerge from a

QFT?

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ PbPb collision evolution

4

Heavy-Ions: Open Questions

➡ Final state particles (what we measure) ➡ Initial state (incoming nuclei) ➡ See talk “Nuclear PDFs” (I.Heleniums) today ➡ Is the QGP strongly coupled? ➡ How is thermalized? ➡ QCD description in all energy range ➡ Quasi-particles?

?

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ PbPb collision evolution

4

Heavy-Ions: Open Questions

➡ Final state particles (what we measure) ➡ Initial state (incoming nuclei) ➡ See talk “Nuclear PDFs” (I.Heleniums) today ➡ Is the QGP strongly coupled? ➡ How is thermalized? ➡ QCD description in all energy range ➡ Quasi-particles?

?

➡ Identify well controlled observables/

probes to assess QGP properties!!

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Soft probes: flow, hydrochemistry, … ✦ Direct result of the QGP evolution ➡ Collective properties and hydrodynamical evolution of the medium

5

QGP Probes

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Soft probes: flow, hydrochemistry, … ✦ Direct result of the QGP evolution ➡ Collective properties and hydrodynamical evolution of the medium ✦ Hard probes: Quarkonia, jets, … ✦ Produced in a high momentum transfer process (hard scattering) ✦ Indirect observation of the QGP effects ➡ Observe the evolution of the QGP (temperature, density,…)

5

QGP Probes

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Soft probes: flow, hydrochemistry, … ✦ Direct result of the QGP evolution ➡ Collective properties and hydrodynamical evolution of the medium ✦ Hard probes: Quarkonia, jets, … ✦ Produced in a high momentum transfer process (hard scattering) ✦ Indirect observation of the QGP effects ➡ Observe the evolution of the QGP (temperature, density,…)

5

QGP Probes

This talk!

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Better theoretical and experimental control! ➡ Like in pp, less sensitive to (unknown) details of

incoming nucleus (nPDFs)

6

Why Hard Probes?

, . . .) ⊗ D(vac)

f →h(z, µ2 F) . →h+rest med

⊗ dσ AA→

(vac) X =

• i jk

fi/A(x1, Q2) ⊗ f j/A(x2, Q2) ⊗ ˆ σi j→ f +k

PDFs Elementary “Hard” cross-section FFs

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Better theoretical and experimental control! ➡ Like in pp, less sensitive to (unknown) details of

incoming nucleus (nPDFs)

6

Why Hard Probes?

, . . .) ⊗ D(vac)

f →h(z, µ2 F) . →h+rest med

⊗ dσ AA→

(vac) X =

• i jk

fi/A(x1, Q2) ⊗ f j/A(x2, Q2) ⊗ ˆ σi j→ f +k

PDFs Elementary “Hard” cross-section FFs

dσ AA→h+rest

(med)

=

=

• i jk

fi/A(x1, Q2) ⊗ f j/A(x2, Q2) ⊗ ˆ σi j→ f +k

X ⊗ Pf (E, L, ˆ

q, . . .) ⊗ D(vac)

f →h(z, µ2 F) .

nPDFs Medium-induced FF “Vacuum” Hadronization (?)

Unmodified by the QGP!

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Formed in the beginning of the collision: ➡ Allow detailed imaging of the QGP ➡ QGP evolution (E.g: thermalisation

process)

✦ Formed by collection of soft to hard

particles

➡ Allow QGP probing by different scales ➡ Scale dependent quantities (Eg.:

“quasi-particles”)

7

Why Jets?

g* Q2 q

?

QGP

Q2

PT Initial Parton What scale sets this transition? Tc

pQCD Scattering from Point-Like Bare Color Charges

µD

pQCD Scattering From Quasiparticles with size ~ µDebye Strong Coupling No Quasiparticles µDebye ! 0

AdS/CFT ?! " ?

What scale sets this transition?

Scattering from Thermal Mass Gluons?

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Formed in the beginning of the collision: ➡ Allow detailed imaging of the QGP ➡ QGP evolution (E.g: thermalisation

process)

✦ Formed by collection of soft to hard

particles

➡ Allow QGP probing by different scales ➡ Scale dependent quantities (Eg.:

“quasi-particles”)

7

Why Jets?

g* Q2 q

?

QGP

Q2

PT Initial Parton What scale sets this transition? Tc

pQCD Scattering from Point-Like Bare Color Charges

µD

pQCD Scattering From Quasiparticles with size ~ µDebye Strong Coupling No Quasiparticles µDebye ! 0

AdS/CFT ?! " ?

What scale sets this transition?

Scattering from Thermal Mass Gluons?

Welcome to the field of jet quenching!

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Formed in the beginning of the collision: ➡ Allow detailed imaging of the QGP ➡ QGP evolution (E.g: thermalisation

process)

✦ Formed by collection of soft to hard

particles

➡ Allow QGP probing by different scales ➡ Scale dependent quantities (Eg.:

“quasi-particles”)

7

Why Jets?

g* Q2 q

?

QGP

Q2

PT Initial Parton What scale sets this transition? Tc

pQCD Scattering from Point-Like Bare Color Charges

µD

pQCD Scattering From Quasiparticles with size ~ µDebye Strong Coupling No Quasiparticles µDebye ! 0

AdS/CFT ?! " ?

What scale sets this transition?

Scattering from Thermal Mass Gluons?

Welcome to the field of jet quenching! But before we start…

Revisiting our baseline: pp

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ “Vacuum” parton shower:

9

From parton to jets in pp

➡ A jet is a subsequent process of single

parton emissions

➡ Avoid non perturbative effects (e.g:

hadronization)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ “Vacuum” parton shower:

9

From parton to jets in pp

➡ A jet is a subsequent process of single

parton emissions

➡ Avoid non perturbative effects (e.g:

hadronization)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ “Vacuum” parton shower:

9

From parton to jets in pp

➡ A jet is a subsequent process of single

parton emissions

➡ Avoid non perturbative effects (e.g:

hadronization)

Revisiting building blocks!

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Gluon bremsstrahlung from an off-shell (virtual) quark:

10

Single parton emission

➡ Soft and collinear divergent ➡ Needs re-summation: evolution

equations (DGLAP, MLLA,…)

ω, k⊥ θ dP q→qg ∼ αsCR dω ω dk2

⊥

k2

⊥

…

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Gluon bremsstrahlung from an off-shell (virtual) quark:

10

Single parton emission

➡ Soft and collinear divergent ➡ Needs re-summation: evolution

equations (DGLAP, MLLA,…)

Are they all independent?

