INTERACTIONS WITH TWO-BODY AND QUASI TWO-BODY FINAL STATES. R. E. Diebold Argonne National Laboratory. E. Fowler Duke University

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1 1 SS INTERACTIONS WITH TWOBODY AND QUASI TWOBODY FINAL STATES R. E. Diebold Argonne National Laboratory E. Fowler Duke University R. M. Heinz Indiana University F. Pipkin Harvard University and J. Prentice University of Toronto ABSTRACT To aid in the design of spectrometer systems at NAL, highenergy reactions with two particles or resonances in the final state are tabulated. This report summarizes in a systematic manner reactions with two particles or resonances in the final state; some threebody finalstate reactions are also given. The main purpose of this summary is to aid in the design of spectrometer systems at NAL. We have considered only proton targets. In many experiments the target will be polarized, and in evaluating the spectrometer systems this should be taken into account. The nuclear contamination in the present polarized targets requires the observation of both the scattered and recoil particle to make an unambiguous measurement. In general one will want to use deuteron and nuclear targets in addition to proton targets. The reaction particles have been divided into four categories: beam particles, stable particles, metastable particles, and unstable particles. Table I summarizes the four categories. The division is based in part on particle lifetime. The stable particles will under ordinary circumstances not decay in the apparatus; the metastable particles, will in some cases decay. and in some cases not decay depending upon their momentathe unstable particles will always decay in a very short distance 1

2 2 885 and thus must be reconstructed from a multibody state. Hyperon beams, gamma beams, electron beams, and muon beams have been treated separately. They usually have special problems which make it necessary to tailor the apparatus to them. For observing the unstable particles, it is necessary to observe one of the many possible decay modes. Table 11 summarizes some of the decay modes for each of the unstable bosons. Where several modes are available, we have chosen the modes consisting of the fewest uncharged particles. Table 111 summarizes the decay modes of the other unstable particles. A summary of the reaction list is the following: 1. Reactions with two stable particles in the final state. 11. (A) Reactions with one stable and one metastable particle in the final state. (B) Reactions with one stable and one unstable particle in the final state. Ill. (A) Reactions with two metastable particles in the final state. (B) Reactions with one metastable and One unstable particle in the final state. (C) Reactions with two unstable particles in the final state. IV. Reactions with hyperon beams. V. Reactions with 'I, e, and f1 beams. VI. Reactions with three particle final states. For each of these reactions, there are in general three kinematic regions: forward scattering, backward scattering, and largeangle scattering. The following classes of particles have not been included just to simplify the table and not because of any judgment as to whether or not they are important. * (K) N with I = 5/2 (K K) Z (8 = i baryons) I = 2, 8 = 0, B = bosons a K O L 2

3 3 SS5 Table 1. Particle Classifications. Stable Metastable Unstable Beam Particles Particles Particles Particles T ~ 10 8 sec T ~ sec T ~ sec Note: ± ± rr rr A rr ± ± ± K K :E T) So, p p :Eo n n 0 (boson)±' p KO K*' ±,o Ii s N)lt.,0,. d T: particle halflife y*: I = 0 or I = 1 hyperon resonances boson: nonstrange boson resonances N*: I = 1/Z or I = 3/Z nonstrange baryon resonances MM: missing mass v: 0, ± MM Table II. Decay Modes for Unstable Bosons. ± (Boson) Classification Decay Examples G = 1 rr ± rr ± p, g ± G = 1 rr rr rr A A 1, 2 ± 0 JP unnatural, G = t 1T 'IT 1T 1T B JP natural, G = ± t 0 KK A Z' N (1016) (Boson)o G = t rr rr po, f G = t co, At' A Z JP unnatural, G = t 1T 1T 1T 1T B JP natural, G = ± t KK q f' :s*' 0, 3

4 4 SS5 Table III. Common Decay Modes for K* N*, v, and::;:* Particle State * * ± K (K) Decay Modes ± 0 K rr (N* ) * (N ) ± K rr rr K rr K rr pit 0 prr rr nn rr o prr nrr prr rr pit 0 prr rr nrr y * (y) * ± o ± :!: rr ± 0 :!: rr ± :!: rr rr. ± ± :!: rr rr (y) * (y) * nk 4

5 5 SS5 Particle State Decay Modes y * (y*)o ATT ~OTTO ± ~ TT pk nko ± l; 1T1T (::=;)* (::=; * ) 2: 1T ::=; TT ::=; TT TT I; K I; K I; K TT AK (::=;0)* ::=; TT 0 :s 1T 1T I; Ko I; KTT AKo I. Two Stable Particles in Final State TT' TT' P P TT P P d K' P K' p p p p p p P TT d P P P p p p n n p P TT TT P P K K n p n p 5

