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}=0.58pm 0.16,text {MeV}.
Highlights
Elitzur and Harari [3] pointed out that if the exchange of Reggeons correctly describes the asymptotic behaviour in the limit ν → ∞ at fixed q2 – an assumption we refer to as Reggeon dominance – the subtraction function obeys a sum rule which fully determines it through the cross section of lepton-nucleon scattering
It will be of considerable interest to compare the result of this analysis for the slope of the subtraction function at Q2 = 0 with the solution of the sum rule that follows from Reggeon dominance constructed in the present paper
We are aware of four recent estimates for the proton–neutron mass difference based on evaluations of the Cottingham formula: Walker-Loud, Carlson and Miller (WCM) [6,9], Erben, Shanahan, Thomas and Young (ESTY) [7], Thomas, Wang and Young (TWY) [8] and Tomalak [10]
Summary
The dispersion relations express the Compton amplitude in terms of the structure functions. These represent the Fourier transform of the current commutator:. The structure functions are experimentally accessible only for q2 ≤ 0 and it is customary to replace q2 by Q2 ≡ −q2. S(q2) represents the subtraction function, ν02 is the subtraction point in the variable ν2 and the lower limit corresponds to the threshold for inelastic reactions, νth = The choice of the subtraction point is arbitrary (provided that ν02 < νt2h), but as pointed out in [1], it is convenient to set ν02. As will be seen below, this choice simplifies the asymptotic behaviour of the subtraction function for Q2 → ∞.
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