Jet fragmentation in a dense QCD medium Jet fragmentation in a dense QCD medium Introduction Jets in the vacuum P. Caucal, E. Iancu, A.H. Mueller, G. Soyez at DLA Jet evolution with a medium at DLA eorique , CEA Institut de Physique Th´ MonteCarlo results beyond DLA October 4, 2018 at the Hard Probes 2018 conference, Conclusion Aix-Les-Bains, France
Jet fragmentation Introduction in a dense QCD medium Introduction Jets in the vacuum at DLA ◮ Jets are important probes of the quark-gluon plasma (QGP) produced in Jet evolution with a medium at DLA heavy-ions collisions at LHC or at RHIC. MonteCarlo results beyond DLA Conclusion ◮ Understanding observables such that the jet R AA or the jet fragmentation function helps to better characterize the QGP. 2/23
Jet fragmentation Important messages in a dense QCD medium Phys.Rev.Lett. 120 (2018) 232001 ◮ Within the double-log approximation of perturbative QCD , the evolution of a jet Introduction factorizes into three steps: Jets in the vacuum at DLA • one vacuum-like shower inside the medium, Jet evolution with • followed by medium-induced mini-jets from by previous sources; a medium at DLA • finally, a vacuum-like shower outside the medium. MonteCarlo results beyond DLA Conclusion hadronization in the medium 0 L 3/23
Jet fragmentation Important messages in a dense QCD medium Phys.Rev.Lett. 120 (2018) 232001 Introduction Jets in the vacuum at DLA hadronization Jet evolution with a medium at DLA in the medium MonteCarlo results beyond DLA Conclusion 0 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. 4/23
Jet fragmentation Bremsstrahlung spectrum in a dense QCD medium ◮ Logarithmic enhancement for soft and collinear emissions. Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion d θ 2 d P ≃ α s C R d ω θ 2 π ω ◮ Formation time due to the virtuality ≃ ωθ 2 of the parent parton: t vac ∼ ω/ k 2 ⊥ ∼ 1 / ( ωθ 2 ) 5/23
Jet fragmentation Iteration of Bremsstrahlung emissions in a dense QCD medium Introduction Angular ordering at DLA Jets in the vacuum at DLA Quantum color coherence implies angular ordering: a jet is described in terms of a Jet evolution with classical shower picture with successive Bremsstrahlung emissions forming the Markov a medium at DLA chains of independent elementary radiation events. MonteCarlo results beyond DLA Conclusion 6/23
Jet fragmentation Phase space and evolution at DLA in a dense QCD medium Transverse momentum cut-off Introduction ⊥ ≃ ω 2 θ 2 > Λ 2 Evolution is stopped by hadronisation: k 2 QCD . Jets in the vacuum at DLA Jet evolution with a medium at DLA ( E, ¯ θ ) MonteCarlo results beyond DLA Conclusion VACUUM PHASE SPACE E ¯ θ k 2 0.1 ⊥ = ω 2 θ 2 = Λ 2 θ 0.01 0.1 1 10 100 ω [GeV] 7/23
