- Email: [email protected]
Further evidence for A Kππ resonance at 1175 MeV
Vo!ume 15. number 1
PHYSICS L E T T E R S
turn trxns~ex, and Z = ± 1 for e ~ - p s c a t t e r i n g . Further, ~s(al) is the smaller (larger) of A E e argi A R p and
l - x In (I - ~) - l+x in (1 + x).
1 March 1965
and ~Ee/Ee and
AEO/F~)
l e s s than 5 % the exact result should not. differ"from that in (2) by m o r e
than 2%.
The largest contribution of the fmtetion o(x),
The a u t h o r w i s h e s to a c k n o w l e d g e h i s i n d e b t h e s s to P r o f . G. KKll~n f o r a d v i c e a n d c r R i c i s m and to N o r d i t a f o r f i n a n c i a l s u p p o r t .
about - g ~ for r e a s o n a b l e v a l u e s of q~, i s obmined w h e n ~ e = AF.p. In the c a l c u l a U ~ n l e a d i n g t o (2) the m a i n approximations w e r e the neglect of strong interaction e f f e c t s (except f o r t h o s e i n c l u d e d in the s t a n d a r d f o r m f a c t o r s ) and the neglect of the t e r m s not g i v i n g r i s e to a n i n f r a r e d d i v e r g e n c e in the h r e m s s t r a h l u n g m a t r i x e l e m e n t s [2]. T h e s i z e of t h e e r r o r c a u s e d by t h i s d e p e n d s m a i n l y on ~ o , AEe, a n d AEp. F o r E o l e s s t h a n 5 GeV,
~efe~-e1~,~s 1. J.Sehwinger, Phys. Rev. 76 (1949) 760. 2. Y.S.Tsai, Phys. Roy. 122 (1961) 1898. 3. A . S . K r u s , Phys. Roy. 125 (196g)2172. 4. N.Meister andD.Yelmie, Phys. Roy. 130 (196,1) 1210. 5. K.Berkelman, M.Feldman, R.M. Littauer, G.Rou~e and R.IR.Wflson, Phys. Rev. 130 (1963) 2061.
o(x)
:
2.
x
FURTHER
x
EVIDENCF
F O R A Klrv R E S O N A N C E
AT
1175
MeV*
D. F . P.IILLER, A. Z. K O V A C S , R. L. M c I L W A I N , T . R . P A L F R E Y a n d G. W. T A U T F E S T
Physics Department, Purd~e University, Lafayette, Indiana Received 26 January 1965
Recently three resonances decaying by a K~r m~e have been reported. Wangler et al. [I] have .,bs.°rved a r e s o n a n c e at 1175 MeV in YK~n f i n a l :-:arcs f r o m --p interactions at 3 GeV/c. The omer resonances, having masses of 1225 [2] and 1270 [3J M e V , w e r e r e p o r t e d f r o m a n t i p r o t o n a n r.ihilations and h a v e o t h e r d e c a y m o d e s such a s ~ . We u~ish to r e p o r t a d d i t i o n a l e v i d e n c e f o r the e x i s t e n c e of the f i r s t m e n t i o n e d r e s o n a n c e in =-p i n t e r a c t i o n s at 2.7 GeV/c. In a r u n of 30 000 p i c t u r e s t a k e n on the L R L A l v a r e z 72 ~ h y d r o g e n c h a m b e r 242 e v e n t s of the type YK~,~ h a v e b e e n a n a l y z e d . T a b l e ! g i v e s the event n u m b e r s and c r o s s s e c t i o n s f o r the ob:~erved final s t a t e s . The Kn~ m a s s s p e c t r u m f o r •,hose e v e n t s i s shown in fig. 1. F o r t h e ~Kn:r •": K - - ) s y s t e m ~ c u p p e r l i m i t of t b e K : ~ p h a s e ~<~3.c~ is 1325 (1245) MeV. T h e d o t t e d c u r v e ~ ",~. -~ith the data in fig. 1 is the sum of the phase spaces for these t~) systems corrected for the a m o u n t s of Y* and K* p r o d u c t i o n obs e r v e d ; the solid line shows the u n c o r r e c t e d " Work s~tpported in part by th,~U.S. Atomic Energy C o.-'...m ission. -4
Table 1 Number of events, c r o s s section and dominant Y* for each ~hannel.
