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

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1 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

2 Parton showers Quarks and gluons in final state, pointlike. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 2/45

3 Parton showers Quarks and gluons in final state, pointlike. Know short distance (short time) fluctuations from matrix element/feynman diagrams: Q few GeV to O(TeV). Measure hadronic final states, long distance effects, Q 0 GeV. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 2/45

4 Parton showers Quarks and gluons in final state, pointlike. Know short distance (short time) fluctuations from matrix element/feynman diagrams: Q few GeV to O(TeV). Parton shower evolution, multiple gluon emissions become resolvable at smaller scales. TeV GeV. Measure hadronic final states, long distance effects, Q 0 GeV. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 2/45

5 Parton showers Quarks and gluons in final state, pointlike. Know short distance (short time) fluctuations from matrix element/feynman diagrams: Q few GeV to O(TeV). Parton shower evolution, multiple gluon emissions become resolvable at smaller scales. TeV GeV. Measure hadronic final states, long distance effects, Q 0 GeV. Dominated by large logs, terms α n S log2n Q Q 0. Generated from emissions ordered in Q. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 2/45

6 Parton showers Quarks and gluons in final state, pointlike. Know short distance (short time) fluctuations from matrix element/feynman diagrams: Q few GeV to O(TeV). Parton shower evolution, multiple gluon emissions become resolvable at smaller scales. TeV GeV. Measure hadronic final states, long distance effects, Q 0 GeV. Dominated by large logs, terms α n S log2n Q Q 0. Generated from emissions ordered in Q. Soft and/or collinear emissions. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 2/45

7 Outline Review Building a parton shower, what s inside? Splitting functions, Sudakov FF, Angular ordering... Jet rates and resummations. Some data comparison. Some non perturbative issues. Covered in other talks: Matching to NLO. Merging higher multiplicity MEs with PS. Subleading Colour. MPI. Alternatve formulations. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 3/45

8 e + e annihilation Good starting point: e + e q qg: Final state momenta in one plane (orientation usually averaged). Write momenta in terms of (x,x 2 ) = (x q,x q ) plane: x i = 2p i q Q 2 (i =,2,3), 0 x i,x + x 2 + x 3 = 2, q = (Q,0,0,0), Q E cm. Fig: momentum configuration of q, q and g for given point (x,x 2 ), q direction fixed. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 4/45

9 e + e annihilation Differential cross section: dσ C F α S x + x 2 = σ 0 dx dx 2 2π ( x )( x 2 ) Collinear singularities: x or x 2. Soft singularity: x,x 2. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 5/45

10 e + e annihilation Differential cross section: dσ C F α S x + x 2 = σ 0 dx dx 2 2π ( x )( x 2 ) Collinear singularities: x or x 2. Soft singularity: x,x 2. Rewrite in terms of x 3 and θ = (q,g): [ dσ C F α S 2 = σ 0 dcosθdx 3 2π sin 2 θ Singular as θ 0 and x ( x 3 ) 2 x 3 x 3 ] Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 5/45

11 e + e annihilation Can separate into two jets as 2dcosθ sin 2 θ = dcosθ cosθ + dcosθ + cosθ = dcosθ cosθ + dcos θ cos θ dθ 2 θ 2 + d θ 2 θ 2 Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 6/45

12 e + e annihilation Can separate into two jets as 2dcosθ sin 2 θ = dcosθ cosθ + dcosθ + cosθ = dcosθ cosθ + dcos θ cos θ dθ 2 θ 2 + d θ 2 θ 2 So, we rewrite dσ in collinear limit as dθ dσ = σ 0 2 α S jets θ 2 2π C F + ( z) 2 dz z 2 Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 6/45

13 e + e annihilation Can separate into two jets as 2dcosθ sin 2 θ = dcosθ cosθ + dcosθ + cosθ = dcosθ cosθ + dcos θ cos θ dθ 2 θ 2 + d θ 2 θ 2 So, we rewrite dσ in collinear limit as dθ dσ = σ 0 2 α S jets θ 2 2π C F dθ = σ 0 2 α S jets θ 2 2π P(z)dz with DGLAP splitting function P(z). + ( z) 2 dz Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 6/45 z 2

