Jet multiplicities in a dense QCD medium Mueller and G. Soyez - - PowerPoint PPT Presentation

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Jet multiplicities in a dense QCD medium Mueller and G. Soyez - - PowerPoint PPT Presentation

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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

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SLIDE 1

Jet multiplicities in a dense QCD medium

  • P. Caucal, E.

Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion

Jet multiplicities in a dense QCD medium

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

Institut de Physique Th´ eorique, CEA, France

January 7, 2018 at JETSCAPE workshop

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SLIDE 2

Jet multiplicities in a dense QCD medium

  • P. Caucal, E.

Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion

Motivations and goal of the talk

◮ Jet evolution in a dense medium : medium induced

emissions versus vacuum-like emissions. How can we include both mechanisms ?

◮ The simplest possible approximation in parton shower :

keep all leading double-logarithm (DL) terms and resum them.

◮ Within this approximation, the time scales in the

evolution factorize.

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SLIDE 3

Jet multiplicities in a dense QCD medium

  • P. Caucal, E.

Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion

Where does double-logarithmic phase space come from ?

Vacuum-like emissions inside the medium

◮ Bremsstrahlung =

⇒ energy and angle logarithms. Formation time due to the virtuality of the parent parton : tvac ∼ ω/k2

⊥ ∼ 1/(ωθ2). ◮ BDMPS-Z (Baier, Dokshitzer, Mueller, Peign´

e, and Schiff; Zakharov 1996–97)

Medium-induced formation time and broadening characteristic time scale : tf ∼

  • ω/ˆ

q. If tvac ≪ tf : emission triggered by the virtuality and not yet affected by the momentum broadening. = ⇒ double-logarithmic enhancement of the probability.

Equivalent conditions

◮ k2 ⊥ ≫ k2 f = √ˆ

qω

◮ ω ≫ (ˆ

q/θ4)1/3 ≡ ω0(θ)

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SLIDE 4

Jet multiplicities in a dense QCD medium

  • P. Caucal, E.

Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion

Where does double-logarithmic phase space come from ?

Vacuum-like emissions outside the medium

◮ tvac ≥ L =

⇒ vacuum-like emission outside the medium triggered by the virtuality of the parent parton.

◮ In terms of energy : ω ≤ 1/(Lθ2).

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SLIDE 5

Jet multiplicities in a dense QCD medium

  • P. Caucal, E.

Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion

How to resum these double logarithms in the medium ?

Iteration of vacuum-like emissions

Large Nc limit

Emission of a soft gluon by an antenna ⇔ splitting of the parent antenna into two daughter antennae.

Decoherence time

◮ In the medium, an antenna loses its color coherence

after a time tcoh = 1/(ˆ qθ2

q¯ q)1/3.

(Mahtar-Tani, Salgado, Tywoniuk, 2010-11 ; Casalderrey-Solana, Iancu, 2011)

◮ Important angular scale, θ2 c such that tcoh(θ2 c) = L. ◮ Reminder : color coherence is responsible for angular

  • rdering in vacuum cascades.
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SLIDE 6

Jet multiplicities in a dense QCD medium

  • P. Caucal, E.

Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion

How to resum these double logarithms in the medium ?

In the leading double-logarithmic approximation, successive in-medium vacuum-like emissions form angular-ordered cascades.

Proof

◮ First case : tvac(ωi, θ2 i ) ≤ tcoh(ωi−1, θ2 i−1), the parent

antenna did not lose its coherence during the time required by the next antenna to be formed ⇒ θ2

i ≪ θ2 i−1. ◮ Second case : tvac(ωi, θ2 i ) ≥ tcoh(ωi−1, θ2 i−1). This

inequality can be rewritten ωi ≤ (ˆ q/θ4

i )1/3 ×

θ2

i−1

θ2

i

1/3 = ω0(θi) × θ2

i−1

θ2

i

1/3 Then, necessarily θ2

i ≤ θ2 i−1, otherwise the condition

tvac(ωi, θ2

i ) ≤ tf (ωi, θ2 i ) is not fulfilled.

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SLIDE 7

Jet multiplicities in a dense QCD medium

  • P. Caucal, E.

Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion

Consequences on the emissions outside the medium

◮ The precedent proof does not apply if the antenna i − 1

is the last inside the medium.

◮ In that case, the formation time of the next antenna is

larger than L.

Last emission inside the medium

◮ If θ2 i−1 ≤ θ2 c : the decoherence time is also larger than L

⇒ angular ordering is preserved.

◮ If θ2 i−1 ≥ θ2 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)

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SLIDE 8

Jet multiplicities in a dense QCD medium

  • P. Caucal, E.

Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion

Phase space

Long story short

10−4 10−3 10−2 10−1 100 ω/E 10−3 10−2 10−1 100 θ2/θ2

q¯ q

ωc θ2

c

VLE emissions inside the medium with angular ordering VLE emissions

  • utside the medium

with angular ordering θ2 =

  • ˆ

q/ω3 θ2 = 1/(ωL)

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SLIDE 9

Jet multiplicities in a dense QCD medium

  • P. Caucal, E.

Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion

What about the energy loss ?

Energy loss is negligible for any parton of the cascade inside the medium (except for the last one)

◮ ωloss ∼ ˆ

qt2 energy of the hardest medium induced emission that can develop during t.

◮ By the inequality tvac(ωi, θ2 i ) ≪ tf (ωi, θ2 i ), one finds

that ωloss ≪ ωi.

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.

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SLIDE 10

Jet multiplicities in a dense QCD medium

  • P. Caucal, E.

Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion

Experimental data

CMS data (CMS PAS HIN-12-013, CMS collaboration)

Differential jet shapes for different centrality bins for jets with pT ≥ 100 GeV/c in PbPb collisions.

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SLIDE 11

Jet multiplicities in a dense QCD medium

  • P. Caucal, E.

Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion

Experimental data

CMS data (CMS PAS HIN-12-013, CMS collaboration)

Fragmentation function in bins of increasing centrality for jets with pT ≥ 100 GeV/c in PbPb collisions.

Similar results by the ATLAS collaboration (Physics Letters B 739 (2014) 320–342)

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SLIDE 12

Jet multiplicities in a dense QCD medium

  • P. Caucal, E.

Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion

Preliminary analytical results

Vacuum DLA cascades : ωθ2 dNvac dωdθ2 = ¯ αI0

  • 2
  • ¯

α log(E/ω) log(θ2

q¯ q/θ2)

  • We have similar analytical formulae for DLA cascades with

medium constraints.

1 10 100 1000 E/ω 1 10 100 1000 10000 θ2

q¯ q/θ2

ωθ2 dNvac

dωdθ2 with E = 200 GeV , θ2

q¯ q = 1

100 101 1 10 100 1000 E/ω 1 10 100 1000 10000 θ2

q¯ q/θ2

ωθ2

dN dωdθ2 with E = 200 GeV , θ2

q¯ q = 1, ˆ

q = 1 GeV 2/fm, L = 4 fm 100 101

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SLIDE 13

Jet multiplicities in a dense QCD medium

  • P. Caucal, E.

Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion

Preliminary analytical results

Qualitative behavior, in agreement with data

◮ Enhancement of the multiplicity at large angles inside the jet and

small energy fractions.

◮ Small suppression at intermediate energy fractions.

1 10 100 1000 E/ω 1 10 100 1000 10000 θ2

q¯ q/θ2 dN dωdθ2/ dNvac dωdθ2 with E = 200 GeV , θ2 q¯ q = 1, ˆ

q = 1 GeV 2/fm, L = 4 fm 1 2 3 4 5 6 7 8 9 10

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SLIDE 14

Jet multiplicities in a dense QCD medium

  • P. Caucal, E.

Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion

Conclusion

In perspective

◮ Calculate the fragmentation function in order to

compare more precisely our results with data.

◮ Go beyond DLA by including full splitting functions

(hence, energy conservation) for the VLE’s.

◮ Include medium-induced radiation not only as a

constraint on the VLE’s = ⇒ energy loss.

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SLIDE 15

Jet multiplicities in a dense QCD medium

  • P. Caucal, E.

Iancu, A.H. Mueller and G. Soyez Introduction DL approximation Resummation to DL accuracy Energy loss Results Conclusion

Thank you for listening !