Probing QGP transport properties with jet correlations Chen Lin - - PowerPoint PPT Presentation
Probing QGP transport properties with jet correlations Chen Lin IoPP, CCNU, China Opportunities and Challenges with Jets at LHC and Beyond - 2018 in collaboration with: W.Lei, G.Qin, S.Wei, B.Xiao, H.Zhang, Y.Zhang based on: PLB 773(672),
IoPP, CCNU, China
in collaboration with: W.Lei, G.Qin, S.Wei, B.Xiao, H.Zhang, Y.Zhang based on: PLB 773(672), arxiv 1612.04202, arxiv 1803.10533 presented in: HP2016, QM2017, QM2018
In relativistic heavy-ion collision experiments at RHIC(BNL) and LHC(CERN), hard partons produced from hard processes traverse through a hot-dense matter known as the Quark-Gluon Plasma QGP . To study the properties of this QGP , we investigate the modifications it has on these hard partons known as Jets. Two main modifications that the QGP medium has on such jets are: Transverse momentum broadening Jet energy loss Their relation is given by (BDMPS): − dE dx = αsNc 4 ˆ qL, ˆ q ≡ d⟨q2
⊥⟩
dL
BDMPS NPB 483 (1997) 291, 484 (1997) 265, 531 (1998) 403
0.5 1 Event Fraction 0.1 0.2
=7.0 TeV s pp PYTHIA CMS
L dt = 35.1 pb
∫
, R=0.5
T
Anti-k
(a) 0.2 0.4 0.6 0.8 1 Event Fraction 0.1 0.2 20-30% (d) 0.2 0.4 0.6 0.8 1 0.1 0.2
=2.76 TeV
NNs PbPb PYTHIA+DATA
50-100% (b)
Iterative Cone, R=0.5
b µ L dt = 6.7
∫
)
T,2
+p
T,1
)/(p
T,2
T,1
= (p
J
A 0.2 0.4 0.6 0.8 1 0.1 0.2 10-20% (e) 0.2 0.4 0.6 0.8 1 0.1 0.2 30-50% (c)
> 120 GeV/c
T,1
p > 50 GeV/c
T,2
p π 3 2 >
12
φ ∆
0.2 0.4 0.6 0.8 1 0.1 0.2 0-10% (f)
(radians) φ ∆
1 2 3 4
) φ ∆ dN/d(
trigger
1/N
0.4 0.6 0.8 1
centrality 20-60% (radians) φ ∆
1 2 3 4
)-flow φ ∆ dN/d(
trigger
1/N
0.1 0.2
p+p Au+Au, in-plane Au+Au, out-of-plane STAR PRL 90 082302, PRL 93 252301 ATLAS 1011.6182v2, CMS 1102.1957v2
Azimuthal angular decorrelation reflects directly on the transverse momentum broadening effect of the QGP medium, and Dijet momentum imbalance describes an intuitive picture on the energy loss effect experienced by the hard jet through the QGP .
AJ ≡ pleading
⊥
− psub−lead
⊥
pleading
⊥
+ psub−lead
⊥
is an observable reflects directly on the energy imbalance. Signs of energy loss
?
Qualitative analysis (of ∆φ distribution) has been lacking. What did we miss? What is the limitation of pQCD ?
ATLAS PRL 105 252303 D0 PRL 94 221801
J
x 0.10.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
J
x d N d N 1 0.5 1 1.5 2 2.5 3 3.5 4
Preliminary ATLAS 0 - 10 % < 126 GeV
T
p 100 < = 2.76 TeV
NN
s = 0.4 jets, R
t
k anti-
2011 Pb+Pb data, 0.14 nb
J
x 0.10.2 0.3 0.4 0.5 0.6 0.70.8 0.9 1
J
x d N d N 1 0.5 1 1.5 2 2.5 3 3.5 4
60 - 80 % Measured Unfolded
J
x 0.10.2 0.3 0.40.5 0.6 0.7 0.8 0.9 1
J
x d N d N 1 0.5 1 1.5 2 2.5 3 3.5 4
pp
data, 4.0 pb pp 2013
paper published by ATLAS in Quark Matter 2015 shows new fully corrected dijet asymmetry results in both pp and PbPb collisions. Note the large difference between the measured and unfolded result. detector (calorimeter) response fluctuations by UEs
these can cause bin migration in the measured p1,⊥, p2,⊥ distributions.
