Jet evolution in a dense QCD medium. Edmond Iancu IPhT Saclay & CNRS. June 19, 2013

Transcription

1 Jet evolution in a dense QCD medium Edmond Iancu IPhT Saclay & CNRS based on work with J.-P. Blaizot, P. Caucal, F. Dominguez, Y. Mehtar-Tani, A. H. Mueller, and G. Soyez ( ) 1.8 June 19, 2013 D(ω)/D vac (ω) q^=1 Gev 2 /fm,l=3 fm q^=2 Gev 2 /fm,l=3 fm q^=2 Gev 2 /fm,l=4 fm solid: Λ=100 MeV dashed: Λ=200 MeV E=200 GeV, θ qq - =0.4, ᾱ s= ω [GeV] INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 1 / 43

2 Outline Jets in heavy ion collisions jet quenching di-jet asymmetry, fragmentation functions Two types of radiation vacuum-like: bremsstrahlung (parton virtualities) medium-induced radiation : BDMPS-Z (collisions in the plasma) Separately well understood How to combine them together (within pqcd)? How is the vacuum-like radiation modified by the medium? INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 2 / 43

3 Jets: pp vs. AA collisions at the LHC Hard processes in QCD typically create pairs of partons which propagate back to back in the transverse plane In the vacuum (pp collisions), this leads to a pair of symmetric jets A spray of collimated particles produced via radiation (parton branching) In AA collisions, the two jets can be differently affected by their interactions with the surrounding, partonic, medium: quark-gluon plasma INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 3 / 43

4 Jets in practice Experimentally, jets are constructed by grouping together hadrons which propagate at nearby angles The jet opening angle 0 (a.k.a. R) is the same for both jets Medium modifications refer both to the jets and to the outer regions INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 4 / 43

5 From di jets in p+p collisions... INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 5 / 43

6 ... to mono-jets in Pb+Pb collisions Central Pb+Pb: mono jet events The secondary jet can barely be distinguished from the background: ET GeV, ET 2 > 25 GeV INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 6 / 43

7 Di jet asymmetry at the LHC Huge difference between the energies of the two jets The missing energy is found in the underlying event: many soft (p? < 2 GeV) hadrons propagating at large angles Very different from the usual jet fragmentation pattern in the vacuum INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 7 / 43

8 Di jet asymmetry : A J (a) CMS -1 L dt = 35.1 pb (b) -1 L dt = 6.7 µb (c) 0.2 pp s=7.0 TeV PbPb s NN =2.76 TeV p > 120 GeV/c T,1 Event Fraction 0.1 PYTHIA Anti-k T, R=0.5 PYTHIA+DATA Iterative Cone, R=0.5 p T,2 φ 12 > 50 GeV/c > 2 π % 30-50% (d) (e) (f) 0.2 Event Fraction % 10-20% 0-10% A J = (p -p T,1 T,2 )/(p +p T,1 T,2 ) Event fraction as a function of the di jet energy imbalance in p+p (a) and Pb+Pb (b f) collisions for different bins of centrality A J = E 1 E 2 E 1 + E 2 (E i p T,i = jet energies) INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 8 / 43

9 Di jet asymmetry : A J (a) CMS -1 L dt = 35.1 pb (b) -1 L dt = 6.7 µb (c) 0.2 pp s=7.0 TeV PbPb s NN =2.76 TeV p > 120 GeV/c T,1 Event Fraction 0.1 PYTHIA Anti-k T, R=0.5 PYTHIA+DATA Iterative Cone, R=0.5 p T,2 φ 12 > 50 GeV/c > 2 π % 30-50% (d) (e) (f) 0.2 Event Fraction % 10-20% 0-10% A J = (p -p T,1 T,2 )/(p +p T,1 T,2 ) N.B. A pronounced asymmetry already in p+p collisions! 3-jets events, fluctuations in the branching process Central Pb+Pb : the asymmetric events occur more often INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 8 / 43

10 The nuclear modification factor for jets The jet yield in Pb+Pb collisions normalized by p+p times the average nuclear thickness function ht AA i R AA 1 N evt ht AA i d2 d 2 N jet dp T dy AA jet dp T dy pp R AA would be equal to one in the absence of nuclear effects stronger suppression for more central collisions Naturally interpreted as a consequence of energy loss inside the medium INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 9 / 43

