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), arxiv 1612.04202, arxiv 1803.10533 presented in: HP2016, QM2017, QM2018

Introduction - motivation 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 . Two main modifications that the QGP medium has on such jets are: Transverse momentum broadening Jet energy loss Their relation is given by (BDMPS): q ≡ d ⟨ q 2 ⊥ ⟩ − dE dx = α s N c To study the properties of this QGP , we investigate the ˆ qL , ˆ 4 dL modifications it has on these hard partons known as Jets. BDMPS NPB 483 (1997) 291, 484 (1997) 265, 531 (1998) 403

Introduction - observable ) φ 1 ∆ centrality 20-60% dN/d( 0.8 trigger 0.6 1/N 0.4 )-flow p+p -1 0 1 2 3 4 Au+Au, in-plane 0.2 ∆ φ Au+Au, out-of-plane (radians) φ ∆ dN/d( 0.1 trigger 1/N 0 ∫ ∫ (a) (b) (c) -1 µ -1 CMS L dt = 35.1 pb L dt = 6.7 b p > 120 GeV/c -1 0 1 2 3 4 0.2 pp s =7.0 TeV 0.2 PbPb s =2.76 TeV 0.2 NN T,1 Event Fraction p > 50 GeV/c PYTHIA PYTHIA+DATA ∆ φ T,2 (radians) ∆ φ 2 π > Anti-k , R=0.5 Iterative Cone, R=0.5 12 3 T 0.1 0.1 0.1 STAR PRL 90 082302, PRL 93 252301 50-100% 30-50% ATLAS 1011.6182v2, CMS 1102.1957v2 0 0.5 1 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 (d) (e) (f) Azimuthal angular decorrelation reflects directly on the 0.2 0.2 0.2 transverse momentum broadening effect of the QGP medium, Event Fraction and 0.1 0.1 0.1 Dijet momentum imbalance describes an intuitive picture on the energy loss effect experienced by the hard jet through the QGP . 20-30% 10-20% 0-10% 0 0 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 A = (p -p )/(p +p ) J T,1 T,2 T,1 T,2

Introduction - complications ( ∆ φ ) − p sub − lead A J ≡ p leading ⊥ ⊥ is an observable reflects directly on the energy imbalance. + p sub − lead p leading ⊥ ⊥ � � ? ⇒ No clear signs of broadening Signs of energy loss ATLAS PRL 105 252303 Qualitative analysis (of ∆ φ distribution) has been lacking. What did we miss? D0 PRL 94 221801 What is the limitation of pQCD ?

Introduction - complications ( x J ) 4 4 4 J J J N N N x x x ATLAS Preliminary 0 - 10 % 60 - 80 % -1 pp d d d d d d 2013 pp data, 4.0 pb Measured 3.5 3.5 3.5 1 N anti- k R = 0.4 jets, s = 2.76 TeV 1 N 1 N Unfolded t NN -1 2011 Pb+Pb data, 0.14 nb 3 3 3 2.5 2.5 2.5 2 2 2 1.5 1.5 1.5 1 1 1 0.5 0.5 0.5 100 < p < 126 GeV T 0 0 0 0.10.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.10.2 0.3 0.4 0.5 0.6 0.70.8 0.9 1 0.10.2 0.3 0.40.5 0.6 0.7 0.8 0.9 1 x x x J J J detector (calorimeter) response paper published by ATLAS in Quark Matter 2015 shows new fully corrected dijet asymmetry results in both pp fluctuations by UEs and PbPb collisions. other detector artefacts. Note the large difference between the measured and these can cause bin migration in the measured p 1 , ⊥ , p 2 , ⊥ unfolded result. distributions.

Formalism - resummation We now focus on the region close to π . Multi-scale problem: Q 2 ≈ p 2 ⊥ ≫ q 2 ⊥ Large logarithm in α s expansion: n ( α s ln 2 p 2 ⊥ ) q 2 ⊥ Ideal QCD expansion: ∞ s ( L i + C ( i ) ) ∑ α i σ 0 i = 0 n − 1 n − 1 s C ( i ) ⇐ pQCD ∑ ∑ α i s L i α i σ 0 σ 0 i = 0 i = 0 ∞ ∞ s C ( i ) ∑ ∑ α i s L i α i σ 0 σ 0 i = n i = n Sun, Yuan, Yuan, PRL 113 232001, PRD 92 (2015) ⇑ ↖ negligible d 2 p ⊥ P ( p ⊥)( 2 π ) 2 δ ( 2 )( q 1 ⊥ + ⋯ + qn ⊥ + p ⊥ − q ⊥) 1 d σ = σ 0 ∑ d 2 q 1 ⊥⋯ d 2 qn ⊥ T ( q 1 ⊥)⋯ T ( qn ⊥) ∫ n ! ∫ d 2 q ⊥ resummation n d 2 b ⊥ e − iq ⊥ ⋅ b ⊥ ˜ T ( b ⊥) P ( b ⊥) e ˜ = σ 0 ∫ pQCD sums finite α s expansion. To sum arbitrary number of soft-gluon emission, we perform integration in resummation (Sudakov) sums Logarithmic T ( b ⊥ ) = − S sudakov b ⊥ space, with ˜ terms to all order. ! Sudakov resummation can effectively take into account the soft gluon radiation (parton shower) effect.

