SOME POLARIZED TARGET EXPERIMENTS FOR ELEMENTARY PARTICLE PHYSICS

R.H. DALITZ Department of Theoretical Physics, Oxford

INTRODUCTION

At the present stage in elementary particle physics, there are three major areas of phenomena where the use of polarized targets may lead to especially illuminating information.

a. High energy scattering, in the energy range where the dominant contributions to the processes observed may arise from Reggion ex­ change. The features of particular interest in these situjtions will be discussed at this meeting by Dr R.J.N. Phillips 1 •

b. Tests of time-reversal (T) invariance for electrom~gnetic pro­ cesses, following the suggestion by Bernstein et al 2) that the CF-violation observed in the weak decay of kaons arises from the existence of an electromagnetic interaction which strongly viola­ tes T-invariance. Evidence for this hypothetical T-violating elec­ tromagnetic interaction can be sought most directly in the study of electromagnetic processes from a polarized proton target, for example in the study of the electro-excitation process e + N-+ e + N* , as discussed by Christ and Lee 3J. The experi~ents proposed will be discussed at this meeting by Dr M. Jacob 4J.

c. Hadron spectroscopy. Very many resonant states have been obser­ ved for masonic and baryonic states. These hadronic states are be­ lieved to correspond to the patterns appropriate to unitary multi­ plets of states, and these unitary multiplets appear to be grouped in supermultiplet patterns. In our attempt to classify and under­ stand all these hadronic states, our first need is for the deter­ mination of the spin and parity for each state. A general survey of the methods available for their determination will be given at 262 R.H. DALITZ

this meeting by Dr M. Jacob 4). In this talk, we wish to discuss briefly some particular situations of interest, in order to illus­ trate the kinds of experiment which appear especially relevant at present.

2 RESONANCE FORMATION EXPERIMENTS

The additional information made available by the use of polarized targets is especially valuable in the case of resonant states which may be formed by direct collisions. Such "resonance forma­ tion experiments" are possible only for resonance states for which there is an entrance channel corresponding to a conveniently long­ lived particle (n*, K~, K~, p, n or p) incident on a proton or neutron target. We shall uiscuss the situations briefly in turn.

The nN system has already been much studied in the resonance re­ gion. Polarized target experiments have been reported for n+p and n-p elastic scattering up to N* mass about 2200 MeV, as summari­ zed by Dr o. Chamberlain 5) at this meeting. The nN scattering processes are described by two amplitudes

(2.1) for total isospin I = 1/2 and 3/2, and it is possible to carry out analysis on the basis of these n:-p elastic scattering data alone. However it will also be desirable to have available the angular distribution and polarization data for the charge ex­ change process n-p _,. n°n, which is governed by the difference (S3/2-s1; 2 ), in order to ,11ow a unique phase shift analysis for the nN system. Lovelace 6) has recently emphasized that these charge-exchange experiments would be of more immediate value for this purpose than the more difficult spin correlation experiments, involving measurement of the Wolfenstein R and A parameters.

Polarization studies of inelastic processes may also prove to be important, especially for those N* resonances which happen to ha­ ve small partial width for the nN channel. The reaction n-p-+ n~ is a rather convenient example, which may be studied at the same time as the charge-exchange process ; at least one resonance, the (1/2-) NfL 2 (1540) resonance which leads to the strong n~ threshold proauction, is known to have particularly large partial width for the n~ channel. Other reactions of the same kind are n-p ~ AK 0 , which also selects I = 1/2 N* states, and the various reactions nN __.. [K, especially the process n+p-+ E+K+ which se- EXPERIMENTS FOR ELEMENTARY PARTICLE PHYSICS 263

