Aunifiedpictureforin-mediumjetevolutioninpQCD Edmond...
Transcript of Aunifiedpictureforin-mediumjetevolutioninpQCD Edmond...
A unified picture for in-medium jet evolution in pQCD
Edmond IancuIPhT Saclay & CNRS
with P. Caucal, A. H. Mueller and G. Soyez (PRL 120 (2018) 232001 + w.i.p.)
June 19, 2013
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fixing ωc
θmax=1, kt,min=0.25 GeVθmax=1, kt,min=0.25 GeVanti-kt(R=0.4), |y|<2.8anti-kt(R=0.4), |y|<2.8
solid: q̂ =1.5, L=4, α- s=0.25solid: q̂ =1.5, L=4, α- s=0.25dashed: q̂ =2.67, L=3, α- s=0.25dashed: q̂ =2.67, L=3, α- s=0.25dotted: q̂ =0.96, L=5, α- s=0.25dotted: q̂ =0.96, L=5, α- s=0.25
R AA
pt [GeV]
nuclear modification factor RAA
ATLASours
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 1 / 23
Outline
Jet evolution in a quark-gluon plasma at weak coupling
Two types of radiation...
vacuum-like: bremsstrahlung (parton virtualities)
medium-induced radiation : BDMPS-Z (collisions in the plasma)
... which are separately well understood
They can be factorized within controlled approximations in pQCD
The “vacuum-like” radiation too is modified by the medium(constraints on the associated phase-space)
Probabilistic picture allowing for Monte-Carlo implementation
Encouraging preliminary results (jet RAA, fragmentation function)
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 2 / 23
Jet evolution in a quark-gluon plasma
The leading particle (LP) is produced by a hard scattering
It subsequently evolves via radiation (branchings) ...
Bremsstrahlung triggered by the parton virtualities
... and via collisions off the medium constituents, leading to...
transverse momentum broadening: ∆k2⊥ ' q̂∆t
additional, medium-induced, radiation
wash out the colour coherence (destroy interference pattern)JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 3 / 23
Jet evolution in a quark-gluon plasma
The leading particle (LP) is produced by a hard scattering
It subsequently evolves via radiation (branchings) ...
Bremsstrahlung triggered by the parton virtualities
... and via collisions off the medium constituents, leading to...
transverse momentum broadening: ∆k2⊥ ' q̂∆t
additional, medium-induced, radiation
wash out the colour coherence (destroy interference pattern)JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 3 / 23
Jets in the vacuum
tf 'ω
k2⊥' 1
ωθ2
dP ' αsCRπ
dω
ω
dθ2
θ2
Formation time tf : the time it takes the daughter partons to lose theirquantum coherence (overlap in transverse direction)
Determined by the virtuality Q2 of the original parton: tf ∼ E/Q2
Log enhancement for soft (ω � E) and collinear (θ � 1) gluons
Parton cascades: successive emissions are ordered in
energy (ωi < ωi−1), by energy conservation
angle (θi < θi−1), by color coherence
Double-logarithmic approximation (DLA): strong double ordering
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 4 / 23
Lund plot for vacuum emissions at DLA
Strong ordering in both energies and angles:[αs ln(E/ω) ln(θ̄/θ)
]nE � ω1 � ω2 � · · · � ω & θ̄ � θ1 � θ2 � · · · � θ
θ̄: the maximal angle allowed for the first emission
Each emission (ωi, θi): a point in the phase-space diagram
E
ω4
ω3
ω2
ω1
θ1
θ2 θ3
θ4
θ̄
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ω [GeV]
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θ
(ω1, θ1)
(ω2, θ2)
(ω3, θ3)
(ω4, θ4)
(E, θ̄)
k 2⊥=ω2θ 2
=Λ2
VACUUM PHASE SPACE
Evolution stopped by hadronisation: k⊥ ' ωθ & ΛQCD
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 5 / 23
Medium-induced radiation
In medium: collisions introduce a lower limit on the transverse momentum ...
tf =ω
k2⊥
& k2⊥ & q̂tf
tf .√ω
q̂
... hence an upper limit on the formation time !