Channel
No. of events
Dominant Y*
A°K°~+~ AK+~-~o E°K°~'+~-
95 75 16
E-K+~+~ E-K°~+~ °
18 II
Y-*K÷Tr-;;-
18
Z+K°~-~°
9
Y~'(1385) y ; o (1385) Y0* (1405) Y~ (1405) Y~ (1405) Y~ (1405)
Cross section (~b)
81 75 31 12 22 14 17
i 9 _+ 9 +7 ±3 +7 ~3 +_6
p h a s e s p a c e . Both a r e n o r m a l i z e d to t h e t o t a l n u m b e r of e v e n t s . An e x c e s s of e v e n t s c a n be s e e n in the r e g i o n of 1175 MeV w h i l e the o t h e r p o r t i o n s of the d a t a t e n d to be d e p l e t e d . S e p a r a t e p l o t s of the d i f f e r e n t f i n a l s t a t e s s h o w no s t a t i s t i c a l l y i n t e r e s t i n g d i f f e r e n c e s f r o m the c o m b i n e d data. T h e r e i s , h o w e v e r , in o u r s a m p l e s i g n i f i c a n t p r o d u c t i o n of K* (885), Y~ {1385) and Y~ (1405)
Volume 15, number 1
PHYSICS
LETTERS
1 Mtreb 1965
,o r N F.~
l
l
25
tO
-t
N [vm~
20
15
tO
1
nn0;
Mx • • GeV
Fig. 2. Klr~ r o s s spectrum after removing Y * band. .8
.9
tO
I.t
t2
t3
MK~r.w GeV
Fig. 1. K ~ mess spectrum for 242 events of the type
YK~. a s well a s s o me indication of hi ghe r r e s o n a n c e s having s t r a n g e p a r t i c l e d e c a y m o d e s . In o r d e r to examine the e f f e c t of t h e s e r e s o n a n c e s f u r t h e . ' , we have u s e d m a s s h i s t o g r a m s with the a p p r o p r i a t e p h a s e s p a c e s of each c h a n nel to obtain the f r a c t i o n of r e s o n a n c e production. In g e n e r a l f o r an) given A K ~ channel one c h a r g e s t a te of th e Y~ p r e d o m i n a t e s o v e r the other . z o . F o r e x a m p l e , the channel A° K+~-~ o shows only y~O and K *° and not the o t h e r c h a r g e st~*?s. T a b l e 1 shows the dominant c h a r g e state f o r Y* p r o d u c t i o n f o r each channel. II the K~n r e s o n a n c e e x i s t s it should not be slmultaneot, qly produced with a Y* in these c]mzznels. All events, therefore, were removed from the sample if the YTr m a s s w a s between 1350-1420 M e V for AK~Ir ard 1370-1440 M e V for 2;KTr~ and had the correct charge (as shown in table 1). The K ~ m ~ . ~ spectrum is shown in fig. 2 for those rem~.mlng events and as can be seen this tends to p~centuate the deviation in the region of 1175. This sample stillcontains a laxge number of K* events, so a further subtraction was m a d e of all events having a (K~)+o m a s s between 835 and 935 M e V . Fig. 3~t shows the K*n m a s s spectrum for these events; no obviotm deviation appears at 1175 M e V . In fig. 3b the Kr~ m a s s spectrum is plotted for those events having no m a s s combination in any y~+-o,~ Y0* o r K *+{5 bands. Once again this s e e m s to a c c e n t u a t e the peak at 1175.
|.0
I-
,
tl
,
1,2
,i
1.3 MK4/T
15
i
.e
.9
I,O
tl
1.'2
h
1.3
MKTr~r
Fig. 3a. K*~ mass spectrum ~fter removing Y* band. b. K ~ mass spectrum after removing all events containing a possible K* or Y*. To determine whether or not the observed anomaly w a s a reflection of s o m e higher resonance in another chav~,el w e examined all m a s s combinations for those events in fig. 3b having a K ~ m a s s between 1140 and 1200 M e V . No enhaJzcement can be seen in any other channel. In particulax there is no enhancement in the ~ m a s s spectrum. R is the above deviations in the K ~ mass spectrum at ~ 1175 M e V which w e interpret as further evidence for the existence of a resonant state.
