Vacuum-like jet fragmentation in a Vacuum-like jet fragmentation in a dense dense QCD medium QCD medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez P.R.L.,120, 2018 P. Caucal, E. Iancu, A.H. Mueller and G. Soyez Introduction P.R.L.,120, 2018 Vacuum-like emissions with a Institut de Physique Th´ eorique, CEA, France medium Parton cascades with a medium August 2, 2018 at the XIIIth Quark Confinement and Fragmentation the Hadron Spectrum conference in Maynooth function University Energy loss by a jet Conclusion
Vacuum-like jet Introduction fragmentation in a dense QCD medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez ◮ Jets are very important probes of the quark-gluon P.R.L.,120, 2018 plasma (QGP) produced in heavy-ions collisions at LHC Introduction or RHIC. Vacuum-like emissions with a medium ◮ Understanding observables such that the jet suppression Parton cascades or the jet fragmentation function will help to better with a medium Fragmentation characterize the QGP. function Energy loss by a jet ◮ From a theoretical point of view, a complete picture of Conclusion the evolution of a jet in a dense medium is still lacking.
Vacuum-like jet Motivations and goal of the talk fragmentation in a dense QCD medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez P.R.L.,120, 2018 ◮ Jet evolution in a dense medium : medium induced Introduction Vacuum-like emissions versus vacuum-like emissions. How can we emissions with a medium include both mechanisms ? Parton cascades with a medium ◮ Our solution is to work with the simplest possible Fragmentation function approximation in parton shower : the leading Energy loss by a double-logarithm approximation (DLA). jet Conclusion
Vacuum-like jet Vacuum emissions vs ... fragmentation in a dense QCD medium Bremsstrahlung spectrum = ⇒ logarithmic enhancement for P. Caucal, E. soft and collinear emissions. Iancu, A.H. Mueller and G. Soyez Formation time due to the virtuality of the parent parton : P.R.L.,120, 2018 t vac ∼ ω/ k 2 ⊥ ∼ 1 / ( ωθ 2 ) Introduction Vacuum-like emissions with a medium Parton cascades with a medium Fragmentation function Energy loss by a jet Conclusion d θ 2 d P ≃ α s C R dx θ 2 π x
Vacuum-like jet ... medium induced radiation fragmentation in a dense QCD medium BDMPS-Z spectrum (Baier, Dokshitzer, Mueller, Peign´ P. Caucal, E. e, and Schiff; Zakharov 1996–97) Iancu, A.H. = ⇒ NOT DOUBLE LOG ! Mueller and G. Soyez P.R.L.,120, 2018 Medium-induced formation time and broadening � q from � k 2 characteristic time scale : t med ∼ ω/ ˆ ⊥ � = ˆ qt Introduction and t f = ω/ k 2 ⊥ . Vacuum-like emissions with a medium Parton cascades with a medium Fragmentation function Energy loss by a jet Conclusion � d ω L q ˆ d P ≃ ¯ α s t med ( ω ) ≃ ¯ α s L ω 3 d ω ω
Vacuum-like jet Vacuum-like emission inside the medium fragmentation in a dense QCD medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez If t vac � t med : emission triggered by the virtuality and not P.R.L.,120, 2018 yet affected by the momentum broadening. Introduction Vacuum-like = ⇒ double-logarithmic enhancement of the probability . emissions with a medium Parton cascades with a medium Fragmentation function Equivalent condition Energy loss by a jet q /θ 4 ) 1 / 3 ≡ ω 0 ( θ ) ω ≥ (ˆ Conclusion
Vacuum-like jet Vacuum-like emission outside the medium fragmentation in a dense QCD medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez P.R.L.,120, 2018 Introduction ◮ t vac ≥ L = ⇒ vacuum-like emission outside the medium Vacuum-like triggered by the virtuality of the parent parton. emissions with a medium Parton cascades with a medium Fragmentation ◮ In terms of energy : ω ≤ 1 / ( L θ 2 ). function Energy loss by a jet Conclusion
Vacuum-like jet Lund diagram : double logarithmic phase space fragmentation in a dense QCD with a QGP for one emission medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez P.R.L.,120, 2018 Introduction Vacuum-like emissions with a medium Parton cascades with a medium Fragmentation function Energy loss by a jet Conclusion The energy scale ω c The condition t med = L defines the energy scale qL 2 . Gluons with energy greater than ω c are always ω c = 1 / 2ˆ vacuum like.
Vacuum-like jet Iteration of vacuum-like emissions fragmentation in a dense QCD medium P. Caucal, E. Large N c limit Iancu, A.H. Mueller and G. Emission of a soft gluon by an antenna ⇔ splitting of the Soyez parent antenna into two daughter antennae. P.R.L.,120, 2018 Introduction Vacuum-like emissions with a medium Decoherence time Parton cascades with a medium ◮ Color coherence is responsible for angular ordering in Fragmentation function vacuum parton cascades. Energy loss by a ◮ In the medium, an antenna loses its color coherence jet q θ 2 q ) − 1 / 3 . after a time t coh = (ˆ Conclusion q ¯ (Mahtar-Tani, Salgado, Tywoniuk, 2010-11 ; Casalderrey-Solana, Iancu, 2011) ◮ In principle, angular ordering could be violated by cascades inside the medium.
