Jet fragmentation in a dense QCD medium Introduction Jets in the - - PowerPoint PPT Presentation

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion

Jet fragmentation in a dense QCD medium

• P. Caucal, E. Iancu, A.H. Mueller, G. Soyez

Institut de Physique Th´ eorique, CEA

October 4, 2018 at the Hard Probes 2018 conference, Aix-Les-Bains, France

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 2/23

Introduction

◮ Jets are important probes of the quark-gluon plasma (QGP) produced in

heavy-ions collisions at LHC or at RHIC.

◮ Understanding observables such that the jet RAA or the jet fragmentation function

helps to better characterize the QGP.

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 3/23

Important messages

Phys.Rev.Lett. 120 (2018) 232001

◮ Within the double-log approximation of perturbative QCD, the evolution of a jet

factorizes into three steps:

• one vacuum-like shower inside the medium,
• followed by medium-induced mini-jets from by previous sources;
• finally, a vacuum-like shower outside the medium.

hadronization in the medium L

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 4/23

Important messages

Phys.Rev.Lett. 120 (2018) 232001

hadronization in the medium L

◮ Because of decoherence induced by the medium, the first emission outside the

medium has no angular constraint. This reopening of the phase space leads to an increase of soft particles inside the jet.

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 5/23

Bremsstrahlung spectrum

◮ Logarithmic enhancement for soft and collinear emissions.

dP ≃ αsCR π dω ω dθ2 θ2

◮ Formation time due to the virtuality ≃ ωθ2 of the parent parton:

tvac ∼ ω/k2

⊥ ∼ 1/(ωθ2)

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 6/23

Iteration of Bremsstrahlung emissions

Angular ordering at DLA

Quantum color coherence implies angular ordering: a jet is described in terms of a classical shower picture with successive Bremsstrahlung emissions forming the Markov chains of independent elementary radiation events.

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 7/23

Phase space and evolution at DLA

Transverse momentum cut-off

Evolution is stopped by hadronisation: k2

⊥ ≃ ω2θ2 > Λ2 QCD.

E ¯ θ

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (E, ¯ θ) k2

⊥ = ω2θ2 = Λ2

VACUUM PHASE SPACE

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 7/23

Phase space and evolution at DLA

Transverse momentum cut-off

Evolution is stopped by hadronisation: k2

⊥ ≃ ω2θ2 > Λ2 QCD.

E ω1 θ1 ¯ θ

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (ω1, θ1) (E, ¯ θ) k2

⊥ = ω2θ2 = Λ2

VACUUM PHASE SPACE

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 7/23

Phase space and evolution at DLA

Transverse momentum cut-off

Evolution is stopped by hadronisation: k2

⊥ ≃ ω2θ2 > Λ2 QCD.

E ω2 ω1 θ1 θ2 ¯ θ

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (ω1, θ1) (ω2, θ2) (E, ¯ θ) k2

⊥ = ω2θ2 = Λ2

VACUUM PHASE SPACE

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 7/23

Phase space and evolution at DLA

Transverse momentum cut-off

Evolution is stopped by hadronisation: k2

⊥ ≃ ω2θ2 > Λ2 QCD.

E ω3 ω2 ω1 θ1 θ2 θ3 ¯ θ

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (ω1, θ1) (ω2, θ2) (ω3, θ3) (E, ¯ θ) k2

⊥ = ω2θ2 = Λ2

VACUUM PHASE SPACE

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 7/23

Phase space and evolution at DLA

Transverse momentum cut-off

Evolution is stopped by hadronisation: k2

⊥ ≃ ω2θ2 > Λ2 QCD.

E ω4 ω3 ω2 ω1 θ1 θ2 θ3 θ4 ¯ θ

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (ω1, θ1) (ω2, θ2) (ω3, θ3) (ω4, θ4) (E, ¯ θ) k2

⊥ = ω2θ2 = Λ2

VACUUM PHASE SPACE

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 8/23

Description of the dense QCD medium

◮ Dense, weekly coupled quark-gluon plasma. ◮ Medium induced radiation “BDMPS-Z”:

• formation time tmed ≫ mean free path.
• multiple soft scattering during one emission.