75
Volume lS. mmber 1
PHYSICS L E T T E R S
Inspection of the Kw m a s s d i s t r i b u t i o n s for this sample and for the t h r e e p a r t i c l e (YKs) final .~ates shows no corresponding anomaly. This could be explained ff the qtumtum n u m b e r s of the IWffiwere 0 " , 1 + 2", etc. F r o m the data we can not rule cat signfftcan~ branching to K*~, which e~uld o c c a r with the above a s s i g n m e n t s . The number of ( K n ) " m a s s e s a r e too few to say whether it e x i s t s in this channel and, t h e r e f o r e , although the I-spin has to be ½ or ~, we can not r u l e out either possibility. The production angular distrilzztion in the m a s s region 1140-1200 MeV i s e s s e n t i a l l y lsotropic and not m a r k e d l y different f r o m the K n angular distribution o u t , d e ibis region. On the b a s i s of the at~)ve data the resonance appears to have a m a s s of 1160 • 10 MeV, a width of 35 ± 10 MeV, with a production c r o s s section of 20 ± 10 microbarns. This cross sectlon Is less them that observed by Wangler et at.,
1 March 1965
[1] a fact p r o b a b l y explained by our c l o s e r proxim i t y to threshold. We wish to acknowledge the g e n e r o s i t y of the A l v a r e z group And the Lawrence Radiation Lab o r a t o r y f o r m a k i n g t h i s run available to us; in p a r t i c u l a r we would like t~ thank P r o f e s s o r Donald H. Miller.
References 1. T.P.W~mgler, A . R . E r w ~ , W.D.Walker, Physics Letters 9 (1964) 71. 2. R.Armenteros, D.N.Edwards, T.Jat~)bsen, L.MontaneL A. Shapira, J. Vandermeulen, ¢'..H. O'Andlm, A. Astier, P. Bafllon, J. Cohen-Ganotma, C.Defolx, J.Siattd, C.Ghesqulerre ~ P.Rlvet, Pl~ysios Letters 9 (1964) 207. 3. R.Book, B.R.French, J.B.Kinson, V.Slmak, J. Badier, M.Bazin, B.Equer, A.Rouge and P.Grleve, Physics Letters 12 (1964) 6S.
A P H Y S I C A L S U M R U L E ON T H E R E A L P A R T O F THe.' PION NUCLEON FORWARD SCATTERING AMPLITUDE A. MARTIN
CERN, Geneva Received 28 January 1965
Recently, Kinoshita and Khuri [1] have proposed a s u m rule on the r e a l p a r t of the f o r w a r d s c a t t e r ing amplitude, which could constitute a test of d i s p e r s i o n relations. In t h i s note we Just want to r e m a r k that one can avoid the difficulty of evaluating the r e a l p a r t of the s c a t t e r i n g smplitude in p a r t of the unphysical region and write a sum r u l e containing only physical quantitites. Foliowlng r e f . 1 we consider the c a s e of pion-nucleon s c a t t e r i n z E t s the total energy of the pionnucleon s c a t t e r i n g amplitude and f , ( g ) r e f e r r e s p e c t i v e l y to ~ p s c a t t e r i n g . We consider the s y m m e trized amplitude f ( E ) = ~ f + ( E ) + f . ( - E ) ] - (pole t e r m s )
(1)
.f(E), as in ref. 1, Js supposed to increase less fast than E 2"~ at infinity. This is a very w e a k asstunption according to ref. 1. Let us just say that a constant high energy cross section corresponds to f(E) ~ E. The syrnmctrized amplitude f(E) is such that f ( E ) = f ( - E ) , with two cuts f r o m E = °~o to ~" : - ~ a.~d E = ~ to E = 4 ~o. R is convenient then to u s e the variable z = E 2 which maps the upper half E plane on the whole z plane with a cut from z = ~t2 to z = oo. F r o m now on we shall u s e t h i s v a r i a b l e without changing the name of the function. Since f ( , 2 ) , the scattering a m p l i t u d e at t h r e s h o l d i s finite, as e x ~ e r h n e n t a l l y established, it is p e r m i s s i b l e to p e r f o r m a subtraction at t h i s point (only one subtraction in z is necessary):
.Let us .now calm:late the quantity 76
PHYSICS L E T T E R S
turn trxns~ex, and Z = ± 1 for e ~ - p s c a t t e r i n g . Further, ~s(al) is the smaller (larger) of A E e argi A R p and
l - x In (I - ~) - l+x in (1 + x).
