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JACoW Publishingdoi:10.18429/JACoW-IPAC2018-THPAK139

LOST MUON STUDIES FOR THE MUON g-2 EXPERIMENT ATFERMILAB∗
S. Ganguly† , K. T. Pitts, University Of Illinois At Urbana-Champaign, Urbana,United States of America
J. D. Crnkovic, Brookhaven National Laboratory, Upton, United States of America
C. C. Polly, Fermi National Accelerator Laboratory, Batavia, United States of America
on behalf of the Muon g-2 Collaboration
Abstract
The Fermilab Muon g-2 experiment aims to measure themuon anomalous magnetic moment aµ with an unprecedented precision of 140 parts per billion (ppb), a four-foldimprovement over the 540 ppb precision obtained by theBNL Muon g-2 experiment. This study presents preliminary work on estimating the muon losses by using double
coincidences in the calorimeters.

INTRODUCTION
The muon magnetic moment is related to the muon spin
via a dimensionless proportionality constant known as themuon g-factor (g). Dirac theory predicts that g = 2 forspin-1/2 point particles such as the muon, while Standard
Model (SM) Quantum Field Theory predicts that g , 2. Thefractional deviation of g from 2 is known as the magnetic
anomaly. The final Brookhaven National Laboratory (BNL)
muon a measurement [1] isaµ ≡g−2= 116 592 091 (54) (33) × 10−11,2(1)with statistical and systematic errors quoted respectively
within the parentheses. The BNL measurement has a morethan 3σ difference [1, 2] from the SM prediction, indicating
the possibility of physics beyond the SM. The Fermi National
Accelerator Laboratory (Fermilab) Muon g-2 experimenthas the goals of increasing the statistics by more than a factorof 20 and reducing systematic errors by a factor of 3.
The Fermilab Muon Campus [3] produces a high intensity
and highly polarized muon beam that is injected into thestorage ring. The muon beam is injected into the storage
ring via the inflector magnet which is designed to minimize
perturbations to the very uniform storage ring magnetic field.
Fast magnetic kickers transfer the injected off orbit muons
onto the central orbit. The Fermilab Muon g-2 experimentuses 24, 6 × 9 segmented PbF2 Cherenkov crystal calorimeters [4, 5] which measure decay positron energy and arrival
time. The muon anomaly can be determined by a precise∗ We thank William M. Morse for his advice and guidance. This document

was prepared by the Muon g-2 Collaboration using the resources of theFermi National Accelerator Laboratory (Fermilab), a U.S. Department ofEnergy, Office of Science, HEP User Facility. Fermilab is managed byFermi Research Alliance, LLC (FRA), acting under Contract No. DEAC02-07CH11359. This manuscript has been authored by the employeesof University of Illinois at Urbana-Champaign, supported by the U.S.
Department of Energy, grant DE-SC0015640.
† sgang28@illinois.edu

measurement of the muon spin precession ωa in the storage
ring and the magnetic field B. When excluding systematiceffects, the decay positron counts (N) can be described by a
5-parameter fit function [6, 7],
N(t) = (N0 /τ) ∗ e−t/τ [1 − A cos(ωa t + φ)],(2)

where t is the arrival time of the positrons from the muon
decays, N0 is normalization, τ is the lab-frame muon lifetime, A is asymmetry, and φ is the intial phase of the muonpolarization. Muons at the edge of the phase space are favorably lost at early times, leading to a deviation from pureexponential muon decay in Eq. 2. The average spin of thelost muons can differ from that of the fully stored muons,
if these 2 muon populations are created at different points
in the production beamline. This difference in average spin
phase can cause a shift in the measured ωa . The Fermilab
experiment has a goal of keeping the relative number of lostmuons below 10−4 per τ.
The Fermilab Muon g-2 experiment is currently in thefirst physics data taking run. This discussion presents lostmuon studies based on preliminary experimental data thatuses double coincident events in the calorimeters. Thesestudies were in part used to avoid muon storage ring betatron resonances [8] when establishing the voltages for theelectrostatic quadrupole system (EQS) that provide vertical focusing and determine the n-value for the storage ringdynamics.

DETECTION OF LOST MUONSThe BNL experiment measured lost muons by searching for three-fold coincidences in consecutive calorimeters.
The energy deposited by MIPs were far below the hardware threshold of the calorimeters used by the BNL experiment. The BNL experiment used scintillator detectors
mounted on the front of the calorimeters. Thanks to better
calorimeter segmentation and timing precision, the Fermilab
experiment is developing lost muon measurement techniques
based on either two or three-fold coincidences in consecutive calorimeters. This discussion only covers lost muon
detection techniques using two-fold coincidences. The redline shows an example decay electron trajectory while theblue line shows a lost muon trajectory. Two detection coincidences in adjacent calorimeters are used to select muoncandidates, where the calorimeters are located every 15◦
around the storage ring. The 3 GeV lost muons typically

