SHRiMPS Status of soft interactions in SHERPA Holger Schulz (IPPP - PowerPoint PPT Presentation

SHRiMPS Status of soft interactions in SHERPA Holger Schulz (IPPP Durham) November 23, 2015 MPI@LHC 2015, Trieste

Introduction Unitarity of S-matrix → optical theorem Relates tree level to loop level diagram 2 ��� ��� �� �� �� �� ��� �� �� p 1 p 1 p 1 ��� �� �� ��� �� �� = ��� �� �� ��� �� �� ��� �� �� p 2 p 2 p 2 ��� �� �� = 1 σ tot ( s ) s Im[ A el ( s , t = 0) ] � �� � � �� � Eikonal ansatz KMR model → SHRiMPS model: MC event generation of elastic, inelastic and diffractive processes in SHERPA based on Khoze-Martin-Ryskin (KMR, arXiv:0812.2407[hep-ph] ) through Multiple Pomeron Scattering H. Schulz SHRiMPS 1 / 16

Eikonal ansatz σ tot ( s ) = 1 s Im[ A el ( s , t = 0)] Rewrite A ( s , t ) → A ( s , b ), b: impact parameter Ansatz: � d b 2 Im[ A ( s , b )] σ tot ( s ) = 2 � d b 2 [ A ( s , b )] 2 σ el ( s ) = 2 σ inel ( s ) = σ tot ( s ) − σ el ( s ) H. Schulz SHRiMPS 2 / 16

Eikonal ansatz σ tot ( s ) = 1 s Im[ A el ( s , t = 0)] Rewrite A ( s , t ) → A ( s , b ), b: impact parameter Ansatz: � d b 2 Im[ A ( s , b )] σ tot ( s ) = 2 � d b 2 [ A ( s , b )] 2 σ el ( s ) = 2 σ inel ( s ) = σ tot ( s ) − σ el ( s ) � 1 − e Ω( s , b ) / 2) � � d b 2 � 1 − e Ω( s , b ) / 2) � A ( s , b ) = i → σ tot ( s ) = 2 H. Schulz SHRiMPS 2 / 16

Eikonal model � 1 − e Ω( s , b ) / 2) � A ( s , b ) = i Good-Walker (GW) states | φ 1 � , | φ 2 � (diffractive eigenstates) N GW � 1 1 | p � = a i | φ i � SHRiMPS: | p � = 2 | φ 1 � + 2 | φ 2 � √ √ i =1 1 1 | N ∗ (1440) � = 2 | φ 1 � − 2 | φ 2 � √ √ H. Schulz SHRiMPS 3 / 16

Eikonal model � 1 − e Ω( s , b ) / 2) � A ( s , b ) = i Good-Walker (GW) states | φ 1 � , | φ 2 � (diffractive eigenstates) N GW � 1 1 | p � = a i | φ i � SHRiMPS: | p � = 2 | φ 1 � + 2 | φ 2 � √ √ i =1 1 1 | N ∗ (1440) � = 2 | φ 1 � − 2 | φ 2 � √ √ N GW � 1 − e Ω( s , b ) / 2) � | a i | 2 · | a k | 2 � 1 − e Ω ik ( s , b ) / 2) � � → i , k =1 One single-channel Ω ik eikonal per combination of GW states N GW � � | a i | 2 · | a k | 2 � 1 − e Ω ik ( s , b ) / 2) � d b 2 → e.g. σ tot = 2 i , k =1 H. Schulz SHRiMPS 3 / 16

KMR modelling of Ω Ω ik : product of colliding (parton) densities ω i ( k ) ω ( i ) k ω i ( k ) : density of GW state i in the presence of k ω ( i ) k : density of GW state k in the presence of i Coupled evolution (in rapidity, y) equations H. Schulz SHRiMPS 4 / 16

