Constraints on new theories using Rivet (Contur)

Jon Butterworth (UCL), DG, Michael Krämer (Aachen), David Yallup (UCL)

David Grellscheid September 23, 2016

IPPP, Durham University

Thanks to David Yallup for the slides!

1 Introduction and Aims

Goal: Create a flexible framework to confront BSM theories with precision SM • measurements OR quantify what room the errors on SM measurements leave for new physics. Requirements: • • Flexible physics input, desire a framework capable of applying to as broad a class of models as possible • Utilize existing pheno tools where possible, rich landscape of mature tools available, utilise this! • Robust statistical testing framework, constrained inputs, machinery can be lightweight. Use unfolded fiducial cross section measurements - Differentiates from current LHC • limit programs using detector level search data

White paper: arXiv:1606.05296 HepForge site (Work in progress): contur.hepforge.org

2 Building a framework

Feynrules - Mathematica package, generate Feynman rules from input Lagrangian • Herwig 7 - Event Generator, Feynman rules to fully hadronized final state • Rivet - Library of analyses, plug and play ATLAS and CMS measurements. (Data • taken from records in HepData)

Illustrate process by considering a simple model. 3 Simplified Dark Matter Model

Simplified Dark Matter model, enable a q¯ ψ, q description of weakly coupled, low mass resonances.

gq gdm, gq µ P µ L ⊃ gdmψγµγ5ψZ 0 + gq q q¯γµqZ 0 Z0 Vector mediator to dark sector, purely vector q ψ,¯ q¯ coupling toSM, purely axial coupling toDM.

Model introducesDM candidate, ψ, dark . Experimental signatures hence typically rely on either ’Mono-X’ style final states or enhancement to dijet production at colliders.

q¯ W ±, Z, γ q¯ g

ψ,¯ q¯ ψ,¯ q¯

Z0 Z0

q ψ, q q ψ, q

4 Standard Model measurements

Standard Model measurements

should not assume Standard Model • but they match the Standard Model very well • can use them to rule out new theories • Make use of all suitable analyses in Rivet simultaneously.

5 Rivet Analysis base

Derive sensitivity from as broad a range of SM measurements as available in HepData/Rivet. Sensitivity in as many final states/variables as possible

Note: Category defines non overlapping signatures, safe to combine into single metrics, more later 6 Examining the Rivet output (Hadronic Final States)

ATLAS Dijet double-differential cross sections (y∗ < 0.5) 6 10 b b b Data 10 5 b M = 500 GeV b z′ Default Rivet output, seek to quantify b = 1000 GeV 4 b Mz′ [pb/TeV] 10 b

∗ b Mz = 1500 GeV to what extent the measured values and 3 b ′

dy 10 b M = 2000 GeV b z′ 12 2 b errors exclude these simulations. 10 b gq = 0.375, gdm = 1

dm b

/ 1 b Mdm = 600 GeV Working under the assumption that b σ 10

2 b d b 1 b what has been measured by the data b 1 10− points is only Standard Model diagrams b 2 10− 3 10−

0.5 1 1.5 2 2.5 m12[TeV]

Data 1.14 0.42 1.12 0.94 Stack simulated signal on data points, 0.74 1.1 0.43 here display ratio. Legend displaying the CLs max 1.08 CL of exclusion obtained from the least 1.06 compatible bin. (MC+Data)/Data 1.04

1.02

1.0 0.5 1 1.5 2 2.5 7 m12[TeV] Results - Combined ‘Strong’ measurements

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CL of exclusion

2000 2000

1600 1500

1200 [GeV] 1000 [GeV] dm dm M

M 800

500 400

500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000

MZ0 [GeV] MZ0 [GeV]

(a) Heatmap of CLs at each point (b) Derived 95% CLs contour

Maps in mass plane for combined sensitivity from Strong measurements gq = 0.375 and gdm = 1 [Perturbative Unitarity bound on ψψ¯ interaction in blue] 8 Sample Rivet EW Measurements

q¯ W ±, Z, γ

ψ,¯ q¯

Z0

q ψ, q

ATLAS W+Jet 7TeV

ATLAS W+ 2 jet differential cross section ≥ b 1 b

12 b b Data b b m b b b M = 100 GeV b b z′

/d b

j 1 b b 2 10− b M = 300 GeV b z′ 1.2

≥ b b + = 600 GeV b Mz′

W b 2 b σ M = 1000 GeV 10− b z′ d b gq = 0.375, gdm = 1 1.15 3 b Mdm = 600 GeV 10− b b 1.1 4 b 10− b (MC+Data)/Data

5 1.05 10−

6 10− 1.0 0 500 1000 1500 2000 0 500 1000 1500 2000 m12 [GeV] m12 [GeV] 9 Results - Combined EW measurements

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CL of exclusion

2000 2000

1600 1500

1200 [GeV] 1000 [GeV] dm dm M

M 800

500 400

500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000

MZ0 [GeV] MZ0 [GeV]

(a) Heatmap of CLs at each point (b) Derived 95% CLs contour

Maps in mass plane for combined sensitivity from EW measurements gq = 0.375 and gdm = 1 [Perturbative Unitarity bound on ψψ¯ interaction in blue] 10 Sample Rivet ‘MET’ Measurements

