determination of the mass of the Λ0 hyperon

IL N U O V O CIMENT{) VoL. X I , N. 5 1 o Marzo 1959

D e t e r m i n a t i o n oI the Mass of th e A ° H y p e r o n .

Z. P*OGDANOWICZ, M. DANYSZ, A. FILIPF, O~VSKI, ]~. ~,IARQUIT, E. SKRZYPCZAK, A. ~VROBLF~,VSKI a n d J . ZAKRZEVVSKI

l~s l i tu te o/ Physics, Warsaw Uuicersi ty Iu.~tilule jo t N u d e a r tCesearch - Warsaw

( r ieevuto il 22 ( i enna io 1959)

A s t ack of 1S0 pellicles l0 em 5:10 em of 600 tzm l l fo rd G-5 emuls ion was ex- posed to t h e Be rke l ey K beam. lit lhe 80 p l a t e s of t he s t ack which were a t our disposal a search was m a d e for de- cays of A ° hyl )crons . T h e r('~ion in w h i c h t h e m a j o r i t y of t h e K - mesons s t o p p e d was are'~ s canned for aK- and a=- sLars. T h e p ion / r a c k s f rom t h e a=- s t a r s were t r aced back to 1heir po in t of or igin: aK- s tars , t ,wo-prong stars , scat- t e r ed p ions f ront t he beam, etc. If no u n a m b i g u o u s or igin was r eached in a d i s t ance of 20 m m f rom t h e a=- Mar, t h e t r a c k was a b a n d o n e d . S ix ty one t w o - p r o n g s t a r s w i t h ~ second out, going t r a c k were found ou t of 660 p ions t h a t were fol lowed in th i s way. In t h r e e eases t he second t r a c k le f t t he s tack. The r e lna in ing 58 w i t h m e a s u r a b l e r anges were i nc luded in lhe analys is .

1 - Calibration

F r o n t an a d d i t i o n a l s cann ing per- fo rmed on a~<- s tars , 22 p ro ton i c decays of t h e Z+ h y p e r o n s a t res t were found. The i r analys is , us ing l he m e t h o d devel-

oped b y Flay a n d WIIITE (1), yie lded for t he s h r i n k a g e f ac to r of our emul s ion t he va lue :

s~ 2.20 _~ 0 .033 .

t he va lue be ing referred 1o s t a n d a r d con- d i t ions in our l a b o r a t o r y , a n d for t h e m e a n r a n g e of t h e decay p ro tons t h e v a l u e :

l,' -- (1 6 7 6 . 2 -ZL 7 . 3 ) ~J.m .

I n d e p e n d e n t i n fo rma t ion on ti le shr ink- age f ac to r was o b t a i n e d f rom an anal- ysis of 53 t w o - p r o n g st, ars classified as good example s of t he A ° h y p e r o n decays (see below).

T a k i n g in to a c c o u n t t he r a n d o m er- rors of t h e i nd iv idua l QA" values a n d also t he i r known dependence on t h e sh r inkage fac tor , we found for t he m o s t p r o b a b l e va lue of the sh r inkage f a c t o r :

s 2 2.23 ~ 0 .045 .

(1) \V. F. FRY alld (1-. If. WHITE: Phys. /?ev., 90, 207 (1953).

7 ~ S J . B O ( H ) A N O I V I C Z , M. I ) A N Y S Z , A. F I L I P K O W S K I , E . M A R Q U I T , E. S K R E Y P C Z K A E T C .

T h e wei,~'hted m e a n of t he two inde- p e n d e n t e s t ima te s .~'~ a n d s.,

S --- 2.21 ± 0.027

was used in f u r t h e r ca lcula t ions . T h e dens i ty of our emuls ion as com-

m u n i c a t e d b y Dr . E. J . LOFGREN was c o n t a i n e d be twe en 3.809 g/era a a n d 3.853 g /em a. l ' s i n g th i s i n f o r m a t i o n we e s t i m a t e d t h e r a t i o of r anges in s tan- d a r d emuls ion ((-~), p. 10) to those in o u r emuls ion :

l~'~t/R = 1.003 3 ~- 0.004 5 .

