# FNAL g-2 Experiment

The simplest magnetic interaction of a charged particle with a B-field is described by the Dirac equation where the magnetic moment of a charged particle of mass m is defined as gsQe/2m where s is the particle's spin and Qe its charge. In the Dirac theory g is exactly two. However interactions involving virtual particles modify this value of g by a small amount (0.1%) and a precise measurement of (g-2) thus gives information about these virtual particles. A comparison of the measured value with the theory incorporating all known particles and interactions can thus indicate whether there are new particles such as those predicted by models of physics beyond the Standard Model.

The simplest higher order interaction, the "QED Schwinger interaction", modifies g-2 by
exactly α/π where α is the EM fine structure
constant (1/137.04). New unknown particle contribute to the (g-2)
proportionally to (m/M)^{2} where m is the mass of the
particle and M the mass of the new particle.

The measurement of the electron's g-2 is the most
precisely determined quantity in physics. It has recently been
measured to 3 parts in 10^{13} and its value
calculated in QED from a
summation of 12,672 Feynman diagrams !
However despite these amazing experimental and theoretical feats, the (m/M)
^{2} contribution from new particles is only discernible for small values
of M (i.e. M < 100 MeV) and presently the measured and predicted
values are in good agreement. In contrast a measurement of the g-2
of the muon, whose mass is 220 times that of the electron,
has a sensitivity to new particles with masses in the range 10 MeV
to 1000 GeV and thus at the upper end is probing a similar mass region to
the LHC experiments but in a very different way. The muon g-2
measurement can also probe low mass physics below the sensitivity of
the LHC.

The current world's best determination of the muon g-2 used data taken in 2001 from an accelerator and muon storage ring at Brookhaven National Laboratory (BNL) on Long Island and differs from that predicted by the SM by approximately 3.5 standard deviations. This has produced much speculation and this result is the second most cited in experimental particle physics (with over 3,000 citations). A 3.5 standard deviation discrepancy is not sufficient to claim evidence for new physics and this motivates a new experiment (and theoretical predictions) to be undertaken with greater precision to conclusively determine whether the BNL measurement is a harbinger of new physics or not. We are seeking to make this new measurement with a precision of 0.14 parts per million which would be the most accurate measurement of any quantity at an accelerator. By comparison the Z mass was determined by the LEP experiments to a precision of 20 parts per million. It is possible to make this new measurement with such a precision by exploiting a new muon beamline at Fermilab and re-using the existing Brookhaven storage ring. This 14m diameter, 17 tonne storage ring provides a uniform magnetic field to better than 0.1 parts per million and is a unique apparatus. It was transported 3000 miles from Brookhaven (Long Island) to Fermilab (Chicago) via road and barge in 2012. The storage ring, new beamlines and detectors have subsequently been commissioned and data taking will begin in 2017.

The magnetic moment is determined by injecting polarised muons of a very specific energy (3.1 GeV) into a storage ring that has a uniform 1.45 T magnetic field and counting the number of decay positrons above 1.9 GeV in 24 calorimeters around the storage ring as a function of time. The direction of the higher energy decay positrons is strongly correlated with the direction of the muon spin which precesses around the magnetic field at a rate determined by (g-2). To achieve the 0.1 parts per million in statistical precision 200 billion decay positrons must be measured by injecting more than 10,000 muons in 120ns bunches 300 million times into the storage ring over a period of 1-2 years. The muons are created from pion decays which in turn come from an 8 GeV proton beam striking a lithium target.

The UK joined the g-2 experiment in 2013 and UCL provides the UK PI (M. Lancaster). The UK is making key contributions to the experiment in five areas:

- Design, construction and commissioning of the straw trackers (Liverpool) that will measure the muon's beam profile, correct for pileup and be used to measure the muon's electric dipole moment.
- Modeling of the injection system (inflector, kicker magnets and quadrupoles) to optimise the beam matching (Cockcroft Institute, Lancaster University)
- Readout, DAQ and control logic for the straw trackers (UCL)
- Analysis of existing and new e
^{+}e^{-}datasets at low energy (√s < 2 GeV) to improve the precision of the SM estimate of g-2.