Cross Sections of Reactions Produced by High Energy Neutrino Beams

1. -T h e e x p e c t e d a v a i l a b i l i t y in t h e n e x t f u t u r e of h i g h i n t e n s i t y b e a m s of h i g h e n e r g y pa r t i c l e s m a k e s i t a p p e a l i n g to t h i n k of poss ib le e x p e r i m e n t s to d e t e c t r e a c t i o n s i n i t i a t e d b y h i g h e n e r g y n e u t r i n o s (1). N e u t r i n o s a re k n o w n to h a v e on ly w e a k i n t e r a c t i o n s a n d t h e i r cross sec t ions a t low e n e r g y are i n d e e d v e r y sma l l (2). N e u t r i n o cross-sec t ions are h o w e v e r s u s p e c t e d to g row-up v e r y f a s t w i t h e n e r g y (3). One wou ld a rgue t h a t , in a r e a c t i o n such as ~ p + e + ~ n t h e p h a s e space v o l u m e wil l e v e n t u a l l y g row-up w i t h t h e s q u a r e of t h e C.1~. energy , wh i l e t h e m a t r i x e l e m e n t de r ived n a i v e l y f rom t h e four l inea r ~ coup l ing wil l r e m a i n c o n s t a n t , t h u s g i v i n g a c ross sec t ion i n c r e a s i n g w i t h t h e s q u a r e of t h e C.~I. energy . T h i s a r g u m e n t is o b v i o u s l y w r o n g a t l eas t becaus e of t h e p re sence of f o r m f ac to r s a n d of new coup l ings i n d u c e d t h r o u g h t h e v i r t u a l fields of pa r t i c l e s w h i c h i n t e r a c t s t r o n g l y w i t h t h e nuc leons , s u c h as p ions , e tc . I n l i s t i ng t h e poss ib le r e a c t i o n s w h i c h can be p r o d u c e d f rom h i g h e n e r g y neut r i n o s one h a s to no t e t h a t m a n y r e a c t i o n s are f o r b i d d e n b y t h e l e p t o n c o n s e r v a t i o n law. T h e i r absence w o u l d a c t u a l l y c o n s t i t u t e t h e m o s t d i rec t p roof of l e p t o n con-