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

SLIDE 1

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

Deciphering the zg distribution in heavy ion collisions

P. Caucal, E. Iancu and G. Soyez

Institut de Physique Th´ eorique

Quark Matter 2019 - November 6 - Wuhan Talk based on JHEP 10(2019)273

0 / 13

SLIDE 2

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

A new pQCD picture for jet evolution in the QGP Caucal, Iancu, Mueller, Soyez, 2018 - QM 2018

utside

ωθ

VETOED

medium medium inside non perturbative

ω =E =log

t

log k log 1/ θ θ ω = ω

c c

Phase space for vacuum-like emissions (VLEs) dictated by pQCD principles. Vetoed region for VLEs: only k⊥ > ˆ qtf or tf > L allowed. Angular ordering of VLEs inside and outside the medium. Factorization between VLEs and medium-induced emissions (MIEs). ⇒ Independent energy loss for VLEs inside with θ > θc = 2/

ˆ

qL3. Monte-Carlo implementation In this talk, first Monte-Carlo results based on this factorized picture (including coherence effects) for the zg distribution and RAA.

1 / 13

SLIDE 3

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

zg distribution in a nutshell Larkoski, Marzani, Soyez, Thaler, 2014

For a given jet of radius R, recluster the constituents of the jet using C/A (ordered in angles). Then iteratively decluster the jet until the SD condition is met: z12 ≡ min(pT1, pT2) pT1 + pT2 ≥ zcut Additional constraint: ∆R12 ≡

∆y 2

12 + ∆φ2 12 ≥ θcut

Add the value of zg to the corresponding bin in your histogram and normalize it either to 1 or to the total number of jets.

2 4 6 8 log(R/ ) 2 4 6 log(k /GeV) = pT 1 2 3 = zcut pT =

cut

primary Lund plane

pT,1 pT,2 1 2 3 ∆R12 = θg pT zg = min(pT,1,pT,2)

pT,1+pT,2

θ1 ≫ θ2 ≫ θ3 = θg 2 / 13

SLIDE 4

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

Why focusing on the zg distribution ?

Not IRC safe but Sudakov safe ⇒ can be calculated in pQCD. Larkoski, Marzani, Thaler, 2015 Example: in the vacuum, with fixed coupling αs: 1 Njets dNi dzg ∝

measure splitting function !

¯ Pi(zg) ∼ 1 zg

3 / 13

SLIDE 5

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

Why is the zg distribution interesting in heavy ion collisons ?

In the presence of the medium, controlled by two basic phenomena:

SoftDrop condition triggered either by a vacuum-like emission or by a medium

induced emission. Mehtar-Tani, Tywoniuk 2017

both subjets lose energy via medium induced emissions, independently as long as

θg ≥ θc = 2/

ˆ
qL3. Mehtar-Tani, Salgado, Tywoniuk, 2010-11 ; Casalderrey-Solana, Iancu, 2011

4 / 13

SLIDE 6

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

Two regimes

Red region: Phase space for vacuum-like emissions inside the medium. ωc = 1

2 ˆ

qL2 maximal energy and Qs = ωcθc = √ˆ qL maximal k⊥ for MIEs.

2 4 6 8 log(R/ ) 2 4 6 log(k /GeV) = pT (

c, c)

= zcutpT =

cut

k =

c c

primary Lund plane - high pT regime

High-pT regime: pTzcut ≫ ωc SD can only select VLEs.

2 4 6 8 log(R/ ) 2 4 6 log(k /GeV) = pT (

c, c)

= zcutpT =

cut

primary Lund plane - low pT regime

Low-pT regime: pTzcut ωc SD can select both VLEs and MIEs.

5 / 13

SLIDE 7

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

High pT regime zcutpT ≫ ωc: energy loss shift effect

pT pT,1 = zpT − Eg pT,2 = (1 − z)pT − Ei

Incoherent energy loss Relate the physical z fraction before energy loss to the measured zg balance. zg = zpT − Eg pT − Eg − Ei ⇒ z = zg + Eg − zg(Eg + Ei) pT ≥ zg

6 / 13

SLIDE 8

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

High pT regime zcutpT ≫ ωc: energy loss shift effect

pT pT,1 = zpT − Eg pT,2 = (1 − z)pT − Ei

0.8 0.85 0.9 0.95 1 1.05 0.1 0.2 0.3 0.4 0.5 pT0,gluon=1 T eV

q ^

=1.5 GeV2/fm, L=4 fm

anti-kt(R=0.4), SD(β=0,zcut=0.1) [mMDT], θg>0.1

R(zg) zg Njets-norm zg distribution - high-pT jets ε=16.5 GeV

zg = zpT − Eg pT − Eg − Ei ⇒ z = zg + Eg − zg(Eg + Ei) pT ≥ zg Assume Eg and Ei constant, RAA(zg) ∝ ¯ Pi(z) ¯ Pi(zg) ∼ zg z ≃ 1 − ∆z zg Ratio increases with zg.

