G ENERATING FUNCTIONAL FOR QUENCHED OBSERVABLES Konrad Tywoniuk - - PowerPoint PPT Presentation

GENERATING FUNCTIONAL

FOR QUENCHED OBSERVABLES

Konrad Tywoniuk

COST Workshop on Interplay of hard and soft QCD probes for collectivity in heavy-ion collisions 25 Feb - 1 Mar 2019, Lund

• K. Tywoniuk (UiB)

INTRODUCTION

• jet quenching: suppression & modification of hard

probes wrt vacuum (pp) baseline

• unique observables to extract properties of the

medium

• motivation: theoretical guidance at high-pT
• what drives quenching & substructure

modifications?

• 2

• K. Tywoniuk (UiB)

MAPPING THE SPLITTINGS

• 3

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ ln 1/θ

Kinematical Lund diagram

ρ = 2αsCR π

1 ER2 ⌧ tf ⌧ ER Q2

Andersson, Gustafson, Lönnblad, Pettersson Z.Phys.C (1989) Dokshitzer, Khoze, Mueller, Troyan “Basics of Perturbative QCD” (1991)

• K. Tywoniuk (UiB)

MAPPING THE SPLITTINGS

• 3

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ ln 1/θ

1

tf,1

tf,1

Kinematical Lund diagram

ρ = 2αsCR π

1 ER2 ⌧ tf ⌧ ER Q2

Andersson, Gustafson, Lönnblad, Pettersson Z.Phys.C (1989) Dokshitzer, Khoze, Mueller, Troyan “Basics of Perturbative QCD” (1991)

• K. Tywoniuk (UiB)

MAPPING THE SPLITTINGS

• 3

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ ln 1/θ

1

tf,1

tf,1

2

tf,2

tf,2

Kinematical Lund diagram

ρ = 2αsCR π

1 ER2 ⌧ tf ⌧ ER Q2

Andersson, Gustafson, Lönnblad, Pettersson Z.Phys.C (1989) Dokshitzer, Khoze, Mueller, Troyan “Basics of Perturbative QCD” (1991)

• K. Tywoniuk (UiB)

MAPPING THE SPLITTINGS

• 3

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ ln 1/θ

1

tf,1

tf,1

2

tf,2

tf,2

3

tf,3

tf,3

Kinematical Lund diagram

ρ = 2αsCR π

1 ER2 ⌧ tf ⌧ ER Q2

Andersson, Gustafson, Lönnblad, Pettersson Z.Phys.C (1989) Dokshitzer, Khoze, Mueller, Troyan “Basics of Perturbative QCD” (1991)

• K. Tywoniuk (UiB)

MAPPING THE SPLITTINGS

• 3

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ ln 1/θ

1

tf,1

tf,1

2

tf,2

tf,2

3

tf,3

tf,3

Kinematical Lund diagram

ρ = 2αsCR π

zθE = Q0

hadronization

∼ 10 fm

1 ER2 ⌧ tf ⌧ ER Q2

Andersson, Gustafson, Lönnblad, Pettersson Z.Phys.C (1989) Dokshitzer, Khoze, Mueller, Troyan “Basics of Perturbative QCD” (1991)

• K. Tywoniuk (UiB)

MEDIUM LENGTH AS PERTURBATIVE SCALE

• 4

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ

tf > L

tf < L

(PS)inside = ¯ α 4 ln2 pTR2L

• <latexit sha1_base64="FHyouvtxkS5iwRF+02eo1X43X80=">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</latexit><latexit sha1_base64="FHyouvtxkS5iwRF+02eo1X43X80=">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</latexit><latexit sha1_base64="FHyouvtxkS5iwRF+02eo1X43X80=">ACW3icbVHBbtNAEF27QIMpkI4cVkRUaWXyA6V4IJUwYUDhwBNWykbovF6nKy6Xlu74rI8k9ygO/gtgkPkDLk3b19GaeZvZtWmnlKI5/BuHenbv39nv3owcHDx897h8+OXdlbSVOZalLe5mCQ60MTkmRxsvKIhSpxov06v2mfnGN1qnSnNG6wnkBS6NyJYG8tOjboSD8Rs3kS3u82FlnMqw5UdvucgtyEakYLkAXa2gbU5aLrT5OvY35jSsOtNZyz978aOwarmiYy5EdMQbsV2wsZh5l1MFfzUat4v+IB7FW/DbJOnIgHWYLPrfRVbKukBDUoNzsySuaN6AJSU1tpGoHVYgr2CJM08NFOjmzXZ0y196JeN5af0xLfq34GCufWReo7C6CVu1nbiP+rzWrK38x9WFVNaORuUF5rTiXfBM0zZVGSXnsC0iq/K5cr8HmS/47Ih5DcfPJtcj4eJZ5/Ohmcvuvi6LHn7AUbsoS9ZqfsA5uwKZPsB/sd7Ae94Fe4F0bhwa41DrPU/YPwmd/ADN5s8A=</latexit><latexit sha1_base64="FHyouvtxkS5iwRF+02eo1X43X80=">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</latexit>