lects I = 3/2 N* states. The AK0 and L+K+ reactions just mentio­ ned are of particular interest in that a polarization analysis of the final state is readily available in consequence of the strong polarization dependence of the decay processes A -pn- and L+ _. pno. Some polarization analyses of these reactions have al­ ready been carried out on this basis, without the use of polari­ zed targets, but these have not been sufficient for a unique ana­ lysis of the reaction amplitudes. Marked oscillations in theAKO polarization angular distribution h~ve been reported in bubble­ chamber data analysed by Schwartz 7J, for pion momenta about 1500- 1700 MeV/c, which are probably associated with an Nf/ 2 resonance not otherwise known 8) ; however, the statistics available even from such large bubble-chamber experiments are not sufficient to determine the details of the phenomena with sufficient precision for a definite interpretation. An investigation of this reaction with a polarized target, together with polarization observations for the final A particle, would be of particular interest, in that this situation would allow a complete determination of the spin properties for this reaction. For the L +K+ reaction, pola­ rization effects have been reported which are associated with the resonance N3; 2 (1920), although the statistics in these bubble­ chamber experiments are r~latively limited, and these have been interpreted by Holladay 9) in terms of interference between reso­ nant and peripheral production amplitudes to give support for the assignment (772+) for the spin-parity of this state. A more ade­ quate study of the polarization pro~erties of this r+K+ reaction could be made also for the higher N3/2 states, with the use of polarized targets.

For the KN systemt there are two elastic amplitudes , of the s0 s1 general form (2.1). The K-p elastic scattering amplitude is 1/2(So ! s ) ; the_ampl~tude for the charge exchange process 0 1 K-p ~ K n is 1/2(s1 - s 0 ). Hence, a complete analysis for the KN system requires angular distribution and polarization data for both the elastic and charge exchange processes. Here, the knowled­ ge of the charge exchange process is essential for. an adequate a­ nalysis, and this process has received very little attention to date ; there is some preliminary bubble-chamber data on angular distributions and total cross-sections, but no information at all on its polarization properties.

The inelastic process K-p -..Ano is of particular interest, both because the final state has I = 1 and is therefore an indicator for If states and because of the polarization analysis possible for the A hyperon. Bubble-chamber studies of this reaction (or of the corresponding reaction K-n - An-) haye already yielded much information on the If resonance states 10). The inelastic reaction K-p -- A~ similarly has special interest, in that the final state has I = 0 and is an indicator for YO stat~s ; apart from the thres­ hold studies, which indicate the existence of a Y (1670) resonance with (1/2-), there is rather little data available0 on this reaction, 264 R.H. DALITZ

essentially none on its polarization properties. These reaction amplitudes are not closely related with the elastic KN amplitu­ des, except for the form of the Breit-Wigner amplitude for the resonant state, since the unitarity relations are complicated, owing to the large number of other competing channels. However, with polarized target and polarization observations for the fi­ nal A particle, complete spin and partial-wave analyses are pos­ sible for these amplitudes alone. Of course, the study of these reactions with polarized targets is made difficult by the fact that the final mesons are neutral, unless targets are available with a very high proportion of polarized protons.

For the KN system, K+p elastic scattering leads directly to the I = 1 amplitude S1 of the form (2.1 ). Polarized target studies are needed for a partial wave analysis for s 1 and experiments are being planned by several groups. At present, these will be of particular interest in the neighbourhood of K+ momentum 1250 MeVJc, where a small)bump has been found recently in the K+p to­ tal cross-section 11 •

