195 lines
7.6 KiB
TeX
195 lines
7.6 KiB
TeX
\documentclass[twocolumn,twoside]{revtex4}
|
||
\usepackage{graphicx}
|
||
\usepackage{fancyhdr}
|
||
\pagestyle{fancy}
|
||
\fancyhead{} % clear all fields
|
||
\fancyhead[C]{\it {
|
||
Flavor Physics and CP Violation Conference, Victoria BC, 2019
|
||
}} \fancyhead[RO,LE]{\thepage}
|
||
\fancyfoot{} % clear all fields
|
||
\fancyfoot[LE,LO]{}
|
||
\usepackage{amsmath}
|
||
|
||
\renewcommand{\headrulewidth}{0pt}
|
||
\renewcommand{\footrulewidth}{0pt}
|
||
\renewcommand{\sfdefault}{phv}
|
||
|
||
\setlength{\textheight}{235mm}
|
||
\setlength{\textwidth}{170mm}
|
||
\setlength{\topmargin}{-20mm}
|
||
\usepackage{hyperref}
|
||
\usepackage[noabbrev, capitalize]{cleveref} % hyperref must be loaded first
|
||
\usepackage[
|
||
detect-weight=true,
|
||
per=slash,
|
||
detect-family=true,
|
||
separate-uncertainty=true]{siunitx}
|
||
|
||
\bibliographystyle{apsrev}
|
||
|
||
% ************* Make changes after here ***************
|
||
|
||
\fancyfoot[LE,LO]{\bf MonB1010}
|
||
|
||
\begin{document}
|
||
|
||
%Title of paper
|
||
\title{Measurements of the muon anomalous magnetic moment}
|
||
\author{Nam H. Tran\\
|
||
on behalf of the Muon $g-2$ Experiment at Fermilab}
|
||
\affiliation{Boston University, Boston, MA, US 02215}
|
||
%
|
||
|
||
\begin{abstract}
|
||
The over 3-sigma discrepancy between the latest experimental and theoretical
|
||
values of the anomalous magnetic of the muon has been one of the best
|
||
hints of new physics beyond the Standard Model. Ongoing efforts
|
||
to settle the issue from the experimental side are happening at Fermilab and
|
||
J-PARC. The E989 at Fermilab is using the same key technologies as the last
|
||
experiment at BNL (E821), but with great improvement in accuracy. The first
|
||
physics data has been taken, and data analysis is going to be finalized soon.
|
||
The E34 at J-PARC adopts a novel approach, is
|
||
well advanced in R\&D, and recently received Stage-2 Approval. The
|
||
experimental principles, techniques, and prospects of these measurements are
|
||
presented.
|
||
\end{abstract}
|
||
|
||
%\maketitle must follow title, authors, abstract
|
||
\maketitle
|
||
|
||
\thispagestyle{fancy}
|
||
|
||
% body of paper here - Use proper section commands
|
||
% References should be done using the \cite, \ref, and \label commands
|
||
% Put \label in argument of \section for cross-referencing
|
||
%\section{\label{}}
|
||
|
||
\section{Introduction}
|
||
The magnetic dipole moment, $\vec{\mu}$, of an elementary particle can be
|
||
expressed in terms of its spin, $\vec{S}$, as:
|
||
\begin{equation}
|
||
\vec{\mu} = g\frac{q}{2m}\vec{S},
|
||
\end{equation}
|
||
where $q$ and $m$ are charge and mass of the particle respectively. The
|
||
dimensionless gyromagnetic ratio $g$ for a spin 1/2, structureless particle can
|
||
be calculated from Dirac equation to be exactly 2. Measured values of $g$ is
|
||
slightly different from 2, this anomaly $a$ is defined as:
|
||
\begin{equation}
|
||
a = \frac{g - 2}{2}.
|
||
\end{equation}
|
||
|
||
The Standard Model (SM) provides very precise predictions of the anomaly of the
|
||
muon, $a_\mu$, at sub-part-per-million level. Experimentally,
|
||
there has been a series of measurements with increasing accuracy at CERN and
|
||
Brookhaven National Laboratory (BNL). The last measurement, the E821 at BNL,
|
||
was done with an uncertainty of 540 part-per-billion (ppb)~\cite{BNL2006}, and
|
||
showed a 3.7 standard deviation from the SM
|
||
prediction by Keshavarzi and colleagues~\cite{Alex2018}. This discrepancy
|
||
motivates new and better measurements of $a_\mu$, two of such experiments are:
|
||
\begin{itemize}
|
||
\item E989 at Fermilab: this is the successor of the E821 experiment,
|
||
inheriting the muon storage ring, general experimental techniques, as well
|
||
as analysis methods. The E989 will improve the precision by four times
|
||
by collecting 20 times more data, and reducing systematic uncertainties.
|
||
\item E34 at Japan Proton Accelerator Research Complex (J-PARC): a completely
|
||
new experiments with novel approaches, aiming for a measurement with
|
||
comparable accuracy compares to that of the BNL experiment. It will be an
|
||
important cross check of results from E821 and E989.
