Test of charge-conjugation symmetry via microwave spectroscopy of positronium

The <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>2</a:mn> <a:msup> <a:mspace width="0.16em"/> <a:mn>3</a:mn> </a:msup> <a:msub> <a:mi>S</a:mi> <a:mn>1</a:mn> </a:msub> <a:mo>→</a:mo> <a:mn>2</a:mn> <a:msup> <a:mspace width="0.16em"/> <a:mn>1</a:mn> </a:msup> <a:msub> <a:mi>P</a:mi> <a:mn>1</a:mn> </a:msub> </a:mrow> </a:math> interval in positronium has been measured via microwave spectroscopy. This transition is strictly forbidden by charge conjugation invariance but may be observed in a magnetic field. Extrapolation of the Rabi frequencies obtained from spectral line shapes measured in different fields to the zero field case was used to test for a possible C-violating interaction with Hamiltonian <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi>H</d:mi> <d:mi>CV</d:mi> </d:msub> </d:math> , characterized by the matrix element <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:msub> <e:mi>M</e:mi> <e:mi>CV</e:mi> </e:msub> <e:mrow> <e:mo>=</e:mo> <e:mo>〈</e:mo> <e:mn>2</e:mn> </e:mrow> <e:msup> <e:mspace width="0.16em"/> <e:mn>1</e:mn> </e:msup> <e:msub> <e:mi>P</e:mi> <e:mn>1</e:mn> </e:msub> <e:mrow> <e:mo>|</e:mo> </e:mrow> <e:msub> <e:mi>H</e:mi> <e:mi>CV</e:mi> </e:msub> <e:mrow> <e:mo>|</e:mo> <e:mn>2</e:mn> <e:msup> <e:mspace width="0.16em"/> <e:mn>3</e:mn> </e:msup> <e:msub> <e:mi>P</e:mi> <e:mn>1</e:mn> </e:msub> <e:mo>〉</e:mo> </e:mrow> </e:mrow> </e:math> . We obtain <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mrow> <h:mo>|</h:mo> </h:mrow> <h:msub> <h:mi>M</h:mi> <h:mi>CV</h:mi> </h:msub> <h:mrow> <h:mo>|</h:mo> <h:mo>=</h:mo> <h:mn>18.6</h:mn> <h:mo>±</h:mo> <h:mn>6.5</h:mn> <h:mspace width="0.28em"/> <h:mi>MHz</h:mi> </h:mrow> </h:mrow> </h:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:mrow> <j:mo>|</j:mo> </j:mrow> <j:msub> <j:mi>M</j:mi> <j:mi>CV</j:mi> </j:msub> <j:mrow> <j:mo>|</j:mo> <j:mo>=</j:mo> <j:mn>37.2</j:mn> <j:mo>±</j:mo> <j:mn>13.4</j:mn> <j:mspace width="4pt"/> </j:mrow> </j:mrow> </j:math> MHz for the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mrow> <l:msub> <l:mi>M</l:mi> <l:mi>J</l:mi> </l:msub> <l:mo>=</l:mo> <l:mo>±</l:mo> <l:mn>1</l:mn> <l:mo>→</l:mo> <l:mo>±</l:mo> <l:mn>1</l:mn> </l:mrow> </l:math> and the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>M</m:mi> <m:mi>J</m:mi> </m:msub> <m:mo>=</m:mo> <m:mn>0</m:mn> <m:mo>→</m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> components, respectively.