Deciphering the z g distribution in heavy ion collisions P. Caucal, - - PowerPoint PPT Presentation

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Deciphering the z g distribution in heavy ion collisions P. Caucal, - - PowerPoint PPT Presentation

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z g distribution in a nutshell General pQCD picture High p T regime Low p T regime Conclusion Deciphering the z g distribution in heavy ion collisions P. Caucal, E. Iancu, A.H. Mueller and G. Soyez Institut de Physique Th eorique, CEA,

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Deciphering the zg distribution in heavy ion collisions

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

Institut de Physique Th´ eorique, CEA, France

May 13, 2019 - Bergen Jet Tools 2019

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Introduction

I will focus mainly on the zg distribution because this allows for comparisons with results from pQCD. How to understand from first principles these measurements ?

CMS Collab. PAS HIN-16-006

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

zg distribution in a nutshell

Jets are first defined with anti-kT. All final particles in one jet are reclustered with Cambridge/Aachen to impose physical angular ordering. A SoftDrop declustering is used the find the first two subjets satisfying zg ≥ zcut. The angle of branching is called θg.

Larkoski, Marzani, Soyez, Thaler, 2014

One can also impose a minimal angle between the two subjets θg ≥ θcut.

θg ≥ θcut pT = pT,1 + pT,2 pT,1 pT,2 zg = min(pT,1,pT,2)

pT,1+pT,2

≥ zcut z1 ≤ zcut z2 ≤ zcut

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

pQCD calculation in the vacuum

Sudakov form factor ∆(R, θg): probability to have no branching between R and θg with z ≥ zcut. ∆i(R, θg) = exp

  • −

R

θg

dθ 1/2

zcut

dzPi(z, θ)

  • Pi(z, θ) = 2Ci

π αs(zpTθ) θ ¯ Pi(z) The probability density pi(zg) to have a given value of zg is pi(zg) = NΘ(zg − zcut) R

θcut

dθg∆i(R, θg)Pi(zg, θg)

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Jet evolution in a dense QCD medium

Phys.Rev.Lett. 120 (2018) 232001

The evolution of a jet factorizes into three steps:

  • one angular ordered vacuum-like shower inside the medium ,
  • medium-induced showers triggered by previous sources;
  • finally, a vacuum-like shower outside the medium.
  • Vetoed region for VLEs: essential for the factorization of VLEs

from MIEs.

θc θqq

c

ω E

ω θ

ω θ = Λ 1 2

(ω,θ)

ω θ

3 4

=2q

  • utside

medium medium inside VETOED ω θ2 L = 2

θ1 θ2 θ ω1 ω2 ω

ωc = 1

2 ˆ

qL2 θc =

2

√

ˆ qL3

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Primary Lund plane - Definition

Density of primary emissions with a given kT = ωθ and 1/θ.

(see e.g. Dreyer, Salam, Soyez, 2018) 0.1 1 10 100

ω [GeV]

0.01 0.1

θ (E, θq¯

q)

ωθ = Λ ω

3

θ

4

= 2 ˆ q ωθ2L = 2 V E T O E D INSIDE OUTSIDE ωc θc 2 4 6 8

log(1/θ)

−2 2 4

log(k⊥/GeV) (ωc,θc) E (large z) INSIDE OUTSIDE VETOED large angles small angles non-perturbative

Primary Lund Plane

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Primary Lund planes (from MC calculations)

New scale for the medium-induced shower: kT = Qs ≡ √ˆ qL.

  • 1

1 2 3 4 1 2 3 4 5 6

log(kt/GeV) log(1/θ)

  • 1

1 2 3 4 1 2 3 4 5 6 0.5 1 1.5 2

VLEs only

q=1 GeV2/fm, L=4 fm, αs=0.25 ratio med/vac

  • 1

1 2 3 4 1 2 3 4 5 6 anti-kt(R=0.4), pt=200 GeV

log(kt/GeV) log(1/θ)

  • 1

1 2 3 4 1 2 3 4 5 6 0.2 0.4 0.6 0.8 1 1.2 1.4

medium-induced shower

q=1 GeV2/fm, L=4 fm, αs=0.25

  • 1

1 2 3 4 1 2 3 4 5 6

log(kt/GeV) log(1/θ)

  • 1

1 2 3 4 1 2 3 4 5 6 0.2 0.4 0.6 0.8 1 1.2 1.4

full shower

q=1 GeV2/fm, L=4 fm, αs=0.25

  • 1

1 2 3 4 1 2 3 4 5 6

log(kt/GeV) log(1/θ)

  • 1

1 2 3 4 1 2 3 4 5 6 0.5 1 1.5 2

med/vac ratio

q=1 GeV2/fm, L=4 fm, αs=0.25

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Two regimes: “high pT” and “low pT”

2 4 6 8

log(1/θ)

2 4 6

log(k⊥/GeV) (ωc,θc) E zcutE θcut

Lund Plane - high pT regime

2 4 6 8

log(1/θ)

2 4 6

log(k⊥/GeV) (ωc,θc) E zcutE θcut

Lund Plane - low pT regime

zg-distribution for “monochromatic” gluon jets in the regimes:

  • “High pT”: zcutpT ≥ ωc and θcut ≥ θc. Medium induced emission

can not be selected by SoftDrop.

