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

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

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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

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SLIDE 1

SHRiMPS Status of soft interactions in SHERPA

Holger Schulz (IPPP Durham) November 23, 2015 MPI@LHC 2015, Trieste

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SLIDE 2

Introduction

Unitarity of S-matrix → optical theorem Relates tree level to loop level diagram

  • 2

=

p2 p1 p2 p1 p2 p1 σtot(s)

Eikonal ansatz

= 1

s Im[Ael(s, t = 0)

  • 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

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SLIDE 3

Eikonal ansatz

σtot(s) = 1

s Im[Ael(s, t = 0)]

Rewrite A(s, t) → A(s, b), b: impact parameter Ansatz: σtot(s) = 2

  • db2Im[A(s, b)]

σel(s) = 2

  • db2[A(s, b)]2

σinel(s) = σtot(s) − σel(s)

  • H. Schulz

SHRiMPS 2 / 16

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SLIDE 4

Eikonal ansatz

σtot(s) = 1

s Im[Ael(s, t = 0)]

Rewrite A(s, t) → A(s, b), b: impact parameter Ansatz: σtot(s) = 2

  • db2Im[A(s, b)]

σel(s) = 2

  • db2[A(s, b)]2

σinel(s) = σtot(s) − σel(s) A(s, b) = i

  • 1 − eΩ(s,b)/2)

→ σtot(s) = 2

  • db2

1 − eΩ(s,b)/2)

  • H. Schulz

SHRiMPS 2 / 16

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SLIDE 5

Eikonal model

A(s, b) = i

  • 1 − eΩ(s,b)/2)

Good-Walker (GW) states |φ1, |φ2 (diffractive eigenstates) |p =

NGW

  • i=1

ai|φi SHRiMPS:|p =

1 √ 2|φ1 + 1 √ 2|φ2

|N∗(1440) =

1 √ 2|φ1 − 1 √ 2|φ2

  • H. Schulz

SHRiMPS 3 / 16

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SLIDE 6

Eikonal model

A(s, b) = i

  • 1 − eΩ(s,b)/2)

Good-Walker (GW) states |φ1, |φ2 (diffractive eigenstates) |p =

NGW

  • i=1

ai|φi SHRiMPS:|p =

1 √ 2|φ1 + 1 √ 2|φ2

|N∗(1440) =

1 √ 2|φ1 − 1 √ 2|φ2

  • 1 − eΩ(s,b)/2)

→

NGW

  • i,k=1

|ai|2 · |ak|2 1 − eΩik(s,b)/2) One single-channel Ωik eikonal per combination of GW states → e.g. σtot = 2

  • db2

NGW

  • i,k=1

|ai|2 · |ak|2 1 − eΩik(s,b)/2)

  • H. Schulz

SHRiMPS 3 / 16

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SLIDE 7

KMR modelling of Ω

Ωik: product of colliding (parton) densities ωi(k) ω(i)k ωi(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

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SLIDE 8

KMR modelling of Ω

Ωik: product of colliding (parton) densities ωi(k) ω(i)k ωi(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 Ωik(s, b) =

1 2β2

  • db1db2δ2(b − b1 + b2)ωi(k)(y, b1, b2)ω(i)k(y, b1, b2)

b2 b b1

  • H. Schulz

SHRiMPS 4 / 16

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SLIDE 9

KMR evolution

dωi(k)(y) dy

= ∆ωi(k) · R(λ, ωi(k), ω(i)k)

dω(i)k(y) dy

= ∆ω(i)k · R(λ, ωi(k), ω(i)k) ∆: parameter for probability for gluon emission

  • H. Schulz

SHRiMPS 5 / 16

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SLIDE 10

KMR evolution

dωi(k)(y) dy

= ∆ωi(k) · R(λ, ωi(k), ω(i)k)

dω(i)k(y) dy

= ∆ω(i)k · R(λ, ωi(k), ω(i)k) ∆: parameter for probability for gluon emission R(λ, ωi(k), ω(i)k): rescattering/absorption with free parameter λ Boundary conditions (form factors):

Y = log

s m2

p − δY , parameter δY

ωi(k)(−Y /2, b1) = Fi(b1, β0, ξ, κ, Λ) ω(i)k(+Y /2, b2) = Fk(b2, β0, ξ, κ, Λ) with tuning parameters β0, ξ, κ, Λ k k i i

  • H. Schulz

SHRiMPS 5 / 16

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SLIDE 11

Event generation

  • Prob. for particular process p:

σp(Y ) σtot(Y ), p ∈ [inel, el, SD, DD]

Elastic scattering, single- and double diffractive easy Inelastic processes more involved (ladder-generation)

  • H. Schulz

SHRiMPS 6 / 16

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SLIDE 12

Event generation

  • Prob. for particular process p:

σp(Y ) σtot(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 Q2 = 0 Pick colliding GW states (i, k in σinel) Choose impace parameter Pomeron exchanges independent → pick N according to Poisson (ν = Ωik) 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

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SLIDE 13

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

Construct overall (now trivial) χ2 ≈

bins (parameterisation−data)2 error2

and Numerically minimize Minuit

p b b b b best p data bin bin interpolation

  • H. Schulz

SHRiMPS 7 / 16

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SLIDE 14

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

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SLIDE 15

Shrimps tuning

Two stages:

1

Tune parameters important for cross-sections to measured cross-sections at various √s

2

Tune parameters of dynamic part of the model to variety of distributions measured at the LHC at 7 TeV (ATLAS, CMS, TOTEM)

  • H. Schulz

SHRiMPS 9 / 16

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SLIDE 16

Cross section tuning

20 40 60 80 100 120 140 160 0.1 1 10 100 σtot,inel,elas [mb] Ec.m. [TeV] total, inelastic and elastic cross section pp data ppbar data TOTEM data LHC data SHRiMPS

  • H. Schulz

SHRiMPS 10 / 16

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SLIDE 17

Tuning of dynamical part of SHRiMPS

Tuned 8 parameters to 7 TeV data Tuned parameters (below) not in latest release Parameter Tuned value

Q 0^2

3.02

Chi S

0.65

Shower Min KT2

1.19

KT2 Factor

3.48

RescProb

1.01

RescProb1

0.18

Q RC^2

0.50

ReconnProb

  • 15.30
  • H. Schulz

SHRiMPS 11 / 16

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SLIDE 18

ATLAS 7TeV MinBias, arXiv:1012.5104

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

Data

b

SHRiMPS 1 2 3 4 5 6 7 Charged particle η at 7 TeV, track p⊥ > 100 MeV, for Nch ≥ 2 1/Nev dNch/dη

  • 2
  • 1

1 2 0.6 0.8 1 1.2 1.4 η MC/Data

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

Data

b

SHRiMPS 10−5 10−4 10−3 10−2 10−1 1 10 1 Charged particle p⊥ at 7 TeV, track p⊥ > 100 MeV, for Nch ≥ 2 1/Nev 1/2πp⊥ dσ/dηdp⊥ 10−1 1 10 1 0.6 0.8 1 1.2 1.4 p⊥ [GeV] MC/Data

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

Data

b

SHRiMPS 0.5 1 1.5 2 2.5 Charged particle η at 7 TeV, track p⊥ > 500 MeV, for Nch ≥ 1 1/Nev dNch/dη

  • 2
  • 1

1 2 0.6 0.8 1 1.2 1.4 η MC/Data

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

Data

b

SHRiMPS 10−6 10−5 10−4 10−3 10−2 10−1 Charged multiplicity ≥ 1 at 7 TeV, track p⊥ > 500 MeV 1/σ dσ/dNch 20 40 60 80 100 120 0.6 0.8 1 1.2 1.4 Nch MC/Data

  • H. Schulz

SHRiMPS 12 / 16

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SLIDE 19

ATLAS 7 TeV UE arXiv:1103.1816

b b b b b b b b

Data

b

SHRiMPS 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Transverse N density vs. pclus1

⊥

, √s = 7 TeV d2N/dηdφ 2 4 6 8 10 12 14 0.6 0.8 1 1.2 1.4 p⊥ (leading particle) [GeV] MC/Data

b b b b b b b b

Data

b

SHRiMPS 0.5 1 1.5 2 Transverse ∑ p⊥ density vs. pclus1

⊥

, √s = 7 TeV d2 ∑ p⊥/dηdφ 2 4 6 8 10 12 14 0.6 0.8 1 1.2 1.4 p⊥ (leading particle) [GeV] MC/Data

  • H. Schulz

SHRiMPS 13 / 16

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SLIDE 20

ATLAS rapidity gaps, arXiv:1201.2808[hep-ex]

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

Data

b

SHRiMPS 10−1 1 10 1 10 2 Rapidity gap size in η starting from η = ±4.9, pT > 400 MeV dσ/d∆ηF [mb] 1 2 3 4 5 6 7 8 0.6 0.8 1 1.2 1.4 ∆ηF MC/Data

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

Data

b

SHRiMPS 10−1 1 10 1 10 2 Rapidity gap size in η starting from η = ±4.9, pT > 800 MeV dσ/d∆ηF [mb] 1 2 3 4 5 6 7 8 0.6 0.8 1 1.2 1.4 ∆ηF MC/Data

  • H. Schulz

SHRiMPS 14 / 16

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SLIDE 21

CMS 13TeV arXiv:1507.05915[hep-ex]

b b b b b b b b b b b b b b b b b b b b

Data

b

SHRiMPS 1 2 3 4 5 6 7 8 9 Selection: inelastic pp, charged hadrons (p, K ,π) cτ > 10mm

1 N dN dη

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 η MC/Data

Encouraging prediction for 13 TeV

  • H. Schulz

SHRiMPS 15 / 16

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SLIDE 22

Summary

MC generation of elastic, inelastic and diffractive processes with one model, based on KMR Satisfying prediction of cross-sections Unsatisfying prediction of minimum bias data at 7 TeV 13 TeV data comparison encouraging SHRiMPS had low priority in the last year within SHERPA Recently convinced ourselves that it’s not tuning problem Currently code cleanup for improvements

  • H. Schulz

SHRiMPS 16 / 16

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SLIDE 23

Backup

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SLIDE 24

1e-05 0.0001 0.001 0.01 0.1 1 0.01 0.1 1 u d g anti-u s

IR continued PDFs

Q

2 = 0 GeV 2 [straight], 1 GeV 2 [dashed], 2 GeV 2 [dotted]