SCET approach to energy loss. Zhongbo Kang Los Alamos National Laboratory

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1 SCET approach to energy loss Zhongbo Kang Los Alamos National Laboratory Symposium on Jet and Electromagnetic Tomography of Dense Matter June 26-27, 2015

2 Outline Introduction SCET G = SCET with Glauber gluons Medium induced splitting from SCET G Evolved fragmentation function in medium Connection to standard energy loss approach Applications single inclusive hadron production in A+A Jet shapes in A+A Summary 2

gluon plasma) created in heavy ion collisions at RHIC

3 Probe of quark gluon plasma Jet quenching has become the excellent/standard probe of the hot dense medium (quark gluon plasma) created in heavy ion collisions at RHIC and LHC Gyulassy, Wang, 92, BDMPS, GLV, AMY, high-twist, 3

4 Jets at LHC and future RHIC High energetic jets have emerged as new tool to study properties of QGP, as well as short-distance dynamics (multiple scattering, parton showering) in the medium 4

5 Soft Collinear Effective Theory (SCET) SCET: an effective theory for highly energetic partons (quark or gluons) interacting with collinear and/or soft gluons Particularly suitable for studying hard particle and jet productions 5

6 QCD factorization QCD factorization of modes (regions) σ = H S Hard: Soft: Collinear: n B i=1 B i k µ = k +,k,k N j=1 k Q [1, 1, 1] k Q λ 2, λ 2, λ 2 k Q 1, λ 2, λ J j + power correction Bauer et al. 01, Pirol et al. 04 RG evolution for each sector: resummation of large logs due to very distinct scales, e.g., Drell-Yan production M >> qt 6

7 Highly successful in p+p studies Advanced QCD theory and phenomenology significantly 25 Stewart, et al, PRL 11 Becher, et al, JHEP 12 Z boson M 2 L =ln q 2 T 20 dσ dq T pb GeV NLL 5 NNLL q T GeV 7

8 Medium: Glauber gluons are important To describe the propagation of an highly energetic jet (quark/ gluon) in the medium t-channel dominance (forward scattering): transverse momentum transfer is the most important degree of freedom k Q λ 2, λ 2, λ Glauber: Gyulassy, Levai, Vitev, 00 Initial formulation of SCET does not contain Glauber gluons Work of Idilbi, Majumder 08, D Eramo, Liu, Rajagopal 10, Ovanesyan, Vitev 11, 12 Recently Fleming showed that Glauber gluon exchange leads to BFKL evolution equation in the small x limit:

9 SCET with Glauber gluons SCET G = SCET with Glauber gluons, new terms describe the interaction between collinear quark/gluon and Glauber gluon Feynman rules are given: Idilbi, Majumder 08, Ovanesyan, Vitev 11 Collinear quark with Glauber gluon Collinear gluon with Glauber gluon 9

10 Medium induced parton splitting Easy implementation to compute medium induced parton splitting functions 10

11 Results of all medium splitting kernels qà qg, gà qq, gà gg Ovanesyan, Vitev, 11 11

12 Small-x approximation Under small x approximation, it reproduces GLV splitting kernel for quarkà quark, and gluonà gluon Now a natural place to study the FINITE x correction and its consequences Kang, Ovanesyan, Vitev, et.al., PRL, 15 12

13 A natural way: using DGLAP evolution So far the calculation is for real diagram (real gluon emission), add the virtual correction can be obtained from Flavor and momentum conservation sum rules Vacuum evolution splitting kernel Perform the same exercises for the medium induced splitting kernels: then integrate over k T to obtain the inclusive splitting function, and the upper scale is set to hard scale (factorization scale) P(x, ; ) 13

14 A natural way: using DGLAP evolution Now we have four splitting kernels: qà q, gà g, qà g, gà q Natural framework is to use DGLAP evolution equations to account for multiple gluon emissions 14

15 Application of the evolution approach Solving the evolution equation in the medium, one obtains the medium modified FFs, which can then be used in the calculation of nuclear modification factor R AA in A+A collisions Choose factorization scale =p T R AA (p T )= H(µ, p T ) PDF(µ) PDF(µ) D med (µ) H(µ, p T ) PDF(µ) PDF(µ) D vac (µ) Connection to the usual energy loss approach? 15

16 Reminder: energy loss approach Of course the comparison is only relevant to small-x approximation limit D quenched c h (z,µ) = 1 z Under soft approximation 0 d P c() (1 ) D c h Standard GLV implementation The parton does not change identity, so the energy loss has its true meaning no flavor changing z 1,µ Any significant fractional energy loss is carried away through multiple gluon bremsstrahlung (Poisson distribution) 16

