Detailed report on the measurement of the positive muon anomalous magnetic moment to 0.20 ppm

Abstract

We present details on a new measurement of the muon magnetic anomaly, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>a</a:mi><a:mi>μ</a:mi></a:msub><a:mo>=</a:mo><a:mo stretchy="false">(</a:mo><a:msub><a:mi>g</a:mi><a:mi>μ</a:mi></a:msub><a:mo>−</a:mo><a:mn>2</a:mn><a:mo stretchy="false">)</a:mo><a:mo>/</a:mo><a:mn>2</a:mn></a:math>. The result is based on positive muon data taken at Fermilab’s Muon Campus during the 2019 and 2020 accelerator runs. The measurement uses <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mn>3.1</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>GeV</e:mi><e:mo>/</e:mo><e:mi>c</e:mi></e:mrow></e:math> polarized muons stored in a 7.1-m-radius storage ring with a 1.45 T uniform magnetic field. The value of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>a</g:mi><g:mi>μ</g:mi></g:msub></g:math> is determined from the measured difference between the muon spin precession frequency and its cyclotron frequency. This difference is normalized to the strength of the magnetic field, measured using nuclear magnetic resonance. The ratio is then corrected for small contributions from beam motion, beam dispersion, and transient magnetic fields. We measure <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>a</i:mi><i:mi>μ</i:mi></i:msub><i:mo>=</i:mo><i:mn>116</i:mn><i:mn>592</i:mn><i:mn>057</i:mn><i:mo stretchy="false">(</i:mo><i:mn>25</i:mn><i:mo stretchy="false">)</i:mo><i:mo>×</i:mo><i:msup><i:mn>10</i:mn><i:mrow><i:mo>−</i:mo><i:mn>11</i:mn></i:mrow></i:msup></i:math> (0.21 ppm). This is the world’s most precise measurement of this quantity and represents a factor of 2.2 improvement over our previous result based on the 2018 dataset. In combination, the two datasets yield <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>a</m:mi><m:mi>μ</m:mi></m:msub><m:mo stretchy="false">(</m:mo><m:mrow><m:mi>FNAL</m:mi></m:mrow><m:mo stretchy="false">)</m:mo><m:mo>=</m:mo><m:mn>116</m:mn><m:mn>592</m:mn><m:mn>055</m:mn><m:mo stretchy="false">(</m:mo><m:mn>24</m:mn><m:mo stretchy="false">)</m:mo><m:mo>×</m:mo><m:msup><m:mn>10</m:mn><m:mrow><m:mo>−</m:mo><m:mn>11</m:mn></m:mrow></m:msup></m:math> (0.20 ppm). Combining this with the measurements from Brookhaven National Laboratory for both positive and negative muons, the new world average is <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mrow><s:msub><s:mrow><s:mi>a</s:mi></s:mrow><s:mrow><s:mi>μ</s:mi></s:mrow></s:msub><s:mo stretchy="false">(</s:mo><s:mi>exp</s:mi><s:mo stretchy="false">)</s:mo><s:mo>=</s:mo><s:mn>116</s:mn><s:mn>592</s:mn><s:mn>059</s:mn><s:mo stretchy="false">(</s:mo><s:mn>22</s:mn><s:mo stretchy="false">)</s:mo><s:mo>×</s:mo><s:msup><s:mrow><s:mn>10</s:mn></s:mrow><s:mrow><s:mo>−</s:mo><s:mn>11</s:mn></s:mrow></s:msup></s:mrow></s:math> (0.19 ppm). Published by the American Physical Society 2024