Optimizing the sensitivity for anomalous quartic gauge couplings in the event selection of WWss

Transcription

1 Optimizing the sensitivity for anomalous quartic gauge couplings in the event selection of WWss Diploma Thesis at TU Dresden Constanze Hasterok MPIK Heidelberg March 27, / 10

2 Outline 1. Effective field theory approach 2. 2 / 10

3 Effective Field Theory (EFT) Motivation No concrete theory has to be known in order to describe effects of high energy physics at low energies The number of free parameters does not have to be known EFT contains an infinite set of free parameters The SM is assumed to be a low energy effect of a more complex theory Extension of the SM-Lagrangian by introducing additional operators: L = L SM + α 4 (tr[v µ V ν ]) 2 + α 5 (tr[v µ V µ ]) 2 α 4 and α 5 are the aqgc parameters of interest 3 / 10

4 The effective Lagrangian can violate unitarity Unitarization of WWss scattering Most general approach: K-Matrix Method ( arxiv: ) Implemented in Whizard projecting the spinisospin-eigenamplitude on the Argand circle ( a K (s) i 2 = 1 2 ) for a(s) the a K (s) converges to the point 0+i: corresponds to an infinitely massive resonance (arxiv: ) Im[a] 1/2 a K (s) Re[a] a(s) 4 / 10

5 aqgc cross section and limits Cross section calculated in fiducial phase space ( talk Ulrike Schnoor T114.4) (ATLAS-CONF ) 1D 95% CL 0.14 < α 4 < < α 5 < 0.24 cross section (in fb) rises with increasing aqgc parameters larger slope in α 4 Scale of New Physics (arxiv: ) Λ = v 650 GeV α 5 / 10

6 aqgc Sensitive Jet Variables in W ± W ± M jj shape changes not much with increasing aqgc peak at M jj = 80 GeV due to W ± W ± W lνlνq q processes has to be cut away Y jj is very sensitive: with increasing aqgc, scattering of high energetic VB is enhanced jets are more forward 6 / 10

7 aqgc Sensitive Lepton Variables in W ± W ± pt ll = p l 1 T + p l 2 T pt ll is very sensitive: with increasing aqgc, scattering of high energetic VB is enhanced for the same reason the angular correlation between the leptons increases with increasing aqgc parameters 7 / 10

8 Cut Optimization (1st Quadrant) According to the shown distributions cuts on Y jj, φ ll and pt ll have the highest impacts on the sensitivity to aqgc 3D optimization All studies are done assuming constant systematic uncertainties for all cuts. (M jj > 500 GeV) Impact of a cut in Y jj of the same order as a φ ll cut A cut in p ll T > 200 GeV has the highest impact on the limits 8 / 10

9 Limits from Optimized Event Selection Cut set with best aqgc parameter limits and highest event yields: Y jj > 3.0, φ ll > 2.25, p ll T > 250 GeV and M jj > 300 GeV Number of expected events: 1.4 Expected Limits (1st Quadrant) α 4 < 0.04 α 5 < % improvement of the aqgc sensitivity! Scale of new physics: Λ 1.2 TeV 9 / 10

10 Summary Set upper limits on aqgc parameters α 4 and α 5 The variables Y jj, φ ll, and pt ll are sensitive to the presence of aqgc Compared to a selection optimised for discovery of WWss-EW an aqgc optimized selection can increase the sensitivity by about 60% Thank you for your attention! 10 / 10

11 Backup 11 / 10

12 The ATLAS Detector Typical onion structure: Trackers around the interaction point, electromagnetic and hadronic calorimeter, and muon system Coordinate System: y Φ x y Y 0 z Y Rapidity: Y ln [ ( )] θ tan 2 12 / 10

13 EWSB Approach EW symmetry breaking is realized by a Σ(x) field (2 2 matrix) Σ(x) can be parametrized linearly (case of a light Higgs boson) or non-linearly Global symmetry breaks down to a custodial symmetry SU(2) cu (isospin symmetry) The effective Lagrangian takes the form (arxiv: ): L eff = v 2 4 tr [VµV µ ] β v 2 8 tr [TVµ]tr [TV µ ] (Q L Σ M Q Q R + L L Σ M L L R + h.c.) L c L Σ M NL 1 + σ 3 2 Σ L L L c R M NR 1 + σ Q L i D Q L + q R i D Q R + L L i D L L + l R i D l R 1 2 tr [WµνWµν ] 1 2 tr [BµνBµν ] µ2 v 2 4 tr [Σ Σ] + λv 4 16 tr [Σ Σ] 2 + L R V µ = Σ(D µσ), T = Σ σ 3 Σ last two terms are the potential terms of the Σ field: only needed if fluctuations of the field are allowed (implies that a particle like the Higgs boson is present) This Lagrangian is valid up to an energy scale of 4πv 3 TeV 13 / 10

14 aqgc Operators Σ(x) can be parametrized by ( ) i Σ(x) = exp v w(x) 3 with w = w a σ a a=1 w a...goldstone bosons, σ a...pauli Matrices Effective Lagrangian with this parametrization is not complete more dimension four operators consistent with the electroweak symmetry can be found five of them respect the custodial symmetry SU(2) cu only two of them additionally modify only quartic couplings: (arxiv: ) 14 / 10

15 Interpretation of constraints on the parameters based on the observed cross section (event counting) The Profile Likelihood Method is used for the measurement which takes into account all experimental uncertainties: L(µ, ν) = Poi(N µs( ν) + i B i ( ν)) j G(ν 0,j, ν j, 1) 15 / 10

16 Correlations of aqgc Sensitive Variables Correlation Coefficients SM α 4 = α 5 = 0.1 φ ll - p ll T Y jj -M jj M jj - p ll T Y jj - p ll T as expected M jj and Y jj strongly correlated no optimization at the same time p ll T and φ ll slightly correlated are chosen to be optimized at the same time The correlation coefficient of two random variables X and Y is defined by C(X, Y ) = Cov(X, Y ) σ(x )σ(y ) with Cov(X, Y ) = E[(X E(X )) (Y E(Y ))] and σ being the positive standard deviation. 16 / 10

17 Background Lepton Distributions 17 / 10

18 Background Jet Distributions 18 / 10

19 Optimization of Limits in α 5 19 / 10

20 Bibliography M. Sekulla: Issues of Unitarisation, compare Kilian/Reuter/Sekulla in prep., Indico Link J. Reuter, W. Kilian, M. Sekulla, Simplified Models for New Physics in Vector Boson Scattering - Input for Snowmass 2013, arxiv: W. Kilian, T. Ohl, J. Reuter, WHIZARD: Simulating Multi-Particle Processes at LHC and ILC, arxiv: Wolfgang Kilian, Electroweak Symmetry Breaking: The Bottom-Up Approach, Springer, 2003 P. Anger et. al: Same Sign W ± W ± Production and Limits on Anomalous Quartic Gauge Couplings, in prep. 20 / 10