Onset of Jet decoherence in dense QCD media

Transcription

1 Onset of Jet decoherence in dense QCD media Yacine Mehtar-Tani In collaboration with Carlos A. Salgado and Konrad Tywoniuk PRL 106 (2011) arxiv: [he-h] arxiv: [he-h] Y. M.-T. and K. Tywoniuk, arxiv: [he-h] Work in rogress Oct 10, 2011 GGI worksho 2011 Florence

2 Outline Introduction to color coherence Antenna radiation attern in a medium Onset of Decoherence (soft limit: Leading Log) Jet Decoherence at higher gluon energies Summary and Outlook

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4 Motivation QCD coherence in Jets: Angular Ordering MLLA: Basseto, Ciafaloni, Marchesini, Mueller (1982) Fadin (1983), Dokshitzer, Diakonov, Troian (1980) θ 3 < θ 2 < θ 1 θ 3 < θ 2 < θ 1 Limiting hase sace for soft gluon radiation θ 3 θ 2 θ 1 θ 3 dn/dξ θ 2 ξ =ln(e jet / h ) Markovian rocess «Building block for QCD evolution» (MC)!"#$%&'()*+,-.#/0$)1,2#,'$

5 Motivation QCD coherence in Jets: Angular Ordering MLLA: Basseto, Ciafaloni, Marchesini, Mueller (1982) Fadin (1983), Dokshitzer, Diakonov, Troian (1980) θ 3 < θ 2 < θ 1 θ 3 < θ 2 < θ 1 Limiting hase sace for soft gluon radiation θ 3 θ 2 θ 1 θ 3 dn/dξ θ 2 ξ =ln(e jet / h ) Markovian rocess «Building block for QCD evolution» (MC) E jet θ ω!"#$%&'()*+,-.#/0$)1,2#,'$ dn α S dω ω dθ θ α S ln 2 E jet

6 Motivation QCD coherence in Jets: Angular Ordering MLLA: Basseto, Ciafaloni, Marchesini, Mueller (1982) Fadin (1983), Dokshitzer, Diakonov, Troian (1980) θ 3 < θ 2 < θ 1 θ 3 < θ 2 < θ 1 Limiting hase sace for soft gluon radiation θ 3 θ 2 θ 1 θ 3 dn/dξ QGP θ 2 ξ =ln(e jet / h )!"#$%&'()*+,-.#/0$)1,2#,'$ Q: How does the QGP alter QCD coherence in a jet?

7 Motivation QCD coherence in Jets: Angular Ordering MLLA: Basseto, Ciafaloni, Marchesini, Mueller (1982) Fadin (1983), Dokshitzer, Diakonov, Troian (1980) θ 3 < θ 2 < θ 1 θ 3 < θ 2 < θ 1 Limiting hase sace for soft gluon radiation QGP θ 1 θ 2 θ 3 θ 2 θ 3 dn/dξ ξ =ln(e jet / h ) Q: How does the QGP alter QCD coherence in a jet?!"#$%&'()*+,-.#/0$)1,2#,'$

8 Antenna in vacuum (Building block of QCD evolution)! k "! " k! "! k " k (2π) 2 ω dn vac γ d 3 k = α sc F ω 2 (R q + R q 2 J ), Destructive interferences

9 Antenna in vacuum (Building block of QCD evolution) dn vac q,γ = α sc F π dω ω sin θ dθ 1 cos θ Θ(cos θ cos θ q q), Θ q q Radiation confined inside the cone Angular ordering in vacuum Why? Gluon emitted at angles larger than the air oening angle cannot resolve its internal structure: Emission by the total charge (suressed for a white antenna) Simler Q: How Does the QGP alter the antenna emission attern?

10 In medium: single emitter Energy loss: Broadening: (BDMPS-Z) Baier, Dokshitzer, Mueller, Peigné, Schiff ( ) Zakharov (1996) Wiedemann (2000) Gyulassy, Levai, Vitev (2000) E = α s C R ω c = α s C R ˆqL 2 k 2 = ω c /L Q 2 s =ˆqL ω di dω ωc ω Medium induced sectrum: Gluon interacts kt-broadening QGP C. A. Salgado, U. A. Wiedemann (2003) No soft/collinear divergence No vacuum-like medium-induced radiation Need two emitters to see QCD coherence and build-u in-medium jet evolution

11 Antenna in medium Y. M.-T., C. A. Salgado and K. Tywoniuk, PRL 106 (2011) arxiv: [he-h]! k "! " k! "! k " k

12 Antenna in medium Y. M.-T., C. A. Salgado and K. Tywoniuk, PRL 106 (2011) arxiv: [he-h] QGP! k " k! "! " QGP! k " k Let s switch on the medium

13 Antenna in medium Y. M.-T., C. A. Salgado and K. Tywoniuk, PRL 106 (2011) arxiv: [he-h] QGP! k " k! "! " QGP! k " k Let s switch on the medium Small angle aroximation θ, θ q q 1 The medium is modeled as a Classical background field A med (x+,x )= 1 2 ρ med (x +,x ), A i med = A + med =0

14 Classical Yang Mills [D µ,f µν ]=J ν, [D µ,j µ ]=0 J J q + J q The eikonal current gets simly color rotated J q (x) =gu (x +, 0) δ (3) (x E t)θ(t) Q q U (x +, 0) = P + ex ig x + 0 dz + T A med z +, + z+ Multile scattering of the quarks (Unitarity imlemented)