6 6 SS5 II. (A) One Stable Particle and One Metastable Particle in the Final Sta te 'II P K ~ 'II P K ~, K ~' P 'II K P K II. (B) One Stable and One Unstable Particle in the Final State,, * 'II P 'II (N ), 'II P P (boson),, 'II P K (y*t,, 'II P d N*', 'II P P (MM) 'II P n (MM) 'II P 'II (MM) 'II P 'II (MM) 'II P K (MM) 'II P K (MM) * 'II 'II (N P 0 'II 'II n P 'II P n (bosont 'II P P (MM) 'II P n (MMt 'II P 'II (MM) p 'II (MM) 'II P K (MM) 'II P K (MM) K' * K' P (N ) K' * p (K), p K P d y*, K P P (MM) K P n (MM) K P 'II (MM) K P 'II (MM) K P K (MM) K P K (MM) K P K O n s 6

7 7 SS5 II. (B) One Stable and One Unstable Particle in the Final State K p (KO{ n K p 1T (Y) K p K (:=:* ) K p p (MM) K p n (MM)o K P 1T (MM) K p 1T (MM) K p K (MM) K p K (MM) ~::: p p p (N ) n ~~ (N ) d (boson) p (MM) n (MM) 1T 1T (MM) (MM) K (MM) K (MM) n p n (N * ) p P p (N*)o d 1T d (boson)o p (MM)o n (MM) 1T (MM)o 1T (MM) K (MM)o K (MM), 1T (boson), K' (K) r, p (N*) (N)'F p n: * 0 (N ) (N)o n p (MM) 7

8 8 SS5 II. (B) One Stable and One Unstable Particle in the Final State p p n (MM)o 1T (MM) 1T (MM) K (MM) K (MMt III. (A) Two Metastable Particles in the Final State 1T P KO s!i. K P KO s 2 P P KO KO s s x A L' L' 0 0 :s :=;0 :=:0 III. (B) One Metastable and One Unstable Particle in the Final State * 1T P!I. (K ) ~::: L (K)!I. (MM) L' (MM), :=:,0 (MM), 0 (MM) K~ (MM) 1T P!I. (K*)o L (K) KO LO S L (K * )!I. (MM)o L' (MM), :=:~ 0 (MMt.,0 0 (MM) KO s (MM)o ~::: K P KO s (N )!I. (MM) L' (MM)' 8

9 9 SS5 III. (B) One Metastable and One Unstable Particle in the Final State :=:,0 K P (MMt' Q (MM) Kg (MM) K P A (boson)o ~' (boson), :=:,0 * (K), K O s (:;::*)0 K~ * 0 (N ) A (MM)o ~' (MM), S,o (MM)'o Q (MM) K O (MM)o s P P K O (K*)o s x (Y*) 0 A (y*)o * ~ (Y ), (y*), ~, _ :=:,0 (:;::*),0..., a (:;::*),0 A (MM)o ~, (MM), :=: r, 0 (MMt,o Q (MM) K~ (MM)o K (MM)o ~ ~, (MM), :=;.0 (MM)'o rr (MM) K~ (MM)o III. (C) Two Unstable Particles in the Final State IT P (boson) (N* ) 0 t,: IT (N ) * 7] (N ) ~o :(: (K ) 9

10 10 SSS III. (C) Two Unstable Particle s in the Final State 1T P 1T P K P (bosont (boson) * (K ) 1T TJ E ~:o: (N ) * (N ) * (Y ) (MM) (MM) (MM) (boson),. (MM)', (K*)'. (MMt,. (N*t', 0, (MMt., (y* ),, (MM)', (::;:<'). (MM)' 1T (N*)o TJ (N*)o EO (K*)o (boson)o (N*)o (boson) (N ) '~) (boson) (N (K ) (Y) * (K)o (y*)o 1T (MM)o TJ (MMjo EO (MMt (boson)', (MM)',0 (K*)''o (MM)',0 (N*t',0, (MM),,0. (y*),,0 (MM)''o (::;:*). (MMt,o :>;: (K) (N*) (K)o ~:: (N ) 1T (MM) TJ (MM) '1:,0 (MM) (boson), (MM)', (K*)', a (MM)', (N<')', v, (MM)o.., 10

11 11 SS5 III. (e) Two Unstable Particles in the Final State K P K p p p n P (y*t r, C::;*), 1T T) 1T T) (boson), (boson)o (K*)' (K*t,o 1T T) L,0 (boson), (K)', (N)., 0, (y*t,, (S':'), (N*t,o 1T T) L, (boson),, * ~ 7 0 (K ) (Nt,, 0, (y)., C::;),o (N*)o, 1T T) L, (boson), (K*t, (Nt', 0, (y,:,),, (S*) (MMt (MM) (y':')o (Y) L,0 L, (Y) L,0 *, (N*t,o ':: (s ). (MM)o (MM)o (MM)o (MM)''o (MM)''o (MM),,0, (MM)',0 (MMt,o (N')' (MM) (MM) (MM) (MM)', (MMt,, (MM)O.,, (MM)', (MM) (N*)' (MM) (MM) (MM) (MM)o,, (MM)o,, (MM),0,, (MM)o,, (MM)' 11

