Sudakov form factor from Markov property

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Dominick Perry
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1 Sudakov form factor from Markov property Unitarity P( some emission ) + P( no emission ) = P(0 < t T) + P(0 < t T) = 1. Multiplication law (no memory) P(0 < t T) = P(0 < t t 1 ) P(t 1 < t T) Stefan Gieseke CTEQ School /98

2 Sudakov form factor from Markov property Unitarity P( some emission ) + P( no emission ) Multiplication law (no memory) = P(0 < t T) + P(0 < t T) = 1. P(0 < t T) = P(0 < t t 1 ) P(t 1 < t T) Then subdivide into n pieces: t i = n i T,0 i n. P(0 < t T) = lim n 1 n i=0 = exp ( P(t i < t t i+1 ) = lim n 1 n i=0 lim n 1 n i=0 P(t i < t t i+1 ) ) ( 1 P(ti < t t i+1 ) ) ( T = exp 0 ) dp(t) dt. dt Stefan Gieseke CTEQ School /98

3 Sudakov form factor Again, no emission probability! So, P(0 < t T) = exp ( T 0 ) dp(t) dt dt dp(first emission at T) = dp(t) P(0 < t T) ( T ) dp(t) = dp(t)exp dt dt That s what we need for our parton shower! Probability density for next emission at t: dp(next emission at t) = dt t z+ z α S (z,t) 2π ˆP(z, t)dz exp 0 [ t dt z+ ] α S (z,t) ˆP(z, t)dz t 0 t z 2π Stefan Gieseke CTEQ School /98

4 Parton shower Monte Carlo Probability density: dp(next emission at t) = dt t z+ z α S (z,t) 2π ˆP(z, t)dz exp [ t dt z+ ] α S (z,t) ˆP(z, t)dz t 0 t z 2π Conveniently, the probability distribution is (t) itself. Stefan Gieseke CTEQ School /98

5 Parton shower Monte Carlo Probability density: dp(next emission at t) = dt t z+ z α S (z,t) 2π ˆP(z, t)dz exp [ t dt z+ ] α S (z,t) ˆP(z, t)dz t 0 t z 2π Conveniently, the probability distribution is (t) itself. Hence, parton shower very roughly from (HERWIG): 1. Choose flat random number 0 ρ If ρ < (t max ): no resolbable emission, stop this branch. 3. Else solve ρ = (t max )/ (t) (= no emission between t max and t) for t. Reset t max = t and goto 1. Determine z essentially according to integrand in front of exp. Stefan Gieseke CTEQ School /98

6 Parton shower Monte Carlo Probability density: dp(next emission at t) = dt t z+ z α S (z,t) 2π ˆP(z, t)dz exp [ t dt z+ ] α S (z,t) ˆP(z, t)dz t 0 t z 2π Conveniently, the probability distribution is (t) itself. That was old HERWIG variant. Relies on (numerical) integration/tabulation for (t). Pythia, now also Herwig++, use the Veto Algorithm. Method to sample x from distribution of the type [ x ] dp = F(x)exp dx F(x ) dx. Simpler, more flexible, but slightly slower. Stefan Gieseke CTEQ School /98

7 Parton cascade Get tree structure, ordered in evolution variable t: Here: t 1 > t 2 > t 3 ; t 2 > t 3 etc. Construct four momenta from (t i,z i ) and (random) azimuth φ. Stefan Gieseke CTEQ School /98

8 Parton cascade Get tree structure, ordered in evolution variable t: Here: t 1 > t 2 > t 3 ; t 2 > t 3 etc. Construct four momenta from (t i,z i ) and (random) azimuth φ. Not at all unique! Many (more or less clever) choices still to be made. Stefan Gieseke CTEQ School /98

9 Parton cascade Get tree structure, ordered in evolution variable t: t can be θ, Q 2, p,... Choice of hard scale t max not fixed. Some hard scale. z can be light cone momentum fraction, energy fraction,... Available parton shower phase space. Integration limits. Regularisation of soft singularities.... Good choices needed here to describe wealth of data! Stefan Gieseke CTEQ School /98

10 Soft emissions Only collinear emissions so far. Including collinear+soft. Large angle+soft also important. Stefan Gieseke CTEQ School /98