17 Vacuum evolution in the soft gluon limit Under soft gluon approximation, quark and gluon evolution decouples Using + function, expanding around z =1 17

$PRL 15 Over most of z range, the suppression of FFs is dominated by the fractional energy loss, amplified by the steepness of D(z) Near threshold (z=1), the modification is$

18 Connection to energy loss approach Evolution of FFs in medium Kang, Ovanesyan, Vitev, et al. PRL 15 Over most of z range, the suppression of FFs is dominated by the fractional energy loss, amplified by the steepness of D(z) Near threshold (z=1), the modification is determined by the probability not to emit a gluon exp ( N g ) Gyulassy, Levai, Vitev, PLB, 02 18

19 Energy loss vs Evolution (soft approximation) Energy loss: multiple gluon emission Poisson distribution Evolution: through DGLAP evolution equation (soft approximation) R AA (p T ) Ratio p T [GeV] Soft gluon energy loss, g=2.0 Soft gluon energy loss, g=2.1 Soft gluon analytic evolution, g=2.0 Soft gluon analytic evolution, g=2.1 ALICE ch. hadron R AA, 0-5% CMS ch. hadron R AA, 0-5% Central Pb+Pb, s 1/2 =2760 GeV p T [GeV] Kang, Ovanesyan, Vitev, et al. PRL 15 19

20 Evolution: full x vs small x Both RHIC and LHC Kang, Ovanesyan, Vitev, et al. PRL 15 R AA (p T ) PHENIX π 0, 0-10% Full evolution numerics, g=2.3 Soft gluon energy loss, g=2.3 Soft gluon analytic evolution, g=2.3 Soft gluon evolution numerics, g=2.3 Central Au+Au, s 1/2 =200 GeV R AA (p T ) Ratio p T [GeV] Full evolution numerics, g=1.9 Full evolution numerics, g=2.0 Soft gluon evolution numerics, g=1.9 Soft gluon evolution numerics, g=2.0 ALICE ch. hadron R AA, 0-5% CMS ch. hadron R AA, 0-5% p T [GeV] 0.2 Central Pb+Pb, s 1/2 =2760 GeV p T [GeV] QCD evolution using full DGLAP evolution in the medium is on the top of the small-x approximation to evolution above (6 GeV for RHIC) and (15 GeV for LHC) At small and intermediate pt, the shape of full x evolution is in slightly better agreement with the data 20

21 Fragmentation functions For single inclusive hadron RAA: the finite x correction is SMALL There should be other observables sensitive to large/finite x correction Differences in the fragmentation functions calculated in different approximations are more visible, especially for gluon FFs at large values of z However, the sensitivity of RAA to this is reduced because gluon FFs in the medium are more quenched D med (z,q) / D vac (z,q) Cental Pb+Pb s 1/2 = 2.76 TeV Q = 40 GeV Gluon fragmentation Q = 40 GeV Quark fragmentation Full evolution, numerics Soft gluon evolution, numerics Soft gluon analytic evolution Soft gluon energy loss hadron parton z = p /pt T The coupling between the jet and the medium is ~15% larger at RHIC (g=2.3) and LHC (g=2.0) 21

22 Other application: Jet shape Jet shape is another very powerful observable to study in-medium parton interaction and showering An observable of r and R, which receives large logarithms of type ln(r/r) and can be naturally resummed through SCET Chien, Vitev, JHEP 14 22

23 Jet shapes in the medium Early predictions based on energy loss approach Not describe the data well at small r/r region Vitev, Wicks, Zhang, 08 This is precisely the region where the theory could be improved through SCET resummation techniques and full medium-induced splitting functions 23

24 Medium modification of Jet shape Jet shapes get modified through the modification of jet energy function Chien, Vitev in preparation 24

25 Summary SCET is a very useful tool to make reliable/precise predictions/ computations for hard particle and jet production at both p+p and A+A collisions Inclusion of Glauber gluons through SCET G Further full development of SCET approach in the medium, along with new observables, could/should advance heavy ion field significantly 25

26 Summary SCET is a very useful tool to make reliable/precise predictions/ computations for hard particle and jet production at both p+p and A+A collisions Inclusion of Glauber gluons through SCET G Further full development of SCET approach in the medium, along with new observables, could/should advance heavy ion field significantly Thank you! 26

Zhong-Bo Kang Los Alamos National Laboratory

Introduction to pqcd and Jets: lecture 3 Zhong-Bo Kang Los Alamos National Laboratory Jet Collaboration Summer School University of California, Davis July 19 21, 2014 Selected references on QCD QCD and