ATLASZZ 7TeV

ATLAS total fiducial cross-section reconstructed ZZ 2l2ν → b Data

[fb] b b = 300 GeV σ Mz′ 100 b = 500 GeV Mz′ b = 1000 GeV Mz′ 80 b = 1500 GeV Mz′ gq = 0.375, gdm = 1 60 Mdm = 100 GeV

40 b

20 b b b b

b 0 b 200 400 600 800 1000 1200 1400 1600 [GeV] MZ′

11 Results - ‘MET’ measurements

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CL of exclusion

2000 2000

1600 1500

1200 [GeV] 1000 [GeV] dm dm M

M 800

500 400

500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000

MZ0 [GeV] MZ0 [GeV]

(a) Heatmap of CLs at each point (b) Derived 95% CLs contour

Maps in mass plane for combined sensitivity from ‘MET’ measurements gq = 0.375 and gdm = 1 [Perturbative Unitarity bound on ψψ¯ interaction in blue] 12 Results - Putting it all together

Test has been constructed to enable combination of all previously shown maps into a single combined LHC Test

2000 2000

1500 1500 [GeV] [GeV] 1000 1000 dm dm M M

500 500

500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000

MZ0 [GeV] MZ0 [GeV]

(a) Heatmap of CLs at each point (b) Derived 95% CLs contour

Maps in mass plane for combined sensitivity from all channels, gq = 0.375 and gdm = 1 [Perturbative Unitarity bound on ψψ¯ interaction in blue] 13 Results - heatmaps

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CL of exclusion

2000 2000

1500 1500 [GeV] [GeV] 1000 1000 dm dm M M

500 500

500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000

MZ0 [GeV] MZ0 [GeV]

(a) gq = 0.25 and gdm = 1 (b) gq = 0.5 and gdm = 1 Heatmap showing two scenarios: a - weakly coupled, b - strongly coupled

14 Results - 95% CL Contours

2000 2000

1500 1500 [GeV] [GeV] 1000 1000 dm dm M M

500 500

500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000

MZ0 [GeV] MZ0 [GeV]

(a) gq = 0.25 and gdm = 1 (b) gq = 0.5 and gdm = 1 95% CL contour showing two scenarios: a - weakly coupled, b - strongly coupled [perturbative unitarity bound in blue]

15 Results cont. - Heatmaps

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CL of exclusion

2000 2000

1500 1500 [GeV] [GeV] 1000 1000 dm dm M M

500 500

500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000

MZ0 [GeV] MZ0 [GeV]

(c) gq = 0.375 and gdm = 1 (d) gq = 0.375 and gdm = 0.25 Heatmap showing two scenarios: c - medium coupling, d - DM suppressed

16 Results cont. - 95% CL contour

2000 2000

1500 1500 [GeV] [GeV] 1000 1000 dm dm M M

500 500

500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000

MZ0 [GeV] MZ0 [GeV]

(c) gq = 0.375 and gdm = 1 (d) gq = 0.375 and gdm = 0.25 95% CL contour showing two scenarios: c - medium coupling, d - DM suppressed [perturbative unitarity bound in blue]

17 Conclusions and Outlook

SM measurements can inform us about what is not happening • Can utilize SM measurements as a test for BSM constraints, • without any prior knowledge of the model Provide utility for model building and • additional motivation for continued precision measurement programmes. • To do:

Extend testing framework • Include additional measurements as/when available • Roll out to other models • Initial paper arXiv:1606.0529 Updated plots and all code available at https://contur.hepforge.org/

18 Backup Statistical Analysis

Lean heavily on Cowan et al. arXiv:1007.1727. Asymptotic formulae for • likelihood-based tests of new physics. Construct Likelihood function for a single bin by bin test of: •

(µs+b)n
1  (m b)2  (s)k
L(µ, b, σb, s) = n! exp − (µs + b) × exp − −2 × k! exp − s √2πσb 2σb

Poisson event count: µ signal strength parameter, modulating between tested • hypothesis.

Gaussian encoding background error: σb, Uncertainty in b count taken from • Rivet/HepData as 1 σ error on a Gaussian (uncertainties quoted as the combination of statistical and systematics uncertainties in quadrature. Typically the systematic uncertainty dominates). Poisson term describing statistical MC error on simulated BSM signal count, s • Note that in the absence of a separate simulation of the background, take • [n] = [m] = b and [k] = s.

20 Statistical Analysis - cont.

Test each bin of each plot of each analysis, selecting the most significant bins to • combine into a total CL of exclusion (a simple extension of the Likelihood function to a product of the bins with the most prominent deviation). Note: guiding principal, construct combined CL limit from statistically independent counts. Selecting a single bin as a representative of a signature =⇒ mitigate impact of • correlations between systematic uncertainties in a single final state Issues: • • Methodology aims to build maximal safe limit out of available info. More advanced treatment possible? • Correlations between systematic errors between final states and datasets not a well posed question. Data certainly not available to account for this currently. • Currently rely on Differential xs measurements, need an event COUNT =⇒ multiply by Integrated Lumi, possible to test additional metrics?

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