REGGAE – Generator for Uniform Filling of LIPS

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REGGAE – Generator for Uniform Filling of LIPS Ivan Melo, Boris Tomášik, Michal Mereš, Vlado Balek, Vlado Černý Zimanyi Winter School 6. 12. 2012
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Ivan Melo , Boris Tomášik, Michal Mereš, Vlado Balek, Vlado Černý. REGGAE – Generator for Uniform Filling of LIPS. Zimanyi Winter School 6 . 12 . 2012. Multiparticle phase space?. LEP : LHC (pp): LHC (Pb Pb):. n ≥ 4 n ≥ 5,6,8 n ≥ 100. 2/20. - PowerPoint PPT Presentation

Transcript of REGGAE – Generator for Uniform Filling of LIPS

  • REGGAE Generator for Uniform Filling of LIPS

    Ivan Melo, Boris Tomik, Michal Mere, Vlado Balek, Vlado ern Zimanyi Winter School 6. 12. 2012

  • 2/20LEP:LHC (pp):LHC (Pb Pb): n 4 n 5,6,8 n 100Multiparticle phase space?

  • Lorentz invariant phase space - LIPSdynamicskinematics & statistics3/20LIPS:

  • to calculate by Monte Carlo integration

    to generate eventsUniform filling of LIPS?4/20

  • Monte Carlo Integration x1x2x3x4x5x6x7x8Sample mean methodxi have to be uniformly distributed5/20nf = |M|2

  • Event generation Take event uniformly distributed in

    Calculate weight w = |M|2 for this event

    Accept this event with probability w/wmax wmaxw = |M|2nwn6/20

  • GENBOD generator (F. James)7/20fills LIPS uniformly

  • Generate M2, M3 uniformly within kinematic limits Calculate weight w Accept M2, M3 with probability w/wmax Generate angles, calculate momenta, boost to Lab systemM2wM3wmaxGenerate events with Genbod8/20 M22 = (p1 + p2) 2 M32 = (p1 + p2 + p3) 2

  • GENBODw/wmax very lowGood for n < 30 RAMBOw/wmax much better, = 1 for massless particlesGood for n < 100 relativistic particles NUPHAZw/wmax best so far, = 1 for massless particlesBetter than RAMBO, relativistic particles GENBOD vs other generators9/20

  • REGGAE (Tomik, Mere, Melo,Balek,ern) Use Genbod in the 1st step to generate event with any w

    Let the particles in the event collide virtually to reach the most probable configurations in the phase space with w 1Aim to generate pure phase space events with high multiplicity and efficiency for both relativistic and nonrelativistic particles(REscattering after Genbod GenerAtor of Events)10/20Computer Physics Communications 182 (2011) 2561-2566.

  • Small wLarge wGas in a boxFor large n Maxwell-Boltzmann with temperature T11/20

  • E(GeV)12/20

  • LIPSMicrocanonical ensembleBoltzmannLIPS-Boltzmannlarge nlarge nE13/20Darwin-Fowler methodV n

  • Information entropy14/20

  • REGGAE vs other generators numerical integration15/20

  • n = 30 particles with mass 1 GeV, pa+pb = (100 GeV, 0, 0, 0)n = 60 particles with mass 1 GeV16/20

  • What next?REGGAE can fill LIPS uniformly for fixed n and chemical composition

    but can we predict if total CM energy prefers to convert to, say, n=50 or n=60 particles? I.e. generate events with different n?17/20

  • From LIPS to microcanonical phase space?

    LIPS counts states in the momentum space, these states are asymptotic (infinite volume)

    Microcanonical counts states both in momentum and configuration spacewhich has finite volume V Vn19/20|M|2 = 2E1 2E2 . 2En Vn

  • Statistical model of hadronizationfireballhadronsfinite V20/20Described by microcanonical phase spaceHeavy ioncollision


  • Question: Molecules colliding in a box give canonical Boltzmann, how is this different from REGGAE collisions which give LIPS-Boltzmann?

    Answer: Molecules in a box collide in both momentum and configuration space

    Question: Can we adjust REGGAE collisions to get canonical Boltzmann?

    Question: If we get canonical Boltzmann, do we also get uniform filling of the microcanonical phase space?18/20

  • Mn 1 + 2 + 3 + + n Mn2 = (pa + pb) 2M2 1 + 2 M22 = (p1 + p2) 2M3 1 + 2 + 3 3 + M2

    M32 = (p1 + p2 + p3) 2Mn Mn-1 M3 M2 n-1n321. . . GENBOD generator (F. James)Each 2-body decay evaluated in the CM frame of 2 daughters

  • Standard Numerical Methods of IntegrationabRectangular



  • where12 variables 2 M22 = (p1 + p2) 2 M32 = (p1 + p2 + p3) 2GENBOD generator (F. James)10/20

  • Pure phase space(Lorentz Invariant Phase Space, LIPS)numerically complicated1Pure multiparticle phase space = LIPSkinematics & statistics4/20

  • Standard methods vs MCSimpsonTrapezoidalRectangularStandard methodsMonte Carlo Number of dimensions12d1/n1/n21/n41/n1/n1/n1/n21/n1/n111n1/dn2/dn4/d(Error scaling with n)8/20