Single top polarization

Here I will discuss theory and MC (TopReX) results.

Interesting papers and talks on EW-top polarization:

Mahlon (1998), Mahlon, Parke (1996) (finds that the optimal reference axis is the d-quark direction)
Christova, Draganov (1997) (angular distribution and t->b spectrum from the decay of polarized top quarks)
Espriu, Manzano (2002) (calculation of some variables sensitive to top polarization; the final section shows the effect of non-zero g_R taking also into account the complex phase)
Boos, Sherstnev (2002) (polarization in Wt-channel)
Talk by Tait @ Thinkshop (1998)
Talk by Mahlon @ Thinkshop (1998)

Strategy:

Plot the angular distribution of the lepton in the top rest frame, with respect to the "optimal" reference axis.
This axis is NOT the helicity axis, since the top cannot be considered as an ultrarelativistic particle. Instead, according to the theoretical literature, the top quarks are 100% polarized along the d-type quark from the udW (or csW) vertex.
In t-channel events, the best approximation to this axis is the recoil jet, i.e. the less b-tagged jet.

Advantages in using t-channel:

The reference axis is well defined (recoil jet)
No ambiguity in top reconstruction (lepton + Et-missing + "best" b-jet)
t-channel enrichment is quite easy (anti-b-tag of one jet, cut on the angular distance between jets)

This is the result after t-channel enrichment (from 1st to 5th: s-ch., t-ch., Wt, tt, Wbb; the 6th plot is the weighted sum with the expected proportions at LHC) with these cuts. The normalized slope (B/A) is 0.95+-0.08, both in the weighted sum and in the pure t-channel sample, demonstrating that the background contamination is well under control.
Note: there is a slight bias towards positive slope, probably due to the cut on the jet-jet angular distance; this can be seen by comparing with the distributions just after preselection and before preselection (note: this last plot shows that the apparent polarization in t-channel is not an artefact of the preselection).
The very forward bins are depleted by the lepton isolation cut; this is to be taken into account in case of A_FB calculation.

New physics with g_R different from zero would rise the baseline of the plot.
This can be risen also by:

unexpectedly large background contamination
recoil jet direction poorly approximating d-type quark direction (we should try several jet-finding algos...)
poor top momentum reconstruction

Further checks:

Replacing the reconstructed top direction with the true top from MC I obtain this (in Wbb, where the true top doesn't exist, it is replaced by the (0,0,0,0) 4-vector; in ttbar, where two true tops are present, one is chosen randomly).
According to Mahlon, the slope for the cosine between b-jet and recoil jet has to be -0.40. From this figure I obtain -0.41+-0.04 for t-channel. (In s-channel, b-jet and recoil jet have to be strongly anticorrelated, since the first one is from top decay and the other is mostly back-to-back with the top.)
This is for the neutrino/recoil-jet angular distribution. Mahlon predicts -0.33 for the slope, I obtain -0.43+-0.05.
How reliably is reconstructed the angle between the top and the recoil jet? Reconstructed top and true MC top; the shapes are very similar for t-channel, but quite different for the other cathegories, maybe explaining the discrepancies.
Probably the best check is to compare TopReX (which takes into account top polarization) with PYTHIA (which doesn't). Since PYTHIA generates the LO process only (qb->q't, and not qg->qbb->q'tb), I have to use IPROC=1 and not IPROC=11 in TopReX. The result for the lepton and the b-jet confirms that the distribution is constant for PYTHIA (low plot).

Talks:

Internal meeting in Pisa, 20/5/2004
Louvain, 29/6/2004 (second half of the talk is devoted to polarization)

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