14 Collinear limit Universal DGLAP splitting kernels for collinear limit: dθ dσ = σ 0 2 α S jets θ 2 2π P(z)dz P q qg (z) = C F + z 2 z P g gg (z) = C A ( z( z)) 2 z( z) P q gq (z) = C F + ( z) 2 z P g qq (z) = T R ( 2z( z)) Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 7/45

15 Collinear limit Universal DGLAP splitting kernels for collinear limit: dθ dσ = σ 0 2 α S jets θ 2 2π P(z)dz Note: Other variables may equally well characterize the collinear limit: dθ 2 θ 2 dq2 Q 2 dp2 p 2 d q2 q 2 dt t whenever Q 2,p 2,t 0 means collinear. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 7/45

16 Collinear limit Universal DGLAP splitting kernels for collinear limit: dθ dσ = σ 0 2 α S jets θ 2 2π P(z)dz Note: Other variables may equally well characterize the collinear limit: dθ 2 θ 2 dq2 Q 2 dp2 p 2 d q2 q 2 dt t whenever Q 2,p 2,t 0 means collinear. θ: HERWIG Q 2 : PYTHIA 6.3, SHERPA. p : PYTHIA 6.4, ARIADNE, Catani Seymour showers. q: Herwig++. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 7/45

17 Resolution Need to introduce resolution t 0, e.g. a cutoff in p. Prevent us from the singularity at θ 0. Emissions below t 0 are unresolvable. Finite result due to virtual corrections: + = finite. unresolvable + virtual emissions are included in Sudakov form factor via unitarity (see below!). Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 8/45

18 Towards multiple emissions Starting point: factorisation in collinear limit, single emission. t dt z+ σ 2+ (t 0 ) = σ 2 (t 0 ) t 0 t dz α S z 2π ˆP(z) t = σ 2 (t 0 ) dtw(t). t 0 Multiple emissions (probabilistic) σ >2 (t 0 ) = σ 2 (t 0 ) k= ( = σ 2 (t 0 ) 2 k ( t ) k dtw(t) = σ 2 (t 0 )( k! t 0 2 (t 0,t) Sudakov Form Factor [ t ] (t 0,t) = exp dtw(t) t 0 ) e 2 t ) dtw(t) t0 Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 9/45

19 Towards multiple emissions Starting point: factorisation in collinear limit, single emission. t dt z+ σ 2+ (t 0 ) = σ 2 (t 0 ) t 0 t dz α S z 2π ˆP(z) t = σ 2 (t 0 ) dtw(t). t 0 Multiple emissions (probabilistic) σ >2 (t 0 ) = σ 2 (t 0 ) k= ( = σ 2 (t 0 ) 2 k ( t ) k dtw(t) = σ 2 (t 0 )( k! t 0 2 (t 0,t) ) e 2 t ) dtw(t) t0 Sudakov Form Factor in QCD [ t ] [ t dt z+ ] α S (z,t) (t 0,t) = exp dtw(t) = exp ˆP(z, t)dz t 0 t 0 t z 2π Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 9/45

20 Sudakov form factor Note that ( ) σ all = σ 2 + σ >2 = σ 2 + σ 2 2 (t 0,t), 2 (t 0,t) = σ 2 σ all. Two jet rate = 2 = P 2 (No emission in the range t t 0 ). Sudakov form factor = No emission probability. Often (t 0,t) (t). Hard scale t, typically CM energy or p of hard process. Resolution t 0, two partons are resolved as two entities if inv mass or relative p above t 0. P 2 (not P), as we have two legs that evolve independently. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 0/45

