PHYSICAL REVIEW D VOLUME 4, NUMBER 6 15 SEPTEMBER 1971 Erratum Electromagnetic Corrections to Nucleon Transitions of the Vector and Axial-Vector Currents, Heinz Pagels [ Phys. Rev. D 3, 610 (1971)]. From remarks made by Professor T. D. Lee it has been found that this paper contains a crucial mistake in the sign of 6M, the electron~agnetic mass shift. In all equations such as (2.6), (2.14), and (2.15), the sign of 6M should be reversed. If obeys an unsubtracted dispersion relation and in the scaling limit w~)(~~, v)- F~)(w)+H(,')(w)/~~ with F ~ ) ( w ) = 0 (see footnote 9 of this paper), then the correct expression for the divergent part of the mass shift is The positivity requirement is [if F$)(w)=o] F(,P)(w)~o, -H$)(w) 3 0. For a free charged Dirac particle or in the naive parton model with spin-; partons, (v2//n/lZq2)w2(v, q2)+ wfll(v, q2) =O and Hi)(w)=-wF:)(w). Then one obtains On these assumptions, if F!)(W) - F?)(W) >O, then the scaling region contributes with the "wrong" sign to 6MP- 61Mn, as was concluded in this paper. If, however, Ff)(w)+ 2H(,')(w)/w >O [for example, if H ~ ) ( w ) = 01, then 6~ $:< 0, and one could account for the observed sign if F',P) (w) - (w) > 0. This important observation was first made by T. D. Lee. It is clear that all conclusions depend crucially on the nonscaling structure function H;'(W), which IS essentially impossible to measure experimentally. Therefore it becomes of interest to examine models or light-cone algebras which imply F!)(LL)) =O and serve to specify H(,"!(w) relative to F?'(W).

Electromagnetic Corrections to Nucleon Transitions of the Vector and Axial-Vector Currents

Download PDF Report

Upload
heinz
View
213
Download
0

Embed Size (px)

Citation preview

Page 1: Electromagnetic Corrections to Nucleon Transitions of the Vector and Axial-Vector Currents

P H Y S I C A L R E V I E W D V O L U M E 4 , N U M B E R 6 1 5 S E P T E M B E R 1 9 7 1

Erratum

Electromagnetic Corrections to Nucleon Transitions of the Vector and Axial-Vector Currents, Heinz Pagels [ Phys. Rev. D 3, 610 (1971)]. From remarks made by Professor T. D . Lee it has been found that this paper contains a crucial mistake in the sign of 6M, the electron~agnetic mass shift. In all equations such a s (2.6), (2.14), and (2.15), the sign of 6M should be reversed. If

obeys an unsubtracted dispersion relation and in the scaling limit

w ~ ) ( ~ ~ , v)- F ~ ) ( w ) + H ( , ' ) ( w ) / ~ ~

with F ~ ) ( w ) = 0 (see footnote 9 of this paper), then the correc t expression for the divergent part of the mass shift i s

The positivity requirement i s [if F$)(w)=o] F ( , P ) ( w ) ~ o , -H$)(w) 3 0. For a free charged Dirac particle or in the naive parton model with spin-; partons,

(v2//n/lZq2)w2(v, q 2 ) + wfll(v, q2 ) = O and Hi)(w)=-wF:)(w).

Then one obtains

On these assumptions, if F!)(W) - F?)(W) >O, then the scaling region contributes with the "wrong" sign to 6MP- 61Mn, a s was concluded in this paper. If, however, Ff)(w)+ 2H(,')(w)/w > O [for example, if H ~ ) ( w ) = 01, then 6~ $:< 0, and one could account for the observed sign if F',P) (w) - (w) > 0. This important observation was f i r s t made by T. D. Lee.

It i s clear that all conclusions depend crucially on the nonscaling structure function H;'(W), which IS

essentially impossible to measure experimentally. Therefore i t becomes of interest to examine models or light-cone algebras which imply F!)(LL)) = O and serve to specify H(,"!(w) relative to F?'(W).