11 The nuclear modification factor for jets The jet yield in Pb+Pb collisions normalized by p+p times the average nuclear thickness function ht AA i R AA 1 N evt ht AA i d2 d 2 N jet dp T dy AA jet dp T dy pp jet spectra are rapidly decreasing with p T they are shifted towards lower p T due to in-medium energy loss R AA is almost flat at very high p T : energy loss increases with p T INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 9 / 43

12 Intra-jet nuclear modifications Jet fragmentation function: energy distribution of hadrons inside the jet D(!)! dn d! = Z R 0 d! dn d d! ) R D(p T ATLAS 126 < p 126 < p jet y < 2.1 anti-k t R=0.4 jets jet < 158 GeV, s NN = 2.76 TeV T jet < 158 GeV, s NN = 5.02 TeV T! p T of a hadron inside the jet ratio of FFs in Pb+Pb and p+p slight suppression at intermediate energies enhancement at low energies (z 1) p [GeV] T Pb+Pb, 0-10% Two classes of nuclear modifications: inside & outside the jet cone We shall argue that they refer to two different types of radiation INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 10 / 43

13 Intra-jet nuclear modifications R D(z) Jet fragmentation function: energy distribution of hadrons inside the jet Similar pattern when the distribution is plotted vs. p T or vs. z = p T /p jet T ATLAS 126 < 126 < jet y < 2.1 anti-k t R=0.4 jets jet p T jet p T < 158 GeV, < 158 GeV, s NN s NN = 2.76 TeV = 5.02 TeV ) R D(p T ATLAS 126 < 126 < jet y < 2.1 anti-k t R=0.4 jets jet p T jet p T < 158 GeV, < 158 GeV, s NN s NN = 2.76 TeV = 5.02 TeV Pb+Pb, 0-10% z 0.5 Pb+Pb, 0-10% p [GeV] T Two classes of nuclear modifications: inside & outside the jet cone We shall argue that they refer to two different types of radiation INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 10 / 43

14 Medium-induced jet evolution The leading particle (LP) is produced by a hard scattering It subsequently evolves via radiation (branchings) and via collisions off the medium constituents Collisions can have several effects transfer energy and momentum between the jet and the medium trigger additional radiation ( medium-induced ) wash out the color coherence (destroy interference pattern) INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 11 / 43

15 Medium-induced jet evolution The leading particle (LP) is produced by a hard scattering It subsequently evolves via radiation (branchings) and via collisions off the medium constituents Collisions can have several effects transfer energy and momentum between the jet and the medium trigger additional radiation ( medium-induced ) wash out the color coherence (destroy interference pattern) INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 11 / 43

16 Transverse momentum broadening An energetic quark acquires a transverse momentum p? via collisions in the medium, after propagating over a distance L x p = 0 p y x + = 0 L L 0 8 Direct amplitude (DA) Complex conjugate amplitude (CCA) Weakly coupled medium =) independent scattering centers Arandomwalkinp? : hp 2? i' ˆqL INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 12 / 43

17 Dipole picture The individual collisions are relatively soft : k? m D E x p = 0 p y x + = 0 L L 0 8 Scattering can be computed in the eikonal approximation: Wilson lines Z V (x) =Pexp ig dx + A a (x +, x)t a Two such Wilson lines (DA CCA) =) a q q color dipole INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 13 / 43

18 Dipole picture y x r x + = 0 dn d 2 p = 1 Z (2 ) 2 e ip r hŝxyi, Ŝ xy 1 tr V r N xv y c Average over the Gaussian distribution of the color fields A a (x +, x): Aa (x +, k) A b (y +, k) = n 0 ab (x + y + g 2 ) (k 2 + m 2 D )2 n = C F n q + N c n g T 3 : color weighted density of thermal quarks & gluons INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 14 / 43 L

19 The tree-level approximation ( MV model ) 1 hŝxyi 0 ' exp 4 Lˆq 0(1/r 2 ) r 2 The tree-level jet quenching parameter ˆq 0 (logarithmic scale dependence): Z Q 2 ˆq 0 (Q 2 ) ng 4 d 2 k k 2 C F (2 ) 2 (k 2 + m 2 ' D )2 4 2 sc F n ln Q2 m 2 D The cross section for p? broadening at tree-level: dn d 2 p = 1 Z (2 ) 2 e ip r e 1 4 Lˆq0(1/r2 ) r 2 ' 1 r Q 2 e p2? /Q2 s s A random walk in transverse momentum: hp 2? i = Q2 s(l) Lˆq 0 (Q 2 s) Power-law tail at large p? Q s : single hard scattering dn d 2 p ' 1 Z 1 (2 ) 2 e ip r r 4 Lˆq 0(1/r 2 ) r 2 ' 4 2 sc F n p 4? INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 15 / 43

