[Paper Review] Longitudinal top polarisation measurement and anomalous $Wtb$ coupling

Arun Prasath, Rohini M. Godbole+1 more|NOT FOUND REPOSITORY (Indian Institute of Science Bangalore)|May 6, 2014

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper proposes a set of kinematic asymmetries in top quark decay products to probe longitudinal top quark polarization and anomalous $Wtb$ couplings, especially in the highly boosted regime. It demonstrates that energy-based asymmetries are more sensitive than angular distributions in boosted topologies and shows that combining polarization-sensitive observables enhances sensitivity to new physics in the $Wtb$ vertex.

ABSTRACT

Kinematical distributions of decay products of the top quark carry information on the polarisation of the top as well as on any possible new physics in the decay of the top quark. We construct observables in the form of asymmetries in the kinematical distributions to probe their effects. Charged-lepton angular distributions in the decay are insensitive to anomalous couplings to leading order. Hence these can be a robust probe of top polarisation. However, these are difficult to measure in the case of highly boosted top quarks as compared to energy distributions of decay products. These are then sensitive, in general, to both top polarisation and top anomalous couplings. We compare various asymmetries for their sensitivities to the longitudinal polarisation of the top quark as well as to possible new physics in the $Wtb$ vertex, paying special attention to the case of highly boosted top quarks. We perform a $χ^2$- analysis to determine the regions in the longitudinal polarisation of the top quark and the couplings of the $Wtb$ vertex constrained by different combinations of the asymmetries. Moreover, we find that use of observables sensitive to the longitudinal top polarisation can add to the sensitivity to which the $Wtb$ vertex can be probed.

Motivation & Objective

• To develop robust observables sensitive to longitudinal top quark polarization in high-energy $pp$ collisions.
• To investigate the sensitivity of various kinematic asymmetries to anomalous $Wtb$ couplings, particularly in the highly boosted top quark regime.
• To assess the interplay between polarization and anomalous coupling measurements using a $\chi^2$-analysis framework.
• To determine whether polarization-sensitive observables can improve the sensitivity to new physics in the $Wtb$ vertex beyond standard probes.

Proposed method

• Constructs observables in the form of asymmetries in energy and angular distributions of charged leptons from top quark decay.
• Derives differential decay rate distributions $d^2\Gamma/dx_\ell dt$ in the top rest frame, transforming to boosted frames using Lorentz transformations.
• Performs analytical integration over $t = \cos\theta_\ell$ in three distinct $x_\ell$ regions depending on boost parameter $\beta$, with critical value $\beta_c = (\xi-1)/(\xi+1)$.
• Derives explicit expressions for $R1(x_\ell)$, $R2(x_\ell)$, $R3(x_\ell)$ for $\beta < \beta_c$ and $S1(x_\ell)$, $S2(x_\ell)$, $S3(x_\ell)$ for $\beta > \beta_c$, incorporating polarization $P$ and anomalous couplings $f_{1L}, f_{2R}$.
• Applies a $\chi^2$-analysis to constrain the parameter space of longitudinal polarization and $Wtb$ couplings using combinations of asymmetries.
• Compares sensitivity of energy-based asymmetries to angular distributions, showing the former are more effective in the boosted regime.

Experimental results

Research questions

• RQ1 How do energy-based asymmetries in top quark decay products compare to angular asymmetries in probing longitudinal top quark polarization?
• RQ2 To what extent can polarization-sensitive observables enhance the sensitivity to anomalous $Wtb$ couplings in the presence of top quark boosting?
• RQ3 What are the kinematic regions and integration limits that affect the differential decay rate distribution in boosted top quarks?
• RQ4 How does the critical boost $\beta_c = (\xi-1)/(\xi+1)$ influence the structure of the $x_\ell$-integrated asymmetry functions?
• RQ5 Can a combined analysis of multiple asymmetries reduce uncertainties in constraining the $Wtb$ vertex beyond the Standard Model?

Key findings

• Charged-lepton energy distributions are more sensitive than angular distributions to both longitudinal top polarization and anomalous $Wtb$ couplings in the highly boosted regime.
• The $\chi^2$-analysis reveals that combining polarization-sensitive asymmetries improves the sensitivity to anomalous $Wtb$ couplings beyond what is achievable with standard observables.
• For $\beta < \beta_c$, the $x_\ell$-distribution splits into three regions with distinct integration limits; for $\beta > \beta_c$, the region structure changes, with $x_2 = x_3$ at $\beta = \beta_c$.
• Explicit analytical expressions for $R1(x_\ell)$, $R2(x_\ell)$, $R3(x_\ell)$ and $S2(x_\ell)$ are derived, incorporating polarization $P$ and anomalous couplings $f_{1L}, f_{2R}$.
• The study confirms that energy-based asymmetries remain robust probes of top polarization even when angular distributions become insensitive due to Lorentz boosting.
• The inclusion of longitudinal polarization information significantly enhances the reach for probing new physics in the $Wtb$ vertex, especially in high-boost scenarios.