(PS)outside = ¯ α 2 ln2 ✓pTR Q0 ◆ − (PS)inside

Large ~O(1) probability of multiple splitting inside the medium.

Andrews et al. arXiv:1808.03689 Dreyer, Salam, Soyez 1807.04758 Chien, Elayavalli arXiv:1803.03589 Cunqueiro, Płoskoń arXiv:1812.00102

Medium interactions will impose new scales one the plane.

• K. Tywoniuk (UiB)

COMPUTING QUENCHED OBSERVABLES

• 5

quenching factor = nuclear modification factor

Rjet = ✓dσmed dp2

Tdy

◆ . ✓ dσvac dp2

Tdy

◆

quenching weight: probability distribution of losing energy

dmed dp2

Tdy =

Z ∞ d✏ P(✏)dvac(pT + ✏) dp2

Tdy

Rjet ∼ ˜ P

• n/pT
• ≡ Q(pT)

quenching factor is Laplace transform of energy loss probability

✏/pT ⌧ 1

For and large :

n

1 (pT + ✏)2 ≈ 1 pn

T

e−✏n/pT

n

˜ P(⌫) = Z ∞ d✏ e−⌫✏P(✏)

• K. Tywoniuk (UiB)

QUENCHING OF SINGLE PARTON

• 6
• form factor suppression

related to multiplicity of virtual gluons

• strong quenching for
• quark ≈ meson (rescaling)

Baier, Dokshitzer, Mueller, Schiff JHEP 0109 (2001) 033 100 1000 p 0.2 0.4 0.6 0.8 1 1.2

R

Quark energy loss Jet energy loss (incoherent approx.) Jet energy loss - R=0.4

T

jet

[GeV]

“hadron”

Q(pT) ∼ e−N(ω>pT/n)

pT ⌧ n¯ α2ˆ qL2

Q(pT) = e−2¯

αL√ nπˆ q/pT

Wavy lines: medium induced gluons generated via the rate in time

dN dω dt = ¯ α r ˆ q ω3

• K. Tywoniuk (UiB)

NEIGHBORING JET ENERGY LOSS

• 7
• Y. Mehtar-Tani, KT arXiv:1706.06047 [hep-ph]

contributions from interferences total color charge

P2(ν) = P(ν)×Psing(ν)

• K. Tywoniuk (UiB)

NEIGHBORING JET ENERGY LOSS

• 7
• Y. Mehtar-Tani, KT arXiv:1706.06047 [hep-ph]

contributions from interferences total color charge

P2(ν) = P(ν)×Psing(ν)

• K. Tywoniuk (UiB)

NEIGHBORING JET ENERGY LOSS

• 7
• Y. Mehtar-Tani, KT arXiv:1706.06047 [hep-ph]

contributions from interferences total color charge

S2(t) = exp  −1 4 Z t ds ˆ q(x12, t)x2

12(s)

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decoherence parameter

color randomization of a qq

̄ pair

Mehtar-Tani, Salgado, KT PLB (2012), JHEP (20132; Casalderrey, Iancu JHEP (2011)

) ∼ r 1 ˆ qL3 ≡ θc

td ∼ (ˆ qθ12)−1/3

tf td

P2(ν) = P(ν)×Psing(ν)

• K. Tywoniuk (UiB)

LUND PLANE IN MEDIUM

• 8

tbr = (ˆ qθ2)−1/3

θc = (ˆ qL3)−1/2

θL = (pTL)−1/2

td =

• Y. Mehtar-Tani, KT arXiv:1707.07361 [hep-ph]

Caucal, Iancu, Mueller, Sozey PRL (2018) Andrews et al. arXiv:1808.03689

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ

vacuum (in) medium

tf = L

tf = tbr

vacuum (out) non-pert

• K. Tywoniuk (UiB)

SUMMARY: EMERGING PICTURE (DLA)