Formalism - factorization Dijet Angular Correlation at the LHC To extract the medium transport coefficient, the vacuum and medium contribution can 6 be considered separately. CMS 0 - 10% qL = 0 GeV 2 l + /q + l + /q + ˆ qL = 8 GeV 2 4 ˆ τ l = L τ l = τ q τ l = τ q 1 1 qL = 20GeV 2 ˆ d ∆ φ dN A+B cancel A+B cancel qL = 100GeV 2 ˆ e l Sudakov Sudakov c n a 1 N c C + 2 B B+C cancel o n u t i v o l ^ e l ⊥ 2 = q τ l B K τ l = L 2 = q τ l ^ ^ l ⊥ q t τ l = r 0 τ l = r 0 ^ 0 q t 2 . 0 2 . 2 2 . 4 2 . 6 2 . 8 3 . 0 ∆ φ 0 ql 0 ^ qL ^ 1/x ⊥ 2 Q 2 l ⊥ 2 0 ql 0 ^ qL ^ 1/x ⊥ 2 Q 2 l ⊥ 2 Dijet Angular Correlation at RHIC Mueller, Wu, Xiao, Yuan, 1608.07339, 1604.04250 Different elements receives different one-loop corrections from separated regions in the 6 qL = 0 GeV 2 ˆ phase space of the radiated gluon. qL = 8 GeV 2 ˆ S AA ( Q , b ) = S pp ( Q , b ) + ⟨ ˆ qL ⟩ b 2 qL = 20GeV 2 ˆ d ∆ φ 4 dN 4 1 N 2 We can see the vacuum Sudakov effect at different kinematic regions: LHC: vacuum Sudakov ≫ medium broadening RHIC: vacuum Sudakov ∼ medium broadening 0 2 . 4 2 . 5 2 . 6 2 . 7 2 . 8 2 . 9 3 . 0 3 . 1 ∆ φ

Implementation - ∆ φ distribution Dihadron azimuthal angular spectrum: ∫ b db J 0 ( q ⊥ ⋅ b ⊥ ) e − S ( Q , b ) d σ a , b , c , d ∫ p h 1 ∑ T ∫ p h 2 T ∫ dz c ∫ dz d d ∆ φ = T dp h 1 T dp h 2 z 2 z d c c ⊗ x a f a ( x a , µ ) ⊗ x b f b ( x b , µ ) ⊗ 1 d σ ab → cd ⊗ D c ( z c , µ ) ⊗ D d ( z d , µ ) d ˆ π t Q 2 d µ 2 µ 2 [ A ln Q 2 S p ( Q , b ) = ∑ µ 2 + B + D ln 1 R 2 ] q , g ∫ µ 2 b Bessel’s function of the first kind. T + p d q ⊥ ≡ p c T Sudakov factor. arXiv:1604.04250 One must convolute the corresponding flavour dependent Sudakov distribution functions of the incoming factor onto the different scattering channels. partons. S ( Q , b ) = S i p ( Q , b ) + S f p ( Q , b ) + S np ( Q , b ) leading order partonic cross-sections. Similarly for hadron-jet, photon-jet, and dijet correlation. final hadron fragmentation function.

