Sum rule for the Compton amplitude and implications for the proton–neutron mass difference
J. Gasser, H. Leutwyler, A. Rusetsky
Abstract
Abstract The Cottingham formula expresses the leading contribution of the electromagnetic interaction to the proton-neutron mass difference as an integral over the forward Compton amplitude. Since quarks and gluons reggeize, the dispersive representation of this amplitude requires a subtraction. We assume that the asymptotic behaviour is dominated by Reggeon exchange. This leads to a sum rule that expresses the subtraction function in terms of measurable quantities. The evaluation of this sum rule leads to $$m_{\mathrm{QED}}^{p-n}=0.58\pm 0.16\,\text {MeV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mrow> <mml:mi>QED</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>-</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>0.58</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.16</mml:mn> <mml:mspace/> <mml:mtext>MeV</mml:mtext> </mml:mrow> </mml:math> .