We now focus on the region close to π. Multi-scale problem: Q2 ≈ p2
⊥ ≫ q2 ⊥
Large logarithm in αs expansion: (αs ln2 p2
⊥ q2 ⊥
)
n
Ideal QCD expansion: σ0
∞
∑
i=0
αi
s (Li + C (i))
σ0
n−1
∑
i=0
αi
sLi
σ0
n−1
∑
i=0
αi
sC (i)
⇐ pQCD σ0
∞
∑
i=n
αi
sLi
σ0
∞
∑
i=n
αi
sC (i)
⇑ ↖ negligible resummation pQCD sums finite αs expansion. resummation (Sudakov) sums Logarithmic terms to all order.
Sun, Yuan, Yuan, PRL 113 232001, PRD 92 (2015) dσ d2q⊥ = σ0 ∑ n 1 n! ∫ d2q1⊥⋯d2qn⊥T(q1⊥)⋯T(qn⊥) ∫ d2p⊥P(p⊥)(2π)2δ(2)(q1⊥ + ⋯ + qn⊥ + p⊥ − q⊥) = σ0 ∫ d2b⊥e−iq⊥⋅b⊥ ˜ P(b⊥)e ˜ T(b⊥)
To sum arbitrary number of soft-gluon emission, we perform integration in b⊥ space, with ˜ T(b⊥) = −Ssudakov ! Sudakov resummation can effectively take into account the soft gluon radiation (parton shower) effect.
2.0 2.2 2.4 2.6 2.8 3.0 2 4 6
∆φ
1 N dN d∆φ
Dijet Angular Correlation at the LHC CMS 0 - 10% ˆ qL = 0 GeV2 ˆ qL = 8 GeV2 ˆ qL = 20GeV2 ˆ qL = 100GeV2 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 2 4 6
∆φ
1 N dN d∆φ
Dijet Angular Correlation at RHIC ˆ qL = 0 GeV2 ˆ qL = 8 GeV2 ˆ qL = 20GeV2
To extract the medium transport coefficient, the vacuum and medium contribution can be considered separately.
l+/q+ l⊥
2
Q2 1
τl = τq Sudakov τl = r0 τl = L qt ^
qL
^
ql0
^ A+B cancel B+C cancel
1/x⊥
2 l⊥
2 = q τl
^
l+/q+ l⊥
2
Q2 1
τl = τq Sudakov τl = r0 τl = L qt ^
qL
^
ql0
^ A+B cancel B + C c a n c e l
1/x⊥
2 B K e v
u t i
l⊥
2 = q τl
^
Mueller, Wu, Xiao, Yuan, 1608.07339, 1604.04250
Different elements receives different one-loop corrections from separated regions in the phase space of the radiated gluon. SAA(Q, b) = Spp(Q, b) + ⟨ˆ qL⟩b2 4 We can see the vacuum Sudakov effect at different kinematic regions: LHC: vacuum Sudakov ≫ medium broadening RHIC: vacuum Sudakov ∼ medium broadening
Dihadron azimuthal angular spectrum: dσ d∆φ = ∑
a,b,c,d ∫ ph1 T dph1 T ∫ ph2 T dph2 T ∫
dzc z2
c
∫ dzd zd
c
∫ b db J0(q⊥ ⋅ b⊥)e−S(Q,b) ⊗ xafa(xa, µ) ⊗ xbfb(xb, µ) ⊗ 1 π dσab→cd dˆ t ⊗ Dc(zc, µ) ⊗ Dd(zd, µ) Sp(Q, b) = ∑
q,g ∫ Q2 µ2 b
dµ2 µ2 [A ln Q2 µ2 + B + D ln 1 R2 ] Bessel’s function of the first kind. Sudakov factor. arXiv:1604.04250 distribution functions of the incoming partons. leading order partonic cross-sections. final hadron fragmentation function. q⊥ ≡ pc
T + pd T
One must convolute the corresponding flavour dependent Sudakov factor onto the different scattering channels. S(Q, b) = Si
p(Q, b) + Sf p (Q, b) + Snp(Q, b)
Similarly for hadron-jet, photon-jet, and dijet correlation.