◮ For present purposes, our medium is characterized by two parameters:

• the jet quenching parameter ˆ

q: k2

⊥ = ˆ

q∆t, transverse momentum acquired by multiple collisions during time ∆t.

• the distance L travelled by the jet in the medium.

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 9/23

Medium induced radiation

◮ BDMPS-Z spectrum (Baier, Dokshitzer, Mueller, Peign´

e, and Schiff; Zakharov 1996–97)

dP ≃ ¯ αs dω ω L tmed(ω) ≃ ¯ αsL

• ˆ

q ω3 dω = ⇒ No energy nor collinear log !

◮ Medium-induced formation time and broadening characteristic time scale:

tmed ∼

• ω/ˆ

q.

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 10/23

Phase space for vacuum-like emissions (VLEs)

◮ Let’s start with the vacuum phase

space.

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (E, ¯ θ) ω θ = Λ VACUUM PHASE SPACE

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 10/23

Phase space for vacuum-like emissions (VLEs)

◮ VLE in the medium: tvac ≪ tmed.

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (E, ¯ θ) ω θ = Λ ω3θ4 = 2ˆ q INSIDE ωc = 1

2 ˆ

qL2

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 10/23

Phase space for vacuum-like emissions (VLEs)

◮ VLE in the medium: tvac ≪ tmed.

• extends to N emissions strongly
• rdered in energy.
• tvac,1 ≪ .. ≪ tvac,N ≪ tmed,N ≪ .. ≪ tmed,1.

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (E, ¯ θ) ω θ = Λ ω3θ4 = 2ˆ q INSIDE ωc = 1

2 ˆ

qL2

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 10/23

Phase space for vacuum-like emissions (VLEs)

◮ VLE in the medium: tvac ≪ tmed. ◮ VLE outside the medium: tvac ≥ L.

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (E, ¯ θ) ω θ = Λ ω3θ4 = 2ˆ q ωθ2L = 2 INSIDE OUTSIDE ωc = 1

2 ˆ

qL2

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 10/23

Phase space for vacuum-like emissions (VLEs)

◮ VLE in the medium: tvac ≪ tmed. ◮ VLE outside the medium: tvac ≥ L.

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (E, ¯ θ) ω θ = Λ ω3θ4 = 2ˆ q ωθ2L = 2 V E T O E D INSIDE OUTSIDE ωc = 1

2 ˆ

qL2

Vetoed region for VLEs

Reduction of the phase space available with respect to the vacuum case: emissions with tmed ≤ tvac ≤ L are forbidden.

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 11/23

(De)coherence in the medium

In the medium, an antenna loses its color coherence after a time tcoh = (ˆ q¯ θ2)−1/3.

(Mahtar-Tani, Salgado, Tywoniuk, 2010-1 ; Casalderrey-Solana, Iancu, 2011)

¯ θ L tcoh = (ˆ q¯ θ2)−1/3

◮ However, no consequences for VLEs in the medium (PC, Iancu, Mueller, Soyez 2018)

• VLE (tvac ≤ tmed) at large angle (θ ≥ ¯

θ) ⇒ tvac ≤ tcoh.

• Large angle emissions forbidden by color coherence.
• Gluon cascades are angular ordered as in the vacuum.

◮ DLA cascades develop also inside the medium.

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 12/23

DLA phase space and evolution with QGP

E ¯ θ L

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (E, ¯ θ) ω θ = Λ ω

3

θ

4

= 2 ˆ q ωθ2L = 2 VETOED INSIDE OUTSIDE ωc = 1

2 ˆ

qL2

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 12/23

DLA phase space and evolution with QGP

E ¯ θ ω1 L

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (ω1, θ1) (E, ¯ θ) ω θ = Λ ω

3

θ

4

= 2 ˆ q ωθ2L = 2 VETOED INSIDE OUTSIDE ωc = 1

2 ˆ

qL2

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 12/23

DLA phase space and evolution with QGP

E ¯ θ θ2 ω1 ω2 L

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (ω1, θ1) (ω2, θ2) (E, ¯ θ) ω θ = Λ ω