|
||
\end{itemize}
|
||
|
||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
\section{Principle of measurements}
|
||
When a muon is injected perpendicularly into a uniform dipole magnetic field,
|
||
$\vec{B}$, it will move in a circle with the cyclotron frequency:
|
||
\begin{equation}
|
||
\vec{\omega}_c = -\frac{e}{\gamma m_\mu}\vec{B},
|
||
\label{eq:omega}_c
|
||
\end{equation}
|
||
where $\gamma$ is the Lorentz factor.
|
||
|
||
Assuming spin of the muon is also perpendicular to the magnetic field, the spin
|
||
will precess with a fixed frequency:
|
||
\begin{equation}
|
||
\vec{\omega}_s = -g_\mu \frac{e}{2m_\mu}\vec{B} -
|
||
(1-\gamma)\frac{e}{\gamma m_\mu}\vec{B}.
|
||
\label{eq:omega_s}
|
||
\end{equation}
|
||
|
||
The difference between $\vec{\omega}_c$ and $\vec{\omega}_s$:
|
||
% \begin{align}
|
||
% \vec{\omega}_a &= \vec{\omega}_s - \vec{\omega}_c \\
|
||
% &= -\frac{g-2}{2}\frac{e}{m_\mu} \vec{B} \\
|
||
% &= -a_\mu \frac{e}{m_\mu}\vec{B}.
|
||
% \end{align}
|
||
\begin{equation}
|
||
\vec{\omega}_a = \vec{\omega}_s - \vec{\omega}_c = -a_\mu \frac{e}{m_\mu}\vec{B}.
|
||
\label{eq:omega_a0}
|
||
\end{equation}
|
||
|
||
The magnetic field strength in~\cref{eq:omega_a0} can be measured most
|
||
precisely using NMR technique using a sample with high hydrogen content.
|
||
Introducing the Larmor precession frequency of the proton in the magnetic
|
||
field, $\omega_p$, the proton magnetic moment, $\mu_p$, the electron
|
||
$g$-factor, $g_e$, the electron mass, $m_e$, and the electron magnetic moment,
|
||
$\mu_e$, the~\cref{eq:omega_a0} can be rearranged into the form:
|
||
\begin{equation}
|
||
a_\mu = \frac{g_e}{2} \frac{\omega_a}{\omega_p} \frac{m_\mu}{m_e} \frac{\mu_p}{\mu_e}.
|
||
\label{eq:omega_a1}
|
||
\end{equation}
|
||
|
||
The ratio $\omega_a/\omega_p$ is experimentally measured in the muon $g$-2
|
||
experiments, while other quantities $g_e/2$, $m_\mu/m_e$, and $\mu_p/\mu_e$ are
|
||
known to 0.26 part-per-trillion, 22 ppb, and 3 ppb,
|
||
respectively~\cite{codata}.
|
||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
\section{The E989 experiment at Fermilab}
|
||
%% TODO: this paragraph is from James Tau 2016, need paraphrasing
|
||
The Muon $g − 2$ experiment at Fermilab aims to measure the anomalous magnetic
|
||
moment of the muon to a precision of 140 ppb, reducing the experimental
|
||
uncertainty by a factor of 4 compared to the previous measurement at E821
|
||
The measurement technique adopts the storage ring concept used for
|
||
E821, with magic-momentum muons stored in a highly uniform 1.45 T magnetic
|
||
dipole field. The spin precession frequency is extracted from an analysis of
|
||
the modulation of the rate of higher-energy positrons from muon decays,
|
||
detected by 24 calorimeters and 3 straw tracking detectors. Compared to the
|
||
E821 experiment, muon beam preparation, storage ring internal hardware, field
|
||
measuring equipment, and detector and electronics systems are all new or
|
||
significantly upgraded.
|
||
|
||
\subsection{Magnetic field}
|
||
\subsection{Muon beam line}
|
||
\subsection{Detector systems}
|
||
\subsection{Status}
|
||
|
||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
\section{The E34 experiment at J-PARC}
|
||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||
\section{Summary}
|
||
|
||
% If you have acknowledgments, this puts in the proper section head.
|
||
%\bigskip % extra skip inserted
|
||
\begin{acknowledgments}
|
||
This work was supported in part by the US DOE, Fermilab.
|
||
\end{acknowledgments}
|
||
|
||
\bigskip % extra skip inserted
|
||
% Create the reference section using BibTeX:
|
||
%\bibliography{basename of .bib file}
|
||
\begin{thebibliography}{9} % Use for 1-9 references
|
||
%\begin{thebibliography}{99} % Use for 10-99 references
|
||
\bibitem{Alex2018} A. Keshavarzi{\em et al.}, Phys.~Rev.~D 97, 114025 (2018).
|
||
\bibitem{BNL2006} G.W. Bennet{\em et al.}, Phys.~Rev.~D 73, 072003 (2006).
|
||
\bibitem{codata} Mohr, Peter J. and Newell, David B. and Taylor, Barry N., Rev.~Mod.~Phys.~88, 035009 (2016).
|
||
|
||
|
||
\end{thebibliography}
|
||
|
||
|
||
\end{document}
|
||
%
|
||
% ****** End of file template.aps ******
|