2.4 2.6 2.8 3.0 0.0 1.0 2.0 3.0 4.0
ptrig
T,h = [5, 10] GeV
passo
T,h = [3, 5] GeV
∆φ
1 σ dσ d∆φ PHENIX pp PHENIX AA 0-20% p2
⊥ = 0 GeV2
p2
⊥ = 13 GeV2
2.4 2.6 2.8 3.0 0.0 1.0 2.0 3.0 4.0
ptrig
T,h = [5, 10] GeV
passo
T,h = [5, 10] GeV
∆φ
1 σ dσ d∆φ PHENIX pp PHENIX AA 0-20% p2
⊥ = 0 GeV2
p2
⊥ = 13 GeV2
2.4 2.6 2.8 3.0 0.0 1.0 2.0 3.0 4.0
ptrig
T,h = [12, 20] GeV
passo
T,h = [3, 5] GeV
∆φ
1 σ dσ d∆φ STAR pp STAR AA 0-10% p2
⊥ = 0 GeV2
p2
⊥ = 13 GeV2
2.4 2.6 2.8 3.0 0.0 2.0 4.0 6.0
ptrig
T,h = [9, 30] GeV
passo
T,J = [12, 18] GeV
∆φ
1 σ dσ d∆φ STAR 60-80% STAR 0-10% p2
⊥ = 0 GeV2
p2
⊥ = 13 GeV2
2.4 2.6 2.8 3.0 0.0 2.0 4.0 6.0
ptrig
T,h = [9, 30] GeV
passo
T,J = [18, 48] GeV
∆φ
1 σ dσ d∆φ STAR 60-80% STAR 0-10% p2
⊥ = 0 GeV2
p2
⊥ = 13 GeV2
2.4 2.6 2.8 3.0 0.0 2.0 4.0 6.0
ptrig
T,h = [20, 50] GeV
passo
T,J = [60, 90] GeV
∆φ
1 σ dσ d∆φ ALICE TT[20, 50] 0-10% ALICE TT[20, 50]-[8, 9] p2
⊥ = 0 GeV2
p2
⊥ = 13 GeV2
p2
⊥ = 26 GeV2
CL, Qin, Wei, Xiao, Zhang PLB 773(672)
√s = 2.76 TeV
2.2 2.4 2.6 2.8 3 10−1 100 101
∆φ
1 σ dσ d∆φ CMS p⊥γ = [40, 50]GeV LO (2 → 3) Resummed √s = 2.76 TeV
2.2 2.4 2.6 2.8 3 10−1 100 101
∆φ
1 σ dσ d∆φ CMS p⊥γ = [50, 60]GeV LO (2 → 3) Resummed √s = 2.76 TeV
2.2 2.4 2.6 2.8 3 10−1 100 101
∆φ
1 σ dσ d∆φ CMS p⊥γ = [60, 80]GeV LO (2 → 3) Resummed √s = 2.76 TeV
2.2 2.4 2.6 2.8 3 10−1 100 101
∆φ
1 σ dσ d∆φ CMS p⊥γ > 80GeV LO (2 → 3) Resummed √s = 5.02 TeV
2.2 2.4 2.6 2.8 3 10−1 100 101
∆φ
1 σ dσ d∆φ ATLAS p⊥γ = [80, 100]GeV LO (2 → 3) Resummed √s = 5.02 TeV
2.2 2.4 2.6 2.8 3 10−1 100 101
∆φ
1 σ dσ d∆φ ATLAS p⊥γ = [100, 150]GeV LO (2 → 3) Resummed CL, Qin, Wang, Wei, Xiao, Zhang, Zhang 1803.10533
The dijet asymmetry implicitly encodes the following: amplitude of the dijet momenta momentum conservation geometric properties of the scattering (angular distribution) AJ ≤ n − 2 n , xJ ≥ 1 n − 1 1 σ dσ dxJ ∣
Improved
= 1 σNLO dσNLO dxJ ∣
0<∆φ<φm
+ 1 σSudakov dσSudakov dxJ ∣
φm<∆φ<π