6 / 13

SLIDE 9

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

How much energy is lost ?

In previous slide, constant energy loss for a jet without VLEs: Eg ∝ ωbr ≡ α2

sωc

Not realistic ! pT ր ⇒ phase space for in-medium VLEs ր ⇒ more sources for energy loss This simple fact explains RAA for the jet cross-section pattern... Caucal, Iancu, Soyez 2019

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 200 500 100 1000

θmax=1(0.75,1.5), k⊥,min=0.25(0.15,0.5) GeV θmax=1(0.75,1.5), k⊥,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

q ^

=1.5 GeV2/fm

q ^

=1.5 GeV2/fm

L=4 fm L=4 fm αs=0.24 αs=0.24 RAA pT,jet [GeV] RAA: varying uncontrolled parameters ATLAS

urs

10 20 30 40 50 60 70 2 5 20 50 200 500 10 100 1000

anti-kt(R=0.4) anti-kt(R=0.4) θmax=R, k⊥,min=0.25 GeV θmax=R, k⊥,min=0.25 GeV

q ^

=1.5 GeV/fm2

q ^

=1.5 GeV/fm2

L=4 fm L=4 fm αs=0.24 αs=0.24 gluon gluon average energy loss [GeV] pT0 [GeV] average energy loss - pT0 dependence MIEs only MIEs+VLEs

21.4+10.6 log(pT0/ωc)+1.46 log2(pT0/ωc)

10 20 30 40 50 60 70 2 5 20 50 200 500 10 100 1000

7 / 13

SLIDE 10

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

How much energy is lost ?

In previous slide, constant energy loss for a jet without VLEs: Eg ∝ ωbr ≡ α2

sωc

Not realistic ! pT ր ⇒ phase space for in-medium VLEs ր ⇒ more sources for energy loss ... and RAA for the Njets normalized zg distribution ! [E → E(zpT)]

0.8 0.85 0.9 0.95 1 1.05 0.1 0.2 0.3 0.4 0.5 pT0,gluon=1 T eV

q ^

=1.5 GeV2/fm, L=4 fm

anti-kt(R=0.4), SD(β=0,zcut=0.1) [mMDT], θg>0.1

R(zg) zg Njets-norm zg distribution - high-pT jets MC ε=εfit(pT) ε=16.5 GeV 10 20 30 40 50 60 70 2 5 20 50 200 500 10 100 1000

anti-kt(R=0.4) anti-kt(R=0.4) θmax=R, k⊥,min=0.25 GeV θmax=R, k⊥,min=0.25 GeV

q ^

=1.5 GeV/fm2

q ^

=1.5 GeV/fm2

L=4 fm L=4 fm αs=0.24 αs=0.24 gluon gluon average energy loss [GeV] pT0 [GeV] average energy loss - pT0 dependence MIEs only MIEs+VLEs

21.4+10.6 log(pT0/ωc)+1.46 log2(pT0/ωc)

10 20 30 40 50 60 70 2 5 20 50 200 500 10 100 1000

7 / 13

SLIDE 11

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

Low pT regime zcutpT ωc: intrajet medium-induced emissions

At low pT, the energy loss shift effect remains. Contradiction with the data ? No, because there is another effect: SD can select relatively hard medium-induced emissions remaining inside the jet cone.

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 anti-kt(R=0.4), pT∈[80,120] GeV, |η|<0.5 q ^ = 1.5 GeV2/fm, L = 4fm, αs=0.24 SD(β=0,zcut=0.1) [mMDT], θg>0.1 Ratio PbPb/pp zg zg distribution - normalized by 1/Njets MC - √s=5.02 T

eV

MC - incoherent energy loss only

ALICE Collaboration, 2018

8 / 13

SLIDE 12

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

Analytical insight

For MIEs, emission probability is: Baier, Dokshitzer, Mueller, Peign´

e, and Schiff; Zakharov 1996–9

d2PMIE = αsCR π

2ωc

pT dz z3/2 × Pbroad(z, θ)dθ

Gaussian-like broadening distribution

⇒ more singular at small z than the vacuum splitting function.