  • “Low pT”: zcutpT ≤ ωc and θcut ≥ θc. Medium induced emissions

might be selected by SoftDrop. Mehtar-Tani, Tywoniuk, 2016

  • In the current LHC data, θcut = 0.1 whereas in our set-up θc ≤ 0.05
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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

High pT regime: incoherent energy loss

In the high pT regime, the only leading medium effect is the incoherent energy loss of the two subjets via medium-induced radiation. Incoherent energy loss because we chose θg ≥ θcut ≥ θc.

Mehtar-Tani, Salgado, Tywoniuk, 2010-1 ; Casalderrey-Solana, Iancu, 2011

Let us call E(pT,1, R1) the energy loss by a subjet.

θg ≥ θcut ≥ θc pT pT,1 = zpT − E(zpT, ∼ θg/2) pT,2 = (1 − z)pT − E((1 − z)pT, ∼ θg/2)

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

High pT regime: pQCD calculation

Vacuum: pi(zg) = NΘ(zg − zcut) R

θcut

dθg∆i(R, θg)Pi(zg, θg) ∆i(R, θg) = exp

  • −

R

θg

dθ 1/2 dzPi(z, θ)Θ(z − zcut)

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

High pT regime: pQCD calculation

Vacuum: z is the physical splitting fraction. pi(zg) = NΘ(zg − zcut) 1 dz R

θcut

dθg∆i(R, θg)Pi(z, θg)δ(z − zg) ∆i(R, θg) = exp

  • −

R

θg

dθ 1/2 dzPi(z, θ)Θ(z − zcut)

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

High pT regime: pQCD calculation

With the medium: pi(zg) = NΘ(zg−zcut) 1 dz R

θcut

dθg∆i(R, θg)Pi(z, θg)δ(Zg(z, θg)−zg)

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

High pT regime: pQCD calculation

With the medium: pi(zg) = NΘ(zg−zcut) 1 dz R

θcut

dθg∆i(R, θg)Pi(z, θg)δ(Zg(z, θg)−zg) ∆i(R, θg) = exp

  • −

R

θg

dθ 1/2 dzPi(z, θ)Θ(Zg(z, θ) − zcut)

  • Zg(z, θ) = min(zpT − E(zpT, θg), (1 − z)pT − E((1 − z)pT, θg))

pT − E(zpT, θg) − E((1 − z)pT, θg)

θg ≥ θcut ≥ θc pT pT,1 = zpT − E(zpT, ∼ θg/2) pT,2 = (1 − z)pT − E((1 − z)pT, ∼ θg/2)

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

The energy loss function E(pT, R)

The importance of the “in-medium” multiplicity of VLEs

For pT ≫ ωbr ≡ ¯ αs2ωc, partonic energy loss via MIEs is constant. For jets with VLEs and MIEs, the energy loss increases because of the VLEs multiplicity inside the medium.

10 20 30 40 50 60 70 2 5 20 50 200 500 10 100 1000 anti-kt(R=0.4) θmax=R, kt,min=0.25 q ^

=1.5 GeV/fm2, L=4 fm, α

  • s=0.25

average energy loss [GeV] pt0 [GeV] average energy loss MI only MI+VLEs fit (C=4.7) 5 10 15 20 25 30 35 40 45 0.2 0.4 0.6 0.8 1 anti-kt(R), pt,0=200 θmax=R, kt,min=0.25 q ^

=1.5 GeV/fm2, L=4 fm, α

  • s=0.25

average energy loss [GeV] R average energy loss MI only MI+VLEs

Analytical estimations: DL and single emission approximation, E(pT, θg) ∝ ωbr pT dω R

θc

dθ d2N dωdθΘin

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

High pT regime: analytical and MC results

0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 0.1 0.2 0.3 0.4 0.5

q=1.5 GeV2/fm, L=4 fm, pT=1 T eV

zg

Ratio med/vac - Normalized to 1

Monte-Carlo 0.8 0.85 0.9 0.95 1 0.1 0.2 0.3 0.4 0.5 q=1.5 GeV2/fm, L=4 fm, pT=1 T eV anti-kt(R=0.4)

zg

Ratio med/vac - Njets normalized

ε=11 GeV ε=20 GeV ε(pT)=ε0+ε1 log(pT/ωc)

Comments pT dependence of energy loss coming from VLEs leading to an increase in the number of sources. This pT dependence is important to achieve a good analytic description of both ways of normalizing zg.

