# A measurement of the anomalous magnetic moment of the muon to 0.14 ppm using the FNAL g-2 experimen (Liverpool)

Lead Research Organisation:
University of Liverpool

Department Name: Physics

### Abstract

The electron is the lightest, stable charged particle and its properties are extremely well measured and underpin life through its role in chemical reactions. In 1937 a similar but heavier charged particle, the muon, was discovered in cosmic rays. The muon has been studied for the past 80 years and it seems to behave like a heavier version of the electron with its properties only modified by virtue of it being

approximately 220 times the mass of the electron. It appears, like the electron, to have no structure and is not an excited state of the electron but a distinct fundamental particle.

Its larger mass means it is unstable and decays with a lifetime of 2 x 1/millionth of a second. Like the electron, the muon is charged and has the quantum mechanical property of spin. This in turn means that the muon acts like a subatomic magnet and has a property called a magnetic moment. This microscopic magnetic moment in the case of an electron ultimately determines the macroscopic magnetic properties of a material. The size of this magnetic moment determines the size of the torque that an external magnetic field will exert on the muon. This torque causes the direction of the muon's spin to precess around the direction of the magnetic field with a certain frequency. This frequency is determined by the muon's magnetic moment and it this frequency and hence magnetic moment that we will measure in this project.

We are seeking to measure the magnetic moment of the muon to a precision of 0.14 parts per million which will be over a factor of 4 better than the previous measurement. The reason for making such a precise measurement is that the value of the muon's magnetic moment is very precisely predicted in quantum mechanics and so we can use the measurement to test the predictions of quantum mechanics to a very high level of precision.

We presently know there are 4 types of force or interaction: the strong nuclear force, the electromagnetic force, the weak nuclear force and the gravitational force. The muon is subject to all these forces (interactions) and these in turn affect its magnetic moment. The gravitational contribution is too tiny to be measured but the others are not. Since we know the properties of these forces very well then using quantum theory, we can then predict the magnetic moment of the muon and compare it to experiment. Should the prediction and the measurement differ significantly then that would be evidence that there are new types of interaction or that the muon is not a fundamental particle after all and has some sort of structure. The previous measurement of the muon's magnetic moment from data taken in 2001 was at odds with the prediction such that the probability of them being consistent was only 0.05%. However in science the benchmark for inconsistency is that the chance of them being consistent has to be extremely small (0.0001%). By making a more precise measurement we can better examine this consistency of the measurement and the prediction and determine whether there is indeed evidence of new physics or not.

We will make this measurement by injecting a beam of muons into a circular storage ring (of 7m radius) which is subject to a 1.45 T magnetic field. By examining the direction of the electrons from the muon decay as a function of time (and measuring very precisely i.e. to better than 0.1 parts per million) the magnetic field we can measure the magnetic moment. This will be done in 2016 at Fermilab in the USA.

The UK institutes (Liverpool, UCL, Oxford, QMUL, RAL) will be making key contributions to this measurement. We will build the detectors that measure the muon beam's trajectory, the device to measure the magnetic field and the magnet that injects the beam into the circular storage ring. We hope by 2018 to have completed the measurement and so know whether there is new physics beyond the four known interactions or not.

approximately 220 times the mass of the electron. It appears, like the electron, to have no structure and is not an excited state of the electron but a distinct fundamental particle.

Its larger mass means it is unstable and decays with a lifetime of 2 x 1/millionth of a second. Like the electron, the muon is charged and has the quantum mechanical property of spin. This in turn means that the muon acts like a subatomic magnet and has a property called a magnetic moment. This microscopic magnetic moment in the case of an electron ultimately determines the macroscopic magnetic properties of a material. The size of this magnetic moment determines the size of the torque that an external magnetic field will exert on the muon. This torque causes the direction of the muon's spin to precess around the direction of the magnetic field with a certain frequency. This frequency is determined by the muon's magnetic moment and it this frequency and hence magnetic moment that we will measure in this project.

We are seeking to measure the magnetic moment of the muon to a precision of 0.14 parts per million which will be over a factor of 4 better than the previous measurement. The reason for making such a precise measurement is that the value of the muon's magnetic moment is very precisely predicted in quantum mechanics and so we can use the measurement to test the predictions of quantum mechanics to a very high level of precision.

We presently know there are 4 types of force or interaction: the strong nuclear force, the electromagnetic force, the weak nuclear force and the gravitational force. The muon is subject to all these forces (interactions) and these in turn affect its magnetic moment. The gravitational contribution is too tiny to be measured but the others are not. Since we know the properties of these forces very well then using quantum theory, we can then predict the magnetic moment of the muon and compare it to experiment. Should the prediction and the measurement differ significantly then that would be evidence that there are new types of interaction or that the muon is not a fundamental particle after all and has some sort of structure. The previous measurement of the muon's magnetic moment from data taken in 2001 was at odds with the prediction such that the probability of them being consistent was only 0.05%. However in science the benchmark for inconsistency is that the chance of them being consistent has to be extremely small (0.0001%). By making a more precise measurement we can better examine this consistency of the measurement and the prediction and determine whether there is indeed evidence of new physics or not.

We will make this measurement by injecting a beam of muons into a circular storage ring (of 7m radius) which is subject to a 1.45 T magnetic field. By examining the direction of the electrons from the muon decay as a function of time (and measuring very precisely i.e. to better than 0.1 parts per million) the magnetic field we can measure the magnetic moment. This will be done in 2016 at Fermilab in the USA.

The UK institutes (Liverpool, UCL, Oxford, QMUL, RAL) will be making key contributions to this measurement. We will build the detectors that measure the muon beam's trajectory, the device to measure the magnetic field and the magnet that injects the beam into the circular storage ring. We hope by 2018 to have completed the measurement and so know whether there is new physics beyond the four known interactions or not.

### Planned Impact

See lead document (P1826803).

### Publications

Grange J

*Muon (g-2) Technical Design Report*
MAXFIELD S
(2014)

*g - 2 AT FNAL*in International Journal of Modern Physics: Conference SeriesDescription | Since the previous submission, data taking by the g-2 experiment has continued and publication of the first results is expected later in 2020. The Straw trackers , built using this grant have continued to perform excellently. They are being successfully exploited not only according to their main purpose of reducing systematic errors on the main measurement of g-2 but have also proved invaluable in monitoring and diagnosing the behaviour of the muon storage ring and other detector and ring components. |

Exploitation Route | See previous submissions. |

Sectors | Education,Healthcare,Other |