KMR modelling of Ω Ω ik : product of colliding (parton) densities ω i ( k ) ω ( i ) k ω i ( k ) : density of GW state i in the presence of k ω ( i ) k : density of GW state k in the presence of i Coupled evolution (in rapidity, y) equations � 1 d b 1 d b 2 δ 2 ( b − b 1 + b 2 ) ω i ( k ) ( y , b 1 , b 2 ) ω ( i ) k ( y , b 1 , b 2 ) Ω ik ( s , b ) = 2 β 2 0 b 1 b 2 b H. Schulz SHRiMPS 4 / 16

KMR evolution d ω i ( k ) ( y ) = ∆ ω i ( k ) · R ( λ, ω i ( k ) , ω ( i ) k ) d y d ω ( i ) k ( y ) = ∆ ω ( i ) k · R ( λ, ω i ( k ) , ω ( i ) k ) d y ∆: parameter for probability for gluon emission H. Schulz SHRiMPS 5 / 16

KMR evolution d ω i ( k ) ( y ) = ∆ ω i ( k ) · R ( λ, ω i ( k ) , ω ( i ) k ) d y d ω ( i ) k ( y ) = ∆ ω ( i ) k · R ( λ, ω i ( k ) , ω ( i ) k ) d y ∆: parameter for probability for gluon emission R ( λ, ω i ( k ) , ω ( i ) k ): rescattering/absorption with free parameter λ Boundary conditions (form factors): s Y = log p − δ Y , parameter δ Y m 2 ω i ( k ) ( − Y / 2 , b 1 ) = F i ( b 1 , β 0 , ξ, κ, Λ) ω ( i ) k (+ Y / 2 , b 2 ) = F k ( b 2 , β 0 , ξ, κ, Λ) with tuning parameters β 0 , ξ, κ, Λ i i k k H. Schulz SHRiMPS 5 / 16

Event generation σ p ( Y ) Prob. for particular process p : σ tot ( Y ) , p ∈ [inel , el , SD , DD] Elastic scattering, single- and double diffractive easy Inelastic processes more involved (ladder-generation) H. Schulz SHRiMPS 6 / 16

Event generation σ p ( Y ) Prob. for particular process p : σ tot ( Y ) , p ∈ [inel , el , SD , DD] Elastic scattering, single- and double diffractive easy Inelastic processes more involved (ladder-generation) 3 val. quarks + 1 val. gluon at Q 2 = 0 Pick colliding GW states (i, k in σ inel ) Choose impace parameter Pomeron exchanges independent → pick N according to Poisson ( ν = Ω ik ) Generate N ladders similar to parton shower (gluon emissions) → correction of the tree-level t-channel t -channel propagators can be colour singlett → rapidity gaps ⊕ parton shower, hadronisation H. Schulz SHRiMPS 6 / 16

Tuning with Professor Random sampling: N parameter points in n -dimensional space Run generator and fill histograms (e.g. Rivet) For each bin: Don’t care about actual dependence on parameters Polynomial approximation ( parameterisation − data ) 2 Construct overall (now trivial) χ 2 ≈ � error 2 bins and Numerically minimize Minuit data bin b b b b bin interpolation best p p H. Schulz SHRiMPS 7 / 16

Professor 2 http://professor.hepforge.org , release 2.1.0 Complete rewrite Parametrisation now in C++ (Eigen) Usage in other codes ( arXiv:1511.05170[hep-ph] , arXiv:1506.08845[hep-ph] ) Python bindings (through cython) for flexibility: 1 import professor2 as prof # X ... parameter points, e.g. 3 − dimensional 3 # Y ... corrsponding values I=prof2.Ipol(X,Y, order=5) 5 print I.val([0, − .5, 13]) HepMC to Rivet to YODA to Professor tool chain of course still supported with set of scripts Much improved command line Parametrisations stored in text files H. Schulz SHRiMPS 8 / 16

Shrimps tuning Two stages: Tune parameters important for cross-sections to measured 1 cross-sections at various √ s Tune parameters of dynamic part of the model to variety of 2 distributions measured at the LHC at 7 TeV (ATLAS, CMS, TOTEM) H. Schulz SHRiMPS 9 / 16