21 Sudakov form factor from Markov property Unitarity P( some emission ) + P( no emission ) = P(0 < t T) + P(0 < t T) =. Multiplication law (no memory) P(0 < t T) = P(0 < t t ) P(t < t T) Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 /45

22 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) =. P(0 < t T) = P(0 < t t ) P(t < t T) Then subdivide into n pieces: t i = n i T,0 i n. P(0 < t T) = lim n n i=0 = exp ( P(t i < t t i+ ) = lim n n i=0 lim n n i=0 P(t i < t t i+ ) ) ( P(ti < t t i+ ) ) ( T = exp 0 ) dp(t) dt. dt Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 /45

23 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 PSR 202 DESY Hamburg 29/5-/6/202 2/45

24 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 PSR 202 DESY Hamburg 29/5-/6/202 3/45

25 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):. Choose flat random number 0 ρ. 2. If ρ < (t max ): no resolvable 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. Determine z essentially according to integrand in front of exp. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 3/45

26 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 PSR 202 DESY Hamburg 29/5-/6/202 3/45

27 Parton cascade Get tree structure, ordered in evolution variable t: Here: t > t 2 > t 3 ; t 2 > t 3 etc. Construct four momenta from (t i,z i ) and (random) azimuth φ. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 4/45

28 Parton cascade Get tree structure, ordered in evolution variable t: Here: t > 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 PSR 202 DESY Hamburg 29/5-/6/202 4/45

29 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 PSR 202 DESY Hamburg 29/5-/6/202 5/45

30 Parton shower kinematics (Herwig++) Sudakov-basis p,n with p 2 = M 2 ( forward ), n 2 = 0 ( backward ), p q = zp + β q n q p g = ( z)p + β g n + q Collinear limit for radiation off heavy quark, [ ] + z P gq (z,q 2,m 2 2 2z( z)m2 ) = C F z q 2 + ( z) 2 m 2 = C ] F [ + z 2 2m2 z z q 2 q 2 q 2 may be used as evolution variable. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 6/45

31 Parton shower kinematics (Herwig++) Introduce a kinematical cutoff Q g in order to avoid the soft gluon singularity (usually z ). Reconstruct transverse momentum q from our definition of q for q qg splitting [µ = max(m q,q g )], z( z) q 2 = q2 z( z) + Q2 g z + z z Allowed phase space, where q real. For large q µ q < z < Q g q. µ 2 Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 7/45

32 Parton shower kinematics (Herwig++) For given q get phase space limits z ± ( q). q qg, uds b bg z z q/gev q/gev (q qg/b bg). Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 7/45

33 Parton shower kinematics (Herwig++) Evolution variables for parton shower evolution in Herwig++. Consider (x, x) phase space for e + e q qg Herwig++ Comparison HERWIG Possible pitfalls: dead regions, overlap. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 8/45

34 Parton shower kinematics (Herwig++ dipole shower) Alternative picture with different evolution variables (Catani Seymour dipole shower)..6. The parton shower x x Lines of const z straight, const q. Soft cutoff blown up. Figure.7: Allowed phase-space regions in terms of Dalitz variables. The blue region is accessible to the emission of parton. The contourplot shows curved grey lines, which define emission at fixed p, and straight grey lines at fixed z. The black solid Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 9/45

35 Soft emissions Only collinear emissions so far. Including collinear+soft. Large angle+soft also important. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 20/45

36 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+ = dσ n dω ω dω α S 2π 2π ij C ij W ij ( QCD Antenna ) with W ij = cosθ ij ( cosθ iq )( cosθ qj ). Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 20/45

37 Soft emissions We define W ij = cosθ ij ( cosθ iq )( cosθ qj ) W(i) ij + W (j) ij with W (i) ij = ( ) W ij +. 2 cosθ iq cosθ qj W (i) ij is only collinear divergent if q i etc. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 2/45

38 Soft emissions We define W ij = cosθ ij ( cosθ iq )( cosθ qj ) W(i) ij + W (j) ij with W (i) ij = ( ) W ij +. 2 cosθ iq 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. cosθ iq (θ iq < θ ij ) 0 otherwise Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 2/45