20 Radiation: Formation time Uncertainty principle: quantum particles are delocalized The gluon has been emitted when it has no overlap with its source? = 1 k? ' 1! k x? ' t &? =) t & t f! k 2? ' 1! 2 Formation time : the time it takes to emit a gluon This argument universally applies to radiation: in vacuum & in the medium In vacuum, t f is measured from the hard scattering INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 16 / 43

21 Medium-induced radiation Collisions introduce a lower limit on the transverse momentum... t f =! k 2? & k 2? & ˆqt f t f. r! ˆq t f <L =)! apple! c ˆqL 2... hence an upper limit on the formation time! Three types of emissions: vacuum-like (usual bremsstrahlung): k? 2 ˆqt f,ort f p!/ˆq medium-induced, single hard scattering: k? 2 ˆqt f,ort f p!/ˆq medium-induced, multiple soft scattering: k 2? ' ˆqt f,or t f ' p!/ˆq INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 17 / 43

22 Radiative corrections to p? broadening Medium-induced emissions contribute to momentum broadening via recoil Formally, a higher-order effect, but amplified by logarithms: evolution k x y 0 y + x + L L x + y k x y 0 y + x + L L 0 8 The quark evolves by emitting a soft gluon ( real or virtual ) soft ()! k + E =) eikonal emission vertices INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 18 / 43

23 In-medium BK/JIMWLK evolution Exchange graphs between q and q, or self energy graphs y k y k x x 0 y + x + L 0 y + x + L All partons undergo multiple scattering: non linear evolution However, and unlike for a shockwave (DIS, pa), the multiple scattering cannot be computed in the eikonal approximation Eikonal scattering: transverse deviation x? during collision time t should be small compared to the transverse wavelength? =1/p? : x? = p?! t? = 1 p? =) t! p 2? = t f But for the soft gluon emissions at hand, one rather has t = t f INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 19 / 43

24 The single scattering approximation The dominant radiative corrections are associated with fluctuations which undergo only a single scattering (Liou, Mueller, Wu, 2013) Power-law spectrum / 1/k? 4 yielding a logarithmic enhancement of the recoil single scattering z k 2? ˆqt f or t f p!/ˆq B(t) Gunion-Bertsch (or GLV) spectrum x y r! dn d! d 2 k ' sn c 2 ˆq 0 L k 4? 0 t 1 t t 2 L The one-loop contribution to p? -broadening to double-log accuracy: Z hp 2?i rad = k 2!,k Z Z dn d! dk 2 d! d 2 k = ˆq? 0L! k? 2 L ˆq INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 20 / 43

25 A renormalization group equation for ˆq (Liou, Mueller, Wu, 2013; Blaizot and Mehtar-Tani, 2014; E.I., 2014) The limits of the double-logarithmic phase space are simpler in terms of the formation time t f =2!/k? 2 (below, 1/T ) ˆq 0 ˆq Z L Z dt ˆqL f dk? 2 = t f ˆqt f k? 2 = 2 ln2 L a relatively large correction =) needs for resummation the general ( BK ) equation reduces to a linear equation : DLA Z L Z dt ˆqL f dk? 2 ˆq(L) =ˆq 0 + t f ˆqt f k? 2 ˆq(t f,k?) 2 not the standard DLA equation: medium-dependent integration limits ˆq(L) =ˆq 0 1 p ln L/ I 1 2 p ln L / L 2p large anomalous dimension s =2 p 1 INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 21 / 43

26 Using a running coupling (E.I., D.N. Triantafyllopoulos, 2014) The running coupling slows down the evolution at large Y ln(l/ ) Z L dt f ˆq(L) =ˆq 0 + =) ln ˆq(L) ' 4 r t f b 0 ln L Z ˆqL ˆqt f dk 2? k 2? (k 2?) ˆq(t f,k 2?) (slower than any exponential) q`shylêq`h0l Y INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 22 / 43

