A sensitive test of quantum electrodynamics

~

Nuclear Physics B23 (1970) 641. North-Holland Publishing Comp., Amsterdam

ERRATUM A. Di Giacomo, A sensitive t e s t of quantum e l e c t r o d y n a m i c s . The 2S-2P e n e r g y d i f f e r e n c e of muonic hydrogen, Nucl. Phys. B l l (1969) 411. The calculation of ref. [1] gives f o r the contribution of the e l e c t r o n v a c u u m p o l a r i z a t i o n to the 2S-2P e n e r g y splitting an "instantaneous" t e r m and a " r e t a r d e d " contribution ~d~R [eqs. (18) and (27)]. T h i s r e t a r d a t i o n t e r m has the unphysical f e a t u r e of being independent of the r a t i o w h e r e a s it should depend on it if it w e r e a genuine r e c o i l correction*. In fact it is c a n c e l l e d by the t e r m s of the k e r n e l r e p r e s e n t e d by the g r a p h s in the f i g u r e

mp./mp,

"

/~

P'~

p~

Explicit calculation of t h e s e g r a p h s by the p e r t u r b a t i o n f o r m u l a [eq. (A.9) of ref. [1]] gives, in the s a m e notation of ref. [1]

dm~(m2)

e 4 f d3p f d 3 p ' f d 3 K f~¢ AE = - - ~ - j - - - - ~ - - - - - ~ j - - - - ~ - j (2~') ° (2~) ° (2~) ° . 2 (m +K2)~ ~m C

1

1

XlKl2 ip+K-p'l 2

X~..(p,) XE(P) .

T h i s c o r r e s p o n d s to an effective potential 4n~2

W'(r)

W'(r)

W'(r)

where is the same as in_eqs. (18) and (20) of ref. [1], and exactly c a n c e l s the r e t a r d e d t e r m ~ R . All the r e s t of the analysis of ref. [1] stays unchanged. The only change

* A discussion with S. I. Brodsky on this point is acknowledged.

642

A. DI GIACOMO

i s t h a t 5/~ R i n eq. (27) h a s to b e c a n c e l l e d . A s a c o n s e q u e n c e , eq. (36) should read -

V = ( - 1.5030 ± 0.0006) o~2Ry .

REFERENCES [1] A.Di Giacomo, Nucl. Phys. B l l (1969} 411.