39 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 PSR 202 DESY Hamburg 29/5-/6/202 22/45

40 Angular ordered parton showers p ordered shower. Angular ordering from additional vetos. Angular ordered shower. Some softer emissions before hardest one. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 23/45

41 Colour coherence from CDF Events with 2 hard (> 00 GeV) jets and a soft 3rd jet ( 0 GeV) Best description with angular ordering. F. Abe et al. [CDF Collaboration], Phys. Rev. D 50 (994) Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 24/45

42 Colour coherence from CDF Events with 2 hard (> 00 GeV) jets and a soft 3rd jet ( 0 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 (994) Best description with angular ordering. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 24/45

43 Parton showers Herwig++ New parton shower variables introduced for Herwig++ [SG, P. Stephens and B. Webber, JHEP 032 (2003) 045 [hep-ph/030083]] More under development dipole shower, based upon Catani Seymour dipoles. Sherpa [SG, S. Plätzer, ]] CS-Shower default by now, always matched via CKKW (see later). Pythia p T ordered shower (simple matching). Interleaved with Multiple partonic interactions. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 25/45

44 Resummation Sudakov FF basis for resummation. Radiator functions Γ i (t,t ) only retaining the leading log terms of the splitting function. Formulate parton shower in terms of generating functionals and obtain jet rates (in e + e, at k T resulution y). f 2 (s,y) = [ q (s) ] 2, f 3 (s,y) = 2 [ q (s) ] s 2 dtγ q (s,t) g (t), t 0 f 4 (s,y) = 2 [ q (s) ] { [ s ] 2 2 dtγ q (s,t) g (t) t 0 s s + dtγ q (s,t) g (t) dt [ Γ g (t,t ) g (t ) + Γ f (t,t ) f (t ) ] }. t 0 t 0 Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 26/45

45 Resummation in the parton shower Herwig++ dipole shower. LO and NLO matched (POWHEG like). Integrated 2-jet rate with Durham algorithm (9.2 GeV) Integrated 3-jet rate with Durham algorithm (9.2 GeV) Integrated 4-jet rate with Durham algorithm (9.2 GeV) R LO NLO data R3 0 0 LO NLO data R4 0 0 LO NLO data MC/data.4.2 MC/data.4.2 MC/data y Durham cut y Durham cut y Durham cut Integrated 5-jet rate with Durham algorithm (9.2 GeV) Integrated 6-jet rate with Durham algorithm (9.2 GeV) R5 MC/data LO NLO data y Durham cut R 6 MC/data LO NLO data y Durham cut OPAL jet rates Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 27/45

46 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 PSR 202 DESY Hamburg 29/5-/6/202 28/45

47 Initial state radiation Available phase space limited by several factors: Real q x < z < z max ( q;q g ). q > Q g Backward branching Maybe kinematics α S (Q) in Herwig++ = frozen at low q. single branching b ac: p b q i c 0.8 x i = x i z i q i x i a 0.6 position qi = αip + βin + q i. Basis (p, n) proton direction. Kinematics of shower from αi = αi q i p i, q i =. z zi 0.2 p 2 i = ( zi)2 q 2 i ziq2 g. ted to parton shower cutoff. Sudakov FF s. Workshop TeV4LHC, BNL, 3 5 Feb 2005, 2 ME z 0.4 Q g p = 0 x=0.02 available PS Q 0 /2, Q 0, 2Q q/gev Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 29/45

48 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 PSR 202 DESY Hamburg 29/5-/6/202 30/45

49 Reconstruction of Kinematics After shower: original partons acquire virtualities q 2 i boost/rescale jets: Started with n s = m 2 i + p2 i i= we rescale momenta with common factor k, s = n i= q 2 i + k p2 i to preserve overall energy/momentum. resulting jets are boosted accordingly. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 3/45

