An introduction to medium induced gluon radiation. Edmond Iancu IPhT Saclay & CNRS

Transcription

1 Edmond Iancu IPhT Saclay & CNRS a review of some relatively old stuff (BDMPS Z, 995) & original work with J. Casalderrey Solana (arxiv:6.3864) June 24th, 2

2 Motivation 2 Antenna pattern 3 BDMPS Z 4 Interference

3 Di jet production at the LHC (cf. talk by A. Baldisseri) A peripheral event 6 p+p collisions, or peripheral Pb+Pb collisions A pair of well collimated, back to back, jets

4 Motivation Antenna pattern BDMPS Z Interference Back up Di jet asymmetry (ATLAS) Central Pb+Pb: mono jet events The secondary jet cannot be distinguished from the background: ET GeV, ET 2 > 25 GeV

5 Di jet asymmetry (CMS) Central Pb+Pb: the secondary jet is barely visible The jet energy has been redistributed in the transverse plane

6 J J J J Di jet asymmetry (ATLAS) ) dn/da (/N % ) dn/da (/N % ) dn/da (/N % ) dn/da (/N s NN =2.76 TeV -% ATLAS Pb+Pb - L int =.7 µb A J A J A J A J ) dn/d φ ) dn/d φ ) dn/d φ ) dn/d φ Pb+Pb Data p+p Data HIJING+PYTHIA (/N (/N (/N (/N φ φ φ φ Event fraction as a function of the di jet energy imbalance A J = E T E T 2 E T + E T...and of the azimuthal angle φ, for different centralities.

7 J J J J Di jet asymmetry (ATLAS) ) dn/da (/N % ) dn/da (/N % ) dn/da (/N % ) dn/da (/N s NN =2.76 TeV -% ATLAS Pb+Pb - L int =.7 µb A J A J A J A J ) dn/d φ ) dn/d φ ) dn/d φ ) dn/d φ Pb+Pb Data p+p Data HIJING+PYTHIA (/N (/N (/N (/N φ φ φ φ Additional energy loss of 2 to 3 GeV due to the medium Typical event topology: still a pair of back to back jets The secondary jet loses energy without being deflected

8 J J J J Di jet asymmetry (ATLAS) ) dn/da (/N % ) dn/da (/N % ) dn/da (/N % ) dn/da (/N s NN =2.76 TeV -% ATLAS Pb+Pb - L int =.7 µb A J A J A J A J ) dn/d φ ) dn/d φ ) dn/d φ ) dn/d φ Pb+Pb Data p+p Data HIJING+PYTHIA (/N (/N (/N (/N φ φ φ φ Additional energy loss of 2 to 3 GeV due to the medium Typical event topology: still a pair of back to back jets The secondary jet loses energy without being deflected Medium induced emissions of soft gluons at large angles

9 J J J J Di jet asymmetry (ATLAS) ) dn/da (/N % ) dn/da (/N % ) dn/da (/N % ) dn/da (/N s NN =2.76 TeV -% ATLAS Pb+Pb - L int =.7 µb A J A J A J A J ) dn/d φ ) dn/d φ ) dn/d φ ) dn/d φ Pb+Pb Data p+p Data HIJING+PYTHIA (/N (/N (/N (/N φ φ φ φ Additional energy loss of 2 to 3 GeV due to the medium Typical event topology: still a pair of back to back jets The secondary jet loses energy without being deflected Medium induced emissions of soft gluons at large angles

10 Medium induced gluon radiation Additional radiation triggered by interactions in the medium Baier, Dokshitzer, Mueller, Peigné, Schiff, Zakharov 995 L k

11 Medium induced gluon radiation Additional radiation triggered by interactions in the medium Baier, Dokshitzer, Mueller, Peigné, Schiff, Zakharov 995 Θ s L This could naturally explain the data in the framework of perturbative QCD (soft gluons, large emission angles) Rencontres... unless Ions Lourds, it is IPNspoilt Orsay 2 by angular An ordering introductionof tosuccessive medium inducedemissions gluon radiation

12 Medium induced gluon radiation Additional radiation triggered by interactions in the medium Baier, Dokshitzer, Mueller, Peigné, Schiff, Zakharov unless it is spoilt by angular ordering of successive emissions