9 / 13

SLIDE 13

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

Analytical insight

The zg distribution without energy loss shift is enhanced by a medium-induced term: 1 Njets dN dzg = 1 Njets dN dzg |vac + R

θcut

dθg ∆VLE

i

(R, θg)∆MIE

i

(R, θg)

no emission with z>zcut between R and θg

(1 + ν)d2PMIE dzgdθg Multiplicity factor 1 + ν because each VLE inside the medium can further radiate a MIE. With the energy loss shift, one has to relate the physical z to the measured zg as before. zg = zpT − Eg pT − Eg − Ei

9 / 13

SLIDE 14

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

Parton with fixed pT,0

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 √s=5.02 T eV, anti-kt(R=0.4) √s=5.02 T eV, anti-kt(R=0.4) q ^

=1.5 GeV/fm2, L=4 fm, αs=0.24

q ^

=1.5 GeV/fm2, L=4 fm, αs=0.24

θmax=R, k⊥,min=0.25 GeV θmax=R, k⊥,min=0.25 GeV

quark R(zg) zg Njets-norm zg distribution: pT0 dependence pT0=100 GeV pT0=200 GeV pT0=500 GeV pT0=1000 GeV 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

q ^

=1.5 GeV/fm2, L=4 fm, αs=0.24

q ^

=1.5 GeV/fm2, L=4 fm, αs=0.24

solid: VLEs+MIEs solid: VLEs+MIEs dashed: VLEs dashed: VLEs quark analytic R(zg) zg Njets-norm zg distribution: pT0 dependence pT0=100 GeV pT0=200 GeV pT0=500 GeV pT0=1000 GeV

Transition low pT → high pT Qualitative agreement between MC and analytical calculations. Competitive effect between small zg peak and energy loss effect. Chang, Cao, Qin 2018

10 / 13

SLIDE 15

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

Results with initial jet spectrum

Bias due to the steeply falling spectrum.

Self-norm zg distribution - CMS-like setup 0.8 0.9 1 1.1 1.2 0.1 0.2 0.3 0.4 0.5 140<pT<160 GeV θg>0.1 R(norm)(zg) zg 0.8 0.9 1 1.1 1.2 160<pT<180 GeV zcut=0.1 R(norm)(zg) 0.8 0.9 1 1.1 1.2 180<pT<200 GeV β=0 R(norm)(zg) 0.8 0.9 1 1.1 1.2 200<pT<250 GeV anti-kt(R=0.4) R(norm)(zg) 0.8 0.9 1 1.1 1.2 250<pT<300 GeV R(norm)(zg) 0.8 0.9 1 1.1 1.2 300<pT<500 GeV R(norm)(zg) (2.0, 4, 0.20) (2.0, 3, 0.29) (1.5, 4, 0.24) (1.5, 3, 0.35)

CMS Collaboration, 2017

11 / 13

SLIDE 16

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

Correlating θg and RAA

Transition between incoherent and coherent energy loss for θg ∼ θc Our Monte-Carlo results for RAA displayed in bins of θg. Possible hint of θc in the data.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 200 500 100 1000

αs=0.24 αs=0.24 q ^

=1.5 GeV2/fm

q ^

=1.5 GeV2/fm

L=4 fm L=4 fm

SD(β=0,zcut=0.1) [mMDT] SD(β=0,zcut=0.1) [mMDT] √s=5.02 T eV, 0-10% cent., anti-kt(R=0.4), |y|<2.5

RAA pT,jet [GeV] Dependence of RAA on θg all jets θg<0.03 0.03<θg<0.1 0.1<θg<0.2 0.2<θg<0.3 0.3<θg 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 200 500 100 1000

12 / 13

SLIDE 17

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

Summary

Take-home messages Energy loss incrases with jet pT, due to a rise in the number of partonic sources via VLEs ⇒ explain both the RAA for jet cross section and zg in the high pT regime. zg distribution in the low pT regime controlled by the incoherent energy loss and medium induced emissions inside jets. Importance of the normalization to Njets in order to capture the bias induced by the initial steeply falling spectrum. Other results nSD distribution: number of splittings selected by iterated SD (see back-up). Fragmentation function from our pQCD factorized picture: MC and analytic results.

13 / 13

SLIDE 18

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

THANK YOU !

13 / 13

SLIDE 19

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

nSD predictions

0.5 1 1.5 2 2.5 1 2 3 4 5 6 7

q ^ =1.5 GeV2/fm, L=4 fm, αs=0.24 √s=5.02 T eV, anti-kt(R=0.4) 130<pT,jet<200 GeV, |y|<0.5 SD(β=0,zcut=0.1) [mMDT]

Ratio PbPb/pp nSD nuclear effects on the nSD distribution medium (full) medium (incoherent energy loss only)

Comment Contrary to the zg distribution, this observable is mostly sensitive to the energy loss: no qualitative difference when intrajet medium-induced emissions are included.