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

High pT regime: analytical and MC results

0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 0.1 0.2 0.3 0.4 0.5

q=1.5 GeV2/fm, L=4 fm, pT=1 T eV

zg

Ratio med/vac - Normalized to 1

Monte-Carlo 0.8 0.85 0.9 0.95 1 0.1 0.2 0.3 0.4 0.5 q=1.5 GeV2/fm, L=4 fm, pT=1 T eV anti-kt(R=0.4)

zg

Ratio med/vac - Njets normalized

ε=11 GeV ε=20 GeV ε(pT)=ε0+ε1 log(pT/ωc)

Comments The effects of the incoherent energy loss on zg have also been discussed in Mehtar-Tani, Tywoniuk, 2016 & Chang, Cao, Qin, 2018 These papers refers to relatively low pT. Indeed, even in that regime, this mechanism represents an ingredient of the full physical scenario.

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Low pT regime: medium induced emissions

Purely medium-induced shower - zg distribution

For MIEs, the evolution variable is the emission time, not the angle. Primary emissions dominate the intrajet activity in the kinematics of interest since zcutpT ≫ ωbr ≡ ¯ α2

sωc. Blaizot, Iancu, Mehtar-Tani, 2013

For such emissions, one can build a fictitious angular ordering that mimics C/A declustering.

t θ ⇐ ⇒

d3Pmed dtdωdθ = αsCi 2π

  • ˆ

q ω3 2ω2θ ˆ q(L−t)e− ω2θ2

ˆ q(L−t)

d2Pmed dθdω = αsCi π

  • 2ωc

ω3 2θω2 Q2

s Γ(0, ω2θ2

Q2

s )

(ω, θ) ω

pi,med(zg) = NΘ(zg − zcut) R

θcut

dθg∆i,med(R, θg)Pi,med(zg, θg) ∆i,med(R, θg) = exp

  • −

R

θg

dθ 1/2 dzPi,med(z, θ)Θ(z − zcut)

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Low pT regime: full parton shower

The zg distribution taking into account both VLEs and MIEs is: pi(zg) = NΘ(zg − zc) R

θcut

dθg∆vac

i (R, θg)∆med i

(R, θg) × 1/2 dz

  • Pvac

i

(z, θg)δ(Z vac

g

− zg) + Pmed

i

(z, θg)δ(Z med

g

− zg)

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Low pT regime: full parton shower

The zg distribution taking into account both VLEs and MIEs is: pi(zg) = NΘ(zg − zc) R

θcut

dθg∆vac

i (R, θg)∆med i

(R, θg) × 1/2 dz

  • Pvac

i

(z, θg)δ(Z vac

g

− zg) + Pmed

i

(z, θg)δ(Z med

g

− zg)

  • Incoherent energy loss for the 2 sub-jets emerging from either a

hard vacuum-like splitting, or a hard medium-induced one. But the respective values for the energy loss are different. However the story is not over !

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Low pT regime: full parton shower

The zg distribution taking into account both VLEs and MIEs is: pi(zg) = NΘ(zg − zc) R

θcut

dθg∆vac

i (R, θg)∆med i

(R, θg) × 1/2 dz

  • Pvac

i

(z, θg)δ(Z vac

g

− zg) + Pmed

i

(z, θg)δ(Z med

g

− zg)

  • A MI branching can be emitted by any of the partonic sources

created via VLEs inside such that ω ≥ zpT and θc ≤ θ ≤ θg.

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Low pT regime: full parton shower

The formula with all the important physical ingredients is pi(zg) = NΘ(zg − zc) R

θcut

dθg∆vac

i (R, θg)∆med i

(R, θg) × 1/2 dz

  • Pvac

i

(z, θg)δ(Z vac

g

− zg) + (1 + ν)Pmed

i

(z, θg)δ(Z med

g

− zg)

  • A MI branching can be emitted by any of the partonic sources

created via VLEs inside such that ω ≥ zpT and θc ≤ θ ≤ θg. The probability Pmed

i

(z, θg) is enhanced by a factor 1 + ν with ν = pT

zpT

dω θg

θc

dθ d2N dωdθΘin and the Sudakov ∆med

i

(R, θg) suppressed accordingly.