ω, k⊥ θ dP q→qg ∼ αsCR dω ω dk2

⊥

k2

⊥

…

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Soft gluon radiation from a quark - anti-quark pair: ✦ color singlet configuration:

11

Jet Coherence

ω, k⊥ θ q1 q2 θ1

+

ω, k⊥ θ q1 q2 θ1

2

dI dΩk = Rq + R¯

q − 2J(1

) = Rcoh + 2

11

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Soft gluon radiation from a quark - anti-quark pair: ✦ color singlet configuration: ✦ No radiation outside of the cone ➡ Angular ordering

11

Jet Coherence

dN ω→0

q

∼ αsCR dω ω sinθ dθ 1 − cos θΘ(cos θ1 − cos θ)

ω, k⊥ θ q1 q2 θ1

+

ω, k⊥ θ q1 q2 θ1

2

dI dΩk = Rq + R¯

q − 2J(1

) = Rcoh + 2 Integrating in azimuthal angle…

11

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Soft gluon radiation from a quark - anti-quark pair: ✦ color singlet configuration: ✦ No radiation outside of the cone ➡ Angular ordering ✦ color octet configuration: ✦ Radiation outside of the cone re-interpreted

as from the initial gluon

11

Jet Coherence

dN ω→0

q

∼ αsCR dω ω sinθ dθ 1 − cos θΘ(cos θ1 − cos θ)

ω, k⊥ θ q1 q2 θ1

+

ω, k⊥ θ q1 q2 θ1

2

dI dΩk = Rq + R¯

q − 2J(1

) = Rcoh + 2 Integrating in azimuthal angle…

11

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Soft gluon radiation from a quark - anti-quark pair: ✦ color singlet configuration: ✦ No radiation outside of the cone ➡ Angular ordering ✦ color octet configuration: ✦ Radiation outside of the cone re-interpreted

as from the initial gluon

➡ Angular ordering preserved

11

Jet Coherence

dN ω→0

q

∼ αsCR dω ω sinθ dθ 1 − cos θΘ(cos θ1 − cos θ)

ω, k⊥ θ q1 q2 θ1

+

ω, k⊥ θ q1 q2 θ1

2

dI dΩk = Rq + R¯

q − 2J(1

) = Rcoh + 2 Integrating in azimuthal angle…

11

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Formation time of an emission:

12

Vacuum formation time

See: Basics of Perturbative QCD, 1991

∆E∆t = 1

∆E = mvirtual

τform = ∆tγboost = ∆t ∆E mvirtual

⇒ τform = 1 mvirtual E mvirtual

Uncertainty principle:

θ

p = ((1 − z)E, ~ p)

k = (! = zE,~ k)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Formation time of an emission:

12

Vacuum formation time

See: Basics of Perturbative QCD, 1991

∆E∆t = 1

∆E = mvirtual

τform = ∆tγboost = ∆t ∆E mvirtual

⇒ τform = 1 mvirtual E mvirtual

Uncertainty principle:

θ

p = ((1 − z)E, ~ p)

k = (! = zE,~ k)

m2

virtual = 2p · k = 2z(1 z)E2(1 cos θ) ' z(1 z)E2θ2

k⊥ ∼ ω sin θ ∼ ωθ

where:

) τform ' 1 zEθ2 = ω k2

⊥

= λ⊥ θ

λ⊥ ∼ k−1

⊥

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Formation time of an emission: ✦ As for subsequent emissions:

12

Vacuum formation time

See: Basics of Perturbative QCD, 1991

∆E∆t = 1

∆E = mvirtual

τform = ∆tγboost = ∆t ∆E mvirtual

⇒ τform = 1 mvirtual E mvirtual

Uncertainty principle:

θ

p = ((1 − z)E, ~ p)

k = (! = zE,~ k)

m2

virtual = 2p · k = 2z(1 z)E2(1 cos θ) ' z(1 z)E2θ2

k⊥ ∼ ω sin θ ∼ ωθ

where:

) τform ' 1 zEθ2 = ω k2

⊥

= λ⊥ θ

λ⊥ ∼ k−1

⊥

θ θ

1 2

τform,2 = λ⊥,2 θ2

r⊥ = θ1τform,2 ⇔ r⊥ λ⊥,2 = θ1 θ2

During this time, the previous “antenna” separated:

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Formation time of an emission: ✦ As for subsequent emissions:

12

Vacuum formation time

See: Basics of Perturbative QCD, 1991

∆E∆t = 1

∆E = mvirtual

τform = ∆tγboost = ∆t ∆E mvirtual

⇒ τform = 1 mvirtual E mvirtual

Uncertainty principle:

θ

p = ((1 − z)E, ~ p)

k = (! = zE,~ k)

m2

virtual = 2p · k = 2z(1 z)E2(1 cos θ) ' z(1 z)E2θ2

k⊥ ∼ ω sin θ ∼ ωθ

where:

) τform ' 1 zEθ2 = ω k2

⊥

= λ⊥ θ

λ⊥ ∼ k−1

⊥

θ θ

1 2

τform,2 = λ⊥,2 θ2

r⊥ = θ1τform,2 ⇔ r⊥ λ⊥,2 = θ1 θ2

During this time, the previous “antenna” separated: θ2 > θ1 ⇒ rT < 휆T → Sensitive to the “antenna” charge θ2 > θ1 ⇒ rT > 휆T → Sensitive to the “leg” charge

Now back to Heavy-Ions

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ A jet (parton shower) is a perturbative object ⇒ calculable within pQCD

14

First Considerations

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ A jet (parton shower) is a perturbative object ⇒ calculable within pQCD ✦ The QGP is a strongly coupled fluid ✦ It is non perturbative… but we will assume a pQCD description for the jet-medium interaction… ➡ Described by a classical field Aμa(x) (recoil effects are neglected)

14

First Considerations

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ A jet (parton shower) is a perturbative object ⇒ calculable within pQCD ✦ The QGP is a strongly coupled fluid ✦ It is non perturbative… but we will assume a pQCD description for the jet-medium interaction… ➡ Described by a classical field Aμa(x) (recoil effects are neglected) ✦ High-energy particles propagating through a medium: ✦ Particle propagation time < timescale for changes in the medium fields ➡ Medium can be considered in a static configuration ➡ Only transverse momentum exchange

14

First Considerations

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Particle moving in the x3 direction: Light Cone Gauge A+ = 0 ✦ Light Cone Coordinates: p+ >> pT >> p- ✦

and

✦ Due to Lorentz contraction one can further assume

15

Light Cone Gauge

x n

+

xn

T

x 1 x 2

T T

x± = x0 ± x3 √ 2

x⊥ = (x1, x2)

A(x+, x−, x⊥) = A(x+, x⊥)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Particle moving in the x3 direction: Light Cone Gauge A+ = 0 ✦ Light Cone Coordinates: p+ >> pT >> p- ✦

and

✦ Due to Lorentz contraction one can further assume

15

Light Cone Gauge

x n

+

xn

T

x 1 x 2

T T

x± = x0 ± x3 √ 2

x⊥ = (x1, x2)

