MeV gamma rays from Q -ball decay

We study the supersymmetric <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>Q</a:mi></a:math> balls which decay at present and find that they create a distinctive spectrum of gamma rays at around O(10) MeV. The charge of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>Q</c:mi></c:math> ball is lepton numbers in order for the lifetime to be as long as the present age of the Universe, and the main decay products are light leptons. However, as the charge of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>Q</e:mi></e:math> ball decreases, the decay channel into pions becomes kinematically allowed towards the end of the decay, and the pions are produced at rest. Immediately, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>π</g:mi><g:mn>0</g:mn></g:msup></g:math> decays into two photons with the energy of 67.5 MeV, half the pion mass, which exhibits a unique emission line. In addition, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>π</i:mi><i:mo>±</i:mo></i:msup></i:math> decay into <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msup><k:mi>μ</k:mi><k:mo>±</k:mo></k:msup></k:math>, which further decay with emitting internal bremsstrahlung, whose spectrum has a sharp cutoff at <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mo>∼</m:mo><m:mn>50</m:mn><m:mtext> </m:mtext><m:mtext> </m:mtext><m:mi>MeV</m:mi></m:math>. If the observations find these peculiar features of the gamma-ray spectrum in the future, it could be a smoking gun of the supersymmetric <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>Q</o:mi></o:math>-ball decay at present.