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Intrinsic Parity Intrinsic parity PH YSI CAL REVIEW VOLUME 88, NUM BER | OCTOBER 1, 1952 The Intrinsic Parity of Elementary Particles G. C. WIcK Carnegie Institute of Technology, Pittsburgh, Pennsylvania AND A. S. WIGHTMAN AND E. P. WIGNER Princeton University, Princeton, Pear Jersey (Received June 16, 1952) The limitations to the concept of parity of quantum-mechanical states and, in particular, of intrinsic parity of elementary particles are discussed. These limitations are shown to follow from "superselection rules, "i.e., from restrictions on the nature and scope of possible measurements. The existence of such super- selection rules is proved for the case of spinor fields; it is also conjectured that a superselection rule operates between states of different total charge. THE POSSIBILITY OF INDETERMINATE PARITIES of a certain kind of particles can be described in two it will be useful to keep both in mind. One can LTHOUGH the present quantum-field-theoretic ways; state the transformation law of the quantized field. scheme to describe elementary particles is full of A One will for instance, that a certainL12 kind of spin- • Parity is a mul$plicave quantum number mathematical holes, it possesses certain features, say, = ( 1) less particles12 are the 1quanta2 of a "pseudoscalar" field, mainly based on invariance properties, that are believed P P P − i.e. a.field such that the transformation law for an • Quarks have intrinsic parity +1 to be of far more permanent value. The importance of , y inversion the origin is these features can hardly be overestimated, since they at • The lighter baryons (offer the most reliableqqqguidance) have posi$ve intrinsic parity. What about light that we have in classi- y'(x, y, s) = —p( —x, —y, —s). (~) fying and interpreting the rapidly growing and already transformation law for an$baryons? very complex experimental picture. Alternatively, one can state the function which The purpose of this paper is to point out the possible the state vector or Schrodinger F, gives the quantum-mechanical description of the state of the • What about mesons? (and in certain cases necessary) existence of limitations ' to one of these general concepts, the concept of "in- field, i.e., one can find the unitary operator I such that trinsic parity" of an elementary particle. Even though F'= IF (2) no radical modification of our thinking is thereby achieved, we believe that the injection of a certain describes the state which is the mirror image of the In 1954, Chinowskyamount of caution and Steinberger demonstrated that the pion has negave in this matter may be useful, as it state described by F. may prevent one from calling "theorems" certain The two alternative descriptions of the transforma- parity (is a assumptions,pseudoscalaror from discarding par$cle) as "impossible" forms tion law are, of course, very simply related, for in of the theory; which under a more flexible scheme are quantum mechanics the "observables" or operator perfectly consistent. Another possible advantage of the quantities, such as the field p(x, y, s) above, transform according to the law following considerations may be to bring a certain — amount of clarity in a field in which a great deal of &'=I&I ', ' confusion exists. when the state vector transforms according to (2). The more or less standard position seems to be that the determines completely "in- Thus unitary operator I every elementary particle must have a definite the transformation law for the field quantities, and un- trinsic parity" factor, which can be determined conversely, the transformation law for the latter is least in ambiguously from experiment' (at principle). sufhcient to determine the operator I. Thus, for in- order to understand the limitations of this view- In stance, if one states that y is a pseudoscalar, this point, it will be useful to recall first some simple points means that about the formalism. — The transformation properties (in our case, the parity) Iy(x, y, z)I '= —s(—x, —y, —s), (4) ' The origin of the present article is an address which was pre- and from this equation one may infer that I is of the sented by the last author at the International Conference on form: Nuclear Physics and the Physics of Elementary Particles in Sep- l)&0+&2+N4+" tember 1951 in Chicago and which was based on a review article IP ~( P (5) which the last two authors are preparing together with V. Barg- mann. In view of several inquiries concerning the above-mentioned where S~ is the number of particles (of the kind de- feel publication of some of address, the authors that a preliminary scribed by &p) with angular momentum / while a& is an the main points