Jet fragmentation in a dense QCD medium Iancu, A.H. Mueller and G. - PowerPoint PPT Presentation

Jet fragmentation in a dense QCD medium P. Caucal, E. Jet fragmentation in a dense QCD medium Iancu, A.H. Mueller and G. Soyez P.R.L.,120, 2018 P. Caucal, E. Iancu, A.H. Mueller and G. Soyez Introduction DL approximation P.R.L.,120, 2018 Resummation up to DL accuracy Institut de Physique Th´ eorique, CEA, France Fragmentation function July 3, 2018 at “Rencontre QGP France” in Etretat Conclusion

Jet fragmentation Introduction in a dense QCD medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez P.R.L.,120, 2018 ◮ Jets are very important probes of the quark-gluon Introduction plasma (QGP) produced in heavy-ions collisions at LHC DL approximation or RHIC. Resummation up to DL accuracy ◮ Understanding observables such that the jet suppression Fragmentation function or the jet fragmentation function will help to better Conclusion characterize the QGP. ◮ From a theoretical point of view, a complete picture of the evolution of a jet in a dense medium is still lacking.

Jet fragmentation Motivations and goal of the talk in a dense QCD medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez P.R.L.,120, 2018 Introduction ◮ Jet evolution in a dense medium : medium induced DL approximation Resummation up emissions versus vacuum-like emissions. How can we to DL accuracy include both mechanisms ? Fragmentation function Conclusion ◮ Our solution is to work with the simplest possible approximation in parton shower : the leading double-logarithm approximation (DLA).

Jet fragmentation Where does the double-logarithmic phase space in a dense QCD medium come from ? P. Caucal, E. Iancu, A.H. Bremsstrahlung law... Mueller and G. Soyez P.R.L.,120, 2018 Bremsstrahlung spectrum = ⇒ energy and angle logarithms. Introduction DL approximation Resummation up to DL accuracy Formation time due to the virtuality of the parent parton : Fragmentation function t vac ∼ ω/ k 2 ⊥ ∼ 1 / ( ωθ 2 ). Conclusion

Jet fragmentation Where does the double-logarithmic phase space in a dense QCD medium come from ? P. Caucal, E. Iancu, A.H. ... vs medium induced radiations Mueller and G. Soyez P.R.L.,120, 2018 BDMPS-Z spectrum (Baier, Dokshitzer, Mueller, Peign´ e, and Schiff; Zakharov 1996–97) Introduction NOT DOUBLE LOG ! DL approximation Resummation up Medium-induced formation time and broadening to DL accuracy � q from � k 2 characteristic time scale : t f ∼ ω/ ˆ ⊥ � = ˆ q ∆ t . Fragmentation function Conclusion

Jet fragmentation Vacuum-like emission inside the medium in a dense QCD medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez P.R.L.,120, 2018 If t vac ≪ t f : emission triggered by the virtuality and not yet affected by the momentum broadening. Introduction DL approximation Resummation up = ⇒ double-logarithmic enhancement of the probability . to DL accuracy Fragmentation function Conclusion Equivalent condition q /θ 4 ) 1 / 3 ≡ ω 0 ( θ ) ω ≫ (ˆ

Jet fragmentation Vacuum-like emission outside the medium in a dense QCD medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez P.R.L.,120, 2018 Introduction DL approximation ◮ t vac ≥ L = ⇒ vacuum-like emission outside the medium Resummation up triggered by the virtuality of the parent parton. to DL accuracy Fragmentation function Conclusion ◮ In terms of energy : ω ≤ 1 / ( L θ 2 ).

Jet fragmentation Summary : double logarithmic phase space with in a dense QCD medium a QGP P. Caucal, E. Iancu, A.H. Mueller and G. Soyez P.R.L.,120, 2018 Introduction DL approximation Resummation up to DL accuracy Fragmentation function Conclusion The energy scale ω c qL 2 . The condition t f = L defines the energy scale ω c = 1 / 2ˆ Gluons with energy greater than ω c are always vacuum like.

Jet fragmentation How to resum these double logarithms in the in a dense QCD medium medium ? P. Caucal, E. Iancu, A.H. Iteration of vacuum-like emissions Mueller and G. Soyez P.R.L.,120, 2018 Large N c limit Introduction Emission of a soft gluon by an antenna ⇔ splitting of the DL approximation parent antenna into two daughter antennae. Resummation up to DL accuracy Fragmentation function Conclusion Decoherence time ◮ Reminder : color coherence is responsible for angular ordering in vacuum cascades ◮ In the medium, an antenna loses its color coherence q θ 2 q ) 1 / 3 . after a time t coh = 1 / (ˆ q ¯ (Mahtar-Tani, Salgado, Tywoniuk, 2010-11 ; Casalderrey-Solana, Iancu, 2011)

Jet fragmentation Coherence in vacuum vs (de)coherence in the in a dense QCD medium medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez P.R.L.,120, 2018 Introduction DL approximation Resummation up to DL accuracy Fragmentation function Conclusion The angular scale θ c 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 .