A(x+, x−, x⊥) = A(x+, x⊥)

igAaT a

AA2 = igAAA2

Additional notation: p1 p2 A1 A2 a

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating through a collection of static scattering centres: ✦ Result will be only a color phase rotation: ➡ In-medium propagator: Wilson Line

16

Eikonal Approximation

W(x0+, L+; x⊥) = P exp

• ig

⇤ L+

x0+

dx+A−(x+, x⊥) ⇥

• Path-ordering

Medium colour field Transverse coordinate

… …

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating through a collection of static scattering centres: ✦ Result will be only a color phase rotation: ➡ In-medium propagator: Wilson Line

16

Eikonal Approximation

W(x0+, L+; x⊥) = P exp

• ig

⇤ L+

x0+

dx+A−(x+, x⊥) ⇥

• Path-ordering

Medium colour field Transverse coordinate

… …

Let’s re-derive this propagator! Starting by two scatterings…

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

17

Eikonal Approximation

p1)

¯ u(p) / AAA2 / p2 = 2p2 · AAA2 ¯ u(p) − ¯ u(p) / p2 / AAA2

See: arXiv:0712.3443

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

See backup slides for more details!

p2

i = 2pi+pi− − p2 i⊥

Consider only the leading terms:

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

17

Eikonal Approximation

p1)

¯ u(p) / AAA2 / p2 = 2p2 · AAA2 ¯ u(p) − ¯ u(p) / p2 / AAA2

See: arXiv:0712.3443

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

See backup slides for more details!

p2

i = 2pi+pi− − p2 i⊥

Consider only the leading terms: sub-leading

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

17

Eikonal Approximation

p1)

¯ u(p) / AAA2 / p2 = 2p2 · AAA2 ¯ u(p) − ¯ u(p) / p2 / AAA2

See: arXiv:0712.3443

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

See backup slides for more details!

p2

i = 2pi+pi− − p2 i⊥

Consider only the leading terms: sub-leading

' 2p2+(A−)AA2 ¯ u(p)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

17

Eikonal Approximation

p1)

¯ u(p) / AAA2 / p2 = 2p2 · AAA2 ¯ u(p) − ¯ u(p) / p2 / AAA2

See: arXiv:0712.3443

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

See backup slides for more details!

p2

i = 2pi+pi− − p2 i⊥

Consider only the leading terms: sub-leading Residues theorem in pi- coordinates will bring the “ordering” of the fields:

Z dp2− 2π eip2−(x1−x2)+ i p2− − (−iε) = θ(x2 − x1)+

' 2p2+(A−)AA2 ¯ u(p)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

17

Eikonal Approximation

p1)

¯ u(p) / AAA2 / p2 = 2p2 · AAA2 ¯ u(p) − ¯ u(p) / p2 / AAA2

See: arXiv:0712.3443

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

See backup slides for more details!

p2

i = 2pi+pi− − p2 i⊥

Consider only the leading terms: sub-leading Residues theorem in pi- coordinates will bring the “ordering” of the fields:

Z dp2− 2π eip2−(x1−x2)+ i p2− − (−iε) = θ(x2 − x1)+

⇒ x1⊥ = x2⊥ = 0

Integrals on pit will just set:

' 2p2+(A−)AA2 ¯ u(p)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

18

Eikonal Approximation

' Z dx1+dx2+ig(A−)AA2(x2+, 0⊥)θ(x2x1)+ig(A−)A2A1(x1+, 0⊥)θ(x1)+u

See: arXiv:0712.3443

p1)

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

)+¯ u(p)Mh(p)

After some work…

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

18

Eikonal Approximation

' Z dx1+dx2+ig(A−)AA2(x2+, 0⊥)θ(x2x1)+ig(A−)A2A1(x1+, 0⊥)θ(x1)+u

See: arXiv:0712.3443

p1)

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

)+¯ u(p)Mh(p)

No interaction term After some work…

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

18

Eikonal Approximation

' Z dx1+dx2+ig(A−)AA2(x2+, 0⊥)θ(x2x1)+ig(A−)A2A1(x1+, 0⊥)θ(x1)+u

See: arXiv:0712.3443

p1)

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

)+¯ u(p)Mh(p)

No interaction term

P exp ( ig Z xn+

x1+

dx+A−(x+, x⊥ = 0) ) = W(xn+, x1+; x⊥ = 0)

summing over all ’n’ interaction terms

∑ ( ) …

After some work…

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a (not so) high energetic particle propagating through a collection of static scattering centres: ✦ Should include a small “kick” in the transverse plane:

19

Non-eikonal corrections

G(x0+, x0⇧; L+, x⇧|p+) = ⌦ r⇤(L+)=x⇤

r⇤(x0+)=x0⇤

Dr⇧(ξ) exp ⌥ ip+ 2 ⌦ L+

x0+

dξ dr⇧ dξ ⇥2 × W(x0+, L+; r⇧(ξ)), (3.10)

Initial/Final coordinates

See: arXiv:0712.3443

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a (not so) high energetic particle propagating through a collection of static scattering centres: ✦ Should include a small “kick” in the transverse plane:

19

Non-eikonal corrections

G(x0+, x0⇧; L+, x⇧|p+) = ⌦ r⇤(L+)=x⇤

r⇤(x0+)=x0⇤

Dr⇧(ξ) exp ⌥ ip+ 2 ⌦ L+

x0+

dξ dr⇧ dξ ⇥2 × W(x0+, L+; r⇧(ξ)), (3.10)

Initial/Final coordinates

See: arXiv:0712.3443

How to get this in-medium propagator?

p2

i = 2pi+pi− − p2 i⊥

sub-leading terms in denominator

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a (not so) high energetic particle propagating through a collection of static scattering centres: ✦ Should include a small “kick” in the transverse plane:

19

Non-eikonal corrections

G(x0+, x0⇧; L+, x⇧|p+) = ⌦ r⇤(L+)=x⇤

r⇤(x0+)=x0⇤

Dr⇧(ξ) exp ⌥ ip+ 2 ⌦ L+

x0+

dξ dr⇧ dξ ⇥2 × W(x0+, L+; r⇧(ξ)), (3.10)

Initial/Final coordinates

Z dpi− 2π eipi−(xi−1−xi)+ i pi− − p2

i⊥

2p+ + iε

= θ(xi − xi−1)+ e

i

p2 i⊥ 2p+ (xi−1−xi)−

Integral in pi-:

See: arXiv:0712.3443

How to get this in-medium propagator?