11 Soft emissions Only collinear emissions so far. Including collinear+soft. Large angle+soft also important. Soft emission: consider eikonal factors, here for q(p + q) q(p)g(q), soft g: u(p) ε p+ q + m ε (p + q) 2 u(p)p m2 p q soft factorisation. Universal, i.e. independent of emitter. In general: dσ n+1 = dσ n dω ω dω α S 2π 2π ij C ij W ij ( QCD Antenna ) with W ij = 1 cosθ ij (1 cosθ iq )(1 cosθ qj ). Stefan Gieseke CTEQ School /98

12 Soft emissions We define W ij = 1 cosθ ij (1 cosθ iq )(1 cosθ qj ) W(i) ij + W (j) ij with W (i) ij = 1 ( ) 1 1 W ij cosθ iq 1 cosθ qj W (i) ij is only collinear divergent if q i etc. Stefan Gieseke CTEQ School /98

13 Soft emissions We define W ij = 1 cosθ ij (1 cosθ iq )(1 cosθ qj ) W(i) ij + W (j) ij with W (i) ij = 1 ( ) 1 1 W ij cosθ iq 1 cosθ qj W (i) ij is only collinear divergent if q i etc. After integrating out the azimuthal angles, we find dφiq 2π W(i) ij = That s angular ordering. 1 1 cosθ iq (θ iq < θ ij ) 0 otherwise Stefan Gieseke CTEQ School /98

14 Angular ordering Radiation from parton i is bound to a cone, given by the colour partner parton j. Results in angular ordered parton shower and suppresses soft gluons viz. hadrons in a jet. i j Stefan Gieseke CTEQ School /98

15 Colour coherence from CDF Events with 2 hard (> 100 GeV) jets and a soft 3rd jet ( 10 GeV) Best description with angular ordering. F. Abe et al. [CDF Collaboration], Phys. Rev. D 50 (1994) Stefan Gieseke CTEQ School /98

16 Colour coherence from CDF Events with 2 hard (> 100 GeV) jets and a soft 3rd jet ( 10 GeV) Pseudorapidity, η, of 3rd jet Fraction of events MC/data CDF data Hw η 3 F. Abe et al. [CDF Collaboration], Phys. Rev. D 50 (1994) Best description with angular ordering. Stefan Gieseke CTEQ School /98

17 Initial state radiation Similar to final state radiation. Sudakov form factor (x = x/z) [ ] tmax dt z+ (t,t max ) = exp dz α S(z,t) x f b (x,t) t t z 2π xf a (x,t) ˆP ba (z,t) b Have to divide out the pdfs. Stefan Gieseke CTEQ School /98

18 Initial state radiation Evolve backwards from hard scale Q 2 down towards cutoff scale Q 2 0. Thereby increase x. With parton shower we undo the DGLAP evolution of the pdfs. Stefan Gieseke CTEQ School /98

19 Dipoles Exact kinematics when recoil is taken by spectator(s). Dipole showers. Ariadne. Recoils in Pythia. Stefan Gieseke CTEQ School /98

20 Dipoles Exact kinematics when recoil is taken by spectator(s). Dipole showers. Ariadne. Recoils in Pythia. New dipole showers, based on Catani Seymour dipoles. QCD Antennae. Goal: matching with NLO. Generalized to IS IS, IS FS. Stefan Gieseke CTEQ School /98

21 Hadronization Stefan Gieseke CTEQ School /98

22 Parton shower Stefan Gieseke CTEQ School /98

23 Parton shower hadrons Stefan Gieseke CTEQ School /98

24 Parton shower hadrons Parton shower terminated at t 0 = lower end of PT. Can t measure quarks and gluons. Degrees of freedom in the detector are hadrons. Need a description of confinement. Stefan Gieseke CTEQ School /98

25 Physical input Self coupling of gluons attractive field lines Stefan Gieseke CTEQ School /98

26 Physical input Self coupling of gluons attractive field lines Linear static potential V(r) κr. Supported by lattice QCD, hadron spectroscopy. Stefan Gieseke CTEQ School /98

27 Hadronization models Older models: Flux tube model. Independent fragmentation. Today s models. Lund string model (Pythia). Cluster model (Herwig). Stefan Gieseke CTEQ School /98

28 Independent fragmentation Feynman Field fragmentation ( 78). Stefan Gieseke CTEQ School 2013 I qq pairs created from vacuum to dress bare quarks. I Fragmentation function fq h (z) = density of momentum fraction z carried away by hadron h from quark q. I Gaussian p distribution. 67/98