The I = 0 KN amplitude s0 is more difficult to reach. One possi­ bility involves the study of the charge exchange reaction K+n _..K~p, whose amplitude is (s1 - s0 )/2f2, and there has alrea­ dy been some study of its angular distrioution from charge ex­ change observations in K+d collisions 12). At present there is particular interest in the study of the I = 0 amplitude in the neighbourhood of K momentum 1150 MeV/c in consequence of a rather marked bump whic~ has been observed recently in the K+d total cross-section 11) and which must be attributed to the I= 0 KN interaction. Polarization information on the I = 0 KN interaction is therefore much desired, in order to assign this bump to a de­ finite spin-parity state for the KN system and to clarify its in­ terpretation. This could be done with a polarized deuterium tar­ get, since the neutron within the deuterium will have polariza­ tion (P+ 1 - P_1 ), where P denotes the percentage of deuterons with magnetic quantum num~er m along the polarization direction. The K? angular distribution observed requires rather substantial corrections at forward scattering angles for the effect of the Pauli principle, arising from the presence of two final protons in the reaction K+d -Kfpp (the differential cross-section neces­ sarily vanishes for 0° scattering with full energy) ; the corres­ ponding corrections to the polarization angular distribution would need to be looked into, since the Pauli principle effects are certainly spin dependent here. The polarization experiment could well be done using a polarized 3He target, using the reac­ tion K+ 3He -Kfppp. The Pauli principle corrections are much lar­ ger (and more difficult to evaluate convincingly, owing to the nu­ clear complications) for this situation than for the deuterium reaction, so that this is a very unfavourable situation for the determination of d~/dQ for the charge-exchange reaction ; however, since the two initial protons have total apin zero, the Pauli EXPERIMENTS FOR ELEMENTARY PARTICLE PHYSICS 265

principle corrections are spin-independent and the determination of the polarization angular distribution would not depend on their evaluation.

Another possibility for the study of the KN charge exchange reac­ tion which should be mentioned here is the reaction K~p - K+n, since this reaction has the advantage of. a proton target. The difficulty is that the K~ beams available to date are not monoe­ nergetic, but have a ratner broad momentum spectrum (typical spread of order± 50 %). In this situation, there are no cons­ traints on the K+ momentum, so that it is exceedingly difficult (if not practically impossible) to separate out the charge ex­ change events occurring from the polarized protons in the target.

The pp system can lead to mesonic resonance states m* with Y = 0 and I= 0 or 1, for mass values above 1876 MeV. A number of such mesonic resonanc~s (with I ~1) have been established recently by Focacci et al 13J, the s--meson at 1929 MeV, the T--meson at 2195 MeV (a neutral meson of mass 2207 MeV has also been reported by Alles-Borelli et al 14)) and the u--meson at 2382 MeV. The spins ~nd parities of these states are not known ; it is specula­ ted 15J that each of these mesonic states are associated with four nonets with total spins J = L + 1, L (twice) and L - 1, and parities (-1)L+1, where L = 3 for the S-mesons, L = 4 for the T­ mesons, L = 5 for the U-mesons, and so on. In principle, these mesons may be formed directly in pp collisions and their existen­ ce may therefore affect the polarization and angular distributions for pp elastic scattering. It is quite likely that these masonic states m* may have small partial widths for the NN channels, since these channels have thresholds lying relatively close to the meson mass values. However, since these mass values appear quite accura­ tely known and these resonances are rather narrow (upper limits typically r ~ 35 MeV), a search for their possible effect on d~/dn and P(e) for pp elastic scattering would be of considerable inte­ rest. Even though the amplitude for pp- m* ~PP may be quite small, polarization effects do depend essentially on interferences between different partial wave amplitudes and can be sensitive to a small, rapidly-energy-dependent amplitude of relatively high or­ bital angular momentum. The determination of the spin-parity va­ lues for these high-lying mesonic states appears quite a difficult problem at the present moment.

3 RESONANCE PRODUCTION EXPERIMENTS

Here we refer to reaction processes in which the resonant state is observed as a final-state interaction among the particles re- 266 R.H. DALITZ

sulting from a multiparticle production process. The simplest examples of such processes are of the type :

m + p -m' + B* B* - B + m" ( 3. 1 )

where B and B* denote a baryon and baryonic resonance state, respectively, and m, m', m" denote various mesons.

First, we consider the semi-stable fermion states. For the spin- 1/2 baryons for which the parities have not already been determi­ ned by other methods, there are experiments under way (at Berke­ ley for the r: +, at CERN for the. S -) to determine their pa:ri ties, using polarized proton targets and the result of Bilenky 16) that the differential cross-section for the reaction

m + B - m' + B' (3.2)

where the mesons m, m' are spinless and the baryons B, B' have spin 1/2, from a polarized B target with polarization Pt is given by :

(3.3) ~~ ( e ) = ( ~~ ( e )) 0 ) 1 + €. ft . P ( e ) \

where (d~/dn (e)) 0 and P(e) are the differential cross-section and B' polarization for the reaction from an unpolarized target and t denotes the product of the intrinsic parities of all the particles m, m', Band B'.