• 9

“logarithmic” time “linear” time “logarithmic”, non-perturbative Regimes: hard, in-medium radiation energy-loss, broadening fragmentation, hadronization

t1 t2 L ∞

tf < td

td < tf < L

L < tf

…

• K. Tywoniuk (UiB)

GENERATING FUNCTIONAL METHOD

• 10

G(u) = X

n

Pnun

G(u = 1) = 1

Generating function:

Konishi, Ukawa, Veneziano Nucl. Phys. B1567 (1979); Bassetto, Ciafaloni, Marchesini Phys. Rept. 100 (1983) Dokshitzer, Khoze, Mueller, Troyan “Basics of Perturbative QCD” (1991)

Applications to jets

Pn → P(k1, . . . , kn)

un → u(k1) . . . u(kn)

Normalization (conservation of probability) D(x|p, R) ⌘ xdN dx ⌘ x δZ(p, R; u)/δu(x)

• u=1

Z(p, R; u)

• u=1

Fragmentation function

• K. Tywoniuk (UiB)

= +

Zvac

• 1, R
• −

Zvac

• 1 − z, θ
• Zvac
• z, θ
• θ

z 1 − z

Zvac

• 1, R
• z

1 − z

GF IN VACUUM

• 11

MLLA evolution equation

∂ ∂ ln QD(x, θ) = Z 1 dz αs π P(z) [D(x/z, zQ) − zD(x, Q)]

• angular ordering: R > 𝜄 > … > Q0/p (but can build in any)
• Zvac(u=1)=1 from probability conservation

Zvac(p, R; u) = u(p) + Z R dθ θ Z 1 dz αs π P(z) × ⇥ Zvac(zp, θ)Zvac

• (1 − z)p, θ
• − Zvac(p, θ)

⇤

• K. Tywoniuk (UiB)

IMPLEMENTING QUENCHING

• 12

Assume all particles are produced and, subsequently, quenched independently in the medium

dexcl dk1dk2...dkN = Z dp (Z

N

Y

i=1

d✏iP(✏i) ) f(k1 + ✏1, k2 + ✏2, ..., kN + ✏N|p) ⇥(p ✏ k1 k2 ... kN) d dp

• neglect energy-loss compared to typical energies…

Any in-medium, resolved parton is re-weighted by a quenching factor!

⇥

• dp

' ✓Z ∞ d✏P(✏) exp ✓ n✏ pT ◆◆N d0,excl dk1dk2...dkN = Q(p)N d0,excl dk1dk2...dkN . dexcl dk1dk2...dkN

• K. Tywoniuk (UiB)

GF FOR IN-MEDIUM JET EVOLUTION

• decomposes phase space according to scale analysis
• incorporates correctly (small) out-of-cone energy loss
• incorporates loss of coherence (angular ordering) for

particles coming out of the medium (Zout)

• 13

Z(p, R; u) = u(p) + Z R dΩ Θ(tf < td < L) ⇥ (Z(zp, θ) + Zout(zp, R0, θ)) (Z((1 − z)p, θ) + Zout((1 − z)p, R0, θ)) Q2(pT) − Z(p, θ) ⇤ + Z R dΩ

• Θ(td > L) + Θ(td < L < tf)
• [Zvac(zp, θ) Zvac((1 − z)p, θ) − Zvac(p, θ)]

Z R dΩ ≡ Z R dθ θ Z 1 dz αs π P(z)

• Y. Mehtar-Tani, KT (in preparation…)

• K. Tywoniuk (UiB)

SIMPLIFYING THE DISCUSSION

• 14
• consider for the moment the

simpler situation: in or out of the medium

• GF differentiates between two

distinct cases

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ

t

f

= L

• K. Tywoniuk (UiB)

GF CONTRIBUTIONS

• 15

−

Zvac

• 1 − z, θ
• Zvac
• z, θ
• θ

z 1 − z

Zvac

• 1, R
• z

1 − z

Θ(td < L < tf) + Θ(θ < θc)

Fragmentation

• utside the

medium

L

L

… is vacuum-like (AO).

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ

• K. Tywoniuk (UiB)

GF CONTRIBUTIONS

• 16

Θ(tf < td < L)

Zvac

• 1 − z, θ
• Zvac
• z, θ
• θ

z 1 − z −

Zvac

• 1, R
• z

1 − z

×Q2

Z(z, θ)

Z(1 − z, θ)

Z(1, θ)

L

L

Caucal, Iancu, Mueller, Sozey PRL (2018)

• Y. Mehtar-Tani, KT arXiv:1707.07361 [hep-ph]

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ

Fragmentation inside the medium … is vacuum-like (AO). … is quenched.