1 March 1965
and ~Ee/Ee and
AEO/F~)
l e s s than 5 % the exact result should not. differ"from that in (2) by m o r e
than 2%.
The largest contribution of the fmtetion o(x),
The a u t h o r w i s h e s to a c k n o w l e d g e h i s i n d e b t h e s s to P r o f . G. KKll~n f o r a d v i c e a n d c r R i c i s m and to N o r d i t a f o r f i n a n c i a l s u p p o r t .
about - g ~ for r e a s o n a b l e v a l u e s of q~, i s obmined w h e n ~ e = AF.p. In the c a l c u l a U ~ n l e a d i n g t o (2) the m a i n approximations w e r e the neglect of strong interaction e f f e c t s (except f o r t h o s e i n c l u d e d in the s t a n d a r d f o r m f a c t o r s ) and the neglect of the t e r m s not g i v i n g r i s e to a n i n f r a r e d d i v e r g e n c e in the h r e m s s t r a h l u n g m a t r i x e l e m e n t s [2]. T h e s i z e of t h e e r r o r c a u s e d by t h i s d e p e n d s m a i n l y on ~ o , AEe, a n d AEp. F o r E o l e s s t h a n 5 GeV,
~efe~-e1~,~s 1. J.Sehwinger, Phys. Rev. 76 (1949) 760. 2. Y.S.Tsai, Phys. Roy. 122 (1961) 1898. 3. A . S . K r u s , Phys. Roy. 125 (196g)2172. 4. N.Meister andD.Yelmie, Phys. Roy. 130 (196,1) 1210. 5. K.Berkelman, M.Feldman, R.M. Littauer, G.Rou~e and R.IR.Wflson, Phys. Rev. 130 (1963) 2061.
o(x)
:
2.
x
FURTHER
x
EVIDENCF
F O R A Klrv R E S O N A N C E
AT
1175
MeV*
D. F . P.IILLER, A. Z. K O V A C S , R. L. M c I L W A I N , T . R . P A L F R E Y a n d G. W. T A U T F E S T
Physics Department, Purd~e University, Lafayette, Indiana Received 26 January 1965
Recently three resonances decaying by a K~r m~e have been reported. Wangler et al. [I] have .,bs.°rved a r e s o n a n c e at 1175 MeV in YK~n f i n a l :-:arcs f r o m --p interactions at 3 GeV/c. The omer resonances, having masses of 1225 [2] and 1270 [3J M e V , w e r e r e p o r t e d f r o m a n t i p r o t o n a n r.ihilations and h a v e o t h e r d e c a y m o d e s such a s ~ . We u~ish to r e p o r t a d d i t i o n a l e v i d e n c e f o r the e x i s t e n c e of the f i r s t m e n t i o n e d r e s o n a n c e in =-p i n t e r a c t i o n s at 2.7 GeV/c. In a r u n of 30 000 p i c t u r e s t a k e n on the L R L A l v a r e z 72 ~ h y d r o g e n c h a m b e r 242 e v e n t s of the type YK~,~ h a v e b e e n a n a l y z e d . T a b l e ! g i v e s the event n u m b e r s and c r o s s s e c t i o n s f o r the ob:~erved final s t a t e s . The Kn~ m a s s s p e c t r u m f o r •,hose e v e n t s i s shown in fig. 1. F o r t h e ~Kn:r •": K - - ) s y s t e m ~ c u p p e r l i m i t of t b e K : ~ p h a s e ~<~3.c~ is 1325 (1245) MeV. T h e d o t t e d c u r v e ~ ",~. -~ith the data in fig. 1 is the sum of the phase spaces for these t~) systems corrected for the a m o u n t s of Y* and K* p r o d u c t i o n obs e r v e d ; the solid line shows the u n c o r r e c t e d " Work s~tpported in part by th,~U.S. Atomic Energy C o.-'...m ission. -4
Table 1 Number of events, c r o s s section and dominant Y* for each ~hannel.
