Measurement of the Weak Mixing Angle

With any measurement, the degree of certainty to which the central value is known is often times as important as the value itself. Here, we detail the steps required to properly calculate the uncertainty on a measured quantity, in this case, on a ratio of numbers of events. To do so, you need to know that:

(1) In a standard counting experiment, the statistical uncertainty on a number N is simply:

(2) The formula for the uncertainty on a function f(x), based on the known variances of parameters a,b,c ... is given by the following equation, assuming the parameters a,b,c are uncorrelated.

(3) From the above formula, it then follows that the uncertainty on a ratio of two functions, , is:

(4) Combining this with (1), then the statistical uncertainty on the ratio, , is simply:

So, for example, to compute the uncertainty on your ratio (R) of NC to CC events, f and g are then your computed numbers of NC (short) and CC (long) events.

Go Back