Cross section tuning total, inelastic and elastic cross section 160 pp data 140 ppbar data TOTEM data 120 LHC data σ tot,inel,elas [mb] 100 SHRiMPS 80 60 40 20 0 0.1 1 10 100 E c.m. [TeV] H. Schulz SHRiMPS 10 / 16

Tuning of dynamical part of SHRiMPS Tuned 8 parameters to 7 TeV data Tuned parameters (below) not in latest release Parameter Tuned value 3.02 Q 0^2 0.65 Chi S 1.19 Shower Min KT2 3.48 KT2 Factor 1.01 RescProb 0.18 RescProb1 0.50 Q RC^2 -15.30 ReconnProb H. Schulz SHRiMPS 11 / 16

b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b ATLAS 7TeV MinBias, arXiv:1012.5104 Charged particle η at 7 TeV, track p ⊥ > 100 MeV, for N ch ≥ 2 Charged particle η at 7 TeV, track p ⊥ > 500 MeV, for N ch ≥ 1 1/ N ev d N ch /d η 1/ N ev d N ch /d η 7 2 . 5 6 2 5 4 1 . 5 3 Data Data 1 SHRiMPS SHRiMPS 2 0 . 5 1 0 0 1 . 4 1 . 4 MC/Data 1 . 2 MC/Data 1 . 2 1 1 0 . 8 0 . 8 0 . 6 0 . 6 - 2 - 1 0 1 2 - 2 - 1 0 1 2 η η Charged particle p ⊥ at 7 TeV, track p ⊥ > 100 MeV, for N ch ≥ 2 Charged multiplicity ≥ 1 at 7 TeV, track p ⊥ > 500 MeV 10 − 1 1/ N ev 1/2 π p ⊥ d σ /d η d p ⊥ 1/ σ d σ /d N ch 10 1 b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b Data Data SHRiMPS SHRiMPS 1 10 − 2 10 − 1 10 − 3 b b b b b b b b b 10 − 2 10 − 4 10 − 3 10 − 4 10 − 5 10 − 5 10 − 6 1 . 4 1 . 4 MC/Data 1 . 2 MC/Data 1 . 2 1 1 0 . 8 0 . 8 0 . 6 0 . 6 10 − 1 1 10 1 20 40 60 80 100 120 p ⊥ [GeV] N ch H. Schulz SHRiMPS 12 / 16

b b b b b b b b b b b b b b b b b b ATLAS 7 TeV UE arXiv:1103.1816 , √ s = 7 TeV , √ s = 7 TeV Transverse N density vs. p clus 1 Transverse ∑ p ⊥ density vs. p clus 1 ⊥ ⊥ � d 2 N /d η d φ � � d 2 ∑ p ⊥ /d η d φ � 1 . 8 2 1 . 6 1 . 4 1 . 5 1 . 2 1 1 0 . 8 Data Data 0 . 6 SHRiMPS SHRiMPS 0 . 5 0 . 4 0 . 2 0 0 1 . 4 1 . 4 1 . 2 1 . 2 MC/Data MC/Data 1 1 0 . 8 0 . 8 0 . 6 0 . 6 2 4 6 8 10 12 14 2 4 6 8 10 12 14 p ⊥ (leading particle) [GeV] p ⊥ (leading particle) [GeV] H. Schulz SHRiMPS 13 / 16

b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b ATLAS rapidity gaps, arXiv:1201.2808[hep-ex] Rapidity gap size in η starting from η = ± 4.9, p T > 400 MeV Rapidity gap size in η starting from η = ± 4.9, p T > 800 MeV d σ /d ∆ η F [mb] d σ /d ∆ η F [mb] 10 2 10 2 Data Data SHRiMPS SHRiMPS 10 1 10 1 1 1 10 − 1 10 − 1 1 . 4 1 . 4 1 . 2 1 . 2 MC/Data MC/Data 1 1 0 . 8 0 . 8 0 . 6 0 . 6 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 ∆ η F ∆ η F H. Schulz SHRiMPS 14 / 16