Jets in QCD media: From Coherence to Decoherence

Transcription

1 Jets in QCD media: From Coherence to Decoherence Yacine Mehtar- Tani In collabora;on with C. Salgado and K. Tywoniuk arxiv: , arxiv: [he- h] Excited QCD February Ecole des Houches

2 What is a Jet? A collimated and energe/c bunch of hadrons roduced in a hard rocess [2- jet event at LEP]

3 What is a Jet? π g π q Originally a jet is born as a hard arton (quark/gluon) which fragments into many artons when the ;me goes by with decreasing virtuality down to a non- erturba;ve scale where hadroniza;on takes lace Parton shower is well described within QCD LPHD: Hadroniza;on does not affect exclusive observables: Jet shae, energy distribu;on, etc. K

4 How about jets in HIC? Jets in vacuum is a fine tuned technology. Once the hard arton is roduced it fragments in vacuum without any further interac;on in the final state as an indeendent object : energy and charge conserva;on, etc. With HIC: Jets do not roagate in vacuum but instead traverse a hot and colored (artonic) medium roduced afer the collision.

5 First jet RHIC, LHC Qualita;ve features: energy conserva;on not ensured, Jets in HIC are broader (less collimated). Issue: Need for theore;cal control! To robe and characterize the roduced QGP

6 Jets in vacuum (basics) Dynamics of an energe;c arton roduced in a hard collision QCD bremsstrahlung : an accelerated charge radiates sof gluons Double logarithmic divergence (DLA): collinear and sof ω E jet ω dn α S dω ω dθ θ α S ln 2 E jet θ E jet What haens when α S ln 2 E jet O(1)?

7 QCD coherence DLA: Successive gluon emissions are ordered in energies and angles E jet E jet ω 1... ω N θ 1 θ 2... θ N ω 1 ω 2 ωn θ 1 θ 2... θ N MLLA: energy conserva;on, running of the couling, etc. A. Basseto, M. Ciafaloni, G. Marchesini, A. H. Mueller (1982) V. S. Fadin (1983)]

8 DLA: Let s have a closer look QCD coherence leads to the dele;on of sof gluons! dn/dξ ξ =ln(e jet / h ) The Hum- backed lateau

9 QCD coherence Successive gluon emissions are ordered in energy and angle E jet E jet ω 1... ω N θ 1 θ 2... θ N ω 1 ω 2 What haens ωn θ 1 θ 2... when one turns the θ QGP on? N

10 From Jet- Quenching to Jets? Radia;ve arton energy loss: inclusive 1- gluon sectrum Remember! Need 2 gluon emissions to see QCD coherence (angular- ordering) t + ω ω t The hard quark loses energy by medium- induced gluon radia;on

11 From Jet- Quenching to Jets? Radia;ve arton energy loss: inclusive 1- gluon sectrum. The emised gluon undergoes mul;le scasering in the medium (BDMPS- ZW- GLV icture ( ) ω t + ω t Collinear and infrared finite sectrum!

12 QCD coherence in medium A missing iece On the market: in- medium jet calculus are erformed by enhancing the vacuum emission by the BDMPS/GLV sectrum: No coherence! [QPYTHIA, QHERWIG,JEWEL...] Are medium modified jets mainly determined by the BDMPS/GLV radia;on asern? We know from studying the gluon cascade in vacuum that the 1- gluon emission sectrum is not enough to build u the N- gluon cascade: Interferences, angular ordering, etc, lay a role at higher orders

13 A simle exercise: QCD coherence from the quark- an;quark antenna! k " k! "! " Probabilis;c interreta;on dn q α s dω ω! k " dn = dn q + dn q dθ k θ k Θ(θ θ k ), Quantum interferences lead to a robabilis;c icture! k

14 A simle exercise: QCD coherence from the quark- an;quark antenna Radia;on off the quark (dn q ) No radia;on outside the cone Why? gluons emised at larger angles than the air oening angle can not resolve the internal structure of the air and thus are suressed (t λ 1 form = ω/k ) 2 t form θ >t form θ = r k

15 A simle exercise: QCD coherence from the quark- an;quark antenna! k "! " k! "! k " k

16 A simle exercise: QCD coherence from the quark- an;quark antenna! k "! " k! "! k " k Let s switch on the medium

17 A simle exercise: QCD coherence from the quark- an;quark antenna! k "! " k! "! k " k Let s switch on the medium single interac;on: one gluon exchange with the medium

18 A simle exercise: QCD coherence from the quark- an;quark antenna! k "! " k! "! k " k Let s switch on the medium single interac;on: one gluon exchange with the medium

19 A simle exercise: QCD coherence from the quark- an;quark antenna! k "! " k! "! k " k Let s switch on the medium single interac;on: one gluon exchange with the medium

20 A simle exercise: QCD coherence from the quark- an;quark antenna! k "! " k! "! k " k Let s switch on the medium single interac;on: one gluon exchange with the medium