3

θ

4

= 2 ˆ q ωθ2L = 2 VETOED INSIDE OUTSIDE ωc = 1

2 ˆ

qL2

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 13/23

First emission outside the medium

◮ tvac ≥ L : parent gluon has lost its color coherence

= ⇒ no angular ordering

E ¯ θ θ2 θ3 ω1 ω2 ω3 L

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (ω1, θ1) (ω2, θ2) (ω3, θ3) (E, ¯ θ) ω θ = Λ ω

3

θ

4

= 2 ˆ q ωθ2L = 2 VETOED INSIDE OUTSIDE ωc = 1

2 ˆ

qL2 θc

◮ Critical angle θc such that tcoh(θc) = L.

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 14/23

Parton shower outside the medium

◮ Subsequent emissions in the vacuum are angular ordered.

E ¯ θ θ2 θ3 θ4 ω1 ω2 ω3 ω4 L

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (ω1, θ1) (ω2, θ2) (ω3, θ3) (ω4, θ4) (E, ¯ θ) ω θ = Λ ω

3

θ

4

= 2 ˆ q ωθ2L = 2 VETOED INSIDE OUTSIDE ωc = 1

2 ˆ

qL2 θc

◮ Evolution is stopped by hadronisation.

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 15/23

Analytical results for the DLA fragmentation function

0.6 0.8 1 1.2 1.4 1.6 1.8 2 1 10 100 solid: Λ=100 MeV dashed: Λ=200 MeV D(ω)/Dvac(ω) ω [GeV] q ^

=1 Gev2/fm,L=3 fm

q ^

=2 Gev2/fm,L=3 fm

q ^

=2 Gev2/fm,L=4 fm

0.6 0.8 1 1.2 1.4 1.6 1.8 2 1 10 100

E=200 GeV, θqq

• =0.4, α
• s=0.3

Small z behavior

The enhancement at small energy is a consequence of decoherence and the re-opening

• f the angular phase space for the first VLE outside the medium.

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 16/23

MonteCarlo implementation

0.1 1 10 100 ω [GeV] 0.01 0.1 θ (E, ¯ θ) ωθ = Λ ω3θ4 = 2ˆ q ωθ2L = 2 V E T O E D INSIDE OUTSIDE ωc = 1

2 ˆ

qL2 θc

Convolution of three showers

Vacuum cascade in the medium (red region)

with full splitting function, running coupling and color representations

⊗ Medium-induced mini-jets with fixed coupling

(Blaizot, Iancu, Mehtar-Tani, 2013)

⊗ Vacuum cascade outside the medium (blue region) after reopening the phase space Pros Cons Based on pQCD Fixed medium length Any jet observables No geometry/fluctuations Include hard matrix elements No hadrons

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 17/23

Preliminary results

10-5 10-4 10-3 10-2 200 250 300 350 400 450 500 550 600 anti-kt(R=0.4), pt,jet>200 GeV

PRELIMINARY

1/Nev dNjet/dpt [GeV-1] jet pt spectrum vacuum q=1.5,L=4,αs,med=0.25 q=1.5, L=4,αs,med=0.30 q=2, L=3,αs,med=0.25 q=2, L=3,αs,med=0.30 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 200 250 300 350 400 450 500 550 600 RAA pt,jet

0.5 1 1.5 2 2.5 0.001 0.01 0.1 1

anti-kt(R=0.4), pt,jet>200 GeV

PRELIMINARY

ratio to vacuum z fragmentation function q=1.5,L=4,αs,med=0.25 q=1.5, L=4,αs,med=0.30 q=2, L=3,αs,med=0.25 q=2, L=3,αs,med=0.30 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

anti-kt(R=0.4), pt,jet>200 GeV

PRELIMINARY

ratio to vacuum zg zg q=1.5,L=4,αs,med=0.25 q=1.5, L=4,αs,med=0.30 q=2, L=3,αs,med=0.25 q=2, L=3,αs,med=0.30

• Good overall qualitative behavior w.r.t data.
• Saturation of RAA due to vacuum-like fragmentation inside the medium.
• Enhancement at small z of the fragmentation function due to decoherence of the

last emission inside the medium (vacuum-like or rare medium-induced still inside the jet).