$I Fragmentation function fq h (z) = density of momentum fraction z carried away by hadron h from quark q.$

29 Independent fragmentation Feynman Field fragmentation ( 78). I qq pairs created from vacuum to dress bare quarks. I Fragmentation function fq h (z) = density of momentum fraction z carried away by hadron h from quark q. I Gaussian p distribution. Problems: I I I I I Stefan Gieseke CTEQ School 2013 last quark. not Lorentz invariant. infrared safety.... I Good at that time. I Still usefull for inclusive descriptions. 67/98

30 Lund string model String model of mesons. L = 0 mesons move in yoyo modes. Area law: m 2 area. Stefan Gieseke CTEQ School /98

31 Lund string model String model of mesons. L = 0 mesons move in yoyo modes. Area law: m 2 area. Simple model for particle production in e + e annihilation: q q pair as pointlike source of string. Stefan Gieseke CTEQ School /98

32 Lund string model String energy intense chromomagnetic field. Additional q q pairs created by QM tunneling. dprob ( ) dxdt exp πm 2 q/κ κ 1GeV. String breaking expected long before yoyo point. Stefan Gieseke CTEQ School /98

33 Lund string model Ajacent breaks form hadrons. Works in both directions (symmetry). Lund symmetric fragmentation function ( f (z,p ) 1 z (1 z)a exp b(m2 h + p2 ) ) z a,b,m 2 h main adjustable parameters. Note: diquarks baryons. Stefan Gieseke CTEQ School /98

34 Lund string model gluon = kink on string = motion pushed into the q q system. Stefan Gieseke CTEQ School /98

35 Lund string model gluon = kink on string = motion pushed into the q q system. Stefan Gieseke CTEQ School /98

36 Lund string model gluon = kink on string = motion pushed into the qq system String effect Stefan Gieseke CTEQ School /98

37 Lund string model Some remarks: Originally invented without parton showers in mind. Stefan Gieseke CTEQ School /98

38 Lund string model Some remarks: Originally invented without parton showers in mind. Stong physical motivation. Very successful desription of data. Universal desription of data (fit at e + e, transfer to hadron-hadron). Many parameters, 1 per hadron. Too easy to hide errors in perturbative description? Stefan Gieseke CTEQ School /98

39 Lund string model Some remarks: Originally invented without parton showers in mind. Stong physical motivation. Very successful desription of data. Universal desription of data (fit at e + e, transfer to hadron-hadron). Many parameters, 1 per hadron. Too easy to hide errors in perturbative description? try to use more QCD information/intuition. Stefan Gieseke CTEQ School /98

40 Colour preconfinement Large N C limit planar graphs dominate. Gluon = colour anticolourpair Stefan Gieseke CTEQ School /98

41 Colour preconfinement Large N C limit planar graphs dominate. Gluon = colour anticolourpair Parton shower organises partons in colour space. Colour partners (=colour singlet pairs) end up close in phase space. Cluster hadronization model Stefan Gieseke CTEQ School /98

42 Cluster hadronization Stefan Gieseke CTEQ School /98

43 Cluster hadronization Stefan Gieseke CTEQ School /98

44 Cluster hadronization Stefan Gieseke CTEQ School /98

45 Cluster hadronization Stefan Gieseke CTEQ School /98

46 Cluster hadronization Primary cluster mass spectrum independent of production mechanism. Peaked at some low mass Primary Light Clusters 1 10 M/GeV Q = 35 GeV Q = 91.2 GeV Q = 189 GeV Q = 500 GeV Q = 1000 GeV Stefan Gieseke CTEQ School /98

47 Cluster hadronization Primary cluster mass spectrum independent of production mechanism. Peaked at some low mass. Cluster = continuum of high mass resonances. Decay into well known lighter mass resonances = discrete spectrum of hadrons. No spin information carried over, i.e. only phase space. Suppression of heavier particles (particularly baryons, can be problematic). Cluster spectrum determined entirely by parton shower, i.e. perturbation theory. Hence, t 0 crucial parameter. Stefan Gieseke CTEQ School /98

48 Cluster hadronization Stefan Gieseke CTEQ School /98

49 Cluster hadronization Stefan Gieseke CTEQ School /98

50 Cluster hadronization Stefan Gieseke CTEQ School /98

51 Hadronization Only string and cluster models used in recent MC programs. Independent fragmentation only for inclusive observables. Strings started non perturbatively, improved by parton shower. Cluster model started mostly on perturbative side, improved by string like cluster fission. Stefan Gieseke CTEQ School /98