2.2 2.4 2.6 2.8 3 10−1 100 101
∆φ
1 σ dσ d∆φ CMS [110, 140]GeV LO (2 → 3) NLO (2 → 4) Resummed
pQCD can describe data at small xJ, but fails to converge at large xJ. Sudakov resummation can describe data close to π. choose φm to switch between pQCD and Sudakov. φm is chosen within the range of 2.8 ≤ ∆φ ≤ 3.0 where the transition between the two formalisms are smooth. choice of φm is not sensitive to result, not free parameter.
0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4
xJ
1 N dN dxJ pp [100-126] Our result
0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4
xJ
1 N dN dxJ pp [126-158] Our result
0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4
xJ
1 N dN dxJ pp [158-200] Our result
0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4
1 N dN dxJ
pp [200-+++] Our result
For the first time, pp baseline established. without smearing, the results were compared directly with fully corrected data. achieved good results at 4 difference pT ranges. results were well described at large xJ due to the Sudakov resummation. results at small xJ were not so good due to the fact that we only use NLO pQCD calculation, higher order expansion should improve the results.
CL, Qin, Wei, Xiao, Zhang PLB accepted June 2018
√s = 5.02 TeV
0.5 1 1.5 2 1 2 3
xJγ
1 σ dσ dxJγ ATLAS pp p⊥γ = [60, 80] GeV pp Sudakov + pQCD Gaussian smeared √s = 5.02 TeV
0.5 1 1.5 2 1 2 3
xJγ
1 σ dσ dxJγ ATLAS pp p⊥γ = [80, 100] GeV pp Sudakov + pQCD Gaussian smeared √s = 5.02 TeV
0.5 1 1.5 2 1 2 3
xJγ
1 σ dσ dxJγ ATLAS pp p⊥γ = [100, 150] GeV pp Sudakov + pQCD Gaussian smeared
√s = 2.76 TeV
0.5 1 1.5 2 1 2 3 4
xJγ
1 σ dσ dxJγ CMS pp p⊥γ = [40, 50] GeV POWHEG + PYTHIA pp Sudakov + pQCD √s = 2.76 TeV
0.5 1 1.5 2 1 2 3 4
xJγ
1 σ dσ dxJγ CMS pp p⊥γ = [50, 60] GeV POWHEG + PYTHIA pp Sudakov + pQCD √s = 2.76 TeV
0.5 1 1.5 2 1 2 3 4
xJγ
1 σ dσ dxJγ CMS pp p⊥γ = [60, 80] GeV POWHEG + PYTHIA pp Sudakov + pQCD √s = 2.76 TeV
0.5 1 1.5 2 1 2 3 4
