Observing $t\bar{t}Z$ spin correlations at the LHC

This project was funded by the Royal Society of Edinburgh under the Saltire Early Career Research Fellowship scheme.

The top quark is the most massive fundamental particle in the Standard Model (SM), and is highly unstable. Its lifetime is in fact shorter than the typical interaction time of the strong nuclear force (QCD), which means that it decays before undergoing hadronisation. While any other quark would have seen their quantum properties (“spin”) diluted and randomised by being forced into colour-neutral composite objects (“hadrons”), the top quark is able to transfer this information, intact, to its decay products. Since the top quark is mostly produced in pairs at the LHC, through the $gg\to t\bar{t}$ process, it is interesting to look at spin correlations of pairs of top quarks; this has recently been done in ATLAS and has led to a small but interesting discrepancy between the SM prediction and the observation in proton collision data.

With fellow top spin expert James Howarth (Glasgow) and his PhD student Ethan Simpson, I started looking at the top process I know best: top pair production in association with a $Z$ boson. Our phenomenological study revealed a couple of interesting features:

• spin correlations are very different in $t\bar{t}Z$ and $t\bar{t}$
• a small polarisation of the top quarks is induced by the $Z$ boson (top quarks from vanilla $t\bar{t}$ are famously unpolarised!)
• measuring the full spin density matrix can provide a new way of constraining the SM Effective Field Theory (SMEFT)

This last item is of great interest, since no sign of new particles have been observed at the ATLAS experiment so far – we can therefore benefit from using precision measurements to constrain the SMEFT and guide our future searches. In this same paper, I also computed the degree of confidence (the “Bayesian $K$-factor”) with which we could claim having observed $t\bar{t}Z$ spin correlations at the LHC: this is what the colourful graph below shows. Using only Run 2 LHC data (collected from 2015 to 2018), it should be possible to obtain strong evidence of this quantum effect – which in frequentist terms could roughly be interpreted as a $3\sigma$ rejection of the null hypothesis, or “evidence” in ATLAS-speak. For a conclusive $5\sigma$ “observation”, we have to wait for combinations of Run 2 and Run 3 data.

The topic of my RSE Saltire Fellowship is precisely to use the LHC Run 2 ATLAS dataset to look for this effect. It is an experimentally challenging measurement, with a very feeble signal (almost a thousand times rare than $t\bar{t}$ production), many different background processes to control and complicated kinematics to reconstruct… Stay tuned!