Effective only so long as tf < L (medium size), hence for ω ≤ ωc ≡ q̂L2
Two types of emissions occurring inside the medium (tf < L):
vacuum-like: k2⊥ � q̂tf , or tf �
√ω/q̂
medium-induced: k2⊥ ' q̂tf , or tf '
√ω/q̂
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 6 / 23
Mini-jets from multiple branching
dP ∼ αsdω
ω
L
tf(ω)∼ αs
√q̂L2
ω
dω
ω(BDMPS-Z)
Multiple branching becomes important when ω . ωbr ≡ α2s q̂L
2
Soft primary gluons with ω . ωbr occur event by event
In turn, they generate mini-jets via democratic branchings: x ∼ 1−x
energy transmitted to many soft quanta which thermalize: ω ∼ Ttypical energy loss by the jet ∆E ∼ ωbr, large fluctuations
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 7 / 23
Mini-jets from multiple branching
dP ∼ αsdω
ω
L
tf(ω)∼ αs
√q̂L2
ω
dω
ω(BDMPS-Z)
Multiple branching becomes important when ω . ωbr ≡ α2s q̂L
2
Soft primary gluons with ω . ωbr occur event by event
Energy loss at large angles: a natural explanation for di-jet asymmetry
J.-P. Blaizot, E. I., Y. Mehtar-Tani, PRL 111, 052001 (2013)JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 7 / 23
Intra-jet nucler modifications
Medium-induced radiation propagates at large angles, outside the jet cone
The LHC data also show nuclear modifications for the energy distributioninside the jet cone
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Can vacuum-like radiation be modified by the medium ?
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 8 / 23
Vacuum-like emissions (VLE)P. Caucal, E.I., A. H. Mueller and G. Soyez, arXiv:1801.09703 (PRL)
A jet initiated by a colorless qq̄ antenna (decay of a boosted γ or Z)
just to simplify the arguments about color coherence
The antenna propagates through the medium along a distance L
Emissions (tf = 1ωθ2 ) can occur either inside (tf ≤ L), or outside (tf > L)
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 9 / 23
VLEs inside the medium
For ω ≤ ωc, the medium introduces an upper limit on tf :
tf .√ω
q̂≤ L
No emission within the range√ω
q̂<
1
ωθ2< L
End point of VETOED at
ωc = q̂L2 , θc =1√q̂L3
VLEs in medium occur like in vacuum, but with a smaller phase-space
typical values: q̂ = 1 GeV2/fm, L = 4 fm, ωc = 50 GeV, θc = 0.05
Energy loss & p⊥-broadening during formation are negligible
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 10 / 23
Color (de)coherence
In vacuum, wide angle emissions (θ > θqq̄) are suppressed by color coherence
the gluon has overlap with both the quark and the antiquark
In medium, color coherence is washed out by collisions after a time tcoh
q̂∆t &1
(θqq̄∆t)2=⇒ ∆t & tcoh =
1
(q̂θ2qq̄)
1/3
(Mehtar-Tani, Salgado, Tywoniuk; Casalderrey-Solana, E. I., 2010–12)
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 11 / 23
Color (de)coherence
In vacuum, wide angle emissions (θ > θqq̄) are suppressed by color coherence
the gluon has overlap with both the quark and the antiquark
In medium, color coherence is washed out by collisions after a time tcoh
tcoh =1
(q̂θ2qq̄)
1/3� L if θqq̄ � θc ' 0.05
Angular ordering could be violated for emissions inside the medium
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 11 / 23
Angular ordering strikes back
But this is not the case for the VLEs !