xJγ
1 σ dσ dxJγ CMS pp p⊥γ > 80GeV POWHEG + PYTHIA pp Sudakov + pQCD
CL, Qin, Wang, Wei, Xiao, Zhang, Zhang 1803.10533
0.4 0.5 0.6 0.7 0.8 0.9 1 0.0 1.0 2.0 3.0 4.0 5.0
1 3
xJ
1 N dN dxJ ATLAS pp [100, 126]GeV PbPb 0 − 10% pp theory ˆ q0 = 2 GeV2/fm ˆ q0 = 6 GeV2/fm
0.4 0.5 0.6 0.7 0.8 0.9 1 0.0 1.0 2.0 3.0 4.0
1 3
xJ
1 N dN dxJ ATLAS pp [126, 158]GeV PbPb 0 − 10% pp theory ˆ q0 = 2 GeV2/fm ˆ q0 = 6 GeV2/fm
0.4 0.5 0.6 0.7 0.8 0.9 1 0.0 1.0 2.0 3.0 4.0
1 3
xJ
1 N dN dxJ ATLAS pp [158, 200]GeV PbPb 0 − 10% pp theory ˆ q0 = 2 GeV2/fm ˆ q0 = 6 GeV2/fm
0.4 0.5 0.6 0.7 0.8 0.9 1 0.0 1.0 2.0 3.0 4.0 5.0
1 3
1 N dN dxJ
ATLAS pp p1⊥ > 200GeV PbPb 0 − 10% pp theory ˆ q0 = 2 GeV2/fm ˆ q0 = 6 GeV2/fm quark jets ˆ q0 = 4 GeV2/fm
Here we use (BDMPS) energy-loss formalism: dσ dp′
⊥1dp′ ⊥2
= ∫ dǫ1dǫ2D(ǫ1)D(ǫ2) dσ dp⊥1dp⊥2 ∣
p⊥1=p′ ⊥1+ǫ1 p⊥2=p′ ⊥2+ǫ2
In the limit ǫ/p⊥ ≪ 1, where:
ǫD(ǫ) = α √ ωc 2ǫ exp ⎛ ⎜ ⎝ − πα2ωc 2ǫ ⎞ ⎟ ⎠ , ωc ≡ ∫ dL ˆ qL, α ≡ 2αs CR π CL, Qin, Wei, Xiao, Zhang PLB accepted June 2018
√s = 5.02 TeV
0.5 1 1.5 2 1 2 3
xJγ
1 σ dσ dxJγ ATLAS pp p⊥γ = [60, 80] GeV pp, Gaussian smeared Scaled ATLAS PbPb 0 − 10% Scaled PbPb ˆ q0 = 2 ∼ 8 GeV2/fm √s = 5.02 TeV
0.5 1 1.5 2 1 2 3
xJγ
1 σ dσ dxJγ ATLAS pp p⊥γ = [80, 100] GeV pp, Gaussian smeared Scaled ATLAS PbPb 0 − 10% Scaled PbPb ˆ q0 = 2 ∼ 8 GeV2/fm √s = 5.02 TeV
0.5 1 1.5 2 1 2 3
xJγ
1 σ dσ dxJγ ATLAS pp p⊥γ = [100, 150] GeV pp, Gaussian smeared Scaled ATLAS PbPb 0 − 10% Scaled PbPb ˆ q0 = 2 ∼ 8 GeV2/fm √s = 2.76 TeV
0.4 0.6 0.8 1 1.2 1.4 1 2 3 4
1 σ dσ dxJγ
PYTHIA + DATA p⊥γ = [60, 90] GeV pp Sudakov + pQCD Scaled ATLAS PbPb 0 − 10% Scaled PbPb ˆ q0 = 2 ∼ 8 GeV2/fm
smearing included to compared with then uncorrected data. (now unfolded) hard radiation probabilities restricted for BDMPS. Shift in xJγ peak, no enhancement in small x distribution. both dijet and photon-jet AA correlations were simulated in a viscous hydrodynamic OSU(2+1) evolution.