13 Angular ordering (in the vacuum) X X X Destructive interference between different sources The only surviving emissions are those inside the antenna What about medium induced radiation? J. Casalderrey Solana & E.I., arxiv: (JHEP)

14 Angular ordering (in the vacuum) X X X Destructive interference between different sources The only surviving emissions are those inside the antenna What about medium induced radiation? J. Casalderrey Solana & E.I., arxiv: (JHEP)

15 A color antenna: pair The simplest device to study interferences: the two sources ( and ) exist from the very beginning Color singlet ( dipole ) : decay of a photon or of a heavy boson * k Antenna opening angle : θ = θ + θ The interactions with the medium are not explicitly represented

16 A color antenna: pair The simplest device to study interferences: the two sources ( and ) exist from the very beginning Color singlet ( dipole ) : decay of a photon or of a heavy boson L * k Antenna opening angle : θ = θ + θ The interactions with the medium are not explicitly represented

17 Direct emissions Emission probability: amplitude complex conjugate amplitude p k k p Vacuum : the bremsstrahlung spectrum Medium : the BDMPS Z spectrum

18 Interference effects Emission by the uark absorption by the antiuark p k k p Vacuum: angular ordering Medium :???

19 The formation time The gluon must lose coherence with respect to its source k k ω θ b θ τ λ 2/k τ 2ω k 2 2 ωθ 2

20 Transverse momentum broadening The gluon decorrelates from its source via medium rescattering Radiative energy loss transverse momentum broadening parton mean free path : l average (momentum) 2 transfer per scattering : µ 2 D L k d k 2 dt µ2 D l ˆ (jet uenching parameter)

21 In medium formation time τ f The gluon acuires a momentum k 2 f ˆ τ f during formation t f L f k f s τ f 2ω/k 2 f k ~ Q s τ f 2ω ˆ, θ f k f ω ( ) 2ˆ /4 ω 3 The smaller the energy ω, the shorter τ f and the larger the formation angle θ f : prompt & soft gluons, large angles!

22 The BDMPS Z spectrum The in medium formation time cannot be larger than L : τ max f = L = maximal energy (ω c ) & minimal angle (θ c ) Θ f Θ c τ f ω c = ˆL 2 /2 & θ c = 2/ ˆL 3

23 The BDMPS Z spectrum After formation, the gluon can still acuire momentum: final momentum Q 2 s = ˆL & final angle θ s = Q s /ω Θ f Θ s τ f L ω ω c = τ f L = θ s θ f θ c

24 The BDMPS Z phase space The gluon can be emitted at any point within the medium Θ s L

25 The BDMPS Z phase space The gluon can be emitted at any point within the medium Θ s L

26 The BDMPS Z phase space The gluon can be emitted at any point within the medium Θ s L The longitudinal phase space is proportional to L

27 The BDMPS Z phase space The gluon can be emitted at any point within the medium Θ s L The longitudinal phase space is proportional to L What about the corresponding interference terms?

28 The BDMPS Z phase space The gluon can be emitted at any point within the medium Θ s L The longitudinal phase space is proportional to L What about the corresponding interference terms?

29 Interference: vacuum The gluon must be coherent (overlap) with both sources λ 2/k k ω θ, r θ τ τ 2/ωθ 2 k θ θ : large angle emission (out of cone) Large angle gluons see only the total color charge (here, zero)

30 Interference: medium Very large dipole angle : θ θ s Θ s Θ No overlap between the BDMPS Z spectrum by one parton and the other parton no interference

31 Relatively large dipole angles: θ s θ θ f Θ f Θ s Θ τ f L The two BDMPS Z spectra overlap with both sources but can they interfere? No, they cannot! (no overlap during formation)

32 Relatively large dipole angles: θ s θ θ f Θ f Θ s Θ τ f L The two BDMPS Z spectra overlap with both sources but can they interfere? No, they cannot! (no overlap during formation)

33 Relatively small dipole angles: θ f θ θ c Θ s Θ τ f L The spectra overlap with both partons during formation. Naively : The typical emission angles being much larger than θ, there should be destructive interference.