The other semi-stable fermion known is the Q --hyperon, believed to belong to the (3/2+) decuplet. About ten examples have been found to date, from the production reaction

(3.4)

at various K- energies. The decay processes, Q -- ../\K- and ~n, occur through weak interactions which do not conserve parity, so that the Q -parity cannot be determined from the study of Q -de­ cay distributions. In due course, it should be possible to deter­ mine the Q spin value from the analysis of the Q -decay distri­ butions, and we may anticipate that the value J = 3/2 will be es­ tablished. The problem is then how to determine whether (3/2+) or (3/2-) holds for the Q --hyperon.

Bilenky and Ryndin 17) have proposed a method for the determina­ tion of the Q --parity which represents an extension of the me­ thod for spin-1/2 baryons based on the relation (3.3). It will be instructive to consider the basis for this method in some de- EXPERIMENTS FOR ELEMENTARY PARTICLE PHYSICS 267

tail. It may be applied to reaction (3.4) in three situations : i) if there exists a o+ resonance m* with the decay modem*- K+K 0 , so that attention can be confined to the reaction K-p - n.-m* ; ii) if attention is confined to final states for which the K+Ko c.m. momentum is sufficiently low as to ensure that ~ = 0 holds for the K+K 0 system ; iii) if attention is confined to events lea­ ding to Q -, K+ and K0 momenta which are coplanar.

In each of these situations there is a unique production piane de­ fined. The method propos~d is based on the Bohr theorem 18) which expresses the invariance of the strong interactions with respect to reflection in this production plane. Since this reflection ope­ ration is equivalent to P x Rn(n), where P denotes the parity ope­ ration and Rn(e) denotes rota~ion of the axes by angle e about the normal n to This plane, this invariance leads to Bohr 1 s result :

(3.5)

where m denotes the spin compo11ent of particle a along the normal Q and Ea denotes the intrinsic parity of particle a, and i, f re­ fer to ihe initial and final particles, respectively. The special feature common to the three situations listed above is that the K­ mesons do not contribute to the spin sums E m in the relation (3.5). With this simplification, then, for i~itial proton spin mi= +1/2 in reaction (3.4), the relation (3.5) allows only mf = +1/2 and -3/2 for the n -spin, for the case of negative a.­ parity ; let us denote these amplitudes by a and a_~/2• For ;2 m. = -1/2, negative Q -parity would allow on1 y mf = -1/2 and +3/2 f5r the Q -spin ; let us denote these amplitudes by a_ / and 1 a~; • For ~ co~pletely polarized target with mi = +1/2, ~hen, the c~bss-section2 is :

2 2 1a1;2I + 1a_3/2 I = cro + O"' 1 (3.6) where

.1. 2 2 2 2 cro = 2 ja3/2 I + 1a1;2I + la_1/2I + la-3/21 ( (3.7a) .1. 2 2 2 2 cr1 = - 2 la3/2 I - la1/2I + 1a_1/2I la-3/21 ( (3.7b)

For positive Q -parity, initial proton spin m. = +1/2 can lead on­ ly to mf = -1/2 or + 3/ 2 for the 0. -spin ; agatn, these amplitudes are denoted by a_ ; and a ; • For mi -1/2, the final spin sta­ 1 2 3 2 = tes are mf = +1/2 and -3/2, with amplitudes a 1 ; 2 and a-3/2• res­ pectively. In this case the cross-section for mi = +1/2 target is 268 R.H. DALITZ

2 2 ) la ; 2 + la_ 1 1 leading to the result ( cr - cr ) • To sum up, ! 2 ! , 0 1 the 3 ~roduction 1 fross-section has the general form :

(3.8) where € denotes the Q -parity and Rt denotes the proton target po­ larization.

