Multiplicity distributions for jet parton showers in the medium

Transcription

1 Multiplicity distributions for jet parton showers in the medium Nicolas BORGHINI in collaboration with U.A. WIEDEMANN CERN N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.1/17

2 Jet parton showers in the medium Jet quenching modelled by medium-induced successive emission of independent soft gluons by a fast parton spectrum of radiated energy per unit length: Novel features of the approach presented here: E ω di dω dl Primary and secondary parton splittings treated equally Energy-momentum conserved at each splitting we implement this as a medium-induced modification of ω E Modified Leading Logarithmic Approximation N.B. & U.A. Wiedemann, hep-ph/ N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.2/17

3 MLLA: main ingredients Resummation of double- and single-logarithms in ln 1 x and ln E jet Λ eff Intra-jet colour coherence: independent successive branchings g gg, g q q, q qg with angular ordering of the sequential parton decays: at each step in the evolution, the angle between father and offspring partons decreases Includes in a systematic way next-to-leading-order corrections O( α s (τ))! Hadronization through Local Parton-Hadron Duality (LPHD) N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.3/17

4 MLLA: generating functional Central object : generating functional Z i [Q,Θ;u(k)] generates the various cross sections ( ggg, ggq q... ) for a jet coming from a parton i (= g, q, q) with energy Q in a cone of angle Θ Z i [Q,Θ;u(k)] = e wi(q,θ) u(q) + Θ dθ 1 Θ dz e w i(q,θ ) w i (Q,Θ) α s(k ) j 0 2π P ji (z)z j [zq,θ ;u]z k [(1 z)q,θ ;u] i Q zq j (1-z)Q k N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.4/17

5 MLLA: generating functional Central object : generating functional Z i [Q,Θ;u(k)] generates the various cross sections ( ggg, ggq q... ) for a jet coming from a parton i (= g, q, q) with energy Q in a cone of angle Θ probability to have Z i [Q,Θ;u(k)] = e wi(q,θ) no branching with angle < Θ u(q) + Θ and Θ Θ dθ 1 Θ dz e w i(q,θ ) w i (Q,Θ) α s(k ) between angular ordering j 0 2π P ji (z)z j [zq,θ ;u]z k [(1 z)q,θ ;u] splitting function i jk i Q zq j (1-z)Q k k z(1 z)q N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.4/17

6 MLLA: limiting spectrum The parton distribution in a jet with energy τ ln Q is given by Λ eff D i (x,τ) Q δ δu(xq) Z i[τ;u(k)] u 1 infrared cutoff Limiting spectrum : D lim (x,τ,λ eff ) = with 4N cτ bb(b + 1) ɛ+i ɛ i A 4N c bν, B a b, a 11 3 N c+ 2N f 3N 2 c dν 2πi x ν Φ( A+B+1, B+2; ντ), b 11 3 N c 2 3 N f N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.5/17

7 MLLA: limiting spectrum dn d ln 1 x Limiting spectrum for a 100 GeV jet ln 1 x Hump-backed plateau Note: hump dominated by the singular parts ( 1 z, 1 1 z ) of the P ji(z) N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.6/17

8 MLLA: limiting spectrum dn d ln 1 x 6 5 Limiting spectrum for a 100 GeV jet maximum multiplicity for ln 1 x = τ ( ) 1 + a αs 2 8πN c 4 3 most particles are here 2 1 hard partons Hump-backed plateau cutoff Λ eff soft partons ln 1 x Note: hump dominated by the singular parts ( 1 z, 1 1 z ) of the P ji(z) N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.6/17

9 MLLA vs. e + e data dn d ln 1 x 6 OPAL s 91 GeV TASSO s 14 GeV e e charged hadrons ln 1 x N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.7/17

10 MLLA vs. e + e data dn d ln 1 x 6 5 OPAL s 91 GeV TASSO s 14 GeV MLLA K h 1.28 MLLA K h 1.46 e e charged hadrons D h (x,τ,λ eff ) = K h Dlim (x,τ,λ eff ) Λ eff = 253 MeV ln 1 x Good description in both RHIC and LHC regimes! N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.7/17