p2

i = 2pi+pi− − p2 i⊥

sub-leading terms in denominator

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a (not so) high energetic particle propagating through a collection of static scattering centres: ✦ Should include a small “kick” in the transverse plane:

19

Non-eikonal corrections

G(x0+, x0⇧; L+, x⇧|p+) = ⌦ r⇤(L+)=x⇤

r⇤(x0+)=x0⇤

Dr⇧(ξ) exp ⌥ ip+ 2 ⌦ L+

x0+

dξ dr⇧ dξ ⇥2 × W(x0+, L+; r⇧(ξ)), (3.10)

Initial/Final coordinates

Z dpi− 2π eipi−(xi−1−xi)+ i pi− − p2

i⊥

2p+ + iε

= θ(xi − xi−1)+ e

i

p2 i⊥ 2p+ (xi−1−xi)−

Integral in pi-: Integral in pT:

Z d2pi⊥ (2π)2 e

i

p2 i⊥ 2p+ (xi−1−xi)−ipi⊥(xi−1−xi)⊥ =

p+ 2πi(xi−1 − xi)+ exp ⇢ ip+ 2 (xi−1 − xi)2

⊥

(xi−1 − xi)+

• =

Z xi⊥

x(i−1)⊥

D(x⊥) exp ( ip+ 2 Z xi+

x(i−1)+

✓dx⊥ dx+ ◆2) = G0(xi+, xi⊥; x(i−1)+, x(i−1)⊥|p+)

See: arXiv:0712.3443

How to get this in-medium propagator?

p2

i = 2pi+pi− − p2 i⊥

sub-leading terms in denominator

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Medium-induced gluon radiation:

20

In-medium gluon emission

g q q g Sin Sin† I II III x0+ x1+ x2+ L+ High energy approximation: ⇒ Decomposition with a fixed number of propagators ⇒ 3 different regions

Mathematical picture Physical picture

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Medium-induced gluon radiation:

20

In-medium gluon emission

g q q g Sin Sin† I II III x0+ x1+ x2+ L+ High energy approximation: ⇒ Decomposition with a fixed number of propagators ⇒ 3 different regions Emission Kernel

Tr D WA(rg)W †

A(0)

E

Mathematical picture Physical picture

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Medium-induced gluon radiation:

20

In-medium gluon emission

g q q g Sin Sin† I II III x0+ x1+ x2+ L+ High energy approximation: ⇒ Decomposition with a fixed number of propagators ⇒ 3 different regions Emission Kernel

Tr D WA(rg)W †

A(0)

E

Classical Broadening

Tr D WA(rg)W †

A(¯

rg) E

Mathematical picture Physical picture

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Medium-induced gluon radiation:

20

In-medium gluon emission

g q q g Sin Sin† I II III x0+ x1+ x2+ L+ High energy approximation: ⇒ Decomposition with a fixed number of propagators ⇒ 3 different regions Emission Kernel

Tr D WA(rg)W †

A(0)

E

Classical Broadening

Tr D WA(rg)W †

A(¯

rg) E

Mathematical picture Physical picture

And, finally, some numerics:

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Medium-induced gluon radiation:

20

In-medium gluon emission

g q q g Sin Sin† I II III x0+ x1+ x2+ L+ High energy approximation: ⇒ Decomposition with a fixed number of propagators ⇒ 3 different regions Emission Kernel

Tr D WA(rg)W †

A(0)

E

Classical Broadening

Tr D WA(rg)W †

A(¯

rg) E

Mathematical picture Physical picture

And, finally, some numerics: LPM (QCD) suppression

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Heuristic discussion on single gluon emission spectrum (BDMPS):

21

LPM effect

k = z p q = (1-z) p

ˆ q = < k2

⊥ >

λmfp

Transport coefficient:

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Heuristic discussion on single gluon emission spectrum (BDMPS):

21

LPM effect

k = z p q = (1-z) p

ˆ q = < k2

⊥ >

λmfp

Transport coefficient:

τform = ω hk2

⊥i =

ω ˆ qτform ) τform = rω ˆ q

⌦ k2

⊥

↵ ∼ ˆ qL

Soft gluons have shorter formation times

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Heuristic discussion on single gluon emission spectrum (BDMPS):

21

LPM effect

k = z p q = (1-z) p

ˆ q = < k2

⊥ >

λmfp

Transport coefficient:

τform = ω hk2

⊥i =

ω ˆ qτform ) τform = rω ˆ q

⌦ k2

⊥

↵ ∼ ˆ qL

Soft gluons have shorter formation times Number of emitted gluons during L: Ng ∝

L τform

Multiple soft emissions (incoherent scatterings)

τform L

τform ⌧ L

Hard gluon spectrum is suppressed (scattering centres act as a whole)

ωc(τform = L) = 1 2 ˆ qL2

Critical energy: ω dI dω

• ω≤ωc

∼ αsCR rωc ω

ω dI dω

• ω>ωc

∼ αsCR ⇣ωc ω ⌘2

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Considering the in-medium singlet quark - antiquark antenna in the simplest case: ➡ Soft gluon emission outside medium

22

Intra-jet (de)coherence?

[Mehtar-Tani, Salgado, Tywoniuk (2010-2011)] [Casalderrey-Solana, Iancu (2011)]

dI dΩk = Rq + R¯

q − 2J(1 − ∆med) = Rcoh + 2J∆med +

ω, k⊥ θ q1 q2 θ1

+

2

ω, k⊥ θ q1 q2 θ1

2

Eikonal approximation: R¯

q ∼ αsCF

q2+ (k · q2) 2J ∼ αsCF  q1+ (k · q1) + q2+ (k · q2) − k+(q1 · q2) (k · q1)(k · q2)

• Rq ∼ αsCF

q1+ (k · q1)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Considering the in-medium singlet quark - antiquark antenna in the simplest case: ➡ Soft gluon emission outside medium

22

Intra-jet (de)coherence?

[Mehtar-Tani, Salgado, Tywoniuk (2010-2011)] [Casalderrey-Solana, Iancu (2011)]

dI dΩk = Rq + R¯

q − 2J(1 − ∆med) = Rcoh + 2J∆med +

ω, k⊥ θ q1 q2 θ1

+

2

ω, k⊥ θ q1 q2 θ1

2

Eikonal approximation: R¯

q ∼ αsCF

q2+ (k · q2) 2J ∼ αsCF  q1+ (k · q1) + q2+ (k · q2) − k+(q1 · q2) (k · q1)(k · q2)

• Rq ∼ αsCF

q1+ (k · q1) Rcoh ∼ αsCF k+(q1 · q2) (k · q1)(k · q2) as in vacuum: 1 − ∆med = 1 N 2

c

Tr D WA(xq)W †

A(x¯ q)

E new in-medium contribution:

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Considering the in-medium singlet quark - antiquark antenna in the simplest case: ➡ Soft gluon emission outside medium

23

Intra-jet (de)coherence?

