Jet multiplicities in a dense QCD medium P. Caucal, E. Iancu, A.H. Jet multiplicities in a dense QCD medium Mueller and G. Soyez Introduction P. Caucal, E. Iancu, A.H. Mueller and G. Soyez DL approximation Resummation to DL accuracy Institut de Physique Th´ eorique, CEA, France Energy loss Results January 7, 2018 at JETSCAPE workshop Conclusion
Jet multiplicities in Motivations and goal of the talk a dense QCD medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez Introduction DL approximation ◮ Jet evolution in a dense medium : medium induced Resummation to emissions versus vacuum-like emissions. How can we DL accuracy include both mechanisms ? Energy loss ◮ The simplest possible approximation in parton shower : Results Conclusion keep all leading double-logarithm (DL) terms and resum them. ◮ Within this approximation, the time scales in the evolution factorize .
Jet multiplicities in Where does double-logarithmic phase space come a dense QCD medium from ? P. Caucal, E. Iancu, A.H. Vacuum-like emissions inside the medium Mueller and G. Soyez ◮ Bremsstrahlung = ⇒ energy and angle logarithms. Introduction Formation time due to the virtuality of the parent DL approximation parton : t vac ∼ ω/ k 2 ⊥ ∼ 1 / ( ωθ 2 ). Resummation to DL accuracy ◮ BDMPS-Z (Baier, Dokshitzer, Mueller, Peign´ e, and Schiff; Zakharov 1996–97) Energy loss Medium-induced formation time and broadening Results � characteristic time scale : t f ∼ ω/ ˆ q . Conclusion If t vac ≪ t f : emission triggered by the virtuality and not yet affected by the momentum broadening. = ⇒ double-logarithmic enhancement of the probability . Equivalent conditions f = √ ˆ ◮ k 2 ⊥ ≫ k 2 q ω q /θ 4 ) 1 / 3 ≡ ω 0 ( θ ) ◮ ω ≫ (ˆ
Jet multiplicities in Where does double-logarithmic phase space come a dense QCD medium from ? P. Caucal, E. Iancu, A.H. Mueller and G. Soyez Vacuum-like emissions outside the medium Introduction ◮ t vac ≥ L = ⇒ vacuum-like emission outside the medium DL approximation triggered by the virtuality of the parent parton. Resummation to ◮ In terms of energy : ω ≤ 1 / ( L θ 2 ). DL accuracy Energy loss Results Conclusion
Jet multiplicities in How to resum these double logarithms in the a dense QCD medium medium ? P. Caucal, E. Iancu, A.H. Iteration of vacuum-like emissions Mueller and G. Soyez Introduction Large N c limit DL approximation Emission of a soft gluon by an antenna ⇔ splitting of the Resummation to DL accuracy parent antenna into two daughter antennae. Energy loss Results Decoherence time Conclusion ◮ 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) ◮ Important angular scale, θ 2 c such that t coh ( θ 2 c ) = L . ◮ Reminder : color coherence is responsible for angular ordering in vacuum cascades.
Jet multiplicities in How to resum these double logarithms in the a dense QCD medium medium ? P. Caucal, E. Iancu, A.H. Mueller and G. In the leading double-logarithmic approximation, successive Soyez in-medium vacuum-like emissions form angular-ordered Introduction cascades . DL approximation Proof Resummation to DL accuracy ◮ First case : t vac ( ω i , θ 2 i ) ≤ t coh ( ω i − 1 , θ 2 i − 1 ), the parent Energy loss antenna did not lose its coherence during the time Results required by the next antenna to be formed ⇒ Conclusion 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 ). This inequality can be rewritten � θ 2 � θ 2 � 1 / 3 � 1 / 3 i ) 1 / 3 × q /θ 4 ω i ≤ (ˆ i − 1 = ω 0 ( θ i ) × i − 1 θ 2 θ 2 i i Then, necessarily θ 2 i ≤ θ 2 i − 1 , otherwise the condition t vac ( ω i , θ 2 i ) ≤ t f ( ω i , θ 2 i ) is not fulfilled.