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Figure 1: Diagram [6] of a lost muon detected by finding
three-fold coincidences among three consecutive calorimeters. The red line shows example decay electron trajectories
while the blue line shows a lost muon trajectory.
correspond to a MIP (minimum ionizing particle) that deposits ∼ 170 MeV into a calorimeter crystal when passing
through it, unlike the decay positrons which typically produce an electromagnetic shower that deposits almost all of
the energy into the calorimeter. These two distinct behaviors allow for the isolation of lost muons. However, lowenergy decay positrons can produce a MIP-like signatureleading to a source of background. A muon typically takes
6.25 ± 0.5 ns (time-of-flight) to travel from one calorimeterto the next calorimeter depositing MIP-like energies in asingle crystal in each calorimeter. Unlike the muon events,decay positron events tend to deposit energy across multiple
crystals. Also a muon candidate tends to curl inwards (awayfrom the ring) while going from the first calorimeter to thenext one where the decay positrons are more abundant near
the storage ring. The low energy decay positrons contributeto two types of backgrounds to the lost muon signal: uncorrelated two low energy e+ backgrounds (random coincidences
occurring when two independent decay positrons or a second lost muon are randomly detected in the coincidence
time window) and correlated single e+ background where asingle e+ can pre-shower and deposit MIP-like energies in
two consecutive calorimeters. Figure 1 shows the detectionof a lost muon through three-fold coincidences among threeconsecutive calorimeters. Using the unique behaviors ofthe muons vs decay positrons a cut-based analysis has been
performed using a MC simulation of the beam originating at
the inflector exit and the same cuts have been applied later toextract the loss function from two-fold coincidences using
experimental data.
A muon cluster is formed by calculating energy weighted
position and time (as given by Eq. 3) of the crystal hits in acalorimeter:(X,Y, t) =Õ

Ext al × (X,Y, t)xt al .Õ

Ext al .
(3)

Three selections [9] have been used to reduce correlated
single e+ backgrounds:
1. E f r ac = Emax /Etot al > 0.8.
2. Spatial distance between the cluster centers in two consecutive calorimeters X2 − X1 < 0.
3. Number of crystal hits in a cluster < 3.

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Cut (1) shows the fraction energy in a cluster where Emax
is the maximum energy in a a single crystal and Etot al is
the total energy in that cluster. Cut (1) provides a good lostmuon signal selection as E f r ac should be ∼1 for muon candidates. Cut (2) removes the positrons side-entering into
the adjacent calorimeter therefore mostly hitting the crystals
closest to the storage volume. Cut (3) removes backgrounddecay positrons as they produce electromagnetic shower hitting more crystals in a cluster compared to the muons hitting
fewer than three crystals. Figure 2 shows the azimuthal distribution of the lost muon signal with > 30 µs after applying
the above-mentioned cuts. The EQS scraping [7] reduces

Figure 2: Preliminary results showing the azimuthal distribution of lost muons observed by detectors placed around thestorage magnet. The variation in the azimuthal muon losses
observed by detectors is a complicated mix of geometricaland detector MIP-detection efficiencies coupled with the underlying muon loss mechanism and placement of collimatorsin the ring. The area under the curve is normalized to unity.
The black lines show the locations of the collimators, andthe cyan bars show the location of the kicker plates.

lost muons during the measurement period. The storage ringhorizontal and vertical tunes are effectively determined by
the EQS operating voltages [7, 10]. Storage ring betatronresonances increase the number of lost muons, and so it isdesirable to find EQS operating voltages that avoid the large
betatron resonances. Figure 3 shows a scan of lost muons
per decay electron in the first calorimeter and with energy> 1.8 GeV as a function EQS storage set-point voltage. Alarge increase in lost muons is clearly seen from the betatronresonances centered near 18.8 and 21.2 kV. These data weretaken without beam scraping, and corresponding decreases
in the number of observed decay e+ are also seen near theseEQS storage set-point voltages [8].

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0.14
0.12
0.1
0.08
0.06
0.04

10− 2−310

0.02

1920212223
Quad HV; kVFigure 3: Fraction of lost muons as a function of EQS storage
set-point voltage for calorimeter 1. An increased lost muon
rate is observed from the betatron resonances centered near
18.8 and 21.2 kV. These resonances are due to 3Q y = 1 andQ x + 2Q y = 2 line in the tune plane.

CONSTRUCTION OF THE LOSSFUNCTION

0

where the integral can be evaluated numerically with τ =64.4 µs, t0 is the canonical fit start time and the parameter
C is allowed to float in the fit, thereby including a sixthparameter into Eq. 2.
Figure 5 shows an example of the loss function using data
integrated over t0 = 30 µs to t = 300 µs.

CONCLUSION
The Fermilab Muon g-2 experiment is currently in thefirst physics data taking phase. Lost muon systematic effects causes a systematic effect on ωa when extracting fromthe 5-parameter fit. MC simulation of the muon beam and100

150

200

250

300
t1;µs

Figure 4: L(t) from double coincidences for calorimeter 1.

510Figure 4 shows the loss function (L(t)) providing the rate
at which muons are lost from the ring as a function of timeafter injection, constructed from double coincidences. Thelosses are normalized with a pure exponential with the expected lifetime of 64.4 µs and an amplitude determined fromthe number of decay electrons with energies > 1.8 GeV
measured in the first calorimeter in a double coincidence.
The ratio of lost muons to decay positrons is expected to
be much higher at early times than at late times. The loss
function (Λ(t) [6]) is a correction factor to N0 (see Eq. (2))
that accounts for muon losses.
∫ t0−t0 /τΛ(t) = 1 − Ce(L(t 0))et /τ dt 0,t050

Counts018104

31050

100150200
250
300t’/τ
L(t’)(t_1; µs) * e in Double coincidence

Figure 5: Loss function from double coincidence forcalorimeter 1, integrated over t0 = 30 µs to t = 300 µs.

storage ring has been used to optimize the lost muon signal by taking advantage of highly segmented calorimeters
to distinguish the lost muons from the much larger decay
positron backgrounds. Preliminary physics data have beenused to determine electrostatic quadrupole operating voltages by looking at fractional muon losses and estimate therate of losses over time using double coincidence calorimeter
events.

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Doubles/Decay electrons with E>1.8GeV

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