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TECHQM Charge to the Working Groups

TECHQM Charge to the Working Groups. Urs Achim Wiedemann CERN PH-TH. Wiedemann, NPB 588 (2000) 303. Radiation off produced parton. Parton undergoes Brownian motion :. Measures target average:. Two approximation schemes:. Harmonic oscillator approximation:.

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TECHQM Charge to the Working Groups

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  1. TECHQMCharge to the Working Groups Urs Achim Wiedemann CERN PH-TH

  2. Wiedemann, NPB 588 (2000) 303 Radiation off produced parton Parton undergoes Brownian motion: Measures target average: Two approximation schemes: Harmonic oscillator approximation: 2. Opacity expansion in powers of The medium-modified Final State Parton Shower

  3. To first order in opacity, there is a generally complicate interference between vacuum radiation and medium-induced radiation. in the parton cascade limit , we identify three contributions: Probability conservation of medium-independent vacuum terms. Transverse phase space redistribution of vacuum piece. Medium-induced gluon radiation of quark coming from minus infinity L 2 2 + + + + Rescattering of vacuum term Bertsch-Gunion term 2 Opacity Expansion - up to 1st order U.A.Wiedemann

  4. Baier, Dokshitzer, Mueller, Peigne, Schiff (1996); Zakharov (1997); Wiedemann (2000); Gyulassy, Levai, Vitev (2000); Wang ... Medium characterized by transport coefficient: • pt-broadening of shower • energy loss of leading parton Salgado,Wiedemann PRD68:014008 (2003) The medium-modified Final State Parton Shower

  5. Probability of propagation without touching medium. Probability of losing energy in medium. Quenching Weights Ideally, we would like to know n-gluon medium-induced emission probabilities, accounting for the loss of a fraction of the parent quark energy. We don’t know how to calculate this rigorously. First attempt: reiterate probabilistically the one-gluon medium-induced emission. The probability of losing the energy via arbitrary n-gluon emission is: Baier, Dokshitzer, Mueller, Schiff, JHEP (2001) 1 2 U.A.Wiedemann

  6. ASW: Quenching Weights for Brick Problem Typical example, more on TECHQM web page

  7. How to implement LPM-effect in MCs? • General assumption about the medium: • The medium gives the projectile the possibility to enter elastic or • inelastic interactions, given by cross sections (scattering centers • QT are distributed with density n • General problem of putting LPM effect in Monte Carlos: • How to decide whether different scattering centers act coherently? • Answer: consider formation time for gluon produced in single scattering If tF < d (distance to next scattering center) then -> gluon produced incoherently, probabilistic implementation trivial If tF > d then -> add qT,i of next (ith) scattering center to get -> recalculate inelastic process under constraint that qtot is transferred from medium (i.e. assume coherent production) -> determine new formation time -> check whether t’F < d , else repeat

  8. Formation time constraint alone gives L^2-dependence of average energy loss K. Zapp, J. Stachel, U.A. Wiedemann, to appear this week Case 1: incoherent limit without energy conservation Case 2: LPM effect without energy conservation Case 3: LPM effect with energy conservation quantitatively consistent with BDMPS, ASW Case 4: incoherent limit with energy conservation

  9. Formation time constraint alone gives sqrt{omega}-dependence of gluon spectrum K. Zapp, J. Stachel, U.A. Wiedemann, to appear this week Case 1: incoherent limit without energy conservation Case 2: LPM effect without energy conservation Case 3: LPM effect with energy conservation quantitatively consistent with BDMPS, ASW Case 4: incoherent limit with energy conservation

  10. In the same way in which quantum interference in the vacuum shower can be treated by a probabilistic algorithm with angular ordering alone, we have shown that the dominant medium-induced quantum interference can be treated by implementation of a formation time constraint alone. We know how to implement the LPM-effect probabilistically in MC simulations. The algorithm is quantitatively consistent with analytical results (BDMPS ASW) The LPM Algorithm extends without further model assumptions to multiple parton branching. We are currently implementing this MC algorithm in JEWEL. This code will be quantitatively consistent in the corresponding limits with all analytical results (not only BDMPS ASW, also collisional e-loss and the baseline of the vacuum parton shower)

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