Channel
No. of events
Dominant Y*
A°K°~+~ AK+~-~o E°K°~'+~-
95 75 16
E-K+~+~ E-K°~+~ °
18 II
Y-*K÷Tr-;;-
18
Z+K°~-~°
9
Y~'(1385) y ; o (1385) Y0* (1405) Y~ (1405) Y~ (1405) Y~ (1405)
Cross section (~b)
81 75 31 12 22 14 17
i 9 _+ 9 +7 ±3 +7 ~3 +_6
p h a s e s p a c e . Both a r e n o r m a l i z e d to t h e t o t a l n u m b e r of e v e n t s . An e x c e s s of e v e n t s c a n be s e e n in the r e g i o n of 1175 MeV w h i l e the o t h e r p o r t i o n s of the d a t a t e n d to be d e p l e t e d . S e p a r a t e p l o t s of the d i f f e r e n t f i n a l s t a t e s s h o w no s t a t i s t i c a l l y i n t e r e s t i n g d i f f e r e n c e s f r o m the c o m b i n e d data. T h e r e i s , h o w e v e r , in o u r s a m p l e s i g n i f i c a n t p r o d u c t i o n of K* (885), Y~ {1385) and Y~ (1405)
Volume 15, number 1
PHYSICS
LETTERS
1 Mtreb 1965
,o r N F.~
l
l
25
tO
-t
N [vm~
20
15
tO
1
nn0;
Mx • • GeV
Fig. 2. Klr~ r o s s spectrum after removing Y * band. .8
.9
tO
I.t
t2
t3
MK~r.w GeV
Fig. 1. K ~ mess spectrum for 242 events of the type
YK~. a s well a s s o me indication of hi ghe r r e s o n a n c e s having s t r a n g e p a r t i c l e d e c a y m o d e s . In o r d e r to examine the e f f e c t of t h e s e r e s o n a n c e s f u r t h e . ' , we have u s e d m a s s h i s t o g r a m s with the a p p r o p r i a t e p h a s e s p a c e s of each c h a n nel to obtain the f r a c t i o n of r e s o n a n c e production. In g e n e r a l f o r an) given A K ~ channel one c h a r g e s t a te of th e Y~ p r e d o m i n a t e s o v e r the other . z o . F o r e x a m p l e , the channel A° K+~-~ o shows only y~O and K *° and not the o t h e r c h a r g e st~*?s. T a b l e 1 shows the dominant c h a r g e state f o r Y* p r o d u c t i o n f o r each channel. II the K~n r e s o n a n c e e x i s t s it should not be slmultaneot, qly produced with a Y* in these c]mzznels. All events, therefore, were removed from the sample if the YTr m a s s w a s between 1350-1420 M e V for AK~Ir ard 1370-1440 M e V for 2;KTr~ and had the correct charge (as shown in table 1). The K ~ m ~ . ~ spectrum is shown in fig. 2 for those rem~.mlng events and as can be seen this tends to p~centuate the deviation in the region of 1175. This sample stillcontains a laxge number of K* events, so a further subtraction was m a d e of all events having a (K~)+o m a s s between 835 and 935 M e V . Fig. 3~t shows the K*n m a s s spectrum for these events; no obviotm deviation appears at 1175 M e V . In fig. 3b the Kr~ m a s s spectrum is plotted for those events having no m a s s combination in any y~+-o,~ Y0* o r K *+{5 bands. Once again this s e e m s to a c c e n t u a t e the peak at 1175.
|.0
I-
,
tl
,
1,2
,i
1.3 MK4/T
15
i
.e
.9
I,O
tl
1.'2
h
1.3
MKTr~r
Fig. 3a. K*~ mass spectrum ~fter removing Y* band. b. K ~ mass spectrum after removing all events containing a possible K* or Y*. To determine whether or not the observed anomaly w a s a reflection of s o m e higher resonance in another chav~,el w e examined all m a s s combinations for those events in fig. 3b having a K ~ m a s s between 1140 and 1200 M e V . No enhaJzcement can be seen in any other channel. In particulax there is no enhancement in the ~ m a s s spectrum. R is the above deviations in the K ~ mass spectrum at ~ 1175 M e V which w e interpret as further evidence for the existence of a resonant state.