T h e r a t i o R:t/R was e v a l u a t e d inde- p e n d e n t l y us ing our va lue o[ t h e m e a n r a n g e of t h e E* decay p r o t o n s (*) a n d t he c o r r e s p o n d i n g v a l u e of th i s r a n g e c a l c u l a t e d for s tandard , emuls ion f rom t h e mass v a l u e of t h e E + h y p e r o n f rom re fe rence (:~). Cal<.ulation y ie lded:

R~JR = 0.9993 ~- 0 . 0 0 5 5 .

"rite w e i g h t e d m e a n v a l u e of these two i n d e p e n d e n t e s t i m a t e s of t h e R,t/R r a t io :

]I1~ e a c h series of I n e l l s U r e l n e l l t s , p r e -

v i o u s l y se lec ted s t a n d a r d s of d e p t h in t h e emuls ion were m e a s u r e d to al low convers ion of t he d a t a to our s t a n d a r d condi t ions .

In e v a l u a t i n g r a n d o m errors of t h e (2-values, e r rors ar i s ing f rom s t ragg l ing and mul t i l ) le s ( ' a t t e r ing were c o m p o u n d e d w i t h er rors of m e a s u r e m e n t s of t h e r anges a n d of p r o j e c t e d a n d dip angles, a n d also w i t h those c o n n e c t e d w i t h hu- m i d i t y f luc tua t ions .

S y s t e m a t i c er rors were spl i t up in to t hose r e su l t i ng f rom the u n c e r t a i n t y in t he sh r inkage fac tor , t he u n c e r t a i n t y in t he s t o p p i n g power of our emuls ion , t h e u n c e r t a i n t y in t he r ange -ene rgy re la t ion , a n d t he u n c e r t a i n t y in t.he va lues of t h e res t mass of p r o t o n s a n d pions.

T he w d u e s of s~raggling were t a k e n f rom the work of B a r k a s a n d Young (4); u n c e r t a i n t y of 0.5 ,q~) in t he B a r k a s range- e n e r g y r e l a t i on (5) was a s sumed (~); t he mass va lues used (a) were

m~, -- (938.213 :~: O.O1) 31eV,

m = - : (139.63 ~ 0 . 0 6 ) M e V .

ll,~/R = 1.001 7 ~- 0.o03 5

was used in f u r t h e r ca lcula t ions .

2 - M e a s u r e m e n t s a n d e r r o r s

3 - R e s u l t s

T h e his tog ' ram in Fig. 1 shows t h e d i s t r i b u t i o n of the Q-values as ca l cu l a t ed for t h e 58 two-p ron~ s tars . F i f t y four

As a l r eady m e n t i o n e d , 58 two-p ron~ s t a r s t e n t a t i v e l y ident i f ied as A°-> p ÷ = - decays were chosen for de ta i l ed analysis . Ranges of t he decay p r o d u c t s were m e a s u r e d to a n accu racy of 1 % • E a c h m e a s u r e m e n t was m a d e i n d e p e n d e n t l y b y two observers . A K o r i s t k a MS2 microscope couple4 to a Zeiss O p t i m e t e r was used for d e p t h m e a s u r e m e n t s . Dur -

~b " 2b" 3'0 4o o , . M , v

F i g . t . l l i s t o g r a m of t h e O - v a l u v ~ for 5S t w ~ - p r o n g s t a r s w i t h b o t h o u t g o i n g p a r t i c l e s s t o p p i n g ill t i l l ' e m n l s i o n . O - v a l u e s w e r e c a l c t f l a t e d as -

SllUling .~," --> p ~ ~ d e c a y .