Jet multiplicities in Consequences on the emissions outside the a dense QCD medium medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez ◮ 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 to DL accuracy larger than L . Energy loss Results 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)
Jet multiplicities in Phase space a dense QCD medium Long story short P. Caucal, E. Iancu, A.H. Mueller and G. Soyez θ 2 = 1 / ( ωL ) θ 2 = � q/ω 3 ˆ 10 0 Introduction DL approximation VLE emissions inside the medium Resummation to with angular ordering DL accuracy 10 − 1 Energy loss Results q ¯ q Conclusion θ 2 /θ 2 10 − 2 VLE emissions outside the medium with angular ordering 10 − 3 θ 2 c 10 − 4 10 − 3 10 − 2 10 − 1 10 0 ω c ω/E
Jet multiplicities in What about the energy loss ? a dense QCD medium P. Caucal, E. Iancu, A.H. Mueller and G. Energy loss is negligible for any parton of the cascade Soyez inside the medium (except for the last one) Introduction qt 2 energy of the hardest medium induced ◮ ω loss ∼ ˆ DL approximation emission that can develop during t . Resummation to DL accuracy ◮ By the inequality t vac ( ω i , θ 2 i ) ≪ t f ( ω i , θ 2 i ), one finds Energy loss that ω loss ≪ ω i . Results Conclusion However... ◮ Energy loss is not negligible for the last antenna inside the medium since it will cross the medium along a distance of order L . ◮ Medium induced gluon cascades are important for large angle radiations.
Jet multiplicities in Experimental data a dense QCD medium P. Caucal, E. Iancu, A.H. CMS data (CMS PAS HIN-12-013, CMS collaboration) Mueller and G. Soyez Differential jet shapes for different centrality bins for jets Introduction with p T ≥ 100 GeV/c in PbPb collisions. DL approximation Resummation to DL accuracy Energy loss Results Conclusion
Jet multiplicities in Experimental data a dense QCD medium P. Caucal, E. Iancu, A.H. CMS data (CMS PAS HIN-12-013, CMS collaboration) Mueller and G. Soyez Fragmentation function in bins of increasing centrality for jets with p T ≥ 100 GeV/c in PbPb collisions. Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion Similar results by the ATLAS collaboration (Physics Letters B 739 (2014) 320–342)
Jet multiplicities in Preliminary analytical results a dense QCD medium Vacuum DLA cascades : P. Caucal, E. Iancu, A.H. ωθ 2 dN vac Mueller and G. � � � α log( E /ω ) log( θ 2 q /θ 2 ) d ω d θ 2 = ¯ α I 0 2 ¯ Soyez q ¯ Introduction We have similar analytical formulae for DLA cascades with DL approximation medium constraints. Resummation to DL accuracy Energy loss ωθ 2 dN vac dN Results dωdθ 2 with E = 200 GeV , θ 2 ωθ 2 dωdθ 2 with E = 200 GeV , θ 2 q = 1 GeV 2 /fm , L = 4 fm q = 1 q = 1 , ˆ q ¯ q ¯ 10000 10000 Conclusion 1000 1000 10 1 10 1 q /θ 2 q /θ 2 100 100 q ¯ q ¯ θ 2 θ 2 10 0 10 0 10 10 1 1 1 10 100 1000 1 10 100 1000 E/ω E/ω
Jet multiplicities in Preliminary analytical results a dense QCD medium Qualitative behavior, in agreement with data P. Caucal, E. Iancu, A.H. ◮ Enhancement of the multiplicity at large angles inside the jet and Mueller and G. Soyez small energy fractions. ◮ Small suppression at intermediate energy fractions. Introduction DL approximation Resummation to dωdθ 2 / dN vac dN dωdθ 2 with E = 200 GeV , θ 2 q = 1 GeV 2 /fm , L = 4 fm q = 1 , ˆ q ¯ DL accuracy 10000 Energy loss 10 9 8 Results 7 1000 Conclusion 6 5 4 q /θ 2 100 3 q ¯ θ 2 2 10 1 1 1 10 100 1000 E/ω
Jet multiplicities in Conclusion a dense QCD medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez Introduction In perspective DL approximation ◮ Calculate the fragmentation function in order to Resummation to DL accuracy compare more precisely our results with data. Energy loss ◮ Go beyond DLA by including full splitting functions Results (hence, energy conservation) for the VLE’s. Conclusion ◮ Include medium-induced radiation not only as a constraint on the VLE’s = ⇒ energy loss.
Jet multiplicities in a dense QCD medium P. Caucal, E. Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to Thank you for listening ! DL accuracy Energy loss Results Conclusion
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