Constraining the top-Z coupling through tt̄Z production at the LHC

We study top pair production in association with a Z-boson at the LHC, focusing on the sensitivity to the topZ couplings. As yet, these couplings have not been studied in a hadronic collider environment. We calculate tt̄Z production to next-to-leading order in perturbative QCD, and include spin correlations in the top and Z-decays to the same order. We use the cross section measurements made by CMS using 4.9 fb−1 of data from the √ s = 7 TeV LHC run to place constraints on the top-Z couplings through a log-likelihood ratio analysis. Looking ahead to the higher energy run, we use the azimuthal angle between the leptons arising from the Z-decay, which is particularly sensitive to the top-Z coupling, to investigate the constraints that could be obtained using 30, 300, and 3000 fb−1 of data. We find that using NLO predictions significantly improves the top-Z coupling constraints, due to the decreased scale uncertainty.


Top-Z Coupling
How well can the top-Z coupling be constrained at the √ s = 13 TeV LHC?
2 Shape of opening angle between leptons from Z decay ∆φ ll sensitive to top-Z couplings.
3 Scale uncertainty is biggest obstacle (on theoretical side)! Also sensitive to top-Z coupling.
Distinguished by number and behavior of jets.
⇒ defer study of top-Z couplings in single top+Z to later. → negligible background to ttZ signal.
In SM, top-Z coupling is Assuming dimension-six, gauge invariant operators, Lagrangian is as anomalous couplingsindependent of kinematics Electric and magnetic top dipole moment.
Zero at tree-level in SM.

Small loop-induced corrections in SM.
Non-renormalizable amplitudes.
Dipole coefficients C 2,V and C 2,A set to zero.
Focus on C 1,V and C 1,A . Define Raoul Röntsch (Fermilab) Constraining the top-Z coupling through ttZ production at the LHC ETH Zürich, 16 July 2014 11 / 35 Full NLO spin correlations for final state particles narrow-width approximation.
Factorization of production and decay : Neglects contributions suppressed by Γt /mt 1%.
Violated by using severe selection cuts or particular distributions (e.g. p T ,Wb ).
Valid approximation for our calculation.
LO production through gg → ttZ and qq → ttZ .
Real corrections open qg andqg channels Soft and collinear singularities regularized using Catani-Seymour dipoles.
Virtual corrections to gg and qq channels calculated using D-dimensional realization of Ossola-Papadopoulos-Pittau procedure. Real and virtual corrections to t → Wb and W → qq decays calculated analytically.
CS dipoles used to regularize soft/collinear singularities.

Details of calculation
Checks performed at parton level: LO and real emission matrix elements checked against MadGraph.
Virtual matrix elements checked against GoSam.
Singularities from integrated dipoles and virtual corrections cancel.

Checks performed at cross-section level:
Cross-section and distributions independent of cut-off in finite dipole phase space.

Comparisons with previous results
Scale uncertainty ±28% at LO and ±14% at NLO.  Don't confuse deviations from SM and NLO QCD effects.

Detour -Binned Log Likelihoods
Binned likelihood function with Poisson distribution P i , with n i events observed and ν i predicted under hypothesis H.

Log-likelihood is then
log L(H| n obs ) = and log-likelihood ratio is test statistic Λ( n obs ) = log L(H0| n obs ) L(H1| n obs ) Constraining the top-Z coupling through ttZ production at the LHC ETH Zürich, 16 July 2014 21 / 35 LL ratio derived from Poisson distribution: and ν H 1 i are calculated/measured binned data according to two hypotheses.
n i,obs are pseudoexperimental data, generated around one of the hypotheses H0 or H1.
Overlap is a measure of statistical separation of hypotheses. Type-I error (falsely reject H0): Type-II error (falsely reject H1): We choose α = β -equal chance of incorrectly rejecting each hypothesis in favor of the other.

Inclusion of Theoretical Uncertainties
Need to include theoretical (scale + pdf) uncertainties.
For H0 and H1, minimize the difference between the total cross-sections within uncertainty.
If cross-sections lie within each other's uncertainty bands, set them both equal to their average.

Rescale all bins by uniformly.
Has effect of minimizing the differences -Λ distributions are closer.

Constraints from CMS data
First observation of ttZ at the LHC: ATLAS sees 1 event with 4.7fb −1 , CMS sees 9 events with 4.9 fb −1 (bg. expectation 3.2 events).
Much tighter constraints at NLO (reduced scale uncertainty; k-factor).
Compare SM calculation to anomalous coupling calculation -measure statistical separation between SM and anomalous top-Z couplings.