For. unpolarized target, the reaction ~3 .4 ). leads to the 0 -spin state mf +3/2 with intensity Ja mr +1/2 with intensity = J. 2 1 , = a 1 2, mf -1/2 with intensity 3 /a_ 1 12, and mf -3/2 with 2 = 1 2 = int~nsity 1a_~/ 12• The quantity cr1 can be determined from the odd moments or the2 n-spin :

1a_1/212) /N (3.9a)

1a_1/212) /N ( (3.9b) where

N = •

In fact

These spin moments can be determined unambiguously from the pola­ rization angular distribution of decay processes Q - - AK- and 3n, as discussed in general by Byers and Fenster 19). Hence, with this determination of cr1 , comparison of the observed cross-section for target polarization ft with the expression (3.8) will lead di- rectly to a determination of the U-parity e: • Bilenky and Ryndin give more general formulae, appropriate to arbitrary spin value for the Q -hyperon, but the above discussion is sufficient for the expected value J = 3/2. Typical examples of the resonance production process ( 3 .1 ) are .

+ 0 *++ *++ + n + p - n + N N - p + n (3.1oa) Ko * * 1t + p - + Yo YO - I:+ n (3.10b) *+ *+ + K + p - n + y1 Yo - A+ n (3.10c) ...... K- + K+ + ';: *- .. * p - ...... - ~ + n (3 .. 10d) EXPERIMENTS FOR ELEMENTARY PARTICLE PHYSICS 269

The spin and parity of the resonance state B* -+-) B + m" can be de­ termined by the method of Byers and Fenster 19 when : i) B* is produced in a state of non-zero polarization (i.e. a state for which some spin tensor of odd rank has non-zero expectation va­ lue), and ii) all components of the polarization of the baryon B can be determined, as is the case especially for the A, ~+and Z particles. ·

The statistics needed to establish these parameters naturally be­ come very large as the degree of polarization available falls to zero, so that it is very desirable to know in advance under what experimental conditions the B* polarization will be large. Many of these production processes are dominantly peripheral in cha­ racter. This is generally the case for reactions of types (3.10 a, b, c), for example ; the non-peripheral processes of the same general kind (for example, the process K-p - n+y;- which requires a charge exchange of two units) generally have significantly smaller cross-sections, perhaps an order of magnitude smaller, than the corresponding peripheral processes. A purely peripheral process (i.e. whose reaction amplitude corresponds exactly to the exchange of a single meson, treated in first Born approxima­ tion) will not generate any B* polarization ; however some pola­ rization may generally be generated as a result of absorptive corrections to the purely peripheral amplitude or as a result of interference of the peripheral amplitude with some non-peripheral amplitudes, which can still be quite appr~ciable.

Hence, although the Byers-Fenster procedure is completely adequa­ te for a spin-parity analysis, one can see at least two ways in which the use of a polarized target may be of benefit for these spin-parity determinations : a. by making a rapid search for energies at which the B* polari­ zation effects are especially strong. This involves measuring the effect of the polarization of the target proton on the B* produc­ tion angular distribution. Although, for spin J > 1/2, there is not a one-to-one cor~elation between this asymmetry and the B* polarization tensors (as exemplified by the above discussion for the U-particle), the observation of a strong asymmetry guaran­ tees that there must be at least one substantial B* polarization tensor)in the experimental conditions examined. However, Chamber­ lain 5 has already pointed out here the difficulties of polari­ zed target experiments at present for reaction processes with no constraints. In these B* production reactions, there is the addi­ tional problem of the finite width for the B* resonance, together with the effects on the asymmetry of the inclusion of non-resonant background. b. even for a purely peripheral process, polarization for the tar­ get proton can ensure that the B* resonance produced has non-zero polarization. This will be especially useful when the proportion 270 R.H. DALITZ

of highly polarized protons in the target can be made high and when a complete picture of the B* production and decay event can be obtained by means of a large magnetic spark chamber. In this situation, the Byers-Fenster analysis can then be used for the B* spin-parity determination. The spark-chamber study of multi­ particle production reactions, including the production and de­ cay of B* resonances, has already been under discussion for so­ me time, although not yet with polarized targets.