50 Dipoles Exact kinematics when recoil is taken by spectator(s). Dipole showers. Ariadne. Recoils in Pythia. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 32/45

51 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 PSR 202 DESY Hamburg 29/5-/6/202 32/45

52 Dipole showers (ARIADNE, of course. Not invented for NLO matching.) Idea to use CS subtraction terms for parton shower immediately clear from Written up in [Nagy, Soper, JHEP 050:024 (2005)] Catani Seymour Dipole cascade codes recently implemented by Schumann, Krauss [ ] (with CKKW like matching) and (independently) Dinsdale, Ternick, Weinzierl [ ] Lund Dipoles revisited [J. C. Winter and F. Krauss, JHEP 0807, 040 (2008)] Similar approach (VINCIA), based on Antenna subtraction by Giele, Kosower, Skands (toy process) [ ] Dipole shower in Herwig++, Coherence/angular ordering clearified see below. [Simon Plätzer, SG, ] Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 33/45

53 Why all those dipoles? Momentum conservation in shower emissions. 2 emissions. No momentum conservation. Kinematic reshuffling needed afterwards. Difficult for matching with NLO. 2 3 emissions. Momentum conservation simple due to recoil against 3rd parton. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 34/45

54 Coherent dipole shower What about angular ordering/soft coherence? Investigate parton showers with local recoils (that s what a CS parton shower is like). Angular ordering/soft coherence manifest in Sudakov anomalous dimension ( Γ q (p 2,Q2 ) = C F ln Q2 p 2 3 ), 2 ( Γ g (p 2,Q2 ) = C A ln Q2 p 2 ). 6 [A. Bassetto, M. Ciafaloni and G. Marchesini, Phys. Rept. 00 (983) 20] [G. Marchesini, B.R. Webber, NPB 238 (984) ] Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 35/45

55 Coherent dipole shower What about angular ordering/soft coherence? Investigate parton showers with local recoils (that s what a CS parton shower is like). Angular ordering/soft coherence manifest in Sudakov anomalous dimension ( Γ q (p 2,Q2 ) = C F 2ln Q2 p 2 3 ), 2 ( Γ g (p 2,Q2 ) = C A 2ln Q2 p 2 ). 6 [A. Bassetto, M. Ciafaloni and G. Marchesini, Phys. Rept. 00 (983) 20] Not correct for virtuality ordered showers. [G. Marchesini, B.R. Webber, NPB 238 (984) ] Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 35/45

56 Coherent dipole showers Result for Herwig++ like shower (ordering in q) with recoils ( Γ AO q (p 2,Q2 ) = C F ln Q2 p 2 3 ) p +C F 2 Q ( Γ AO g (p 2,Q2 ) = C A ln Q2 p 2 6 ) +2C A p Q ( 2λ Q2 s ik ( λ Q2 ) + O ( p 2 s ik Q 2 ), ) ( p 2 ) + O Q 2 Recoil power correction, beyond NLL. (Only enters in phase space ( λ) as spectator is only rescaled.) [Simon Plätzer, SG, ]. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 36/45

57 Coherent dipole showers Result for CS dipole shower with p ordering and right choice of phase space boundaries. ( Γ CS q (p 2, ) = C F ln s ik Γ CS g (p 2, ) = C A p ( ln s ik p 2 6 ) C F πλ p sik + O ) C A πλ p sik + O Hard scale Q 2 = s ik = dipole inv mass. Recoil power correction, beyond NLL. p ordering simple POWHEG matching. ( p 2 ), Q 2 ( p 2 Q 2 ). [Simon Plätzer, SG, ] Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 36/45

58 How well do parton showers work? Jet shapes, jet rates, event shapes, identified particles... Tuning of parameters (e + e hadrons, mostly at LEP). Want to get everything right with one parameter set. Compare to literally 00s of plots. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 37/45