Jet fragmentation Phase space and evolution at DLA in a dense QCD medium Transverse momentum cut-off Introduction ⊥ ≃ ω 2 θ 2 > Λ 2 Evolution is stopped by hadronisation: k 2 QCD . Jets in the vacuum at DLA Jet evolution with a medium at DLA ( E, ¯ θ ) MonteCarlo results beyond DLA ( ω 1 , θ 1 ) Conclusion VACUUM PHASE SPACE E θ 1 ¯ θ k 2 0.1 ⊥ = ω 2 θ 2 = Λ 2 ω 1 θ 0.01 0.1 1 10 100 ω [GeV] 7/23
Jet fragmentation Phase space and evolution at DLA in a dense QCD medium Transverse momentum cut-off Introduction ⊥ ≃ ω 2 θ 2 > Λ 2 Evolution is stopped by hadronisation: k 2 QCD . Jets in the vacuum at DLA Jet evolution with a medium at DLA ( E, ¯ θ ) MonteCarlo results beyond DLA ( ω 1 , θ 1 ) Conclusion VACUUM PHASE SPACE E θ 1 ¯ θ θ 2 ω 2 k 2 ( ω 2 , θ 2 ) 0.1 ⊥ = ω 2 θ 2 = Λ 2 ω 1 θ 0.01 0.1 1 10 100 ω [GeV] 7/23
Jet fragmentation Phase space and evolution at DLA in a dense QCD medium Transverse momentum cut-off Introduction ⊥ ≃ ω 2 θ 2 > Λ 2 Evolution is stopped by hadronisation: k 2 QCD . Jets in the vacuum at DLA Jet evolution with a medium at DLA ( E, ¯ θ ) MonteCarlo results beyond DLA ( ω 1 , θ 1 ) Conclusion VACUUM PHASE SPACE E θ 1 ¯ θ θ 2 ω 2 θ 3 k 2 ( ω 2 , θ 2 ) 0.1 ⊥ = ω 2 θ 2 = Λ 2 ω 3 ω 1 θ ( ω 3 , θ 3 ) 0.01 0.1 1 10 100 ω [GeV] 7/23
Jet fragmentation Phase space and evolution at DLA in a dense QCD medium Transverse momentum cut-off Introduction ⊥ ≃ ω 2 θ 2 > Λ 2 Evolution is stopped by hadronisation: k 2 QCD . Jets in the vacuum at DLA Jet evolution with a medium at DLA ( E, ¯ θ ) MonteCarlo results beyond DLA ( ω 1 , θ 1 ) Conclusion VACUUM PHASE SPACE E θ 1 ¯ θ θ 2 ω 2 θ 3 ω 4 k 2 ( ω 2 , θ 2 ) 0.1 ⊥ = ω 2 θ 2 = Λ 2 θ 4 ω 3 ω 1 θ ( ω 3 , θ 3 ) ( ω 4 , θ 4 ) 0.01 0.1 1 10 100 ω [GeV] 7/23
Jet fragmentation Description of the dense QCD medium in a dense QCD medium ◮ Dense, weekly coupled quark-gluon plasma. Introduction Jets in the vacuum at DLA ◮ Medium induced radiation “BDMPS-Z”: Jet evolution with a medium at DLA MonteCarlo results • formation time t med ≫ mean free path. beyond DLA • multiple soft scattering during one emission. Conclusion ◮ For present purposes, our medium is characterized by two parameters: • the jet quenching parameter ˆ q : � k 2 ⊥ � = ˆ q ∆ t , transverse momentum acquired by multiple collisions during time ∆ t . • the distance L travelled by the jet in the medium. 8/23
Jet fragmentation Medium induced radiation in a dense QCD medium ◮ BDMPS-Z spectrum (Baier, Dokshitzer, Mueller, Peign´ e, and Schiff; Zakharov 1996–97) Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA MonteCarlo results beyond DLA Conclusion � d ω L q ˆ d P ≃ ¯ α s t med ( ω ) ≃ ¯ α s L ω 3 d ω ω = ⇒ No energy nor collinear log ! ◮ Medium-induced formation time and broadening characteristic time scale: � t med ∼ ω/ ˆ q . 9/23
Jet fragmentation Phase space for vacuum-like emissions (VLEs) in a dense QCD medium ( E, ¯ θ ) Introduction VACUUM PHASE SPACE Jets in the vacuum at DLA ◮ Let’s start with the vacuum phase ω Jet evolution with 0.1 θ = a medium at DLA Λ space. θ MonteCarlo results beyond DLA Conclusion 0.01 0.1 1 10 100 ω [GeV] 10/23