If a polarized target can be used for a B* production experiment where B* polarization is already generated with an unpolarized target, then it is possible to obtain still further tests fo~O) the B* spin and parity. This has been discussed by Gaillard for an instructive but relatively special situation. Consider a reaction of type (3.1 ), where m' is a spinless meson, and let us take together all B* decay events for a given B* production di­ rection, taking no note of the azimuth of the decay (i.e. avera­ ging the B* decay around the normal to the production plane). This reduces the B* density matrix to diagonal form, with res­ pect to the axis n (which means giving up a large fraction of the information ~ontained in these decay distributions).

The remaining elements of the B* density matrix are then :

2 m-1 Pmm = N I am I ( 1 + Pt ( -1 ) 2 ) / 2 ( 3 • 11 ) where Pt denotes the target polarization along n, N is a normali­ zation constant such that LmPmm = 1, and am again denotes the amplitude leading from an initial proton spin state to B* state with spin component m. The structure of this expression (3e11) is determined by the Bohr relation (3.5). For Pt= +1, we have mi = +1/2 for the target proton and the elements Pmm are zero for Im - mif = odd integer when the B* parity E has value +1, or for Im - mil = zero or even integer, when the B* parity € has value -1, as required by this relation. The density matrix-ele­ ments Pmm/N are linearly dependent on the target polarization Pt and therefore int7rvo1ate linearly between the values lam12(1 + (-1)m-1 2)/2 for Pt= +1, just given by the Bohr rela­ tion, and the values lamJ2/2 for Pt = O.

As sho~n explicitly by Byers and Fenster, the B* decay angular distribution is determined by the spin tensors of even rank ; after averaging around n, these spin tensors are completely deter­ mined by the even combinations (p_m_ + o __ ). The nolarization · ill 1 -m -m ~ distributions for the baryon B resulting from B* decay are deter- mined entirely by the spin tensors of odd rank, which are deter­ mined entirely by the odd combinations (Prom - p -m -m). These combinations are given by '

1 m-1 \ N A (3.12a) p mm + p -m,-m = 2 m + Pt (-1 ) 2 Bm \ EXPERIMENTS FOR ELEMENTARY PARTICLE PHYSICS 271

(3.12b)

2 2 2 2 where A == I a I + I a I , B = I a I - I a I • From the P t-depen- dence of the~* decay-~ngularmdistr~bution,-~oth the coefficients Am and E Bm may be deduced from expression (3.12a). With expression (3.12b), this then leads to a prediction of the odd spin tensors, as function of P ; their absolute sign is proportional to € • For a given set of od! spin tensors, the angular distribution of the longitudinal (P.~) and transverse (Etr = P - kP.~) components of the polarization of the baryon B (momentum alon~ the unit vector k in the B* rest frame) are definite (for given J), apart from their relative sign ; the observation of this relative sign constitutes the Byers-Fenster determination of the B* parity£ • With (3.12b), the observation of the absolute sign of the longitudinal polar~za­ tion (and of its dependence on Pt) also constitutes an independent determination of the parity € • Explicit expr~ssions for these re­ lationships have been obtained by Gaillard 20) for arbitrary J, and we shall not give the details here, since the qualitative con­ clusion that these polarized target observations allow independent determinations for the resonance parity is already clear. The ob­ servation of these polarized-target effects would be of interest, although it appears that whenever these effects are prominent, the Byers-Fenster method is necessarily also available and adequate for the spin-parity determination desired.