27 Radiation from multiple soft scattering (Baier, Dokshitzer, Mueller, Peigné, Schiff; Zakharov; ) The single hard scattering regime does not also control the energy loss Z h Ei rad =!,k! dn Z!c Z ˆqL d! d 2 k = ˆq dk? 2 0L d! ˆqt f k? 4 without the k? 2 -weighting, the integral is controlled by its lower limit k? 2 ˆqt f pˆq! r! & t f ˆq The BDMPS-Z spectrum for medium-induced radiation! dn d! d 2 k ' L t f (!) 1 pˆq! e k 2? pˆq! the emission can occur anyway inside the medium: a factor L/t f (!) transverse momentum broadening during formation: hk 2? i'pˆq! Maximal! for this mechanism: t f apple L )! apple! c ˆqL 2 INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 23 / 43

28 Angular distribution Transverse momentum broadening during formation & after formation formation angle: f (!) ' (ˆq!)1/4! ' 1/4 ˆq! 3 the minimal angle final angle c = f (! c )= 1 pˆql 3 (!) ' pˆql! = c! c! Soft gluons!! c : small formation times (t f L) &largeangles( c ) Gluons with angles larger than the jet opening angle 0 move outside the jet INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 24 / 43

29 The average energy loss Differential probability for one emission (integrated over k? )! dp d! ' L r t f (!) '!c! (! <! c ˆqL 2 /2) The average energy loss by a particle with energy E>! c E = Z!c d!! dp d! s! c sˆql 2 integral dominated by its upper limit! =! c Hard emissions with!! c :probabilityofo( s ) rare events but which take away a large energy small emission angle c ) the energy remains inside the jet Irrelevant for the di-jet asymmetry and also for the typical events INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 25 / 43

30 Multiple branching J.-P. Blaizot, E. I., Y. Mehtar-Tani, PRL 111, (2013) When!(dP/d!) 1, multiple branching becomes important! dp r d! '!c! 1=)!.! br(l) 2ˆqL 2 LHC: the leading particle has E 100 GeV! br 5GeV In a typical event, the LP emits... anumberofo(1) of gluons with!! br a large number of softer gluons with!! br The primary gluons with!.! br keep splitting INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 26 / 43

31 Multiple branching J.-P. Blaizot, E. I., Y. Mehtar-Tani, PRL 111, (2013) When!(dP/d!) 1, multiple branching becomes important! dp r d! '!c! 1=)!.! br(l) 2ˆqL 2 LHC: the leading particle has E 100 GeV! br 5GeV In a typical event, the LP emits... anumberofo(1) of gluons with!! br a large number of softer gluons with!! br The primary gluons with!.! br keep splitting INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 26 / 43

32 Democratic branchings The primary gluons generate mini-jets via democratic branchings daughter gluons carry comparable energy fractions: z 1 z 1/2 contrast to asymmetric splittings in the vacuum: z 1 Via successive democratic branchings, the energy is efficiently transmitted to softer and softer gluons, which eventually thermalize Energy appears in many soft quanta propagating at large angles X INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 27 / 43

33 Democratic branchings The primary gluons generate mini-jets via democratic branchings daughter gluons carry comparable energy fractions: z 1 z 1/2 contrast to asymmetric splittings in the vacuum: z 1 Via successive democratic branchings, the energy is efficiently transmitted to softer and softer gluons, which eventually thermalize CMS: The jet transverse momentum profile P ( r) (p T in annular rings) A natural explanation for the di-jet asymmetry and for jet shapes INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 27 / 43

34 Intra-jet nucler modifications How to understand the excess of soft particles inside the jet cone ( <R)? ratios of fragmentation functions in PbPb / pp 2.5 ATLAS jet y < 2.1 anti-k t R=0.4 jets 2.5 ATLAS jet y < 2.1 anti-k t R=0.4 jets R D(z) 2 jet 126 < p < 158 GeV T jet 200 < p < 251 GeV T jet 316 < p < 398 GeV T ) R D(p T 2 jet 126 < p < 158 GeV T jet 200 < p < 251 GeV T jet 316 < p < 398 GeV T Pb+Pb, pp, s 2 10 s NN -1 = 5.02 TeV, 0.49 nb, 0-10% -1 = 5.02 TeV, 25 pb Martin Rybar, Wednesday z 0.5 Pb+Pb, pp, s s NN = 5.02 TeV, 0.49 nb, 0-10% -1 = 5.02 TeV, 25 pb 2 10 p [GeV] T!7 Medium-induced soft radiation should be pushed at large angles >R Can vacuum-like radiation be modified by the medium? INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 28 / 43