11 Influence of the medium: a possibility The hump of the limiting spectrum is mostly due to the singular parts of the splitting functions In medium, the emission of soft gluons by a fast parton increases One can model medium-induced effects by modifying the parton splitting functions P ji (z)... (see e.g. Guo & Wang, PRL 85 (2000) 3591)... and especially their singular parts: P qq (z) = 4 3 f med > 0 Bremsstrahlung increases [ ] 2(1 + fmed ) (1 + z) (1 z) + N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.8/17

12 Influence of the medium on the parton spectrum dn d ln 1 x 7 6 Limiting spectra for a jet with E jet 15 GeV in medium, f med 0.8 in vacuum ln 1 x f med fixed to reproduce R AA redistribution of radiated partons: high p T (large x) low p T (small x) N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.9/17

13 Medium-induced modification of the associated multiplicity Ideal case: photon + jet photon gives jet energy E T Count how many jet particles have a momentum larger than some given cut PT cut after propagating through the medium: N(P T PT cut) medium For a jet in vacuum with energy E T, the spectrum is known one knows (measurement / in vacuum MLLA) Compare N(P T P cut T N(P T PT cut) vacuum ) medium with N(P T PT cut) vacuum N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.10/17

14 Medium-induced modification of the associated multiplicity 1.2 P T P cut T in medium P T P cut, E jet 15 GeV T in vacuum P T cut GeV In the presence of a medium, less particles for P T 1.5 GeV (particle excess for P T 1.5 GeV!) N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.11/17

15 Medium-induced modification of the associated multiplicity P T P cut T in medium P T P cut, E jet 15 GeV T in vacuum AA/pp % top 5% p (GeV/c) 8 10 P T cut GeV In the presence of a medium, less particles for P T 1.5 GeV (particle excess for P T 1.5 GeV!) cf. nucl-ex/ N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.11/17

16 Medium-induced modification of the associated multiplicity P T P cut T in medium P T P cut T in vacuum E jet 200 GeV E jet 100 GeV E jet 15 GeV Measurement more promising at LHC: P T cut GeV the additional soft jet multiplicity can more easily be detected above the event background N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.12/17

17 Nuclear modification factor R AA P T Nuclear modification factor in s NN 200 GeV collisions 1 PHENIX Au Au Π 0, 0 10% centrality 0.8 MLLA, f med 0.8, n P T GeV N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.13/17

18 Nuclear modification factor R AA P T Nuclear modification factor in s NN 200 GeV collisions 1 PHENIX Au Au Π 0, 0 10% centrality 0.8 MLLA, f med 0.8, n 7 MLLA, f med 0.6, n n p T P T GeV R AA (P T ) decreases since higher P T higher Q more splitting parton energy loss may depend on Q? e.g. f med 1/Q 2 N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.13/17

19 MLLA parton shower in medium MLLA analytical description of the particle distribution within a jet Formalism generalized to the propagation in a medium Consistent treatment of parton branchings energy-momentum conservation all branchings treated on an equal footing Phenomenological consequences distortion of the hump-backed plateau large P T range accessible at LHC will test Q 2 -dependence of parton energy loss (in progress) multiplicity above a trigger cutoff First step towards further studies: Intra-jet two-particle correlations Monte-Carlo: geometry, f med (Q 2 )... N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.14/17

20 MLLA parton shower in medium Extra slides N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.15/17

21 Parton shower in medium Write the parton-distribution evolution equation with modified splitting functions. D lim (x,τ) = 4N cτ(1+f med ) ɛ+i dν b ˆB( ˆB + 1) 2πi x νφ( Â+ ˆB+1, ˆB+2; ντ) ɛ i  4N c(1 + f med ) â, ˆB bν b, â f med 3 N c + 2N f 3N 2 c Hadronization (LPHD) still takes place in vacuum: K h unchanged N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.16/17

22 Hadron spectra What if the jet energy is unknown... The measured hadron spectrum is the convolution of a parton spectrum 1/(p T ) n (with a p T -dependent n to account for experimental biases) the fragmentation function D h (x,τ) dn dx 1 dp T x 2 p D dx h (x,p n T ) = T x 2 x n ( P D h x, P T n T x which can be computed within MLLA for both a jet in vacuum and a jet propagating through a medium ) gives the nuclear modification factor R AA N. BORGHINI, Multiplicity distributions for jet parton showers in the medium p.17/17