12 12 SS5 III. (e) Two Unstable Particles in the Final State IV. (A) Incident A p P 1T 0 1T 1T I] 0 1T (boson)o I] I] I] (boson)o :l;0 :l;0 :l;0 (Y':')O ~ (y)o :?,: (K) ':: (K ) (K'~)O (K':')O, (N')', 0, (N*)', 0, (y~,), r (Y'),, C=:*),o (:=:), 1T (MM)o I] (MM)o :l;0 (MM)o :l;0 (MM)o (boson)',0 (K)', (MM)''o (MM)''o (N*t',, (MM)',,0 (N'~)',, (MMt',, (y,,),, (MM)''o (y),, (MM)',0 c::*),0 (MM)'o (:::), (MM)'o 1. Two Stable Particles in Final State 2. One Stable A P _ d (MM)o Stable a. With Metastable A P A P :l; n K~ d 12

13 13 SSs IV. (A) Incident A b. With Unstable A P ~o P *0 K d *0 y P 3. Neither Stable P (MM)o n (MM) d (MM)o K (MM)o K a. Two Metastable None IV. (B) Incident :!:, (MM),, (MM)o (MM) P (MM) b. One Metastable, One Unstable * A P A N N*o * N c. Two Unstable A ~O * P N :t:~ Y *0 N y * N*o * * Y N 1. Two Stable ~ P L ~' P P 2. One Stable a. One Metastable L p ~ p ~ P P K d (MM), Stable K~ n 13

14 14 SS5 IV. (B) Incident 2:: ' a. One Stable b. One Unstable 2:: y*' P P P (MM) n (MM). 1T (MM)' K' (MM) P (MM) 0 2:: P 2:: n 3. Neither Stable K*' d y*' p y*'o n * ::=: K P a. Two Metastable None (MM) n (MM)o. 1T (MM) K' (MM), p (MM) b. One Metastable and One Unstable :E p:e N*' A N * :E P A N*'o :E N* K~ N*'o c. Two Unstable :E P y* N'\ y*o N :Eo N*' :E P :Eo N*' y*~oj, N~~JOJ. 14

15 15 SS5 v. y, e. f1 Note: For inelastic e or f1 scattering one can replace: yp X by ep 1X 2 ex 1X 2 or f1p f'.x X Both Stable 2. One Stable y P Y P 1T n n d e P e P f1 P f1 P a. Other Metastable y P K A b. Other Unstable 0 y 1T P P 1] P K 0 ~ N':o 1T 1T N*' K y*.o (boson)o P (boson) n (N'~. 0) d Ii d ~::. N':' Y ~:(, e P e N ~J: f1 P f1 N 3. Neither Stable a. Both Metastable KO Y P ~ b. One Metastable, One Unstable y P KO y. K*'o ~ K, A 15

16 16 SS5 V. y, e, fl 3. Neither Stable c. Both Unstable y P rr 0 N:''':~ I) N':', (boson)o N':', (bosont N':',o (boson) N':' K' :1: 0 K' y':'.o K,o y'~' VI. Three Particle Final States In addition to quasi two body reactions, it is probable that there will be considerable interest in more than twobody final states resulting from multiperipheral processes, cascade decays of resonances, etc. Using an extension of the classification system employed in Sees. I to Ill, it is possible to write lists of reactions for threebody and quasi threebody final states. This has been done only for the three stable particle case. It is shown that all the reactions of Sec. VI are already included in the decay products of quasi twobody final states if one includes sufficiently massive (boson)±' 0, N*, v, and E * to permit decays such as :=:*, 0 rl K. This is equally true of the threebody kinematic configurations if one includes forward, backward, and largeangle production as well as sequential decays of heavy resonances. 16

17 j 7 SS5 VI. Three Stable Particle Final States Already Beam Target Final State Included, e.g.. P P 0 p p p K n) n [ n N' * (boson)o n (boson) p K n [ K Y' * (boson)o n p P p n (bosonjo n P K' P K P n d N*' d K ~ n K'N*' K P K 0 d K N*' KO L p P p K K rl K ';:;'*1 0 N' P N>:C, n n p n [ * P 0 d (boson) d p P 0 p N, p;i1n*,o P n N*,o n;j5n*. p 0 d PN*'; iln*'o n p ~/ n n N n p p N*' P n 0 d (bosonjo d p j5 d (bosonjo d K K d {bosonjo d ' d (boson)o d K ii d d Y*. 17

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