59 How well does it work? Smooth interplay between shower and hadronization. Partons Hadrons Herwig++.0 ΛQCD = 25 MeV ΛQCD = 500 MeV δ =.7 GeV δ = 2.3 GeV δ = 3.2 GeV Herwig++.0 ΛQCD = 25 MeV ΛQCD = 500 MeV δ =.7 GeV δ = 2.3 GeV δ = 3.2 GeV OPAL njet 5 njet ycut ycut Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 38/45

60 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 PSR 202 DESY Hamburg 29/5-/6/202 38/45

61 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 = 9.2 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 = 9.2 GeV) ALEPH data Hw++ Hw++-Powheg ln(ycut) 5-jet fraction (E CMS = 9.2 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 = 9.2 GeV) ALEPH data Hw++ Hw++-Powheg ln(ycut) 6-jet fraction (E CMS = 9.2 GeV) ALEPH data Hw++ Hw++-Powheg ln(ycut) Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 38/45

62 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 PSR 202 DESY Hamburg 29/5-/6/202 38/45

63 How well does it work? p (Z 0 ) intrinsic k (LHC 7 TeV). /σdσ/dp [GeV ] 0 Z p reconstructed from dressed electrons ATLAS data Hw++ Hw++-Powheg MC/data p (ee) [GeV] Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 38/45

64 Nonperturbative issues (Drell Yan) ) Born level process. Net p vanishes. 2) p p from recoil against gluon emissions. Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 39/45

65 Nonperturbative issues (Drell Yan) Primordial k from soft, non perturbative(?) gluons. Gaussian smearing. Default: p = 2.GeV! Modeled by non perturbative gluon emissions < M ll /GeV < 00 Herwig++ CDF no IPT p /GeV [SG, M. Seymour, A. Siodmok, JHEP 0806 (2008) 00] Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 40/45

66 Transverse thrust ) C /N dn/d ln(-t GeV pp Jets Central Transverse Thrust (cms-pt090) CMS Herwig++ Perugia 200 Pythia 8 ) C /N dn/d ln(-t GeV pp Jets Central Transverse Thrust (cms-pt25) CMS Herwig++ Perugia 200 Pythia CMS_20_S Herwig , Pythia 6.424, Pythia Ratio to CMS ln(-t ) C mcplots.cern.ch CMS_20_S Herwig , Pythia 6.424, Pythia Ratio to CMS ln(-t ) C mcplots.cern.ch Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 4/45

67 Integral jet shapes not too hard, central (30 < p T /GeV < 40;0 < y < 0.3) Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 42/45

68 Integral jet shapes harder, more forward (80 < p T /GeV < 0;.2 < y < 2.) Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 42/45

69 Nonperturbative physics and jets Hadronization and UE effects both present in jet substructure! ρ(r) 0 Jet shape ρ for p GeV, y ATLAS data MC (jets-sho) MC (jets-had) MC (jets-all) ρ(r) 0 0 Jet shape ρ for p GeV, y ATLAS data MC (jets-sho) MC (jets-had) MC (jets-all) MC/data r MC/data r ρ(r), energy flow at r < R within jet of radius R. (Herwig shower/+hadronization/+mpi) Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 43/45

70 Nonperturbative physics and jets Hadronization and UE effects both present in jet substructure! Jet shape Ψ for p GeV, y Jet shape Ψ for p GeV, y Ψ(r) Ψ(r) ATLAS data MC (jets-sho) MC (jets-had) MC (jets-all) ATLAS data MC (jets-sho) MC (jets-had) MC (jets-all) MC/data r MC/data r Ψ(r), integrated energy flow. (Herwig shower/+hadronization/+mpi) Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 43/45

71 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] 0 0 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 PSR 202 DESY Hamburg 29/5-/6/202 44/45

72 Conclusion Parton shower MCs amongst core tools for LHC. Devil s in the details. Strong ties between perturbative/non perturbative physics. Use resummation to clearify entanglement of perturbative/non perturbative interplay? Stefan Gieseke PSR 202 DESY Hamburg 29/5-/6/202 45/45