[Mehtar-Tani, Salgado, Tywoniuk (2010-2011)] [Casalderrey-Solana, Iancu (2011)]

dN ω→0

q

∼ αsCR dω ω sin θdθ 1 − cos θ [Θ(cos θ1 − cos θ) + ∆medΘ(cos θ − cos θ1)]

Integrating over azimuthal angle (soft limit):

∆med ≈ 1 − e− 1

12 Q2 sr2 ⊥

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Considering the in-medium singlet quark - antiquark antenna in the simplest case: ➡ Soft gluon emission outside medium

23

Intra-jet (de)coherence?

[Mehtar-Tani, Salgado, Tywoniuk (2010-2011)] [Casalderrey-Solana, Iancu (2011)]

Q−1

s

dN ω→0

q

∼ αsCR dω ω sin θdθ 1 − cos θ [Θ(cos θ1 − cos θ) + ∆medΘ(cos θ − cos θ1)]

Integrating over azimuthal angle (soft limit):

∆med ≈ 1 − e− 1

12 Q2 sr2 ⊥

r⊥ ∆med → 0

Angular ordering Antenna Transverse resolution: r⟂ = θ L Medium Transverse Scale: Qs-1= √(q L)-1

^

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Considering the in-medium singlet quark - antiquark antenna in the simplest case: ➡ Soft gluon emission outside medium

23

Intra-jet (de)coherence?

[Mehtar-Tani, Salgado, Tywoniuk (2010-2011)] [Casalderrey-Solana, Iancu (2011)]

Q−1

s

dN ω→0

q

∼ αsCR dω ω sin θdθ 1 − cos θ [Θ(cos θ1 − cos θ) + ∆medΘ(cos θ − cos θ1)]

Integrating over azimuthal angle (soft limit):

∆med ≈ 1 − e− 1

12 Q2 sr2 ⊥

r⊥ ∆med → 0

Angular ordering Antenna Transverse resolution: r⟂ = θ L Medium Transverse Scale: Qs-1= √(q L)-1

^

r⊥ Q−1

s

Anti-Angular ordering

∆med → 1

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Single gluon radiation beyond eikonal limit: ✦ Small 훕form: parton shower can as incoherent sum

• f gluon radiation

24

More th developments

[J.-P. Blaizot, F. Dominguez, E. Iancu, and Y. Mehtar-Tani (12), Jeon, Moore (05)]

t* 휏form L ⇒ Rate equations

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Single gluon radiation beyond eikonal limit: ✦ Small 훕form: parton shower can as incoherent sum

• f gluon radiation

✦ Non-eikonal corrections to QCD antenna

24

More th developments

[J.-P. Blaizot, F. Dominguez, E. Iancu, and Y. Mehtar-Tani (12), Jeon, Moore (05)]

t* 휏form L ⇒ Rate equations

[LA, N. Armesto, G. Milhano, C. Salgado (17)]

dI dΩqdΩ¯

qdΩk

= ∆0

coh(Rq + R¯ q) − 2(1 − ∆0 med)J

⇒ Interplay Coherence/Decoherence

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Single gluon radiation beyond eikonal limit: ✦ Small 훕form: parton shower can as incoherent sum

• f gluon radiation

✦ Non-eikonal corrections to QCD antenna ✦ Hard emission from In-medium antenna:

24

More th developments

[J.-P. Blaizot, F. Dominguez, E. Iancu, and Y. Mehtar-Tani (12), Jeon, Moore (05)]

t* 휏form L ⇒ Rate equations

[Domínguez, Salgado and Vila (18) ]

⇒ Effective emitters in the parton shower

[LA, N. Armesto, G. Milhano, C. Salgado (17)]

dI dΩqdΩ¯

qdΩk

= ∆0

coh(Rq + R¯ q) − 2(1 − ∆0 med)J

⇒ Interplay Coherence/Decoherence

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Single gluon radiation beyond eikonal limit: ✦ Small 훕form: parton shower can as incoherent sum

• f gluon radiation

✦ Non-eikonal corrections to QCD antenna ✦ Hard emission from In-medium antenna: ✦ Effects of the medium on vacuum-like emissions: ✦ First radiation outside the medium can violate

24

More th developments

[J.-P. Blaizot, F. Dominguez, E. Iancu, and Y. Mehtar-Tani (12), Jeon, Moore (05)]

t* 휏form L ⇒ Rate equations

[Domínguez, Salgado and Vila (18) ]

⇒ Effective emitters in the parton shower

angular-ordering

[Caucal, Iancu, Mueller, Soyez (18) & QM18]

⇒ Medium effects on vacuum emissions

[LA, N. Armesto, G. Milhano, C. Salgado (17)]

dI dΩqdΩ¯

qdΩk

= ∆0

coh(Rq + R¯ q) − 2(1 − ∆0 med)J

⇒ Interplay Coherence/Decoherence

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Single gluon radiation beyond eikonal limit: ✦ Small 훕form: parton shower can as incoherent sum

• f gluon radiation

✦ Non-eikonal corrections to QCD antenna ✦ Hard emission from In-medium antenna: ✦ Effects of the medium on vacuum-like emissions: ✦ First radiation outside the medium can violate

24

More th developments

[J.-P. Blaizot, F. Dominguez, E. Iancu, and Y. Mehtar-Tani (12), Jeon, Moore (05)]

t* 휏form L ⇒ Rate equations

[Domínguez, Salgado and Vila (18) ]

⇒ Effective emitters in the parton shower

angular-ordering

[Caucal, Iancu, Mueller, Soyez (18) & QM18]

⇒ Medium effects on vacuum emissions See K. Tywoniuk (Thursday)

[LA, N. Armesto, G. Milhano, C. Salgado (17)]

dI dΩqdΩ¯

qdΩk

= ∆0

coh(Rq + R¯ q) − 2(1 − ∆0 med)J

⇒ Interplay Coherence/Decoherence

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Resulting picture of a medium-modified parton

shower:

25

Resulting picture

Finite size “pp-like” structures (Angular Ordering)

[1401.8293]

Medium-induced radiation (not collinear)

[See also: 1801.09703]

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Resulting picture of a medium-modified parton

shower:

25

Resulting picture

Finite size “pp-like” structures (Angular Ordering)

[1401.8293]

Medium-induced radiation (not collinear)

[See also: 1801.09703]

hard structure: unmodified

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Resulting picture of a medium-modified parton

shower:

25

Resulting picture

Finite size “pp-like” structures (Angular Ordering)

[1401.8293]

Medium-induced radiation (not collinear)

[See also: 1801.09703]

increase of soft fragments hard structure: unmodified

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Resulting picture of a medium-modified parton

shower:

26

Resulting picture

Finite size “pp-like” structures (Angular Ordering) Medium-induced radiation (not collinear) Soft fragments radiated up to large angles

arXiv:1803.00042

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Resulting picture of a medium-modified parton

shower:

26

Resulting picture

Everything seems to work, we can go home! Finite size “pp-like” structures (Angular Ordering) Medium-induced radiation (not collinear) Soft fragments radiated up to large angles

arXiv:1803.00042

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Quantitative comparisons show some disagreement… ✦ Monte Carlo approaches based on in-medium single gluon

radiation fail to describe some of the intra-jet features!