CL, Qin, Wang, Wei, Xiao, Zhang, Zhang 1803.10533
Utilizing the CERN MINUIT χ2 minimization package, we found that: ⟨p2
⊥⟩ = 13+5 −4 GeV2
for a quark jet at RHIC peak energy. We can also plot the q⊥ distribution for different energy scale, one can see that ˆ q should be more sensitive to RHIC energy scale than LHC scale. q∗2
⊥AA ≃ q∗2 ⊥pp + ⟨p2 ⊥⟩
By investigating the energy loss effect in the medium, we can further extract the effective length of the propagating jet. Or vice-versa.
10 20 30 40 1 2 3 4 5
⊥(GeV2)
HJ[9, 30]+[12, 18] HJ[9, 30]+[18, 48] HH[5, 10]+[3, 5] HH[5, 10]+[5, 10] HH[12, 20]+[3, 5] Global fit
5 10 15 20 25 0.00 0.05 0.10 0.15 0.20 0.25
1 σ dσ dq⊥
RHIC HJ [9, 30]+[12, 18] HJ [9, 30]+[18, 48] HH [5, 10]+[3, 5] HH [5, 10]+[5, 10] HH [12, 20]+[3, 5] LHC HJ [9, 30]+[18, 48] HJ [20, 50]+[60, 90] HH [5, 10]+[5, 10]
The Sudakov factor can be written as: S(Q, b) =Si
p(Q, b) + Sf p (Q, b) + Snp(Q, b)
+ b2 4 (⟨p2
⊥⟩c + ⟨p2 ⊥⟩d)
For a more realistic modelling of the medium, we used OSU (2+1)D viscous hydro to extract the space-time evolution of the medium, relating the leading-order ˆ q to the medium temperature ˆ q ∝ T 3. The double-log resummed expression is: ⟨p2
⊥⟩ = ˆ
qL I1 [2√ ¯ αs ln ( L2
l2
)] [√ ¯ αs ln ( L2
l2
)] , ¯ αs = αsNc 4π we have ˆ q0 = 3.9+1.5
−1.2 GeV2/fm for quark jet at τ0 = 0.6 fm/c at
the center of the medium in central AA collision at RHIC.
We also modelled energy loss effect for associate/both jets and found moderate effect on angular distribution. 10 20 30 40 50 2 4 6
Global fit (p2 ⊥ = 7 GeV2, ∆Easso/E=0%) Global fit (p2 ⊥ = 7 GeV2, ∆Easso/E=5%) Global fit (p2 ⊥ = 7 GeV2, ∆Easso/E=10%) Global fit (p2 ⊥ = 7 GeV2, ∆Eboth/E=5%) Global fit (p2 ⊥ = 7 GeV2, ∆Eboth/E=10%)
2.4 2.6 2.8 3.0 2 4 6
ptrig
T,h = [9, 30] GeV
passo
T,J = [12, 18] GeV
1 σ dσ d∆φ
STAR 60-80% STAR 0-10% p2 ⊥ = 0 GeV2 p2 ⊥ = 7 GeV2, ∆Easso/E=0% p2 ⊥ = 7 GeV2, ∆Easso/E=5% p2 ⊥ = 7 GeV2, ∆Easso/E=10% p2 ⊥ = 7 GeV2, ∆Eboth/E=5% p2 ⊥ = 7 GeV2, ∆Eboth/E=10%
We begin with a brief introduction of the observable that we are using to probe the energy loss of the QGP system.
leading jet (jet with highest pT )≡ pT1. sub-leading jet (jet with second highest pT )≡ pT2. for any 2 → n process: ∣pT1∣ ≥ ∣pT2∣ ≥ ⋯ ≥ ∣pTn∣ Dijet asymmetry ratio: AJ ≡ pT1 − pT2 pT1 + pT2 xJ ≡ pT2 pT1 Similarly: AJ = 1 − xJ 1 + xJ ; xJ = 1 − AJ 1 + AJ The dijet asymmetry ratio AJ and xJ can provide a direct and qualitative approach in probing the energy loss mechanism