Most of the Y* resonances can be studied by the resonance formation experiments, with the use of polarized targets. Only the r5 (1405) (spin-parity not yet established directl~ but believed to be (1/2-) from other considerations) and Yf (1385) (spin-parity (3/2+) esta­ blished) are energetically inaccessible in this way, lying below the KN threshold. There may also be a number of exceptional cases (for example, Yf (1660)) where the amplitude for d~rect formation happens to be particularly small (i.e. with small KN partial width) and where spin-parity analysis by the Byers-Fenster procedure in a resonance production experiment is therefore particularly advanta­ geous. On the other hand, the 2* (and n *) resonances are accessi­ ble only through resonance production experiments. The observation and analysis of the ~* resonances especially will be of great im­ portance for our understanding of the B* unitary multiplets. Many Z* resonances are expected to exist, in fact there will be one Z * resonance expected corresponding to each N* resonance established. So far, long bubble-chamber experiments have given rather little information about these 2 * resonances, beyond 2* ( 1 530), 2 * ( 1820) and S* (1930), owing to the extreme smallness of their production cross-sections. It seems quite likely that the complete study of 2 * resonances will require counter experiments, with selection of the 2* mass value by momentum selection for the K+ in the production reaction (3.10d) and with the use of a large magnetic spark chamber system for the analysis of the S* decay products and their polari­ zation properties. If polari~ed targets are available with a high 272 R.H. DALITZ

proportion of highly polarized protons by that time, their use might be rather well justified in such 3* studies, in order to obtain the most efficient indications of the 2.* spin and parity for the rather limited number of events which will be available.

References

1) R.J.N. Phillips, Polarization questions in high energy scatte­ ring, Proc. Conf. on Polarized Targets and Polarized Ion Sour­ ces (Saclay, 1966). 2) J. Bernstein, G. Feinberg and T.D. Lee, Phys. Rev., 1965, .12..91!, 1650. 3) N. Christ and T.D. Lee, Phys. Rev., 1966, _ill, 1310. 4) M. Jacob, Definition and determination of spin amplitudes : so­ me applications of polarized targets in high energy physics, Proc. Conf. on Polarized Targets and Polarized Ion Sources (sa­ clay, 1966). 5) O. Chamberlain, Experiments with polarized targets in high ener­ gy physics, Proc. Conf. on Polarized Targets and Polarized Ion Sources (Saclay, 1966). 6) c. Lovelace, Pion-nucleon phase shifts, Proc. 1966 Intern. Conf. on High Energy Physics (Berkeley, September 1966), (in press). 7) J.A. Schwartz, Associated Production from 1.5 to 2.4 BeV/c, Lawrence Radiation Laboratory Rept. UCRL-11360 (June 29, 1964). 8) G.J. Hoff and R.B. Hoff, Evidence for a T = 1/2, S = 0 resonan­ ce near 1 .5 BeV/c (Enrico Fermi Institute preprint EFINS 66-6, January, 1966). 9) W.G. Holladay, Phys. Rev., 1965, .1.L9., B1348. 10) W.M. Smart, A. Kernan, G.E. Kalmus and R.P. Ely, Phys. Rev. Letters, 1966, 11, 556. 11) R.L. Cool, G. Giacomelli, T.F. Kycia, B.A. Leontic, K.K. Li, A. Lundby and J. Teiger, Phys. Rev. Letters, 1966, 11, 102. 12) W.E. Slater, D.H. Stork and H.K. Ticho, Phys. Rev. Letters, 1961, 1, 378. 13) M.N. Focacci, W. Kienzle, B. Levrat, B.C. Maglic and M. Martin, Phys. Rev. Letters, 1966, 11, 890. 14) V. Alles-Borelli, B. French, A. Frisk, L. Michejda and E. Paul, Antiproton-proton annihilations into five pions at 5.7 GeV/c, CERN Rept. TC 66-25 (October, 1966). 15) R.H. Dalitz, Symmetries and the strong interactions, Proc. 1966 Intern. Conf. on High Energy Physics (Berkeley, 1966), (in press 16) S.M. Bi1enky, Nuovo Cimento, 1958, J...Q., 1049. 17) S.M. Bilenky and R.M. Ryndin, Phys. Letters, 1965, .1..§., 346. 18) A. Bohr, Nucl. Phys., 1959, 1.Q., 486. 19) N. Byers and S. Fenster, Phys. Rev. Letters, 1963, 1J., 52. 20) M.K. Gaillard, Nuovo Cimento, 1964, ,2.g, 1306.