L E T T E R E A L

NUOVO CIMENTO A C U R A D E L L A S O C I E T A I T A L I A N A DI F I S I C A

VOL. I, N. 10 Serie pr ima 1 ° Apr i l e 1969

Exotic Mesons and Baryons.

S. MI~AM1

Department o] Physics, Osaka City University - Osaka

( r iccvuto il 3 F e b b r a i o 1969)

I t h a s been shown b y m a n y au t ho r s (l-a) t h a t t h e absence of (( exo t ic r e sonances ~) ( I = 2 or kS = 1 or I ~ ~ b a r y o n a n d I ~ 2 meson in the T:-r: sy s t em) leads to va r ious k inds of i n t e r e s t i n g conclus ions such as exchange degeneracy re l a t ions for t he Regge t ra jec tor ies . W e now t h i n k i t wor th -wh i l e to s t u d y t he exot ic r e sonances f rom a phe- nomenolog iea l v i ewpoin t . The pu rpose of t h i s p a p e r is to g ive a s y s t e m a t i c desc r ip t ion of t h e m .

P a y i n g a t t e n t i o n to t he fac t s t h a t i) t h e r e is no re sonance w i t h double cha rge excep t for t he JW~ a n d ii) t he re is no re sonance w i t h I/z] = 2 excep t for t he ~ - , we define a q u a n t i t y E w i t h t he express ion

(1) E = X ( X - - 1 ) ( I - - ~- + ISI) -4- lr(I/zl- 1)(Isl- a ) l ,

where ~ = N ÷ S a n d X ~ I + lYl/2. The X cor responds to t he m a x i m u m va lue of t he charge [Q] of t h e resonance .

Needless to say, E is equa l to zero for t he r e sonances w i t h X~< 1 a n d IY] < 1. Owing to t he fac to rs ( I - - ~ ÷ ISI) a n d ( I S I - - 3 ) i n t r o d u c e d in t he f irst a n d second te rms , respec t ive ly , E = 0 for b o t h t he J ~ w i t h X = 2 a n d t he ~2- w i t h Y = - - 2. I t wou ld be necessary to add some e x p l a n a t i o n a b o u t t h e effect of t he f ac to r ( I S [ - - 3 ) . W h e n IS[= 3, we o b t a i n the fol lowing resul t s : a) F o r t h e meson fami ly , I~1 = 3 a n d x = z + 1~1/2 is l a rger t h a n one. There fo re X ( X - - 1 ) ( 1 - - ~ - 4 - I S I ) > o. T h a t is, E # 0 for t h e meson f a m i l y w i t h l /zl~>2, b) F o r t h e b a r y o n ( a n t i b a r y o n ) fami ly , 37 = - - 2 ( + 2) for t h e case S = - - 3 ( ÷ 3). There fore X can be equa l to one, if I is equa l to zero. I t is t he

(1) (~. SCIE~IID: Phys. Rev. Left., 20, 689 (1968). (3) H. tIARAI~I: Proeeedings o] the X I V Internafional Con/erence on ltigh-Energy Physics, Vienna, 1968;

T. KAWAI and T. SAITO: private communication. (a) C. LOVELAOE: CERN preprint, TIt. 950 (1968).

4 8 6 s. 3IIN '~MI

I ~ s t a l e on ly l ln / t sa t i s i i c s lh(, ('(,lldili(~n E I) in t h e case (,f bar3oH w i t h Y 2

( a n t i l m v y o u w i t h Y 2). T h i s s t a t e eovresp()nd,~ to lh(, ~5--- (~(_)-). I t can e a s i l y he ~,.on t h a t

(2) E- o

fol' t]ll' \ \ (!]]-~ 's talJish( 'd r('sollRIl('(,~ I)f Iiil'SOllN ~/l|d t);tr,v[)/l~. ()11 th( ' o thc l ' hal l ( | .

(3) E o

[I)r t]IU lll(',~Oll-lll0SOIl SyS~('ll lS O1' IlIO~OII-]~II',VOll S VS|( 'HIS l l H ' l l t [ O l l o d })('lOW:

1) : : sS',~tclH wi~h I 2.

2) l ( -= (or K-=) s y s t e m wit]l I - a .

3) K - K (or I<-K) s s s h ' l l l ,

4) " = - , V s y s h m l w i t h I > ~.

5) rz . -N s 3 s t e m with I - - 2 .

~i) r: _= s s ' s h q n w i t h I - ~.

7) K - . \ ' s y s t e m (or l m v y o u s w i t h Y :2) .

A . y v( ,sonanc(,s in l l w s c s y s t e m s h a v e n o t y e t been well e s t a b l i s h e d a n d s o m e of

l h e m h a v e bccn ea lh ,d ~, e x o t i c l'psol/allCCs ,>. \V(, c h a r a c t e r i z e t h e e x o t i c r e s o n a n c e

ill 101'lllg Of E - 11 (*). Thl l s . the E de / i , ed b 9 eq. (1) c a . be regarded as . quantum

, u m b e r by wkick we can uee wketke~' the ~'e.so,auee ix e.rolie or ~lot.

