Flipping a coin to help measure charge asymmetries

The top figure is the invariant mass distribution of all Ds± meson candidates, with a clear signal peak shown in red, together with a number of background processes. For the lower figure, each point is the difference between the number of positive (Ds+) and negative (Ds) candidates, for a set of 10 simulations showing what a negative charge asymmetry of 1 percent would look like for the signal.

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Our understanding of particle physics is grounded in the idea of symmetries. For instance, we observe all charged fundamental particles to have a “mirror image” antiparticle partner, which among other differences has equal but opposite electric charge. Because of this, searches for, and measurements of, charge asymmetries in particle behavior can be very interesting. They can indicate where our assumptions may be not quite right and where potential improvements or additions (or revolutions!) to our Standard Model may be needed.

The DZero collaboration has made several such charge asymmetry measurements in recent years, helped by the unique detector conditions that cancel or suppress many challenging background effects. In a brand new measurement, they are now using the same well-tested techniques to investigate a new area: charge asymmetries in the decay of charmed-strange mesons (Ds±). In the Standard Model, the positively and negatively charged mesons should decay with exactly the same rate into the final state φπ±. A direct measurement of the asymmetry in these rates not only allows this prediction to be tested, but it also provides a benchmark “zero” point for other experiments to use in testing other decays.

An asymmetry measurement is a two-stage process. First, the raw asymmetry is determined by counting the number of positive and negative signal events. Next, the possible effects of detector asymmetries need to be subtracted from this quantity to reach the underlying physical asymmetry of interest. For the Ds± decays, unlike most prior DZero analyses, the detector asymmetries happen to be very small and less important than the precision and accuracy of the raw asymmetry extraction.

To help develop the method for extracting the raw asymmetry and to verify that the measurement is accurate and has correct uncertainties, analysts use an elegant “charge-randomization” technique. In this method, the true charge of the Ds± meson is hidden, and a random charge is assigned instead, effectively using a computerized coin toss. By using “coins” of known bias, scientists can simulate various input asymmetries and test the results of the analysis against these inputs. The above figure shows an example of 10 such simulations with an input asymmetry of -1 percent (that is, 101 Ds mesons for every 99 Ds+).

The results of these simulations confirm that the raw asymmetry can be extracted without bias over a range of different inputs, and so the measurement can proceed using the true meson charges. The final results agree with the Standard Model, with a measured charge asymmetry of around −0.4 percent, consistent with zero, and a precision five times better than existing measurements. Such benchmark asymmetries as this one will allow future experiments to test other decays for unexpected contributions from new physics.

Mark Williams

Iain Bertram was the primary analyzer for this measurement. Peter Garbincius also made an important contribution in his role as chairperson of the editorial board responsible for the internal review of the analysis and paper. 
The DZero administrative team provides a broad range of truly invaluable services to DZero collaborators, including everything from travel arrangements to battery recycling, from organizing social gatherings to fixing printer problems. We give special thanks to Julie Saviano, who is now transitioning to other projects, and welcome Barbara Hehner to the group.