θ > θqq̄ & tf =1
ωθ2> tcoh =⇒ tf &
√ω
q̂: not a VLE
Wide angle VLEs (θ > θqq̄) have tf � tcoh, hence they are suppressed
Emissions at smaller angles (θ < θqq̄) can occur at any time
Color decoherence via collisions plays no role for the VLEsJETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 12 / 23
Vacuum-like cascades at DLA
Previous arguments extend to a sequence of angular-ordered VLEs
rigorous in the double-logarithmic approximation
Formation time for the cascade ≈ that of the last gluon
a typical VL cascade has a formation time � L
After formation, gluons propagate in the medium along a distance ∼ Ladditional sources for medium-induced radiation... and for vacuum-like emissions outside the medium
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 13 / 23
First emission outside the medium
The respective formation time is necessarily large: tf & L
In-medium sources with θ � θc lose coherence in a time tcoh � L
First outside emission can violate angular ordering
re-opening of the angular phase-space
Subsequent “outside” emissions obey angular-ordering, as usual
Vetoed region + lack of angular-ordering for the first “outside” emission
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 14 / 23
Gluon distribution at DLA
Double differential distribution in energies and emission angles:
T (ω, θ) ≡ ωθ2 d2N
dωdθ2
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T/Tvac
E = 200 GeV, θqq̄ = 0.4
q̂ = 2 GeV2/fm, L = 3 fm
T/Tvac = 0 in the excluded region
T/Tvac = 1 inside the medium andalso for ω > ωc and any θ
T/Tvac < 1 outside the mediumat small angles . θc
T/Tvac > 1 outside the mediumat large angles ∼ θqq̄
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 15 / 23
Jet fragmentation function at DLA
D(ω) ≡ ωdN
dω=
∫ θ2qq̄
Λ2/ω2
dθ2
θ2T (ω, θ)
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T/Tvac
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Slight suppression at intermediate energies (from 3 GeV up to ωc)
the phase-space is reduced by the vetoed regionthe amount of suppression increases with L and q̂
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 16 / 23
Jet fragmentation function at DLA
D(ω) ≡ ωdN
dω=
∫ θ2qq̄
Λ2/ω2
dθ2
θ2T (ω, θ)
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Significant enhancement at low energy (below 2 GeV)
reopening of the phase-space by the first emission outside the medium
Related proposal by Mehtar-Tani and Tywoniuk, arXiv:1401.8293JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 16 / 23
Monte Carlo implementation(P. Caucal, E.I., A. H. Mueller and G. Soyez, in preparation)
So far, conceptually simple, but DLA approximations are very crude:
no energy conservation (small-x, gluons only), fixed couplingno k⊥-broadening, no medium-induced radiation
Factorization remains true when assuming strong angular ordering alone
Probabilistic (Markovian) description separately for
vacuum-like parton cascades with angular orderingmedium-induced cascades with BDMPS-Z branching rates
MC implementation: convolution of three showers:
vacuum cascade inside the medium but outside the vetoed regionmedium-induced cascade (in energy)vacuum cascade outside the medium, down to the hadronisation line
Leading parton selected according to the cross-section for pp→ 2 partons
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 17 / 23
Monte Carlo implementation(P. Caucal, E.I., A. H. Mueller and G. Soyez, in preparation)
So far, conceptually simple, but DLA approximations are very crude:
no energy conservation (small-x, gluons only), fixed couplingno k⊥-broadening, no medium-induced radiation
Leading-logarithmic approximation (angular ordering), with obvious benefits
full splitting functions, running coupling, quarks and gluons, Nc = 3
Gaussian k⊥-broadening ascribed by handreconstruction of the geometry in 3 dimensionsenergy loss: partons with angles θ > θ̄ are leaving the jetno angular ordering for the first emission outside the mediumall the partons inside the medium can act as sources for it
Not yet fully realistic for phenomenology:over-simplified medium description: no expansion, no hydro, just q̂no hadrons, just partons
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 17 / 23
MC: preliminary results
Focus on 2 observables:
nuclear modification factor RAAratio of FFs in AA and pp
Various choices for q̂, L and αs,med
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 18 / 23
Medium-induced radiation alone
Initial parton with energy E ≡ pt0 generating a medium-induced cascade
Left: fragmentation function (or spectrum) D(ω) = ω dNdω
pronounced leading-particle peak so long as E � ωs = α2sωc
BDMPS-Z spectrum D(ω) ∝ 1√ωat ω < ωc
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JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 19 / 23
Medium-induced radiation alone
Initial parton with energy E ≡ pt0 generating a medium-induced cascade
Right: average energy loss by the jet + its fluctuations
〈∆E〉 becomes independent of E when E � ωs
sizeable dependence upon the jet opening angle for R ≤ 0.8
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JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 19 / 23
Boldly adding the data: RAA
Not a fit: just a set of “reasonable” values for the physical parameters
“Uncontrolled parameters” = kinematical cuts: kt,min ≡ Λ, θmax ≡ θ̄
results are remarkably robust
Right plot: RAA depends upon the medium only via ωc = q̂L2/2
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nuclear modification factor RAA
ATLASours
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R AA
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nuclear modification factor RAA
ATLASours
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 20 / 23
Boldly adding the data: RAA
Not a fit: just a set of “reasonable” values for the physical parameters
Left plot: fixing θc, that is, the product q̂L3
results are changing, as expected
Right plot: RAA depends upon the medium only via ωc = q̂L2/2
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nuclear modification factor RAA
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solid: q̂ =1.5, L=4, α- s=0.25solid: q̂ =1.5, L=4, α- s=0.25dashed: q̂ =2.67, L=3, α- s=0.25dashed: q̂ =2.67, L=3, α- s=0.25dotted: q̂ =0.96, L=5, α- s=0.25dotted: q̂ =0.96, L=5, α- s=0.25
R AA
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nuclear modification factor RAA
ATLASours
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 20 / 23
Boldly adding the data: FragmentationThe same “canonical” values for the medium parameters as in the “best”description of RAA (ATLAS data from arXiv:1805.05424)
Fixing ωc = q̂L2/2: very small variations (except at very low z)
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JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 21 / 23
Boldly adding the data: FragmentationThe same “canonical” values for the medium parameters as in the “best”description of RAA (ATLAS data from arXiv:1805.05424)
Fixing θc, that is, q̂L3: very small variations as well ...