15 Classical Yang Mills Reduction formula or k 0 y + L Linear resonse of the medium (LC-gauge) F. Gelis, Y. M.-T. (2005), Y. M.-T (2007)

16 Classical Yang Mills Gluon roagator (Brownian motion in the transverse lan) k The amlitude for gluon radiation off the quark 0 y + L n = / +

17 Classical Yang Mills

18 Classical Yang Mills Indeendent emission off the quark (BDMPS-Z sectrum) x = k + / +

19 Classical Yang Mills Interferences Y. M.-T. and K. Tywoniuk [he-h] J. Casalderrey-Solana and E. Iancu arxiv: (JHEP 2011) x = k + / + Decoherence arameter

20 Leading Log (ω 0) The amlitude in the soft limit (no gluon-medium interaction) x = k + / + κ λ M λ (k) = ig x ( k) U (L, 0) Q q + κ λ x ( k) U (L, 0) Q q R q g2 C F x( k) 4g2 C F ω 2 θ 2 k Medium effects cancel out ( UU =1) No soft-div in BDMPS-Z sectrum Interferences lead to medium-induced soft-divergence J g2 C F Nc 2 1 Tr U q(l, 0)U q κ κ (L, 0) x x ( k)( k)

21 Leading Log (ω 0) soft-gluon radiation off an antenna in a singlet state (2π) 2 ω dn tot γ d 3 k = α sc F ω 2 R vac q + R vac q 2(1 med )J vac The decoherence arameter med =1 1 N 2 c 1 Tr U (L, 0)U (L, 0) Multile soft scattering aroximation med 1 e 1 12 ˆq θ2 q q L3 " dn/d"d!! vacuum radiation medium-induced radiation !

22 Leading Log (ω 0) med 0 (Coherence) Θ q q med 1 (Decoherence) dn tot q,γ = α sc F π dω ω sin θ dθ 1 cos θ [Θ(cos θ cos θ q q)+ med Θ(cos θ q q cos θ)]. Total decoherence in oaque media 12 dn tot q,γ oaque = α sc F π dω ω sin θ dθ 1 cos θ. " dn/d"d!! vacuum radiation medium-induced radiation !

23 Memory loss Antenna in the octet reresentation (gluon): additional out-of-cone radiation off the total charge of the air (2π) 2 ω dn tot g d 3 k =(2π)2 ω dn tot γ d 3 k + α sc A ω 2 (1 med ) J In the oaque limit: med 1 dng tot oaque = dnγ tot oaque Emission off the total charge of the air is suressed

24 Gaussian aroximation Multile soft-scattering aroximation A a med(x +, q)a b med(x +, q ) δ ab n(x + ) δ(x + x + )(2π) 2 δ (2) (q q )V 2 (q), Harmonic oscillator 1 2 nσ(r) 1 4 ˆq r2 1 N 2 c 1 Tr U(r)U (0) =ex 14 ˆqLr2

25 Decoherence at high gluon energies The decoherence arameter med 1 ex[ 1 12 Q2 s r 2 ] (A two scale roblem) Q 2 s =ˆqL r = θ q q L r <Q 1 s (Diole regime) r >Q 1 (Decoh. regime) s Θ q q r Q 1 s Θ q q r Q 1 s med 1 12 Q2 s r 2 med 1 screening length Hard scale: Q max (r 1 and,q s) k <Q

26 Angular distribution ( r <Q 1 ) s Diole regime ˆq =1GeV 2 /fm θ q q =0.1 L =5fm Θ q q 10 vacuum 10 vacuum 8 BDMPS TOTAL 8 vac. decoh. BDMPS ωdn/dωdϑ med. interf. ω =1GeV ωdn/dωdϑ TOTAL med. interf. ω = 10 GeV ω dn ind q θ R ind q J ind integrating over the azimuth ω θ " dn/d"d!! vacuum radiation medium-induced radiation

27 Energy sectrum in the diole regime ind dn /dn ind θ q q L ˆq ω r ωdn /dω ind dn ind q dense dilute 1 10 ω R ind q L J ind ˆq Hard scale set by Q r 1 =(θ q ql) 1

28 Angular distribution ( r >Q 1 ) s Decoherence regime ˆq =5GeV 2 /fm θ q q =0.1 L = 10 fm Θ q q 10 vacuum 10 vacuum 8 vac. decoh. BDMPS 8 vac. decoh. BDMPS ωdn/dωdϑ TOTAL med. interf ω θ ωdn/dωdϑ Decoherence ω Coherence: k >Q s θ TOTAL med. interf. " dn/d"d!! vacuum radiation medium-induced radiation

29 Energy sectrum in the decoh. regime ind R L ˆq BDMPS ωdn /dω ind dense L ˆq dilute ind ind J /J ω/qs med. ind. interf. Q s = GeV L ˆq 0.01 dn ind q 1 10 ω R ind q Hard scale set by J ind ω/qs Q Q s = ˆqL

30 Decoherence: a new mechanism Geometrical searation (medium/vacuum rad.) Medium-induced soft-gluon radiation at large angles Suorted by new LHC data! " dn/d"d!! vacuum radiation medium-induced radiation ! vacuum-like frag. func. R<0.3 Momentum in dijets balanced by low t art. at large angles CMS

31 Summary and Outlook Gradual decoherence of the antenna: Onset of a out-of-cone medium-induced soft divergence (novel mechanism for soft-gluon radiation) Decoherence survives at higher energies u to a tyical transverse scale Qs Toward Medium-modified QCD evolution equations... Partial decoherence in the dilute(diole) regime Total decoherence in the oaque limit (memory loss)