21 A simle exercise: QCD coherence from the quark- an;quark antenna! k "! " k! "! k " k Let s switch on the medium single interac;on: one gluon exchange with the medium QGP: classical background field A µ 0 (x)

22 Classical icture: Yang- Mills equa;ons Inut: the classical current limit: E, θ 0, gauge: A + =0 The gluon radia;on amlitude off the quark M i,a 1(q) = ig2 f abc C c where J air = J q + J q J µ q = g µ E δ(3) (x E t) Θ(t) Ca t a d 2 q (2π) 2 q t2 v (k +, (k q)2 2k +, (k q) i ) t 1 dta b 0(t, q ) ν i v 1 e i v t E + κi v k ei E t Is the quark- medium momentum exchange ν = + k + (k q) κ = + k + k

23 Classical icture: Yang- Mills equa;ons The gluon radia;on amlitude off the quark M i,a 1(q) = ig2 f abc C c d 2 q (2π) 2 t2 t 1 dta b 0(t, q ) ν i v 1 e i v t E + κi v k ei E t

24 Classical icture: Yang- Mills equa;ons The gluon radia;on amlitude off the quark M i,a 1(q) = ig2 f abc C c d 2 q (2π) 2 t2 gluon interac;on with the medium quark t 1 dta b 0(t, q ) ν i v 1 e i v t E + κi v k ei E t an;quark

25 Classical icture: Yang- Mills equa;ons The gluon radia;on amlitude off the quark M i,a 1(q) = ig2 f abc C c d 2 q (2π) 2 t2 t 1 dta b 0(t, q ) ν i v gluon bremsstrahlung 1 e i v t E + κi v k ei E t quark quark an;quark an;quark

26 Classical icture: Yang- Mills equa;ons The gluon radia;on amlitude off the quark M i,a 1(q) = ig2 f abc C c d 2 q (2π) 2 t2 t 1 dta b 0(t, q ) ν i v Similarly for the an;quark 1 e i v t E + κi v k ei E t quark quark an;quark an;quark

27 Induced gluon radia;on sectrum Squaring the amlitude M 2 M q + M q 2 = M q 2 + M q 2 +2ReM q M q

28 Induced gluon radia;on sectrum Squaring the amlitude M 2 M q + M q 2 = M q 2 + M q 2 +2ReM q M q BDMPS/GLV (1- scasering)

29 Induced gluon radia;on sectrum Squaring the amlitude M 2 M q + M q 2 = M q 2 + M q 2 +2ReM q M q BDMPS/GLV (1- scasering) Interference term

30 where The sectrum

31 The sectrum GLV (quark)

32 The sectrum GLV (quark) GLV (an;quark)

33 The sectrum GLV (quark) GLV (an;quark) Interferences

34 The sectrum GLV (quark) GLV (an;quark) Interferences Bremsstrahlung interference (sof divergence)

35 The sof limit and an;- angular ordering ω 0, the quark on the z axis (2π) 2 ω dn soft d 3 k κ κ ( k)( k) L 0 dt d 2 q (2π) 2 V (q )(1 cos q Ē t) an;quark quark L

36 The sof limit and an;- angular ordering ω 0, the quark on the z axis (2π) 2 ω dn soft d 3 k κ κ ( k)( k) L 0 dt d 2 q (2π) 2 V (q )(1 cos q Ē t) A med ˆqL r 2 ln 1 r m D Diole scasering amlitude an;quark r Ē L θ L quark L z

37 The sof limit and an;- angular ordering ω 0, the quark on the z axis (2π) 2 ω dn soft d 3 k κ κ ( k)( k) L 0 dt Integra;ng over the azimuth d 2 q (2π) 2 V (q )(1 cos q Ē t) dn dωdθ 1 ω sin θ 1 cos θ Θ(cos θ cos θ)a med (θ )

38 The sof limit and an;- angular ordering ω 0, the quark on the z axis (2π) 2 ω dn soft d 3 k κ κ ( k)( k) L 0 dt Integra;ng over the azimuth d 2 q (2π) 2 V (q )(1 cos q Ē t) dn dωdθ 1 ω sin θ 1 cos θ Θ(cos θ cos θ)a med (θ ) No emissions inside the air!

39 The sof limit and an;- angular ordering Sof divergence and an;- angular ordering vacuum+medium: (ω 0) dn q = 1 2π α dω sc F ω Vacuum emission: inside the cone sin θdθ 1 cos θ [Θ(cos θ cos θ ) + A med (θ )Θ(cos θ cos θ)] Medium emissions: outside the cone! Angular ordering in vacuum! Anti-angular ordering in the medium

40 L=20 GeV - 1 = 4 fm Full sectrum (some numerics) ω dn/dωdϑ ω dn/dωdϑ ω = 1 GeV Sum, calc(y=y*cos(x) Quark interference, c 3000 GLV quark, calc(y=y* GLV anti-quark, calc( Gluon interference, c ω = 0.5 GeV ω = 5 GeV ω = 2 GeV ϑ qq = 0.1 Quark brems. Interf. GLV ϑ ϑ ϑ ϑ GLV interf.