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 18/23

Conclusion

Summary

◮ A pQCD approach of jet evolution leads to a factorization of vacuum-like emissions

inside the medium from the medium-induced radiations.

◮ This picture is well-suited for MonteCarlo implementation which gives qualitatively

good preliminary results.

In perspective

◮ Systematic applications to the phenomenology. ◮ Implementation of the medium expansion and geometry. ◮ Effects of hadronization.

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 19/23

Thank you for listening !

hadronization

in the medium L

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 20/23

Analytical study of jets at DLA

Double differential gluon distribution

T(ω, θ2 | E, θ2

q¯ q) ≡ ωθ2 d2N dωdθ2

⇒ probability of emission of a gluon with energy ω and angle θ2 from an antenna with energy E and opening angle θ2

q¯ q.

In the vacuum at DLA, this quantity satisfies the simple master equation Tvac(ω, θ2 | E, θ2

q¯ q) = ¯

αs+ θ2

q¯ q

θ2

dθ2

1

θ2

1

1

ω/E

dz1 z1 ¯ αsTvac(ω, θ2 | z1E, θ2

1)

With a medium, this equation holds only inside the medium ⇒ mathematically,

• ne must take into account “jumps” over the vetoed region.

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 21/23

Ratio T(ω, θ2)/Tvac(ω, θ2)

0.02 0.05 0.2 0.4 0.01 0.1 0.1 1 10 100 θ ω [GeV] 0.02 0.05 0.2 0.4 0.01 0.1 0.1 1 10 100 0.85 2 5 1

E=200 GeV, θqq=0.4, α

• s=0.3, q

^

=2 Gev2/fm, L=3 fm

T/Tvac

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 22/23

Dependence of MonteCarlo results on θmax and kt,min

Estimation of uncertainties

anti-kt(R=0.4), pt,jet>200 GeV

P R E L I M I N A R Y

1/Nev dNjet/dpt [GeV-1] jet pt spectrum vacuum q=1.5,L=4,αs,med=0.25 q=2, L=3,αs,med=0.25 10-5 10-4 10-3 10-2 200 250 300 350 400 450 500 550 600

(θmax,kt,min)={(1,0.25),(1,0.5),(0.75,0.25),(1.5,0.25)}

RAA pt,jet 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 200 250 300 350 400 450 500 550 600 anti-kt(R=0.4), pt,jet>200 GeV

P R E L I M I N A R Y

z/Njets dNparticle/dz fragmentation function vacuum q=1.5,L=4,αs,med=0.25 q=2, L=3,αs,med=0.25 1 2 3 4 5 6 0.001 0.01 0.1 1

(θmax,kt,min)={(1,0.25),(1,0.5),(0.75,0.25),(1.5,0.25)}

ratio to vacuum z 0.5 1 1.5 2 2.5 0.001 0.01 0.1 1 anti-kt(R=0.4), pt,jet>200 GeV

P R E L I M I N A R Y

1/Njets dNmMDT/dzg zg vacuum q=1.5,L=4,αs,med=0.25 q=2, L=3,αs,med=0.25 1 2 3 4 5 6 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

(θmax,kt,min)={(1,0.25),(1,0.5),(0.75,0.25),(1.5,0.25)}

ratio to vacuum zg 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion 23/23

In-medium intrajet multiplicity and decoherence effects

anti-kt(R=0.4), pt,jet>200 GeV

P R E L I M I N A R Y

1/Nev dNjet/dpt [GeV-1] jet pt spectrum vacuum no quenching no dechoerence quench before VLEs

• ur quenching

10-5 10-4 10-3 10-2 200 250 300 350 400 450 500 550 600 RAA pt,jet 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 200 250 300 350 400 450 500 550 600 anti-kt(R=0.4), pt,jet>200 GeV

P R E L I M I N A R Y

z/Njets dNparticle/dz fragmentation function vacuum no quenching no dechoerence quench before VLEs

• ur quenching

1 2 3 4 5 6 0.001 0.01 0.1 1 ratio to vacuum ξ 0.5 1 1.5 2 2.5 0.001 0.01 0.1 1