0.1 0.2 0.3 10 r 0.1 0.2 0.3

pp

(r) ρ /

PbPb

(r) ρ 0.5 1 1.5 0.1 0.2 0.3 10 r 0.1 0.2 0.3 0.5 1 1.5 0.1 0.2 0.3 10 r 0.1 0.2 0.3 0.5 1 1.5 0.1 0.2 0.3 10 r 0.1 0.2 0.3 0.5 1 1.5 0.1 0.2 0.3 10 r 0.1 0.2 0.3 0.5 1 1.5 70-100%

• 1

10 50-70%

• 1

10 30-50%

• 1

10 10-30%

• 1

10 0-10%

= 2.76 TeV

NN

s CMS,

jets: R = 0.3 anti-k

PbPb

• 1

L dt = 5.3 pb

∫

pp,

• 1

b µ L dt = 150

∫

PbPb,

27

Not so fast…

R 0.05 0.1 0.15 0.2 0.25 0.3

= 0 q

(r)

• /
• q

(r)

• 0.5

1 1.5 2 2.5 3 3.5 4

Q-PYTHIA 2.76TeV ptgen = 70 GeV

• 1

fm

= 1 GeV q

• 1

fm

= 4 GeV q

• 1

fm

= 8 GeV q

ρ(r) = 1 δr 1 Njet ∑

jets

∑

tracks ∈ [ra, rb)

ptrack

T

pjet

T

[L.Apolinário, QCD Forward Physics 2014]

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Quantitative comparisons show some disagreement… ✦ Monte Carlo approaches based on in-medium single gluon

radiation fail to describe some of the intra-jet features!

0.1 0.2 0.3 10 r 0.1 0.2 0.3

pp

(r) ρ /

PbPb

(r) ρ 0.5 1 1.5 0.1 0.2 0.3 10 r 0.1 0.2 0.3 0.5 1 1.5 0.1 0.2 0.3 10 r 0.1 0.2 0.3 0.5 1 1.5 0.1 0.2 0.3 10 r 0.1 0.2 0.3 0.5 1 1.5 0.1 0.2 0.3 10 r 0.1 0.2 0.3 0.5 1 1.5 70-100%

• 1

10 50-70%

• 1

10 30-50%

• 1

10 10-30%

• 1

10 0-10%

= 2.76 TeV

NN

s CMS,

jets: R = 0.3 anti-k

PbPb

• 1

L dt = 5.3 pb

∫

pp,

• 1

b µ L dt = 150

∫

PbPb,

27

Not so fast…

Let’s go back again…

R 0.05 0.1 0.15 0.2 0.25 0.3

= 0 q

(r)

• /
• q

(r)

• 0.5

1 1.5 2 2.5 3 3.5 4

Q-PYTHIA 2.76TeV ptgen = 70 GeV

• 1

fm

= 1 GeV q

• 1

fm

= 4 GeV q

• 1

fm

= 8 GeV q

ρ(r) = 1 δr 1 Njet ∑

jets

∑

tracks ∈ [ra, rb)

ptrack

T

pjet

T

[L.Apolinário, QCD Forward Physics 2014]

Qualitative disagreement…

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ A jet in pp: ✦ Defined with a jet clustering algorithm based (or not) in QCD principles: anti-kT, kT, C/A,… ➡ Have an object that can be related to the parton shower ➡ Have an object that can be equally treated at parton, particle or calorimetric level

28

What is a jet?

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ A jet in heavy-ions: ✦ Defined with a jet clustering algorithm based (or not) in QCD principles: anti-kT, kT, C/A,… ➡ Have an object that can be related to the parton shower ➡ Have an object that can be equally treated at parton, particle or calorimetric level

29

What is a jet?

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ A jet in heavy-ions: ✦ Defined with a jet clustering algorithm based (or not) in QCD principles: anti-kT, kT, C/A,… ➡ Have an object that can be related to the parton shower ➡ Have an object that can be equally treated at parton, particle or calorimetric level

29

What is a jet?

???

How to define a jet in a heavy-ion?

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ The way we see and define a jet should include all momentum scales:

31

Jet Quenching v2.0

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ The way we see and define a jet should include all momentum scales:

31

Jet Quenching v2.0

Expanding Medium In-medium parton shower

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ The way we see and define a jet should include all momentum scales:

31

Jet Quenching v2.0

Expanding Medium Medium-induced energy loss In-medium parton shower

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ The way we see and define a jet should include all momentum scales:

31

Jet Quenching v2.0

Expanding Medium Medium-induced energy loss In-medium parton shower Collisional energy loss

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ The way we see and define a jet should include all momentum scales:

31

Jet Quenching v2.0

Expanding Medium Medium-induced energy loss In-medium parton shower Collisional energy loss Medium recoils

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ The way we see and define a jet should include all momentum scales:

31

Jet Quenching v2.0

Expanding Medium Medium-induced energy loss In-medium parton shower Collisional energy loss Medium recoils Medium effects on Hadronization?

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ The way we see and define a jet should include all momentum scales:

31

Jet Quenching v2.0

Expanding Medium Medium-induced energy loss In-medium parton shower Collisional energy loss Medium recoils Medium effects on Hadronization?

Q2

PT Initial Parton What scale sets this transition? Tc

pQCD Scattering from Point-Like Bare Color Charges

µD

pQCD Scattering From Quasiparticles with size ~ µDebye Strong Coupling No Quasiparticles µDebye ! 0

AdS/CFT ?! " ?

What scale sets this transition?

Scattering from Thermal Mass Gluons?

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ The way we see and define a jet should include all momentum scales:

31

Jet Quenching v2.0

Expanding Medium Medium-induced energy loss In-medium parton shower Collisional energy loss Medium recoils Medium effects on Hadronization?

Q2

PT Initial Parton What scale sets this transition? Tc

pQCD Scattering from Point-Like Bare Color Charges

µD

pQCD Scattering From Quasiparticles with size ~ µDebye Strong Coupling No Quasiparticles µDebye ! 0

AdS/CFT ?! " ?

What scale sets this transition?

Scattering from Thermal Mass Gluons?