Jet fragmentation Phase space for vacuum-like emissions (VLEs) in a dense QCD medium ( E, ¯ θ ) Introduction INSIDE ω 3 θ 4 = 2ˆ Jets in the vacuum q at DLA Jet evolution with ω 0.1 θ = a medium at DLA Λ ◮ VLE in the medium: t vac ≪ t med . θ MonteCarlo results beyond DLA Conclusion 0.01 ω c = 1 2 ˆ qL 2 0.1 1 10 100 ω [GeV] 10/23
Jet fragmentation Phase space for vacuum-like emissions (VLEs) in a dense QCD medium ( E, ¯ θ ) Introduction INSIDE ω 3 θ 4 = 2ˆ Jets in the vacuum q at DLA ◮ VLE in the medium: t vac ≪ t med . Jet evolution with ω 0.1 θ = • extends to N emissions strongly a medium at DLA Λ θ ordered in energy. MonteCarlo results beyond DLA • t vac , 1 ≪ .. ≪ t vac , N ≪ t med , N ≪ .. ≪ t med , 1 . Conclusion 0.01 ω c = 1 2 ˆ qL 2 0.1 1 10 100 ω [GeV] 10/23
Jet fragmentation Phase space for vacuum-like emissions (VLEs) in a dense QCD medium ( E, ¯ θ ) Introduction INSIDE ω 3 θ 4 = 2ˆ Jets in the vacuum at DLA q Jet evolution with ω ωθ 2 L = 2 0.1 a medium at DLA θ ◮ VLE in the medium: t vac ≪ t med . = Λ θ MonteCarlo results beyond DLA ◮ VLE outside the medium: t vac ≥ L . OUTSIDE Conclusion 0.01 ω c = 1 2 ˆ qL 2 0.1 1 10 100 ω [GeV] 10/23
Jet fragmentation Phase space for vacuum-like emissions (VLEs) in a dense QCD medium ( E, ¯ θ ) Introduction V INSIDE E T O ω 3 θ 4 = 2ˆ Jets in the vacuum E D at DLA q Jet evolution with ω ωθ 2 L = 2 0.1 a medium at DLA θ ◮ VLE in the medium: t vac ≪ t med . = Λ θ MonteCarlo results beyond DLA ◮ VLE outside the medium: t vac ≥ L . OUTSIDE Conclusion 0.01 ω c = 1 2 ˆ qL 2 0.1 1 10 100 ω [GeV] Vetoed region for VLEs Reduction of the phase space available with respect to the vacuum case: emissions with t med ≤ t vac ≤ L are forbidden. 10/23
Jet fragmentation (De)coherence in the medium in a dense QCD medium q ¯ θ 2 ) − 1 / 3 . In the medium, an antenna loses its color coherence after a time t coh = (ˆ (Mahtar-Tani, Salgado, Tywoniuk, 2010-1 ; Casalderrey-Solana, Iancu, 2011) Introduction Jets in the vacuum at DLA Jet evolution with a medium at DLA ¯ θ MonteCarlo results beyond DLA Conclusion L q ¯ θ 2 ) − 1 / 3 t coh = (ˆ ◮ However, no consequences for VLEs in the medium (PC, Iancu, Mueller, Soyez 2018) • VLE ( t vac ≤ t med ) at large angle ( θ ≥ ¯ θ ) ⇒ t vac ≤ t coh . • Large angle emissions forbidden by color coherence. • Gluon cascades are angular ordered as in the vacuum. ◮ DLA cascades develop also inside the medium. 11/23
Jet fragmentation DLA phase space and evolution with QGP in a dense QCD medium Introduction Jets in the vacuum ( E, ¯ θ ) at DLA INSIDE VETOED Jet evolution with ω 3 L θ a medium at DLA 4 = 2 q ˆ E MonteCarlo results ¯ θ beyond DLA ω ωθ 2 L = 2 0.1 θ = Conclusion Λ θ OUTSIDE 0.01 ω c = 1 2 ˆ qL 2 0.1 1 10 100 ω [GeV] 12/23
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