Results - HH, HJ ∆ φ distribution 4 . 0 4 . 0 4 . 0 PHENIX pp PHENIX pp STAR pp PHENIX AA 0-20% PHENIX AA 0-20% STAR AA 0-10% 3 . 0 3 . 0 3 . 0 � p 2 ⊥ � = 0 GeV 2 � p 2 ⊥ � = 0 GeV 2 � p 2 ⊥ � = 0 GeV 2 � p 2 ⊥ � = 13 GeV 2 � p 2 ⊥ � = 13 GeV 2 � p 2 ⊥ � = 13 GeV 2 d ∆ φ p trig d ∆ φ p trig d ∆ φ p trig T,h = [5 , 10] GeV T,h = [5 , 10] GeV T,h = [12 , 20] GeV dσ 2 . 0 dσ 2 . 0 dσ 2 . 0 p asso p asso p asso T,h = [3 , 5] GeV T,h = [5 , 10] GeV T,h = [3 , 5] GeV 1 σ 1 σ 1 σ 1 . 0 1 . 0 1 . 0 0 . 0 0 . 0 0 . 0 2 . 4 2 . 6 2 . 8 3 . 0 2 . 4 2 . 6 2 . 8 3 . 0 2 . 4 2 . 6 2 . 8 3 . 0 ∆ φ ∆ φ ∆ φ 6 . 0 6 . 0 6 . 0 STAR 60-80% STAR 60-80% ALICE TT[20 , 50] 0-10% STAR 0-10% STAR 0-10% ALICE TT[20 , 50]-[8 , 9] � p 2 ⊥ � = 0 GeV 2 � p 2 ⊥ � = 0 GeV 2 � p 2 ⊥ � = 0 GeV 2 4 . 0 4 . 0 4 . 0 � p 2 ⊥ � = 13 GeV 2 � p 2 ⊥ � = 13 GeV 2 � p 2 ⊥ � = 13 GeV 2 � p 2 ⊥ � = 26 GeV 2 d ∆ φ d ∆ φ d ∆ φ dσ p trig dσ p trig dσ T,h = [9 , 30] GeV T,h = [9 , 30] GeV p asso p asso p trig T,J = [12 , 18] GeV T,J = [18 , 48] GeV T,h = [20 , 50] GeV 1 σ 1 σ 1 σ 2 . 0 2 . 0 2 . 0 p asso T,J = [60 , 90] GeV 0 . 0 0 . 0 0 . 0 2 . 4 2 . 6 2 . 8 3 . 0 2 . 4 2 . 6 2 . 8 3 . 0 2 . 4 2 . 6 2 . 8 3 . 0 ∆ φ ∆ φ ∆ φ CL, Qin, Wei, Xiao, Zhang PLB 773(672)

Results - γ J ∆ φ distribution 10 1 10 1 10 1 CMS p ⊥ γ = [40 , 50]GeV CMS p ⊥ γ = [50 , 60]GeV CMS p ⊥ γ = [60 , 80]GeV LO (2 → 3) LO (2 → 3) LO (2 → 3) Resummed Resummed Resummed √ s = 2 . 76 TeV √ s = 2 . 76 TeV √ s = 2 . 76 TeV d ∆ φ 10 0 d ∆ φ 10 0 d ∆ φ 10 0 dσ dσ dσ 1 σ 1 σ 1 σ 10 − 1 10 − 1 10 − 1 2 . 2 2 . 4 2 . 6 2 . 8 3 2 . 2 2 . 4 2 . 6 2 . 8 3 2 . 2 2 . 4 2 . 6 2 . 8 3 ∆ φ ∆ φ ∆ φ 10 1 10 1 10 1 ATLAS p ⊥ γ = [80 , 100]GeV ATLAS p ⊥ γ = [100 , 150]GeV CMS p ⊥ γ > 80GeV LO (2 → 3) LO (2 → 3) LO (2 → 3) Resummed Resummed Resummed √ s = 2 . 76 TeV √ s = 5 . 02 TeV √ s = 5 . 02 TeV d ∆ φ d ∆ φ d ∆ φ 10 0 10 0 10 0 dσ dσ dσ 1 σ 1 σ 1 σ 10 − 1 10 − 1 10 − 1 2 . 2 2 . 4 2 . 6 2 . 8 3 2 . 2 2 . 4 2 . 6 2 . 8 3 2 . 2 2 . 4 2 . 6 2 . 8 3 ∆ φ ∆ φ ∆ φ CL, Qin, Wang, Wei, Xiao, Zhang, Zhang 1803.10533

Implementation - x J distribution The dijet asymmetry implicitly encodes the following: amplitude of the dijet momenta momentum conservation geometric properties of the scattering (angular distribution) A J ≤ n − 2 1 x J ≥ n − 1 , n ∣ ∣ + ∣ 1 d σ 1 d σ NLO 1 d σ Sudakov = σ dx J σ NLO dx J 0 < ∆ φ < φ m σ Sudakov dx J φ m < ∆ φ < π Improved CMS [110 , 140]GeV LO (2 → 3) 10 1 pQCD can describe data at small x J , but fails to converge at large x J . NLO (2 → 4) Resummed Sudakov resummation can describe data close to π . d ∆ φ dσ 10 0 choose φ m to switch between pQCD and Sudakov. 1 σ φ m is chosen within the range of 2 . 8 ≤ ∆ φ ≤ 3 . 0 where the transition between the two formalisms are smooth. 10 − 1 choice of φ m is not sensitive to result, not free parameter. 2 . 2 2 . 4 2 . 6 2 . 8 3 ∆ φ