52 Hadronic Decays Stefan Gieseke CTEQ School /98

53 Hadronic decays Stefan Gieseke CTEQ School /98

54 Hadronic decays Stefan Gieseke CTEQ School /98

55 Hadronic decays Many aspects: B 0 γb 0 B 0 e ν e D + π + D 0 K ρ + π + π 0 e + e γ Stefan Gieseke CTEQ School /98

56 Hadronic decays Many aspects: B 0 γb 0 B 0 e ν e D + π + D 0 K ρ + π + π 0 e + e γ EM decay. Stefan Gieseke CTEQ School /98

57 Hadronic decays Many aspects: B 0 γb 0 B 0 e ν e D + π + D 0 K ρ + π + π 0 e + e γ Weak mixing. Stefan Gieseke CTEQ School /98

58 Hadronic decays Many aspects: B 0 γb 0 B 0 e ν e D + π + D 0 K ρ + π + π 0 e + e γ Weak decay. Stefan Gieseke CTEQ School /98

59 Hadronic decays Many aspects: B 0 γb 0 B 0 e ν e D + π + D 0 K ρ + π + π 0 e + e γ Strong decay. Stefan Gieseke CTEQ School /98

60 Hadronic decays Many aspects: B 0 γb 0 B 0 e ν e D + π + D 0 K ρ + π + π 0 e + e γ Weak decay, ρ + mass smeared. Stefan Gieseke CTEQ School /98

61 Hadronic decays Many aspects: B 0 γb 0 B 0 e ν e D + π + D 0 K ρ + π + π 0 e + e γ ρ + polarized, angular correlations. Stefan Gieseke CTEQ School /98

62 Hadronic decays Many aspects: B 0 γb 0 B 0 e ν e D + π + D 0 K ρ + π + π 0 e + e γ Dalitz decay, m ee peaked. Stefan Gieseke CTEQ School /98

63 Hadronic decays Tedious. 100s of different particles, 1000s of decay modes, phenomenological matrix elements with parametrized form factors... Stefan Gieseke CTEQ School /98

64 Hadronic decays Stefan Gieseke CTEQ School /98

65 A few plots Stefan Gieseke CTEQ School /98

66 How well does it work? e + e hadrons, mostly at LEP. Jet shapes, jet rates, event shapes, identified particles... Tuning of parameters. Want to get everything right with one parameter set. Compare to literally 100s of plots. Stefan Gieseke CTEQ School /98

67 How well does it work? Smooth interplay between shower and hadronization. Partons Hadrons Herwig ΛQCD = 125 MeV ΛQCD = 500 MeV δ = 1.7 GeV δ = 2.3 GeV δ = 3.2 GeV Herwig ΛQCD = 125 MeV ΛQCD = 500 MeV δ = 1.7 GeV δ = 2.3 GeV δ = 3.2 GeV OPAL njet 5 njet ycut ycut Stefan Gieseke CTEQ School /98

68 How well does it work? N ch at LEP. Crucial for t 0 (Herwig ) Total charged multiplicity 2/σdσ/dn ch ALEPH data Hw++ Hw++-Powheg MC/data n ch Stefan Gieseke CTEQ School /98

69 How well does it work? Jet rates at LEP. R n = σ(n jets)/σ(jets) R 6 = σ(> 5 jets)/σ(jets) (Herwig ) MC/data σ(2 jet)/σ(inclusive) jet fraction (E CMS = 91.2 GeV) ALEPH data Hw++ Hw++-Powheg ln(ycut) MC/data σ(5 jet)/σ(inclusive) MC/data σ(3 jet)/σ(inclusive) jet fraction (E CMS = 91.2 GeV) ALEPH data Hw++ Hw++-Powheg ln(ycut) 5-jet fraction (E CMS = 91.2 GeV) ALEPH data Hw++ Hw++-Powheg ln(ycut) MC/data σ( 6 jet)/σ(inclusive) MC/data σ(4 jet)/σ(inclusive) jet fraction (E CMS = 91.2 GeV) ALEPH data Hw++ Hw++-Powheg ln(ycut) 6-jet fraction (E CMS = 91.2 GeV) ALEPH data Hw++ Hw++-Powheg ln(ycut) Stefan Gieseke CTEQ School /98