35 Vacuum-like emissions (VLE) P. Caucal, E.I., A. H. Mueller and G. Soyez, PRL 120 (2018) A jet initiated by a colorless q q antenna (decay of a boosted or Z) The antenna propagates through the medium along a distance L Emissions (t f = 1! 2 ) can occur either inside (t f apple L), or outside (t f >L) Evolution stopped by hadronisation: k? '! & QCD INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 29 / 43

36 The vetoed region Remember: the medium introduces an upper limit on the formation time t f. r! ˆq apple L No emission within the range r! ˆq < 1! 2 <L End point of VETOED at! c =ˆqL 2, c = 1 pˆql 3 VLEs in medium occur like in vacuum, but with a smaller phase-space gluons within VETOED should have k? 2 ˆqt f,whichisnotpossible a leading-twist effect: DGLAP splitting functions typical values: ˆq =1GeV 2 /fm, L =4fm,! c = 50 GeV, c =0.05 INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 30 / 43

37 Jet in the vacuum (DLA) Radiation triggered by the parton virtualities: bremsstrahlung dp ' sc R d!! d 2 2 Log enhancement for soft (! E) andcollinear ( 1) gluons Parton cascades: successive emissions are ordered in energy (! i <! i angle ( i < i 1 ), by energy conservation 1 ), by color coherence Double-logarithmic approximation (DLA): strong double ordering d 2 N d!d 2 ' X! 2 n 0 n apple 1 n! ln E n apple n 1 ln 2 0! n! 2 INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 31 / 43

38 Color (de)coherence In vacuum, wideangleemissions( > q q )aresuppressedbycolor coherence the gluon has overlap with both the quark and the antiquark In medium, colorcoherenceiswashed out by collisions after a time t coh ˆqt & 1 r 2? (t) 1 ( q q t) 2 =) t & t coh = 1 (ˆq 2 q q) 1/3 (Mehtar-Tani, Salgado, Tywoniuk; Casalderrey-Solana, E. I., ) INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 32 / 43

39 Color (de)coherence In vacuum, wideangleemissions( > q q )aresuppressedbycolor coherence the gluon has overlap with both the quark and the antiquark In medium, colorcoherenceiswashed out by collisions after a time t coh t coh = 1 (ˆq 2 q q) 1/3 L if q q c ' 0.05 Angular ordering could be violated for emissions inside the medium INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 32 / 43

40 Angular ordering strikes back... But this is not the case for the VLEs! > q q & t f = 1! 2 >t coh =) t f r! ˆq Wide angle emissions ( > q q ) have t f t coh, hence they are suppressed Emissions at smaller angles ( < q q )canoccuratany time DLA cascades inside the medium are still strongly ordered in angles INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 33 / 43

41 There is a life after formation... The VLEs inside the medium have short formation times t f L After formation, gluons propagate in the medium along a distance L They can suffer significant energy loss and momentum broadening additional sources for medium-induced radiation They contribute to the jet multiplicity (fragmentation function) They can emit (vacuum-like) gluons outside the medium INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 34 / 43

42 First emission outside the medium The respective formation time is necessarily large: t f & L An antenna with opening angle c loses coherence in a time t coh L In-medium sources lose color coherence and can also radiate at larger angles After the first outside emission, one returns to angular-ordering, asusual Medium effects at DLA (leading twist): vetoed region + lack of angular-ordering for the first outside emission INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 35 / 43

43 Gluon distribution at DLA Double differential distribution in energies and emission angles: ω [GeV] d2 N T (!, )! 2 d!d 2 E = 200 GeV, q q =0.4 T/T vac ˆq =2GeV 2 /fm, L =3fm θ T/T vac =0in the excluded region T/T vac =1inside the medium and also for!>! c and any E=200 GeV, θ qq =0.4, ᾱ s=0.3, q^ =2 Gev 2 /fm, L=3 fm T/T vac < 1 outside the medium at small angles. c T/T vac > 1 outside the medium at large angles q q INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 36 / 43

44 Jet fragmentation function at DLA ω [GeV] T/T vac 0.2 E=200 GeV, θ qq =0.4, ᾱ s=0.3, q^ =2 Gev 2 /fm, L=3 fm D(!)! dn Z 2 d! = q q d 2 T (!, ) 2 /! θ 0.01 D(ω)/D vac (ω) q^=1 Gev 2 /fm,l=3 fm q^=2 Gev 2 /fm,l=3 fm q^=2 Gev 2 /fm,l=4 fm solid: Λ=100 MeV dashed: Λ=200 MeV E=200 GeV, θ qq - =0.4, ᾱ s= ω [GeV] Slight suppression at intermediate energies (from 3 GeV up to! c ) the phase-space is reduced by the vetoed region the amount of suppression increases with L and ˆq INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 37 / 43