U) ~V. H . llXRK-~S et al. : UCl~L-376,5 (1957) . (*) T h e m e a n r a n g e R = ( 1 6 7 9 . 2 ~ 7 . 3 ) ~ . m

w a s o b t a i n e d b y u s i n g t i m w e i g h t e d v a l u e of s. (~) ~,V. H . BARKAS a n d A. 1-[. I~OSENFELI):

U C I I L - 8 0 3 0 {1958}, V I - l l .

( ' ) \V. [[. BARKAS a n d I) . 3[. VOUN(I: 15CI{1,-2579 (1951).

(~) \V. l l . BARKAS: U C I { L - 3 7 6 9 (1957) . (") \V. [{. I~AI~Ir.AS el (tl. : P(tdltct-re}ti('c Co~

Jercm.e (1957), V I - t l .

DETERMINATION OF THE MASS OF THeE A 0 HYPERON 729

Of t h e m are c o n c e n t r a t e d in t he v ic in i ty of t h e m e a n va lue ; in one of t h e m the ,-:--meson is ine las t ica l ly s ca t t e r ed and i ts e n e r g y was d e t e r m i n e d by ioniza t ion m e a s u r e m e n t s ; t he r e fo re the Q-value for t h i s e v e n t ha s a r a t h e r large er ror (Q = = (39 ~ 7) MeV). T h e r e m a i n i n g four e v e n t s are wel l ou t of th i s g roup ing ; of these four even t s , one ( Q = 41 MeV) is s i t u a t e d 2 mm f r o m the edge of the emuls ion in a s t rong ly d i s to r t ed region, w h e r e m e a s u r e m e n t s are no t rel iable. T h r e e to f ive e v e n t s of our s ample t hus a p p e a r to be ba(~kground. F i f t y t h r ee

~Areo correS~r pdmg

~5 35 37 38 39 ~0 0 ,n MeV

Fig. 2. -- Const,~nt are~ histogram for O-wtlucs of 53 two-prong stars (~ee lcxt).

e v e n t s y ie ld ing elosely c o n e e n t r a t e d Q- va.lues were ana ly sed in g r ea t e r deta i l . A c o n s t a n t a rea h i s t o g r a m of t h e 53 (2- va lues where t he r a n d o m er rors were | a k e n in to ac( .ount is shown in Fig. 2.

The weigh ted m e a n va lue of t he Q d i s t r i b u t i o n is

Q - (37.58 :L 0.18) MeV,

in good a g r e e m e n t wi th t he B a r k a s v a l u e (~)

Q - - (37.45 + 0-17) M e V .

T h e e r ror quo ted includes b o t h r a n d o m a n d s y s t e m a t i c errors . The s t a n d a r d dev ia t ion of t h e m e a n of t h e d i s t r i bu t ion due to r a n d o m er rors is 0.082 MeV, in good a g r e e m e n t w i t h t he s t a n d a r d de- v i a t i o n of t h e mean , c~ lcu la ted f rom t he s p r e a d of t he obse rved Q-values - 0.084 MeV.

F o r t h e mass of t he A ° hype ron we o b t a i n :

m = (1 115.42 ! 0.19) M e V .

W e are g r ea l l y i ndeb t ed to Dr. E. S~:c,I¢~:: fur m a k i n g t h e s t ack avai lable , to ])r . E. J . LOV('R)~'N for exposure of t he s t ack a n d to Dr. S. GOL1)tIABEI'~ for pr()eessing t h e emuls ion . W e wish to t h a n k Dr. P. Z~LI~SKI for m a n y val- uab l e diseussions. W e also would l ike to express our appree i a t ion to t he scan- n i n g s taff of our l a b o r a t o r y : Mrs. K. BOBI]~SKA, M r . R . D d B R O W S K I , Mrs. M. ])AZI)ANOWSKA, Miss W. ~ANIEWSKA f o r

t h e i r carefu l work a n d especial ly Mrs. I. t)RZYPKOWSKA for he r efficient he lp in scanning , m e a s u r e m e n t s a n d calcula t ions .

4 7 - I I N u o v o C i m e n t o .