70 How well does it work? Hadron Multiplicities at LEP (e.g. π +, Λ 0 b ). Multiplicity MC/data Mean π + multiplicity PDG data Hw++ Hw++-Powheg Multiplicity MC/data Mean Λ 0 b multiplicity PDG data Hw++ Hw++-Powheg Stefan Gieseke CTEQ School /98

71 How well does it work? p (Z 0 ) intrinsic k (LHC 7 TeV). 1/σdσ/dp [GeV 1 ] 10 1 Z p reconstructed from dressed electrons ATLAS data Hw++ Hw++-Powheg MC/data p (ee) [GeV] Stefan Gieseke CTEQ School /98

72 Transverse thrust ) C 1/N dn/d ln(1-t GeV pp Jets Central Transverse Thrust (cms1-pt090) CMS Herwig++ Perugia 2010 Pythia 8 ) C 1/N dn/d ln(1-t GeV pp Jets Central Transverse Thrust (cms1-pt125) CMS Herwig++ Perugia 2010 Pythia CMS_2011_S Herwig , Pythia 6.424, Pythia Ratio to CMS ln(1-t ) C mcplots.cern.ch CMS_2011_S Herwig , Pythia 6.424, Pythia Ratio to CMS ln(1-t ) C mcplots.cern.ch Stefan Gieseke CTEQ School /98

73 Integral jet shapes not too hard, central (30 < p T /GeV < 40;0 < y < 0.3) Stefan Gieseke CTEQ School /98

74 Integral jet shapes harder, more forward (80 < p T /GeV < 110;1.2 < y < 2.1) Stefan Gieseke CTEQ School /98

75 Limits of parton shower W + jets, LHC 7 TeV. Inclusive jet multiplicity (electron channel) p of 2nd jet (electron channel) σ(w + Njet jets) [pb] ATLAS data Hw++ Hw++-Powheg dσ/dp [pb/gev] ATLAS data Hw++ Hw++-Powheg MC/data Njet MC/data p (2nd jet) [GeV] Higher jets not covered by parton shower only matching. Stefan Gieseke CTEQ School /98

76 Multiple Partonic Interactions (very sketchy) Stefan Gieseke CTEQ School /98

77 What about the remnants? Stefan Gieseke CTEQ School /98

78 What about the remnants? Stefan Gieseke CTEQ School /98

79 What about the remnants? Stefan Gieseke CTEQ School /98

80 What about the remnants? Stefan Gieseke CTEQ School /98

81 What about the remnants? Stefan Gieseke CTEQ School /98

82 What about the remnants? Stefan Gieseke CTEQ School /98

83 What about the remnants? Stefan Gieseke CTEQ School /98

84 What about the remnants? Stefan Gieseke CTEQ School /98

85 What about the remnants? Stefan Gieseke CTEQ School /98

86 Eikonal model basics Mulitple hard interactions h 1 h 2 Stefan Gieseke CTEQ School /98

87 Eikonal model basics Starting point: hard inclusive jet cross section. σ inc (s;p min t ) = i,j dp2 p min 2 t f i/h1 (x 1, µ 2 ) d ˆσ i,j t dp 2 t σ inc > σ tot eventually (for moderately small p min t ). f j/h2 (x 2, µ 2 ), Stefan Gieseke CTEQ School /98

88 Eikonal model basics 250 (mb) tot : DL '92 tot : DL '04 QCD2 2, p T >2GeV s (GeV) Stefan Gieseke CTEQ School /98

89 Eikonal model basics Starting point: hard inclusive jet cross section. σ inc (s;p min t ) = i,j dp2 p min 2 t f i/h1 (x 1, µ 2 ) d ˆσ i,j t dp 2 t σ inc > σ tot eventually (for moderately small p min t ). f j/h2 (x 2, µ 2 ), Interpretation: σ inc counts all partonic scatters that happen during a single pp collision more than a single interaction. σ inc = nσ inel. Stefan Gieseke CTEQ School /98

90 Eikonal model basics Use eikonal approximation (= independent scatters). Leads to Poisson distribution of number m of additional scatters, Then we get σ inel : σ inel = P m ( b,s) = n( b,s) m e n( b,s). m! d 2 b m ( m=1p b,s) = d 2 b (1 e n( b,s) ). Stefan Gieseke CTEQ School /98

