We know what the relative probability of seeing various values of
&theta* for different W boson helicities (
&theta*
tends to be small for positive helicity W bosons, large for negative
helicity W bosons, and around 90 degrees for zero helicity W bosons)
. For technical reasons, the measurement is
easier if we take the cosine of
&theta*. All we need to do is compare the values of cos
&theta*
in our data sample to the expected distributions. The results,
for a set of data corresponding to one of the signatures the top quark can leave in our detector, are shown below:
In this plot, our data is shown by the points with error bars. The red line represents what we'd see if all the W bosons
had negative helicity, the green line shows the case where they all have
zero helicity, and the blue line shows the case where they all
have positive helicity. The shaded area is the estimated background (meaning
events that don't really have top quarks in them but still sneak into
our sample). Numerically, we
can say that the fractions of W bosons with positive and zero
helicities is:
Fraction with zero helicity:
f0 = 0.425
+/- 0.195
Fraction with positive helicity:
f+ = 0.119 +/- 0.104
Remember that we expected
f0 to be 0.7, and
f+
to be very close to zero. So we don't find exactly what we
expected. To see whether we can claim that this means there's
physics beyond the
Standard Model, we need to assess the probability of
our result happening just by random chance if the
Standard Model is correct. Graphically, the result looks like:
The star shows the
Standard Model value, and our measurement is the dot
(the triangle represents the limit of all "reasonable" measurements in
which none of the helicity fractions are negative). The bigger of
the two ellipses is the 95%
confidence interval, meaning that if we were to repeat the experiment many times, we'd find an answer outside that ellipse 5% of the time. Since the
Standard Model value is well within this ellipse, our result certainly
cannot be used to claim that the
Standard Model is incomplete. In
other words, with the current sample size, it's not
really unlikely that the discrepancy comes about just due to chance --
but we will look again when more data is available. The top quark
may yet hold surprises for us!
More information about this measurement is available in
our full article on the measurement. This article was submitted to Physical Review Letters on October 31, 2007.
Primary Authors: Ken Johns, Jessica Leveque, and Erich W. Varnes (University of Arizona)