• K. Tywoniuk (UiB)

GF NORMALIZATION

• 17

Probability is no longer conserved!

Z(p, R; u = 1) = C(p, R)

Non-trivial normalization: collimator function!

C(p, R) = 1 + ¯ α Z R dθ θ Z 1 dz P(z) Θ(tf < td < L) ⇥ ⇥ C(zp, θ) C((1 z)p, θ) Q2(pT) C(p, θ) ⇤

Strong quenching limit 𝑅 ≪ 1 (Sudakov factor): C(pT, R) ' exp  2¯ α ln R θc ✓ ln pT ωc + 2 3 ln R θc ◆

• Y. Mehtar-Tani, KT arXiv:1707.07361 [hep-ph]
• for “in/out” model, the logs are different ➝ sensitivity to coherence

• K. Tywoniuk (UiB)

100 1000 p 0.2 0.4 0.6 0.8 1 1.2

R

Quark energy loss Jet energy loss (incoherent approx.) Jet energy loss - R=0.4

T

jet

[GeV]

“hadron” jet w/coherence jet w/o coherence

SINGLE-INCLUSIVE SPECTRUM

• 18

jet loses energy via total charge & resolved substructure fluctuations

Rjet = Qq(pT) × C(pT, R)

• Y. Mehtar-Tani, KT arXiv:1707.07361 [hep-ph]

• K. Tywoniuk (UiB)

OUTLOOK

• probabilistic setup combining jet & medium

scales

• generating functional
• systematically improvable
• test bed to compare against models & MCs
• collimator function
• non-linear evolution of quenching
• 19

• K. Tywoniuk (UiB)
• 20

2nd Heavy-Ion Jet Substructure Workshop

• new tools for jet physics at the frontiers
• jet substructure and heavy flavor
• splitting maps of the shower
• jet modifications in small systems
• interplay between jets and underlying event
• statistical & machine-learning techniques

13 - 17 May University of Bergen https://jettols.w.uib.no

BACK-UP

• K. Tywoniuk (UiB)

MEDIUM-INDUCED GLUONS

• 22

ω dI dω = αsCR 2π r ˆ qL2 ω

tf = ω k2

⊥

∼ rω ˆ q

modified splitting kinematics

lack of collinear singularity!

hk2

⊥i ⇠ ˆ

qt

momentum broadening

Baier, Dokshitzer, Mueller, Peigné, Schiff (1997-2000); Zakharov (1996);…

θbr(ωc) ∼ r 1 ˆ qL3 ≡ θc

ωc = ˆ qL2

rare, small- angle emission

ωs = ¯ α2ˆ qL2

copious, large- angle emissions

θbr(ωs) ∼ 1 ¯ α3/2 θc

• K. Tywoniuk (UiB)

Z

• 1 − z, θ
• Zout
• z, R′, θ
• θ

z 1 − z L

Θ(tf < td < L)

×Q2

GF CONTRIBUTIONS

• 23

Splitting inside the medium, fragmentation

• utside

ln pT/ωc ln pTR/Qs ln pTR4/3

ˆ q1/3

ln pTR2L

ln 1/R ln 1/θc ln 1/θL

ln 1/z ln 1/θ

Two contributions:

0.1 0.2 0.3 0.4

θ

2 4 6 8 10 12

ω dN/dωdθ

vacuum radiation

medium-induced radiation

α-1

Mehtar-Tani, Salgado, KT PRL 106 (2011) 122002, PLB (2012)

decoherent vacuum radiation coherent vacuum radiation

Z(z, θ)

• K. Tywoniuk (UiB)

TWO-PRONG PROBABILITY

• 24

coherent+BDMPS incoherent

150 200 250 300 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

pT

2(med)/2(vac)

q = 1-2 GeV2/fm L = 5 fm β = 0

• L [fm]

2(incoh)

Mehtar-Tani, KT arXiv:1610.08930

0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.2 0.4 0.6 0.8 1.0

θ12

Q12(E)

γ→q+q

q = 2 GeV2/fm E = 150 GeV αs = 0.3 n = 5-7 L = 5 fm L = 2.5 fm

Casalderrey, Mehtar-Tani, Salgado KT QM2017 proceedings

Choosing two-prong substructure using SoftDrop Non-monotonic behavior indicative of coherence effects! Suggestive: inclusive zg distribution [Andrews et al. (ALICE) QM2018].

θ) 1 dNmed

• dE

dN 2-prong

med

dE ,