34 Relatively small dipole angles: θ f θ θ Two Partons: Small c An τcoh! " f θf! s The two fronts overlap at formation: they can in The pair rotates color before emission. At But this is spoilt by color rotations which wash out the color coherence of the pair over a time τ coh L ( ) ( ) 2/3 2/3 θc θc τ coh = L τ coh L Lθ θ The color of each uark is randomized No in L

35 Very small dipole angles: θ θ c Θ f Θ Θ c τ f Color coherence is preserved throughout the medium. Quantum coherence is ensured during formation. Destructive interference total contribution is zero

36 Summary Medium induced gluon radiation à la BDMPS Z : a natural mechanism for jet decollimation in perturbative QCD Interference effects are negligible (no angular ordering) the associated phase space is parametrically suppressed as compared to direct emissions The total medium induced radiation by the dipole the incoherent sum of the 2 contributions by the and the preserves large angle emissions during the jet evolution opens the way for Monte Carlo generators (J. Stachel, U. Wiedemann, C. Zapp, 2, w.i.p.) Can pqcd describe the di jet asymmetry seen at the LHC?

37 In medium jet evolution The second gluon is emitted from a uark gluon antenna rad f f g θ g k rad /ω with k 2 rad = ˆτ rad τ rad : typical time between two successive emissions τ P rad (τ) α s C R τ rad τ f θ g θ f τ f α s C R g In medium jet evolution proceeds via independent emissions

38 p T asymmetry (CMS) > (GeV/c) 4 2 T (a) PYTHIA+HYDJET 3-% (b) >.5 GeV/c.5 -. GeV/c GeV/c GeV/c GeV/c > 8. GeV/c -3% <p -2-4 p > 2GeV/c T, p > 5GeV/c T,2 φ > 2 π η <.6,2 3,2 > (GeV/c) 4 2 T (c) CMS Pb+Pb s NN=2.76 TeV - L dt = 6.7 µb 3-% 4 2 (d) -3% <p A J A J

39 In out asymmetry (CMS) > (GeV/c) 4 2 T (a) PYTHIA+HYDJET -3% In-Cone R< (b) >.5 GeV/c.5 -. GeV/c GeV/c GeV/c GeV/c > 8. GeV/c Out-of-Cone R.8 <p p > 2GeV/c T, p > 5GeV/c T,2 φ > 5 π η <.6,2 6,2 > (GeV/c) 4 2 T (c) CMS -3% Pb+Pb s NN=2.76 TeV - L dt = 6.7 µb In-Cone R< (d) Out-of-Cone R.8 <p A J A J

40 R AA at RHIC & the LHC : ALICE R AA - 5% Pb-Pb = 2.76 TeV s NN Nuclear modification factor 7-8% R AA (p ) Yield(A + A) Yield(p + p) A 2 Strong suppression at moderate p T Rapid increase for larger p T Current models do not account for all these features (GeV/c) p T

41 The bremsstrahlung spectrum Direct emission by a uark in the vacuum p k k p dn vac ω dωdk 2 α sc F k 2 α s C F θ 2 τ 2 Vertex suared (θ 2 ) longitudinal phase space (τ 2 ) Mostly soft (ω ) and collinear gluons (θ )

42 Angular ordering Direct emissions plus interferences in the vacuum p k k p ω dn vac dip d 3 k α sc F ( θ τ θ τ ) 2 The interference term ( 2θ θ τ τ ) cancels direct emissions when θ, θ θ = angular ordering

43 Vacuum medium interference A vacuum like gluon emitted at a large angle θ by one of the partons can interfere with the other parton. Θ s Θ This provides a BDMPS Z like contribution to the spectrum.

44 Vacuum medium interference A vacuum like gluon emitted at a large angle θ w.r.t. one parton can interfere with the second parton τ int Θ s Θ... but this has a very small phase space: τ int = ωθ 2 L

45 Relatively large dipole angles: θ s θ θ f Θ f Θ s Θ τ f L Vacuum medium interference is still possible... but it is again suppressed by its small phase space (τ int L)

46 Summary So long as θ θ c, interference is parametrically suppressed when θ θ f, it is suppressed by uantum decoherence when θ f > θ θ c, it is suppressed by color decoherence When θ θ c, the total medium induced radiation vanishes The total medium induced radiation by the dipole the incoherent sum of the 2 contributions by the and the This paves the way to Monte Carlo generators (J. Stachel, U. Wiedemann, C. Zapp, 2, w.i.p.) Can pqcd describe the di jet asymmetry seen at the LHC?