75
Volume lS. mmber 1
PHYSICS L E T T E R S
Inspection of the Kw m a s s d i s t r i b u t i o n s for this sample and for the t h r e e p a r t i c l e (YKs) final .~ates shows no corresponding anomaly. This could be explained ff the qtumtum n u m b e r s of the IWffiwere 0 " , 1 + 2", etc. F r o m the data we can not rule cat signfftcan~ branching to K*~, which e~uld o c c a r with the above a s s i g n m e n t s . The number of ( K n ) " m a s s e s a r e too few to say whether it e x i s t s in this channel and, t h e r e f o r e , although the I-spin has to be ½ or ~, we can not r u l e out either possibility. The production angular distrilzztion in the m a s s region 1140-1200 MeV i s e s s e n t i a l l y lsotropic and not m a r k e d l y different f r o m the K n angular distribution o u t , d e ibis region. On the b a s i s of the at~)ve data the resonance appears to have a m a s s of 1160 • 10 MeV, a width of 35 ± 10 MeV, with a production c r o s s section of 20 ± 10 microbarns. This cross sectlon Is less them that observed by Wangler et at.,
1 March 1965
[1] a fact p r o b a b l y explained by our c l o s e r proxim i t y to threshold. We wish to acknowledge the g e n e r o s i t y of the A l v a r e z group And the Lawrence Radiation Lab o r a t o r y f o r m a k i n g t h i s run available to us; in p a r t i c u l a r we would like t~ thank P r o f e s s o r Donald H. Miller.
References 1. T.P.W~mgler, A . R . E r w ~ , W.D.Walker, Physics Letters 9 (1964) 71. 2. R.Armenteros, D.N.Edwards, T.Jat~)bsen, L.MontaneL A. Shapira, J. Vandermeulen, ¢'..H. O'Andlm, A. Astier, P. Bafllon, J. Cohen-Ganotma, C.Defolx, J.Siattd, C.Ghesqulerre ~ P.Rlvet, Pl~ysios Letters 9 (1964) 207. 3. R.Book, B.R.French, J.B.Kinson, V.Slmak, J. Badier, M.Bazin, B.Equer, A.Rouge and P.Grleve, Physics Letters 12 (1964) 6S.
A P H Y S I C A L S U M R U L E ON T H E R E A L P A R T O F THe.' PION NUCLEON FORWARD SCATTERING AMPLITUDE A. MARTIN
CERN, Geneva Received 28 January 1965
Recently, Kinoshita and Khuri [1] have proposed a s u m rule on the r e a l p a r t of the f o r w a r d s c a t t e r ing amplitude, which could constitute a test of d i s p e r s i o n relations. In t h i s note we Just want to r e m a r k that one can avoid the difficulty of evaluating the r e a l p a r t of the s c a t t e r i n g smplitude in p a r t of the unphysical region and write a sum r u l e containing only physical quantitites. Foliowlng r e f . 1 we consider the c a s e of pion-nucleon s c a t t e r i n z E t s the total energy of the pionnucleon s c a t t e r i n g amplitude and f , ( g ) r e f e r r e s p e c t i v e l y to ~ p s c a t t e r i n g . We consider the s y m m e trized amplitude f ( E ) = ~ f + ( E ) + f . ( - E ) ] - (pole t e r m s )
(1)
.f(E), as in ref. 1, Js supposed to increase less fast than E 2"~ at infinity. This is a very w e a k asstunption according to ref. 1. Let us just say that a constant high energy cross section corresponds to f(E) ~ E. The syrnmctrized amplitude f(E) is such that f ( E ) = f ( - E ) , with two cuts f r o m E = °~o to ~" : - ~ a.~d E = ~ to E = 4 ~o. R is convenient then to u s e the variable z = E 2 which maps the upper half E plane on the whole z plane with a cut from z = ~t2 to z = oo. F r o m now on we shall u s e t h i s v a r i a b l e without changing the name of the function. Since f ( , 2 ) , the scattering a m p l i t u d e at t h r e s h o l d i s finite, as e x ~ e r h n e n t a l l y established, it is p e r m i s s i b l e to p e r f o r m a subtraction at t h i s point (only one subtraction in z is necessary):
.Let us .now calm:late the quantity 76