in the present paper is justified, even though they which remains must refer the reader to the review article to appear later for a arbitrary factor of modulus unity, more exhaustive and consistent presentation of the whole subject. ' This is no doubt an oversimplified version even of "current" ' In this particular kind of discussion it seems to be a good idea belief, especially in the case of spin ~ particles. This case, however, to avoid the chameleon-like term wave function. We shall adhere will be discussed later in greater detail. strictly to state-vector in one case and field function in the other. ioi Charge conjugation C - interchanges par$cles & an$par$cles It reverses all the internal quantum numbers such as charge, lepton number, baryon number, and strangeness. It does not affect mass, energy, momentum or spin. What are the eigenstates of charge conjugaon? C-parity or charge parity ⇒ photon, neutral pion… What about positronium, neutrino? • Maxwell equaons are invariant under C • C reverses the electric field • Photon has charge parity ηC=-1 • Is the following decay possible? h@p://pdg.lbl.gov/2014/tables/contents_tables.html Other Symmetries CP - violated in K0 decay (1964 Cronin & Fitch experiment) VOLUME 1$, NUMBER 4 P H Y SI CAL RE V I E%' LETTERS 27 JULY 1964 EVIDENCE FOR THE 2rr DECAY OF THE Km MESON*1 J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay~ Princeton University, Princeton, New Jersey (Received 10 July 1964) This Letter reports the results of experimental The analysis program computed the vector mo- studies designed to search for the 2m decay of the mentum of each charged particle observed in the K, meson. Several previous experiments have decay and the invariant mass, m*, assuming served"~ to set an upper limit of 1/300 for the each charged particle had the mass of the fraction of K2 's which decay into two charged pi- charged pion. In this detector the Ke3 decay ons. The present experiment, using spark cham- leads to a distribution in m* ranging from 280 ber techniques,CPTproposed - follows from relavis$c invariance to extend this limit. MeV to -536 MeV; the K&3, from 280 to -516; and In this measurement, K,' mesons were pro- the K&3, from 280 to 363 MeV. We emphasize duced at the Brookhaven AGS in an internal Be that m* equal to the E' mass is not a preferred target bombarded by 30-BeV protons. A neutral result when the three-body decays are analyzed beam was defined at 30 degrees relative to the in this way. In addition, the vector sum of the The CPT theorem appeared for the first $me in the work of Julian Schwinger in 1951 to 1 1 circulating protons by a 1&-in. x 12-in. x 48-in. two momenta and the angle, |9, between it and the prove the connec$on between spin and stas$cs. In 1954, collimator at an average distance of 14.5 ft. from direction of the K,' beam Lüderswere determined. and Pauli derived This the internal target. This collimator was followed angle should be zero for two-body decay and is, more explicit proofs. At about the same $me, and independently, this theorem was also by a sweeping magnet of 512 kG-in. at -20 ft. in general, different from zero for three-body and a 6-in. x 6-in. x 48-in. collimator at 55 ft. A decays. proved by John Stewart Bell. These proofs are based on the principle of Lorentz 1~-in. thickness of Pb was placed in front of the An important calibration of the apparatus and invariance and the principle of locality in the interac$on of quantum fields. first collimator to attenuate the gamma rays in data reduction system was afforded by observing the beam. the decays of K,' mesons produced by coherent The experimental layout is shown in relation to regeneration in 43 gm/cm' of tungsten. Since the the beam in Fig. 1. The detector for the decay K,' mesons produced by coherent regeneration Since products consisted is violated, of two spectrometers each has to be violated as well! have the same momentum and direction as the composed ofCPtwo spark chambers for track Tdelin- K,' beam, the K,' decay simulates the direct de- eation separated by a magnetic field of 178 kG-in. cay of the K,' into two pions. The regenerator The axis of each spectrometer was in the hori- was successively placed at intervals of 11 in. zontal plane and each subtended an average solid along the region of the beam sensed by the detec- angle of 0.7&& 10 steradians. The squark cham- tor to approximate the spatial distribution of the bers were triggered on a coincidence between K,"s. The K,' vector momenta peaked about the water Cherenkov and scintillation counters posi- forward direction with a standard deviation of tioned immediately' behind the spectrometers.
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