Vacuum-like jet Coherence in vacuum vs (de)coherence in the fragmentation in a dense QCD medium medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez P.R.L.,120, 2018 Introduction Vacuum-like emissions with a medium Parton cascades with a medium Fragmentation function Energy loss by a jet The angular scale θ c Conclusion The condition t coh = L gives the definition of the critical � qL 3 . Antennae with angles greater than θ c angle θ c = 2 / ˆ always lose their coherence propagating over a distance L .
Vacuum-like jet Parton cascade in the medium fragmentation in a dense QCD medium But decoherence is impossible for vacuum-like emissions P. Caucal, E. (VLE) ! Iancu, A.H. Mueller and G. Soyez t vac ( ω i , θ i ) ≥ t coh ( θ i − 1 ) and θ i ≥ θ i − 1 ⇒ t vac ( ω i , θ i ) ≥ t med ( ω i ) P.R.L.,120, 2018 Introduction ⇒ not a VLE Vacuum-like emissions with a medium In the leading double-logarithmic approximation, successive Parton cascades with a medium in-medium vacuum-like emissions form angular-ordered Fragmentation cascades . function Energy loss by a jet Conclusion Consequence : at DLA successive VLEs are strongly ordered in ◮ energy ω i ≪ ω i − 1 because of energy conservation ◮ angle θ i ≪ θ i − 1 by color coherence at DLA .
Parton shower inside the medium
Vacuum-like jet Last antenna inside the medium fragmentation in a dense QCD medium P. Caucal, E. Iancu, A.H. ◮ The precedent proof does not apply if the parent Mueller and G. Soyez antenna is the last inside the medium . P.R.L.,120, 2018 ◮ In that case, the formation time of the next antenna is Introduction larger than L . Vacuum-like emissions with a medium Parton cascades Last emission inside the medium with a medium ◮ If θ ≤ θ c : the coherence time is also larger than L ⇒ Fragmentation function angular ordering is preserved. Energy loss by a jet ◮ If θ ≥ θ c : the antenna has lost its coherence during the Conclusion formation time of the next antenna ⇒ no constraint on the angle of the next antenna. (Y. Mehtar-Tani, K. Tywoniuk, Physics Letters B 744, 2015)
Parton shower inside and outside the medium Three important (leading-twist) effects : ◮ Reduction of the available phase space due to the VLE constraint. ◮ Angular ordering in the in-medium region. ◮ One violation of angular ordering by the first emission outside the medium.
Vacuum-like jet Analytical study of jets at DLA fragmentation in a dense QCD medium Double differential gluon distribution P. Caucal, E. Iancu, A.H. T ( ω, θ 2 | E , θ 2 q ) ≡ ωθ 2 d 2 N Mueller and G. q ¯ d ω d θ 2 Soyez ⇒ probability of emission of a gluon with energy ω and angle P.R.L.,120, 2018 θ 2 from an antenna with energy E and opening angle θ 2 q . q ¯ Introduction Vacuum-like emissions with a In the vacuum at DLA, this quantity satisfies the simple medium Parton cascades master equation with a medium Fragmentation T vac ( ω, θ 2 | E , θ 2 q ) = ¯ α s + function q ¯ � θ 2 � 1 Energy loss by a d θ 2 dz 1 q ¯ q jet α s T vac ( ω, θ 2 | z 1 E , θ 2 1 ¯ 1 ) θ 2 Conclusion z 1 θ 2 ω/ E 1 With a medium, this equation holds only inside the medium ⇒ mathematically, one must take into account “jumps” over the vetoed region.
Numerical results : ratio T ( ω, θ 2 ) / T vac ( ω, θ 2 ) Vacuum-like jet fragmentation in a dense QCD medium ω [GeV] P. Caucal, E. 0.1 0.1 1 1 10 10 100 100 Iancu, A.H. 0.4 0.4 Mueller and G. Soyez T/T vac P.R.L.,120, 2018 0.2 0.2 Introduction Vacuum-like 0.1 0.1 emissions with a medium Parton cascades θ with a medium 0.05 0.05 Fragmentation function Energy loss by a jet 0.02 0.02 Conclusion 0.01 0.01 - =2 Gev 2 /fm, L=3 fm ^ E=200 GeV, θ qq =0.4, α s =0.3, q 5 2 1 0.85
Vacuum-like jet Fragmentation function with fixed-coupling fragmentation in a dense QCD medium Definition P. Caucal, E. Iancu, A.H. Integral over angle between the k ⊥ cut-off and θ q ¯ Mueller and G. q Soyez � θ 2 Λ 2 /ω 2 d θ 2 ⇒ D ( ω ) ≡ ω dN q ¯ q θ 2 T ( ω, θ 2 ) d ω = P.R.L.,120, 2018 Introduction Vacuum-like emissions with a medium Parton cascades with a medium Fragmentation function Energy loss by a jet Conclusion (CMS collaboration, Phys. Rev. C 90, 2014)
Numerical results for the fragmentation function
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