41 dn q = 1 2π α dω sc F ω Decoherence in Oaque media sin θdθ 1 cos θ [Θ(cos θ cos θ ) + A med (θ )Θ(cos θ cos θ)] First order in the scasering center density: A med =ˆqL r 2 1 ln r m D " dn/d"d!! vacuum radiation medium-induced radiation !!! Angular ordering in vacuum Anti-angular ordering in the medium r Ē L θ L

42 dn q = 1 2π α dω sc F ω Decoherence in Oaque media sin θdθ 1 cos θ [Θ(cos θ cos θ ) + A med (θ )Θ(cos θ cos θ)] Resumming mul;le scaserings: A med =1 e ˆqL r2 ln 1 r m D " dn/d"d!! vacuum radiation medium-induced radiation !!! Angular ordering in vacuum Anti-angular ordering in the medium r Ē L θ L

43 dn q = 1 2π α dω sc F ω Decoherence in Oaque media sin θdθ 1 cos θ [Θ(cos θ cos θ ) + A med (θ )Θ(cos θ cos θ)] In the high density limit dn q 1 2π α dω sc F ω A med 1 sin θdθ 1 cos θ A. Leonidov, V. Nechitailo, [arxiv: [nucl- th]]. " dn/d"d!! vacuum radiation medium-induced radiation !!! Angular ordering in vacuum Anti-angular ordering in the medium r Ē L θ L

44 Decoherence in Oaque media Antenna in a singlet state dnq γ = 1 2π α dω sc F ω sin θdθ 1 cos θ Θ(cos θ cos θ ) Colored antenna (g* to qq or gg) dnq g = 1 2π α dω s ω sin θdθ C F Θ(cos θ cos θ ) + C A Θ(cos θ cos θ) 1 cos θ Extra iece: large angle emissions of the total charge of the air ( C A for a gluon )

45 Decoherence in Oaque media Antenna in a singlet state (in- medium) dnq γ = 1 2π α dω sc F ω Colored antenna (g* to qq or gg) (in- medium) dnq g = 1 2π α dω s ω sin θdθ 1 cos θ [Θ(cos θ cos θ ) + A med (θ )Θ(cos θ cos θ)] sin θdθ C F [Θ(cos θ cos θ ) + Θ(cos θ cos θ)a med (θ )] 1 cos θ +C A Θ(cos θ cos θ)(1 A med (θ ))

46 Decoherence in Oaque media Antenna in a singlet state (in- medium) dnq γ = 1 2π α dω sc F ω Colored antenna (g* to qq or gg) (in- medium) dnq g = 1 2π α dω s ω sin θdθ C F [Θ(cos θ cos θ ) + Θ(cos θ cos θ)a med (θ )] 1 cos θ +C A Θ(cos θ cos θ)(1 A med (θ )) Memory loss in the oaque limit sin θdθ 1 cos θ [Θ(cos θ cos θ ) + A med (θ )Θ(cos θ cos θ)] A med 1 dn g q = dnq γ = 1 2π α dω sc F ω sin θdθ 1 cos θ

47 Toward medium modified jets? Coherence (neglected so far) lays an imortant role in medium- jet modifica;on Geometrical seara;on between vacuum radia;on and medium induced one. Total decoherence in oaque media (Memory loss). Logarithmic sof divergence: resumma;on of LL QCD evolu;on eqs. in medium

48 Back u slides

49 L=20 GeV - 1 = 4 fm Full sectrum (some numerics) ω dn/dωdϑ ω dn/dωdϑ ω = 1 GeV Sum, calc(y=y*cos(x) Quark interference, c 3000 GLV quark, calc(y=y* GLV anti-quark, calc( Gluon interference, c ω = 0.5 GeV ω = 5 GeV ω = 2 GeV ϑ qq = 0.1 Quark brems. Interf. GLV ϑ ϑ ϑ ϑ GLV interf.

50 Classical icture: Yang- Mills equa;ons [D µ,f µν ]=J ν [D µ,j µ ]=0 Sof gluons are described by a classical field M a,µ (k) = lim k 2 0 k2 A a,µ (k) The gluon roduc;on cross- sec;on: (2π) 3 2ω dn d 3 k = M a (k) λ 2 Linear resonse λ=±1 A µ A µ 0 + Aµ ind

51 Medium average Gaussian white noise A a 0(t, q )A b 0 (t, q ) =ˆq δ ab δ(t t )δ (2) (q q )V (q ) 2- dimen;onal Coulomb oten;al (µ=m D ) V (q )= 1 (q 2 + µ2 ) 2

52 The sectrum Rearranging the terms according to the hases Ω 1, Ω 2, Ω 12 GLV GLV (interf) Interferences L L

53 Full sectrum (integra;ng the angle) ω dn/dω GLV - GLVinterf. Liatov^2 interf. Total The sectrum is droing exonen;ally ω dn dω e ω/ω max 0.01 ω max (θ 2 L) ω [GeV] GLV is cancelled by art of the gluon interferences