Measuring the electric-dipole moment of the muon at BNL E821
Does the muon carry a tiny separation of electric charge along its spin? Finding one would break a basic symmetry of nature. I worked out how the g−2 experiment could look for it without fooling itself.
S. O. Giron. Adviser: Prof. Priscilla B. Cushman. Ph.D. dissertation, University of Minnesota (2004).
A downloadable copy of the full dissertation is coming.
A muon is a heavier cousin of the electron. It spins, and because it spins it acts like a tiny magnet. The g−2 experiment measured that magnet very precisely.
My dissertation asked a different question about the same particle: does it also have an electric dipole moment, a slight separation of charge along its spin? The Standard Model predicts one far too small to see. A bigger one would mean time-reversal symmetry is broken in a new way, a sign of new physics.
The hard part isn’t seeing a signal. It’s knowing the signal is real. A slightly tilted detector, a mis-steered beam or a stray magnetic field can all fake an EDM. So I studied three ways of measuring it, and for each one I simulated over 200 million events to learn exactly how it responds to a real EDM and to each kind of flaw. Then I ran all three on the 1999 data, 20 million events.
One method came out ahead: the least fooled by systematic biases, the sharpest response to a real EDM, the best at telling the two apart, and the loosest tolerances for a tenfold improvement on the limit.
My part Mine. My Ph.D. dissertation in experimental high-energy particle physics.
The day the dice ran out
Simulating an experiment means rolling dice, hundreds of millions of times: where each muon decays, which way its positron flies, how the positron showers in the detector. A computer’s dice are a pseudo-random number generator, a recipe that produces numbers that look random but eventually loops back to where it started.
Mine looped sooner than I knew. I was asking it for so many numbers that it ran out and started over, several times. I didn’t find out from the code. I found out from the data: a pattern sat in the simulated events that had no business being there. The same stretch of “random” events kept coming back.
Nature doesn’t repeat itself like that, so the simulation was lying to me in a very orderly way. I swapped in a better generator, and seeded it with another random number generator so no run started in the same place twice. The pattern disappeared, and the studies could be trusted.
It’s still one of my favorite lessons in measurement: the most dangerous error is the one that looks like structure. Check every instrument, including the invisible ones.
Open any part
Why look for a muon EDM?
Every particle with spin can, in principle, have an electric dipole moment. A nonzero value would violate time-reversal symmetry, and through the CPT theorem, CP symmetry too. Chapter 1 covers the classical and quantum descriptions, what the Standard Model predicts, what theories beyond it predict, and the earlier EDM experiments.
How an EDM shows up in the ring
Moving through the ring’s magnetic field, the muon feels an electric field in its own frame. An EDM couples to it and tilts the plane the spin precesses in. The decay positrons then drift up and down in step with the g−2 rhythm, a quarter-cycle out of phase with it. Chapter 2 derives this and describes the beam, the storage ring and the detectors.
The indirect method, and why it isn’t enough
An EDM would also make the measured g−2 slightly larger, so a deviation from the Standard Model could, in principle, be an EDM. But that route can’t tell an EDM apart from any other new physics in g−2. That’s why a direct measurement is required.
Three direct methods
Method I follows the average vertical position of the positrons over time. Method IIa measures how the g−2 phase changes with vertical position. Method IIb measures the phase difference between upper and lower detector segments. Each was tested in simulation and then on the 1999 data from the segmented detectors.
The systematic studies
Most of the work lives here. Using the g2geant simulation, I measured how each method responds to every flaw that could fake an EDM: detector misalignment, muon beam misalignment, vertical spin polarization, energy calibration of each detector segment, a radial magnetic field, detector inefficiencies and signal timing. Then I developed two tests that separate a true EDM from a systematic bias, by how the oscillation amplitude and the phase change with the detector’s vertical offset.
What came out of it
A side-by-side comparison of the methods’ false-EDM responses, estimated limits on false signals in the 1999 run, and the uncertainties the experiment would need for a tenfold better EDM limit. The collaboration’s 2009 EDM paper cites the dissertation for the constant that converts the measured phase slope into an EDM, and for the simulation scale factors in its systematic error estimates.
Each part opens to a short summary. Where a free copy exists, the link takes you to that section of the paper.