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ QGP part that become correlated with the jet (not to be subtracted!) ✦ Seen as (pQCD approach): ✦ Recoils from jet-medium interactions with a thermal/3D hydro particle distribution ➡ Recoiled particle makes part of the jet: JEWEL

32

Medium response

E.g: JEWEL

dˆ σ dˆ t (ˆ s, |ˆ t|) ' CR2πα2

s

(|ˆ t| + µ2

D)2

JEWEL: [Elayavalli, Zapp (17)] LBT: [Cao, Luo, Qin, Wang (16) He, Luo, Wang, Zhu (17)] MARTINI: [Schenke, Gale, Jeon (09)]

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ QGP part that become correlated with the jet (not to be subtracted!) ✦ Seen as (pQCD approach): ✦ Recoils from jet-medium interactions with a thermal/3D hydro particle distribution ➡ Recoiled particle makes part of the jet: JEWEL ➡ Recoiled particle can further interact with medium constituents: MARTINI, LBT

32

Medium response

E.g: JEWEL

dˆ σ dˆ t (ˆ s, |ˆ t|) ' CR2πα2

s

(|ˆ t| + µ2

D)2

E.g: MARTINI

JEWEL: [Elayavalli, Zapp (17)] LBT: [Cao, Luo, Qin, Wang (16) He, Luo, Wang, Zhu (17)] MARTINI: [Schenke, Gale, Jeon (09)]

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Magnitude of the medium recoil component to the jet varies from model to model… ✦ Coupled Jet-Fluid (Analytical approach) ✦ MARTINI (Monte Carlo approach based on in-medium gluon radiation)

33

There are still problems…

Couple Jet-Fluid: [arXiv: 1701.07951]

without recoil

[MARINI: Park QM18]

without recoil

Recoil component Best observed in the “jet radial profile”

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Within the same model, not so easy to simultaneously describe jet radial

profile and jet mass:

34

And more problems…

[JEWEL:1707.01539] [JEWEL:1707.01539]

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Within the same model, not so easy to simultaneously describe jet radial

profile and jet mass:

34

And more problems…

[JEWEL:1707.01539] [JEWEL:1707.01539] [MARTINI:1807.06550] [MARTINI:1807.06550]

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Within the same model, not so easy to simultaneously describe jet radial

profile and jet mass:

34

And more problems…

See K. Zapp (Thursday) for news about JEWEL

[JEWEL:1707.01539] [JEWEL:1707.01539] [MARTINI:1807.06550] [MARTINI:1807.06550]

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Quenching parameter (qhat) at RHIC larger is than at LHC ✦ Not clearly understood so far…

35

And even more problems…

[Jet collaboration (13)] [Andrés, Armesto, Luzum, Salgado, Zurita (17)] [Casalderrey-Solana, Hulcher, Milhano, Pablos, Rajagopal (18)]

both pQCD and non-pQCD approaches!

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Theoretical developments that address elementary jet processes: ✓ Able to build up a clear qualitative picture X Not suited for describing medium recoil component (essential to withdraw QGP properties)

36

JQ Phenomenology

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Theoretical developments that address elementary jet processes: ✓ Able to build up a clear qualitative picture X Not suited for describing medium recoil component (essential to withdraw QGP properties)

36

JQ Phenomenology

Being highly developed within Monte Carlo approaches (see references at backup slides)!

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Theoretical developments that address elementary jet processes: ✓ Able to build up a clear qualitative picture X Not suited for describing medium recoil component (essential to withdraw QGP properties)

36

JQ Phenomenology

Being highly developed within Monte Carlo approaches (see references at backup slides)! Based on phenomenological assumptions… But Jet Quenching must feed (and be fed) with jet phenomenology!

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Theoretical developments that address elementary jet processes: ✓ Able to build up a clear qualitative picture X Not suited for describing medium recoil component (essential to withdraw QGP properties) ✦ To ultimately assess QGP properties, also need new jet observables (from pp and new for heavy-ions): ✦ Sensitive to selected jet quenching effects (establish a baseline): ✦ Probing different QGP timescales:

36

JQ Phenomenology

Being highly developed within Monte Carlo approaches (see references at backup slides)! Based on phenomenological assumptions… But Jet Quenching must feed (and be fed) with jet phenomenology!

[LA, Milhano, Ploskon, Zhang (17)] Initial times: [Andres, Armesto, Niemi, Paatelainen, Salgado (19)] Final times: [LA, Milhano, Salgado, Salam (18)]

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Theoretical developments that address elementary jet processes: ✓ Able to build up a clear qualitative picture X Not suited for describing medium recoil component (essential to withdraw QGP properties) ✦ To ultimately assess QGP properties, also need new jet observables (from pp and new for heavy-ions): ✦ Sensitive to selected jet quenching effects (establish a baseline): ✦ Probing different QGP timescales:

36

JQ Phenomenology

Being highly developed within Monte Carlo approaches (see references at backup slides)! Based on phenomenological assumptions… But Jet Quenching must feed (and be fed) with jet phenomenology!

[LA, Milhano, Ploskon, Zhang (17)] Initial times: [Andres, Armesto, Niemi, Paatelainen, Salgado (19)] Final times: [LA, Milhano, Salgado, Salam (18)]

See L. Apolinário (Thursday)

Wrapping-up

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ This was a brief lecture/overview of “jet quenching”: ✦ Things I didn’t cover: Heavy-quarks, AdS/CFT approaches, Monte Carlo approaches,… ✦ Several developments towards the understanding of what is a jet in a heavy-ion environment! ✦ But no consistent picture has emerged yet… ✦ Not clear the role of medium recoil effects, missing in-medium evolution equation (coupled to

vacuum radiation), …

➡ Several developments in building new observables (particular QGP effect, a particular type of

probe (q/g-jets) and/or different QGP timescales ⇒ Jet substructure!)

38

Summary

See J. Barata (Thursday)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ This was a brief lecture/overview of “jet quenching”: ✦ Things I didn’t cover: Heavy-quarks, AdS/CFT approaches, Monte Carlo approaches,… ✦ Several developments towards the understanding of what is a jet in a heavy-ion environment! ✦ But no consistent picture has emerged yet… ✦ Not clear the role of medium recoil effects, missing in-medium evolution equation (coupled to

vacuum radiation), …

➡ Several developments in building new observables (particular QGP effect, a particular type of

probe (q/g-jets) and/or different QGP timescales ⇒ Jet substructure!)

38

Summary

Questions?