Jet fragmentation How to resum these double logarithms in the in a dense QCD medium medium ? P. Caucal, E. Iancu, A.H. Mueller and G. Soyez In the leading double-logarithmic approximation, successive P.R.L.,120, 2018 in-medium vacuum-like emissions form angular-ordered Introduction cascades . DL approximation Resummation up to DL accuracy Proof Fragmentation function ◮ First case : t vac ( ω i , θ 2 i ) ≤ t coh ( ω i − 1 , θ 2 i − 1 ), the parent Conclusion antenna did not lose its coherence during the time required by the next antenna to be formed ⇒ θ 2 i ≪ θ 2 i − 1 . ◮ Second case : t vac ( ω i , θ 2 i ) ≥ t coh ( ω i − 1 , θ 2 i − 1 ) ⇒ t vac ( ω i , θ 2 i ) ≥ t f ( ω i , θ 2 i ) or θ 2 i ≤ θ 2 i − 1 ⇒ θ 2 i ≤ θ 2 i − 1

Jet fragmentation Consequences on the emissions outside the in a dense QCD medium medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez P.R.L.,120, 2018 ◮ The precedent proof does not apply if the antenna i − 1 Introduction is the last inside the medium . DL approximation ◮ In that case, the formation time of the next antenna is Resummation up larger than L . to DL accuracy Fragmentation function Last emission inside the medium Conclusion ◮ If θ 2 i − 1 ≤ θ 2 c : the decoherence time is also larger than L ⇒ angular ordering is preserved. ◮ If θ 2 i − 1 ≥ θ 2 c : the antenna has lost its coherence during the 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 in a QGP

Jet fragmentation Analytical study of jets at DLA in a dense QCD medium Double differential gluon distribution P. Caucal, E. Iancu, A.H. Mueller and G. T ( ω, θ 2 | E , θ 2 q ) ≡ ωθ 2 d 2 N Soyez q ¯ d ω d θ 2 P.R.L.,120, 2018 ⇒ probability of emission of a gluon with energy ω and angle θ 2 from an antenna with energy E and opening angle θ 2 Introduction q . q ¯ DL approximation Resummation up to DL accuracy In the vacuum at DLA, this quantity satisfies the simple Fragmentation function master equation Conclusion T vac ( ω, θ 2 | E , θ 2 q ) = ¯ α s + q ¯ � θ 2 � 1 d θ 2 dz 1 q ¯ q α s T vac ( ω, θ 2 | z 1 E , θ 2 1 ¯ 1 ) θ 2 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 ) Jet fragmentation in a dense QCD medium ω [GeV] P. Caucal, E. Iancu, A.H. 0.1 0.1 1 1 10 10 100 100 Mueller and G. 0.4 0.4 Soyez P.R.L.,120, 2018 T/T vac Introduction 0.2 0.2 DL approximation Resummation up to DL accuracy 0.1 0.1 Fragmentation function θ 0.05 0.05 Conclusion 0.02 0.02 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

Jet fragmentation Fragmentation function with fixed-coupling in a dense QCD medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez Definition P.R.L.,120, 2018 Integral over angle between the k ⊥ cut-off and θ q ¯ q Introduction � θ 2 Λ 2 /ω 2 d θ 2 ⇒ D ( ω ) ≡ ω dN q ¯ θ 2 T ( ω, θ 2 ) d ω = q DL approximation Resummation up to DL accuracy Remarks Fragmentation function ◮ Formula reliable only for ω ≪ E at DLA. Conclusion ◮ Different from the fragmentation function given by experimentalists represented as a function of the ratio ω/ E where E is the total energy of the jet. Here, “our” E is an unobservable parameter since in practice, the jet loses energy via medium-induced radiations.

Jet fragmentation Numerical results for the fragmentation function in a dense QCD medium 2 2 =1 Gev 2 /fm,L=3 fm ^ P. Caucal, E. q =2 Gev 2 /fm,L=3 fm ^ Iancu, A.H. 1.8 1.8 q =2 Gev 2 /fm,L=4 fm ^ Mueller and G. q 1.6 1.6 Soyez D( ω )/D vac ( ω ) P.R.L.,120, 2018 solid: Λ =100 MeV 1.4 1.4 dashed: Λ =200 MeV Introduction 1.2 1.2 DL approximation 1 1 Resummation up 0.8 0.8 to DL accuracy - E=200 GeV, θ qq - =0.4, α s =0.3 0.6 0.6 Fragmentation 1 1 10 10 100 100 function ω [GeV] Conclusion (CMS collaboration, Phys. Rev. C 90, 2014)