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Low pT regime: analytical and MC results

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.2 0.3 0.4 0.5

q=1.5 GeV2/fm, L=4 fm, pT=200 GeV

zg

zg distribution - Medium induced jet

MC Analytical 0.8 0.9 1 1.1 1.2 1.3 0.1 0.2 0.3 0.4 0.5 anti-kt(R=0.4)

zg

Full shower - Ratio med/vac - Njets normalized

MC reference ν=0 cste energy loss

Comments For curve “reference”, ν is overestimated in the DLA approximation: ν = ¯ αs log(1/z) log(θg/θc). Curve “cste energy loss”: taking a constant energy loss for vacuum-like subjets does not reproduce the flat behavior at large zg.

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Full MC results with initial jet cross section

So far, only “monochromatic” initial jet cross section. The normalization factor for zg distributions is sensitive to the steeply falling spectrum. N.B. Change of the global shape around pT ≃ 500 GeV ∼ ωc/zcut.

q ^

=1.5, L=4, α

  • s=0.25

q ^

=1.5, L=4, α

  • s=0.25

θmax=1(0.75,1.5), kt,min=0.25(0.15,0.5) GeV θmax=1(0.75,1.5), kt,min=0.25(0.15,0.5) GeV anti-kt(R=0.4), |y|<2.8 anti-kt(R=0.4), |y|<2.8 √s=5.02 T eV, 0-10% centrality √s=5.02 T eV, 0-10% centrality

RAA pt [GeV] RAA: varying uncontrolled parameters ATLAS

  • ur result

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 200 500 100 1000 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 0.1 0.2 0.3 0.4 0.5 √s=5.02 T eV, anti-kt(R=0.4) q ^

=1.5 GeV/fm2, L=4 fm, α

  • s=0.25

θmax=1 (0.75,1.5), kt,min=0.25 GeV (0.2,0.35) ratio PbPb/vacuum zg zg distribution: pt dependence pt=100 GeV pt=200 GeV pt=500 GeV pt=1000 GeV

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

zg distributions for realistic initial jet cross section

Variation with ωbr (fixed ωc and θc)

ωbr is the scale controlling the energy loss and the BDMPS-Z rate. RAA decreases when ωbr increases. High-pT zg distribution: global normalization decreases when ωbr increases. Low-pT zg distribution: peak increases when ωbr increases.

q ^

=1.5, L=4

q ^

=1.5, L=4

θmax=1, kt,min=0.25 GeV, α

  • s=0.25

θmax=1, kt,min=0.25 GeV, α

  • s=0.25

anti-kt(R=0.4), |y|<2.8 anti-kt(R=0.4), |y|<2.8 √s=5.02 T eV, 0-10% centrality √s=5.02 T eV, 0-10% centrality

RAA pt [GeV] RAA: fixed θc,ωc, vary ωbr ATLAS ωbr=2.4 GeV (α

  • s=0.2)

ωc=3.75 GeV (α

  • s=0.25)

ωc=6.67 GeV (α

  • s=0.33)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 200 500 100 1000 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 0.1 0.2 0.3 0.4 0.5 √s=5.02 T eV, anti-kt(R=0.4) θmax=1, kt,min=0.25 GeV dashed: ωbr=2.4 GeV solid: ωbr=3.75 GeV dotted: ωbr=6.67 GeV ratio PbPb/vacuum zg zg distribution: fixed θc,ωc, vary ωbr pt=100 GeV pt=500 GeV

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Conclusion

Take-home messages

Recall: the phase-space constraint refers to the VLEs. First phase space effect: the zg distribution in the high pT ≫ ωc/zcut and low pT ≪ ωc/zcut regime cannot be explained without the in-medium multiplicity of VLEs which introduces a pT dependence of the energy loss. We predict a change of behavior of the nuclear modification factor for the zg distribution around pT ∼ ωc/zcut. Second phase space effect: the zg distribution in the low pT regime is affected by the in-medium multiplicity of VLEs that enhances the probability to have a MIE selected by SoftDrop.

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

THANK YOU !

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Back-up - Sudakov form factors

0.2 0.4 0.6 0.8 1 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 q=1.5 GeV2/fm, L=4 fm Δg(R,θg) θg MIE VLE

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Back-up - In-medium VLEs multiplicity

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2 5 20 50 200 500 10 100 1000 anti-kt(R=0.4) θmax=R q ^

=1.5 GeV/fm2, L=4 fm

average multiplicity pt0 [GeV] average in-medium multiplicity all pt pt>10 GeV

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zg distribution in a nutshell General pQCD picture High pT regime Low pT regime Conclusion

Back-up - Transition low pT/high pT

0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 0.1 0.2 0.3 0.4 0.5 anti-kt(R=0.4) θmax=R, kt,min=0.25 q ^

=1.5 GeV/fm2, L=4 fm, α

  • s=0.25

ratio PbPb/vac zg 100 200 500 1000