See J. Barata (Thursday)

• L. Apolinário

Acknowledgements

COST THOR School, “Jet Quenching” 39

Backup Slides

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ MLLA: only the leading behaviour, ✦ Good description in the hard region (two different energies)

41

Experimental Evidences

ξp = log(1 z ) = log( pjet phad )

Soft jet fragments Hard jet fragments

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

42

Eikonal Approximation

p1)

See: arXiv:0712.3443

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

42

Eikonal Approximation

p1)

No dependence on xi-:

See: arXiv:0712.3443

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

42

Eikonal Approximation

p1)

Z dx1−dx2−eix2−(p−p2)+ix1−(p2−p1)+ = (2π)2δ(p − p2)+δ(p2 − p1)+

No dependence on xi-:

⇒ p+ = p1+ = p2+

See: arXiv:0712.3443

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

42

Eikonal Approximation

p1)

Z dx1−dx2−eix2−(p−p2)+ix1−(p2−p1)+ = (2π)2δ(p − p2)+δ(p2 − p1)+

¯ u(p) / AAA2 / p2 / AA2A1 / p1Mh(p1) ' 2p2 · AAA2 2p1 · AA2A1 ¯ u(p)Mh(p1)

¯ u(p) / AAA2 / p2 = 2p2 · AAA2 ¯ u(p) − ¯ u(p) / p2 / AAA2

No dependence on xi-:

⇒ p+ = p1+ = p2+

Dirac structure:

See: arXiv:0712.3443

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

42

Eikonal Approximation

p1)

Z dx1−dx2−eix2−(p−p2)+ix1−(p2−p1)+ = (2π)2δ(p − p2)+δ(p2 − p1)+

¯ u(p) / AAA2 / p2 / AA2A1 / p1Mh(p1) ' 2p2 · AAA2 2p1 · AA2A1 ¯ u(p)Mh(p1)

¯ u(p) / AAA2 / p2 = 2p2 · AAA2 ¯ u(p) − ¯ u(p) / p2 / AAA2

No dependence on xi-: sub-leading

⇒ p+ = p1+ = p2+

Dirac structure:

See: arXiv:0712.3443

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

43

Eikonal Approximation

i2p2 · (igAAA2) p2

2 + iε

' i2p2+(igA−)AA2 2p2+p2− + iε = (igA−)AA2 i p2− + iε

Resulting fractions:

See: arXiv:0712.3443

p1)

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

43

Eikonal Approximation

Z dp2− 2π eip2−(x1−x2)+ i p2− − (−iε) = θ(x2 − x1)+

i2p2 · (igAAA2) p2

2 + iε

' i2p2+(igA−)AA2 2p2+p2− + iε = (igA−)AA2 i p2− + iε

Resulting fractions: Integral in pi-: Residues theorem (and same for x1)

See: arXiv:0712.3443

p1)

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

43

Eikonal Approximation

Z dp2− 2π eip2−(x1−x2)+ i p2− − (−iε) = θ(x2 − x1)+

i2p2 · (igAAA2) p2

2 + iε

' i2p2+(igA−)AA2 2p2+p2− + iε = (igA−)AA2 i p2− + iε

Resulting fractions: Integral in pi-: Residues theorem (and same for x1) Integral in pT:

Z d2p2⊥ (2π)2 d2p1⊥ (2π)2 e−i(x1−x2)⊥−i(0−x1)⊥ = δ2(x1 − x2)⊥δ2(x1)

⇒ x1⊥ = x2⊥ = 0

See: arXiv:0712.3443

p1)

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

44

Eikonal Approximation

' Z dx1+dx2+ig(A−)AA2(x2+, 0⊥)θ(x2x1)+ig(A−)A2A1(x1+, 0⊥)θ(x1)+u

See: arXiv:0712.3443

p1)

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

)+¯ u(p)Mh(p)

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

44

Eikonal Approximation

' Z dx1+dx2+ig(A−)AA2(x2+, 0⊥)θ(x2x1)+ig(A−)A2A1(x1+, 0⊥)θ(x1)+u

See: arXiv:0712.3443

p1)

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

)+¯ u(p)Mh(p)

No interaction term

• L. Apolinário

COST THOR School, “Jet Quenching”

✦ Consider a high energetic particle propagating interacting twice with the medium:

44

Eikonal Approximation

' Z dx1+dx2+ig(A−)AA2(x2+, 0⊥)θ(x2x1)+ig(A−)A2A1(x1+, 0⊥)θ(x1)+u

See: arXiv:0712.3443

p1)

Mh(p1) p1 p2 p x1 x2 A1 A2 A a1 a2

S2 = Z d4x1d4x2 d4p1 (2π)4 d4p2 (2π)4 ¯ u(p)eix2(p−p2)+ix1(p2−p2)A

) /

AAA2(x2+, x2⊥) i / p2 p2

2 + iεig /

AA2A1(x1+, x1⊥) i / p1 p2

1 + iεMh(

p1)

)+¯ u(p)Mh(p)

No interaction term

P exp ( ig Z xn+

x1+

dx+A−(x+, x⊥ = 0) ) = W(xn+, x1+; x⊥ = 0)

summing over all ’n’ interaction terms

∑ ( ) …

• L. Apolinário

Jets in QCD matter: Monte Carlo approaches

✦ Monte Carlo models for jet quenching: ✦ Hybrid Strong/Weak coupling: ✦ JETSCAPE: ✦ JEWEL: ✦ LBT/Co-LBT: ✦ MARTINI: ✦ MATTER: ✦ PYQUEN: ✦ Q-PYTHIA:

45

MC Bibliography

[Casalderrey-Solana, Gulhan, Milhano, Pablos, Rajagopal (14;17); Helcher, Pablos, Rajagopal (18)] [Armesto, Cunquero, Salgado (09)] [Krauss, Wiedemann, Zapp(13); Zapp (14); Elayavalli, Zapp (16;17)] [Wang and Y. Zhu (16); Cao, Luo, Qin, Wang (15); He, Luo, Wang, Zhu (17);] [Schenke, Gale, Jeon (09); Park, Jeon, Gale (18)] [Lokhtin, Snigirev (06)] [Majumder (13); Kordell, Majumder (17); Cao, Majumder (18)] [JETSCAPE Collab. (17)]

• L. Apolinário

Jets in QCD matter: Monte Carlo approaches

✦ Monte Carlo models for heavy-ions: ✦ AMPT: ✦ BAMPS: ✦ CUJET: ✦ HiJING/HIJING++: ✦ HYDJET/HYDJET++: ✦ Analytical approaches: ✦ Coupled Jet-Fluid:

46

MC Bibliography

[Xu, Greiner (03; 07)] [Gyulassy, Wang (91; 94); Barnaföldi et al (17)] [Ko, Li, Lin, Pal, Zhang (00; 01)] [Buzzatti and Gyulassy (11; 12)] [Tachibana, Chang, Qin (17)] [Lokhtin, Malinina, Petrushanko, Snigirev , Arsene, Tywoniuk (09)]