45 Jet fragmentation function at DLA D(!)! dn Z 2 d! = q q d 2 T (!, ) 2 /! 2 2 D(ω)/D vac (ω) q^=1 Gev 2 /fm,l=3 fm q^=2 Gev 2 /fm,l=3 fm q^=2 Gev 2 /fm,l=4 fm solid: Λ=100 MeV dashed: Λ=200 MeV E=200 GeV, θ qq - =0.4, ᾱ s= ω [GeV] Significant enhancement at low energy (below 2 GeV) lack of angular ordering for the first emission outside the medium the enhancement is slowly increasing with the jet energy E (= p T ) INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 37 / 43

46 Jet fragmentation function at DLA D(!)! dn Z 2 d! = q q d 2 T (!, ) 2 /! 2 2 D(ω)/D vac (ω) q^=1 Gev 2 /fm,l=3 fm q^=2 Gev 2 /fm,l=3 fm q^=2 Gev 2 /fm,l=4 fm solid: Λ=100 MeV dashed: Λ=200 MeV E=200 GeV, θ qq - =0.4, ᾱ s= ω [GeV] Significant enhancement at low energy (below 2 GeV) A related proposal by Mehtar-Tani and Tywoniuk, arxiv: INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 37 / 43

47 Beyond DLA: Running coupling & NDLA Remember the double-logarithmic approximations: strong ordering in both energies (P gg ' 1/z) andangles fixed coupling no higher-twist effects: no collisions, no medium-induced radiation DLA - = 150 MeV running coupling - = 150 MeV next-to-dla - = 150 MeV next-to-dla wihout decoherence - next-to-dla - = 150 MeV = 150 MeV D( )/Dvac( ) Jet: E = 200 GeV and =0.4 Medium: ˆq =1GeV 2 /fm and L =3fm D( )/Dvac( ) Jet: E = 200 GeV and =0.4 Medium: ˆq =1GeV 2 /fm and L =3fm [GeV] Adding a running coupling: (k 2? )= 1 b ln! 2 2 2, b = 11/ [GeV] Finite-part of the splitting function: P gg (z) ' 1 z + R 1 0 dz0 P gg (z 0 ) 1 z 0 INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 38 / 43

48 Beyond DLA: Monte Carlo implementation (P. Caucal, E.I., A. H. Mueller and G. Soyez, in preparation) Convolution of three showers: vacuum cascades inside the medium but outside the vetoed region full splitting functions, running coupling, quarks and gluons, N c =3 medium-induced cascade in energy with democratic branchings fixed coupling, energy loss, transverse momentum broadening partons with angles > 0 are leaving the jet vacuum cascade outside the medium no angular ordering for the first emission outside the medium all the partons inside the jet (vacuum-like & medium-induced) can act as sources cascades stop at the hadronisation line Leading parton selected according to the cross-section for pp! 2 partons experimental bias towards events with small energy loss typical energy loss: E 2! c, rather than average: h Ei! c INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 39 / 43

49 MC: preliminary results INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 40 / 43

50 MC: preliminary results (2) Focus on 2 observables: R AA : jet yield in AA normalized to pp ratio of FFs in AA and pp Various choices for ˆq, L and s, med INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 41 / 43

51 MC: preliminary results (3) No quenching : just VLEs no energy loss: R AA =1 suppression in FF at small No decoherence : strict angular ordering (including first outside emission) no effect on energy loss (R AA ) little enhancement at small Quenching before VLEs : no VLEs inside the medium R AA larger & increasing with p T,jet Partons created inside the medium via medium-induced emissions significantly contribute to the soft radiation outside the medium INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 42 / 43

52 Conclusions & perspectives Vacuum-like emissions inside the medium can be factorized from the medium-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 Qualitative agreement with the LHC data for jet fragmentation VLEs inside the medium act as sources for medium-induced radiation DLA: fine for multiplicity, but not for energy flow Probabilistic picture, well suited for Monte-Carlo implementations INT Program 18-3, Seattle, Nov 2018 Jet evolution in a dense medium Edmond Iancu 43 / 43