A study of top polarization in single-top production at the LHC

TL;DR

This work analyzes the sensitivity of LHC single-top production in the s-channel to the Wtb effective couplings g_L and g_R, with explicit mb corrections and within the narrow-width approximation. It formulates the polarized production and decay cross sections, introduces a diagonal spin basis to minimize quantum interference, and provides analytic expressions for both t- and s-channel processes. A numerical study under realistic cuts shows that small right-handed couplings (g_R ~ 5×10^-2) could produce measurable deviations, particularly in anti-lepton–bottom correlations, making polarization a crucial handle for beyond-Standard-Model tests. Overall, the paper demonstrates that s-channel analyses, when combined with mb effects and appropriate spin bases, can yield meaningful constraints on the chirality structure of the Wtb vertex at the LHC.

Abstract

This paper complements the study of single top production at the LHC aiming to estimate the sensitivity of different observables to the magnitude of the effective couplings. In a previous paper the dominant $W$-gluon fusion mechanism was considered, while here we extend the analysis to the subdominant (10% with our set of experimental cuts) s-channel process. In order to distinguish left from right effective couplings it is required to consider polarized cross-sections and/or include $m_b$ effects. The spin of the top is accessible only indirectly by measuring the angular distribution of its decay products. We show that the presence of effective right-handed couplings implies necessarily that the top is not in a pure spin state. We discuss to what extent quantum interference terms can be neglected in the measurement and therefore simply multiply production and decay probabilities clasically. The coarsening involved in the measurement process makes this possible. We determine for each process the optimal spin basis where theoretical errors are minimized and, finally, discuss the sensitivity in the s-channel to the effective right-handed coupling. The results presented here are all analytical and include $m_b$ corrections. They are derived within the narrow width approximation for the top.

Figures (14)

• Figure 1: Feynman diagrams contributing single top production subprocess. In this case we have a $d$ as spectator quark
• Figure 2: Feynman diagram contributing to single top production in the subdominant $s$-channel process. The top decay is also shown in this figure
• Figure 3: Distribution of the cosines of the polar angles of the bottom and anti-bottom with respect to the beam line. The plot corresponds to single top production at the LHC with top decay included. The calculation was performed at the tree level in Standard Model. For the parton distribution functions we use $\mu ^{2}=\hat{s}=\left( q_{1}+q_{2}\right) ^{2}$.
• Figure 4: Anti-bottom transversal momentum distribution corresponding to single top production at the LHC. The calculation has been performed at tree level in the SM ($g_{L}=1$, $g_{R}=0$).
• Figure 5: Distribution of the invariant mass of the lepton (electron or muon) plus bottom system arising in top decay from single top production at the LHC. The calculation was performed at the tree level in Standard Model with $\mu ^{2}=\hat{s}=\left( q_{1}+q_{2}\right) ^{2}$.