\\%, n o w d i s c u s s t h e effect of t h e s e (qmd l o r m of eq. (1). If t h e ~eeond t e r m is no l

b l e l u d c d i~l t h e c x p r v s s i o n of E.

( t ' t E ' - - X ( X l / ( I ~ - - i S i ) .

t hq ' e i t s h o u l d be n o t e d t h a i E t u r n s m l t to be e q u a l to zero for i) t h e K - K (or K - K ) s y s t e m w i t h 1 = o ov ii) t h e K - & ' s 3 s t e m w i t h i 11. Y h o l l . is i t i m p o s s i b l e to

rc~avd t h e E' as a ~ o o d p a r a m e t e r ? In o r d e r to e x a m i n e t h i s p r o b l e m , le t u s c o n s i d e r t h e f o l l o w i n g s t a t e s wi ib 1 " - - 2 :

J) .Y : 0 al ld N L ) ( K - K ~,vstem).

ii) 2V= 1 a n d N ! ( K - , V s h m e m h

i i i ) _ V = 2 a l l d N:- - (1 ( ~ r - ~ \ ~ s y s t e m ) .

A c e o v d i n ~ to t h e U - s p i n d e f i n e d b y MESlIKOV el (d. (4),

. ) K - a n d = (= a n d K ) c, . ' re ,~p(uM, r e s p e c t i v e l y , lo t h e U~ ½ a n d U~ ½ coll l])ollel l ls of l" .a :

b) p a n d \ .2 (V a n d _= ) c m ' r e ~ p o n d , r e s p e c t i v e l y , to l h c U: = ½ a n d U . = --½ c o m p o n e n i s of U }:

c) n a n d ._-0 (K 0 a n d l~ °) c o n c s p , m d , r ( , spec t iw , ly , to t h e U.. = 1 a n d U~ ]

components of U-- 1.

(*) In order' to apply this condition E =0 to the . -baryon system (. ~2 ) , it is necessary t(. lllOdify t h0 0x1)ress4iol/ of / ' , because E is (.'qlHI1 [O z( 'ro ill the . . \ - sys tem. for ex~mlple.

(l) ~. 3[ESllKOV, @. A . [,EVINSON ~Ild ][I. J . L1PKIN: PhYs. l~ev. Lelt., 10, 361 (1963).

EXOTIC MESONS AND BARYONS 487

F r o m these, we can ob ta in t he fol lowing re la t ions for the e las t ic -sca t te r ing ampl i tudes (*) :

(K+.KOIK+KO) = (~+g01z+/£o),

(pK°tpK") = (2:+~olZ+KO), (4)

(nK+lnK+) = (_=oz+I_=oz+) ,

=

E a c h sca t t e r ing is descr ibed in t e rms of the ampl i tude for t he U = } s ta te only. Note t h a t re la t ions (4) do no t necessar i ly hold in low-energy p h e n o m e n a such t h a t the to ta l energy is less t han the sum of the masses of the coll iding part icles. Since E ' ¢ 0 for the u+_~o, Z+]~0, E0=+ and E°-Z + sys tems wi th I = - ~ , we can say the following: If there is ne i ther any resonan t s ta te nor any b o u n d s ta te in the rc+-K, e, Z+-K Q, G"-rc+ or ZQ-Z + sys tem, and i f there is a h o u n d s t a te ins tead of a r e sonan t s t a t e in the K - K , K - ~ or n-p sys tem wi th I = 0, t hen the E ' = X ( X - - l ) ( I - - ~ + [S]) can be a good p a r a m e t e r (**) and the E ' = 0 is i n t e r p r e t e d as a condi t ion for t he ex is tence of a reso- n a n t s ta te or a b o u n d s ta te .

As is well known, there exis ts a b o u n d s ta te (deuteron) in the n-p sys tem wi th I = 0. And the g/- can be r ega rded as a b o u n d s ta te in t he ~ - K s y s t e m wi th t Y I = 2 and I = 0. In order to examine exper imen ta l ly the exis tence of a bound s t a te in the K-J~' or K - K sys tem wi th I = 0, i t is necessary to measure the miss ing-mass spec- t r u m for the reac t ions

K+ +p-~ ~ + +~+

and

K + + p ~ M ' + + E +

in the regions where t he masses of M + and M '+ are near ly equal to or less t h a n m~ + m ~ and 2mK, respect ively .

(*) We have also other relations similar to (4). For example,(K+p]K÷p)=(~,+X+Jg+Z+)=(:,-Z-]u -Z-) = = (K-S-[~-~-) . Note that E' ~=0 for these K+-p, ~+-Z + and K --~'- systems.

(**) If there is no hound state in the K-K or K-2~ system with I = 0, the E" cannot be regarded as a good parameter.