Discrepancy in Standard Model Prediction
for Z⁰ Asymmetry Measurements at SLAC and CERN?

The weak mixing angle can be determined from asymmetry measurements in Z⁰ interactions with leptons and also from asymmetry measurements in Z⁰ interactions with quarks.  These two techniques give results that differ by 3.5 standard deviations (see summary plot of weak mixing angle results).  The reason for this discrepancy could be a statistical fluctuation, an experimental technique problem, or the influence of new physics beyond the Standard Model.  

     The probability for 2 measurements to disagree by 3.5 standard deviations (3.5s) is much less than 0.1%.  This means that in a sample of 1000 measurements, it is unlikely for any 2 of the 1000 measurements to disagree by 3.5s or more.  And for any random comparison of 2 measurements, it is highly unlikely to observe such a large disagreement.
     The leptonic asymmetry results measure the lepton-asymmetry parameter, A_l, which is very sensitive to the weak mixing angle.  There is a similar b-quark asymmetry parameter, A_b, that describes the asymmetry in the strength of the Z⁰ interaction between left-handed b quarks and right-handed ones. A_b is insensitive to the value of the weak mixing angle and is predicted to be 0.935 by the Standard Model.  With the availability of a polarized electron beam, the SLD experiment makes a direct measurement of this parameter.  At CERN, the 4 LEP experiments do not have a polarized electron beam, but can measure a forward-backward asymmetry in Z⁰ decays to b quarks, A_b^FB, and this asymmetry is proportional to the product of A_b times A_l.   The observed discrepancy in the weak mixing angle determination between the lepton and quark asymmetry measurements could result from new physics affecting A_b.   In this case it is very interesting to examine the self-consistency of the A_l, A_b and A_b^FB measurements.  This is done in the plot below.