13 / 13

SLIDE 20

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

Quark vs gluon energy loss - pT,0 dependence

10 20 30 40 50 60 70 2 5 20 50 200 500 10 100 1000

anti-kt(R=0.4) anti-kt(R=0.4) θmax=R, k⊥,min=0.25 GeV θmax=R, k⊥,min=0.25 GeV

q ^

=1.5 GeV/fm2

q ^

=1.5 GeV/fm2

L=4 fm L=4 fm αs=0.24 αs=0.24 gluon gluon average energy loss [GeV] pT0 [GeV] average energy loss - pT0 dependence MIEs only MIEs+VLEs

21.4+10.6 log(pT0/ωc)+1.46 log2(pT0/ωc)

10 20 30 40 50 60 70 2 5 20 50 200 500 10 100 1000 5 10 15 20 25 30 35 2 5 20 50 200 500 10 100 1000

anti-kt(R=0.4) anti-kt(R=0.4) θmax=R, k⊥,min=0.25 GeV θmax=R, k⊥,min=0.25 GeV

q ^

=1.5 GeV/fm2

q ^

=1.5 GeV/fm2

L=4 fm L=4 fm αs=0.24 αs=0.24 quark quark average energy loss [GeV] pT0 [GeV] average energy loss - pT0 dependence MIEs only MIEs+VLEs

11.6+5.0 log(pT0/ωc)+0.63 log2(pT0/ωc)

5 10 15 20 25 30 35 2 5 20 50 200 500 10 100 1000 13 / 13

SLIDE 21

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

Quark vs gluon energy loss - R dependence

10 20 30 40 0.2 0.4 0.6 0.8 1

anti-kt(R=0.4), θmax=R, k⊥,min=0.25 GeV anti-kt(R=0.4), θmax=R, k⊥,min=0.25 GeV pT0=200 GeV pT0=200 GeV

q ^

=1.5 GeV/fm2

q ^

=1.5 GeV/fm2

L=4 fm L=4 fm αs=0.24 αs=0.24 gluon gluon average energy loss [GeV] R average energy loss - R dependence MIEs only MIEs+VLEs 10.2+4.0/√R 10 20 30 40 0.2 0.4 0.6 0.8 1 5 10 15 20 0.2 0.4 0.6 0.8 1

anti-kt(R=0.4), θmax=R, k⊥,min=0.25 GeV anti-kt(R=0.4), θmax=R, k⊥,min=0.25 GeV pT0=200 GeV pT0=200 GeV

q ^

=1.5 GeV/fm2

q ^

=1.5 GeV/fm2

L=4 fm L=4 fm αs=0.24 αs=0.24 quark quark average energy loss [GeV] R average energy loss - R dependence MIEs only MIEs+VLEs 4.6+1.7/√R 5 10 15 20 0.2 0.4 0.6 0.8 1 13 / 13

SLIDE 22

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs 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.

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

−

R

θg

dθ 1/2 dzPi,MIE(z, θ)Θ(z − zcut)

13 / 13

SLIDE 23

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

zg distribution, pQCD calculation in PbPb

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.

13 / 13

SLIDE 24

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

In-medium VLEs multiplicity

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

=1.5 GeV/fm2, L=4 fm

average multiplicity pT0 [GeV] average in-medium multiplicity MC result DLA result

13 / 13

SLIDE 25

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

zg distribution for gluon jets with fixed pT,0

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

√s=5.02 T eV, anti-kt(R=0.4) √s=5.02 T eV, anti-kt(R=0.4) q ^

=1.5 GeV/fm2, L=4 fm, αs=0.24

q ^

=1.5 GeV/fm2, L=4 fm, αs=0.24

θmax=R, k⊥,min=0.25 GeV θmax=R, k⊥,min=0.25 GeV

gluon

R(zg) zg Njets-norm zg distribution: pT0 dependence pT0=100 GeV pT0=200 GeV pT0=500 GeV pT0=1000 GeV 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

q ^

=1.5 GeV/fm2, L=4 fm, αs=0.24

q ^

=1.5 GeV/fm2, L=4 fm, αs=0.24

solid: VLEs+MIEs solid: VLEs+MIEs dashed: VLEs dashed: VLEs

gluon analytic

R(zg) zg Njets-norm zg distribution: pT0 dependence pT0=100 GeV pT0=200 GeV pT0=500 GeV pT0=1000 GeV 13 / 13

SLIDE 26

Introduction High pT regime: energy loss only Low pT regime: energy loss and MIEs Conclusion

zg distribution: sensitivity to uncontrolled parameters

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) √s=5.02 T eV, anti-kt(R=0.4) q ^

=1.5 GeV/fm2, L=4 fm, αs=0.24

q ^

=1.5 GeV/fm2, L=4 fm, αs=0.24

θmax=1 (0.75,1.5), k⊥,min=0.25 (0.15,0.5) GeV θmax=1 (0.75,1.5), k⊥,min=0.25 (0.15,0.5) GeV R(zg) zg Njets-norm zg distribution: pT,jet dependence pT,jet>100 GeV pT,jet>200 GeV pT,jet>500 GeV pT,jet>1000 GeV

13 / 13