η and η′ Production in J/ψ Radiative …

We present a first principles calculation within quantum chromodynamics (QCD) of the radiative decays of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>J</a:mi><a:mo>/</a:mo><a:mi>ψ</a:mi></a:math> into the light pseudoscalar mesons <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>η</c:mi></c:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>η</e:mi><e:mo>′</e:mo></e:msup></e:math>. Within a lattice computation we obtain the transition form factors as a function of photon virtuality from the timelike region, accessible experimentally via the “Dalitz” decay <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>J</g:mi><g:mo>/</g:mo><g:mi>ψ</g:mi><g:mo stretchy="false">→</g:mo><g:msup><g:mi>e</g:mi><g:mo>+</g:mo></g:msup><g:msup><g:mi>e</g:mi><g:mo>−</g:mo></g:msup><g:msup><g:mi>η</g:mi><g:mrow><g:mo stretchy="false">(</g:mo><g:mo>′</g:mo><g:mo stretchy="false">)</g:mo></g:mrow></g:msup></g:math>, through to the real photon point corresponding to <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>J</l:mi><l:mo>/</l:mo><l:mi>ψ</l:mi><l:mo stretchy="false">→</l:mo><l:mi>γ</l:mi><l:msup><l:mi>η</l:mi><l:mrow><l:mo stretchy="false">(</l:mo><l:mo>′</l:mo><l:mo stretchy="false">)</l:mo></l:mrow></l:msup></l:math>. This is the first calculation in lattice QCD with two (heavier than physical) degenerate flavors of light quark and a heavier strange quark, in which the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msup><q:mi>η</q:mi><q:mo>′</q:mo></q:msup></q:math> appears as the state with pseudoscalar isoscalar quantum numbers. We access it reliably by using variationally , the use of which also improves the purity of the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>J</s:mi><s:mo>/</s:mo><s:mi>ψ</s:mi></s:math> and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>η</u:mi></u:math> signals, reducing systematic uncertainties. High quality results at a large number of kinematic points are obtained in a typically noisy disconnected process by using a novel correlator averaging procedure. Our results show the expected enhanced production of the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msup><w:mi>η</w:mi><w:mo>′</w:mo></w:msup></w:math> over the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>η</y:mi></y:math> in this process, and suggest that the demonstrated lattice technology is suitable for future calculations considering processes in which light meson are produced.