Top Quark Spin Correlations at the Tevatron Page: 2 of 8
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TIM HEAD ON BEHALF OF THE CDF AND DO COLLABORATIONS
2. - Observables
In strong interactions the top and anti-top quark are produced unpolarised at hadron
colliders, however the ti system is in a definite spin state. At the Tevatron about 85 %, at
next to leading order, of top quark pairs are produced via quark anti-quark annihilation.
At threshold these ti systems will be in a 3S1 state, whereas the 15% of top quark
pairs produced via gluon fusion will be in a 'So state. In the first case the top and
anti-top quark will tend to have their spins parallel, in the second case they tend to be
anti-parallel. One therefore expects to observe a correlation between the direction of the
spins.
The strength of the correlation due to the production mechanism can be expressed as
the asymmetry A,
(1) A - NTT N-I NT
NTT+NI +NIT+NTI
between the number of events with spins parallel, NTT and Nj1, and the number of events
with spins anti-parallel, NTl and NTT.
In order to measure the direction of the spin vector a quantisation axis needs to be
defined. At the Tevatron three sets of quantisation axes, referred to as "spin basis", are
commonly used. They are shown in Figure 1.
The simplest is the so called "beamline basis" in which the direction of one of the
incoming hadrons is used as quantisation axis. This basis is easy to construct and is
optimal for tt systems produced at threshold. The production asymmetry has been
calculated at next to leading order (NLO) in QCD as A = 0.777 [3].
The second basis is the "helicity basis" in which the momentum of the (anti)top quark
in the top-anti-top quark zero momentum frame is used to quantise the (anti)top quark
spin. At the Tevatron the strength of the correlation is smaller than in the "beamline
basis", in NLO QCD A = -0.352. The opposite sign arises due to the fact that the spins
tend to be anti-parallel in this basis.
Finally the third basis is the "off-diagonal basis". The direction of the quantisation
axes are defined by the angle o with respect to the (anti)top quark momentum. The
angle o is given by tanLo 1 - 32 tan 0, where ) is the speed of the top quark and
O is its scattering angle. This basis interpolates between the "beamline basis" close to
threshold (low )) and the "helicity basis" above threshold (large )). The production
asymmetry is A = 0.782. While this is slightly larger than in the "beamline basis" it is
more complex to reconstruct.
The angular distribution of decay product i in the top quark rest frame is given by:
(2) 1 d 1 - a, - cos 0,)
o d cos 0, 2
where 0, is the angle between the direction of flight of decay product i and the direction
of the spin vector; a2 is the so-called spin analysing power. From Equation 2 it is clear
that the angular distribution of a decay product with a2 = 0 contains no information
about the direction of the top quark spin and the angular distribution of a decay product
with a2 = 1 will contain most information. The spin analysing power of the various top
quark decay products are listed in Table I. The particles with the highest spin analysing
power are the lepton and the down type quark from the W boson decay.2
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Head, Tim. Top Quark Spin Correlations at the Tevatron, article, July 1, 2010; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc1013637/m1/2/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.