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200 < pt < 251 GeV200 < pt < 251 GeV
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ATLASours
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251 < pt < 316 GeV251 < pt < 316 GeV
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ATLASours
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0.005 0.02 0.05 0.2 0.5 0.01 0.1 1
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variations at fixed θc
anti-kt(R=0.4), |y|<2.1
θmax=1, kt,min=0.25 GeV
solid: q̂ =1.5, L=4, α- s=0.25dashed: q̂ =3.56, L=3, α- s=0.25dotted: q̂ =0.77, L=5, α- s=0.25
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ATLASours
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 21 / 23
Boldly adding the data: FragmentationThe same “canonical” values for the medium parameters as in the “best”description of RAA (ATLAS data from arXiv:1805.05424)
Equally good results when plotted as a function of the constituent pt ...
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ATLASours
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ATLASours
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ATLASours
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2 5 20 50 200 1 10 100
316 < pt < 398 GeV316 < pt < 398 GeV
variations at fixed ωc
anti-kt(R=0.4), |y|<2.1
θmax=1, kt,min=0.25 GeV
solid: q̂ =1.5, L=4, α- s=0.25dashed: q̂ =2.67, L=3, α- s=0.25dotted: q̂ =0.96, L=5, α- s=0.25
ratio
PbP
b/pp
pt [GeV]
ATLASours
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 21 / 23
Boldly adding the data: FragmentationThe same “canonical” values for the medium parameters as in the “best”description of RAA (ATLAS data from arXiv:1805.05424)
... but stronger variability with respect to the “uncontrolled parameters” :
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ATLASours
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ATLASours
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ATLASours
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251 < pt < 316 GeV251 < pt < 316 GeV
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z
ATLASours
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0.005 0.02 0.05 0.2 0.5 0.01 0.1 1
316 < pt < 398 GeV316 < pt < 398 GeV
varying uncontrolled parameters
anti-kt(R=0.4), |y|<2.1
q̂ =1.5, L=4, α- s=0.25
solid: θmax=1, kt,min=0.25 GeVdashed: vary kt,min (0.15, 0.2, 0.35, 0.5)dotted: vary θmax (0.75, 1.5)
ratio
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b/pp
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ATLASours
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 21 / 23
Conclusions & perspectives
Vacuum-like emissions inside the medium can be factorized from themedium-induced radiation via systematic approximations in pQCD
Medium effects enter already at leading-twist level :
reduction in the phase-space for VLEs inside the medium
violation of angular ordering by the first emission outside the medium
Angular ordering is preserved for VLEs inside the medium, like in the vacuum
VLEs inside the medium act as sources for medium-induced radiation
Probabilistic picture, well suited for Monte-Carlo implementations
Preliminary MC results, which look promising
qualitative and even semi-quantitative agreement with the LHC datafor jet fragmentation and the nuclear modification factor
Perspectives: more realistic description of the medium, implementation inJETSCAPE
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 22 / 23
MC: preliminary results (2)
“No quenching”: just VLEs
no energy loss: RAA = 1
suppression in FF at small ξ
“No decoherence”: strict angular ordering(including first “outside” emission)
no effect on energy loss (RAA)
little enhancement at small ξ
“Quenching before VLEs”: no VLEsinside the medium
RAA larger & increasing with pT,jet
Partons created inside the medium via medium-induced emissionssignificantly contribute to the soft radiation outside the medium
JETSCAPE, Texas A&M, Jan 2019 In-medium jet evolution in pQCD Edmond Iancu 23 / 23