91 Eikonal model basics Use eikonal approximation (= independent scatters). Leads to Poisson distribution of number m of additional scatters, Then we get σ inel : σ inel = P m ( b,s) = n( b,s) m e n( b,s). m! d 2 b m ( m=1p b,s) = d 2 b (1 e n( b,s) ). Cf. σ inel from scattering theory in eikonal approx. with scattering amplitude a( b,s) = 1 2i (e χ( b,s) 1) σ inel = d 2 b (1 e 2χ( b,s) ) χ( b,s) = 1 2 n( b,s). χ( b,s) is called eikonal function. Stefan Gieseke CTEQ School /98

92 Eikonal model basics Calculation of n( b,s) from parton model assumptions: n( b,s) = L partons (x 1,x 2, b) dp 2 d ˆσ ij t = ij δ ij ij dx 1 dx 2 d 2 b dp 2 t d ˆσ ij dp 2 t dp 2 t D i/a (x 1,p 2 t, b )D j/b (x 2,p 2 t, b b ) Stefan Gieseke CTEQ School /98

93 Eikonal model basics Calculation of n( b,s) from parton model assumptions: n( b,s) = L partons (x 1,x 2, b) dp 2 d ˆσ ij t = ij δ ij ij dx 1 dx 2 d 2 b dp 2 t d ˆσ ij dp 2 t dp 2 t D i/a (x 1,p 2 t, b )D j/b (x 2,p 2 t, b b ) 1 = dx 1 dx 2 d 2 b dp 2 d ˆσ ij t 1 + δ ij ij dp 2 t f i/a (x 1,p 2 t )G A ( b )f j/b (x 2,p 2 t )G B ( b b ) = A( b)σ inc (s;p min t ). Stefan Gieseke CTEQ School /98

94 Eikonal model basics Calculation of n( b,s) from parton model assumptions: n( b,s) = L partons (x 1,x 2, b) dp 2 d ˆσ ij t = ij δ ij ij dx 1 dx 2 d 2 b dp 2 t d ˆσ ij dp 2 t dp 2 t D i/a (x 1,p 2 t, b )D j/b (x 2,p 2 t, b b ) 1 = dx 1 dx 2 d 2 b dp 2 d ˆσ ij t 1 + δ ij ij dp 2 t f i/a (x 1,p 2 t )G A ( b )f j/b (x 2,p 2 t )G B ( b b ) = A( b)σ inc (s;p min t ). χ( b,s) = 1 2 n( b,s) = 1 2 A( b)σ inc (s;p min t ). Stefan Gieseke CTEQ School /98

95 Overlap function A(b) = d 2 b G A ( b )G B ( b b ) G( b) from electromagnetic FF: A(b) [1/mb] µ 2 = 1.80 GeV 2 µ 2 = 0.71 GeV G p ( b) = G p ( b) = d 2 k (2π) 2 But µ 2 not fixed to the electromagnetic 0.71 GeV 2. Free for colour charges. e i k b (1 + k 2 /µ 2 ) 2 Two main parameters: µ 2,p min t impact parameter b [ mb] Stefan Gieseke CTEQ School /98

96 Unitarized cross sections σ [mb] 3 10 from DL σ tot σ inc, p > 2 GeV T σ inel, p σ inc, p σ inel, p > 2 GeV T > 3.1 GeV T > 3.1 GeV T CM energy [GeV] 4 Stefan Gieseke CTEQ School /98

97 Colour reconnection at hadron colliders Colour preconfinement Shorten colour string/lower mass clusters. Stefan Gieseke CTEQ School /98

98 Colour reconnection at hadron colliders Colour preconfinement Shorten colour string/lower mass clusters. Stefan Gieseke CTEQ School /98

99 Monte Carlo training studentships London Lund Durham Manchester Louvain Göttingen CERN Karlsruhe 3-6 month fully funded studentships for current PhD students at one of the MCnet nodes. An excellent opportunity to really understand the Monte Carlos you use! Application rounds every 3 months. funded by: MARIE CURIE ACTIONS for details go to: Stefan Gieseke CTEQ School /98

Parton Showers. Stefan Gieseke. Institut für Theoretische Physik KIT. Event Generators and Resummation, 29 May 1 Jun 2012

Parton Showers. Stefan Gieseke. Institut für Theoretische Physik KIT. Event Generators and Resummation, 29 May 1 Jun 2012 Parton Showers Stefan Gieseke Institut für Theoretische Physik KIT Event Generators and Resummation, 29 May Jun 202 Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 /45 Parton showers Quarks and gluons