a1 + a2 ⇔ b1 + b2normalandinversekinematics!

Time Reversal symmetry and nuclear reactions

Intrinsic parityPH YSI CAL REVIEW VOLUME 88, NUM BER | OCTOBER 1, 1952

The Intrinsic Parity of Elementary ParticlesG. C. WIcK

Carnegie Institute of Technology, Pittsburgh, Pennsylvania

AND

A. S. WIGHTMAN AND E. P. WIGNERPrinceton University, Princeton, Pear Jersey

(Received June 16, 1952)

The limitations to the concept of parity of quantum-mechanical states and, in particular, of intrinsicparity of elementary particles are discussed. These limitations are shown to follow from "superselectionrules, "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 operatesbetween states of different total charge.

THE POSSIBILITY OF INDETERMINATE PARITIES

A LTHOUGH the present quantum-field-theoreticscheme to describe elementary particles is full of

mathematical holes, it possesses certain features,mainly based on invariance properties, that are believedto be of far more permanent value. The importance ofthese features can hardly be overestimated, since theyoffer the most reliable guidance that we have in classi-fying and interpreting the rapidly growing and alreadyvery complex experimental picture.The purpose of this paper is to point out the possible

(and in certain cases necessary) existence of limitationsto one of these general concepts, the concept of "in-trinsic parity" of an elementary particle. Even thoughno radical modification of our thinking is therebyachieved, we believe that the injection of a certainamount of caution in this matter may be useful, as itmay prevent one from calling "theorems" certainassumptions, or from discarding as "impossible" formsof the theory; which under a more flexible scheme areperfectly consistent. Another possible advantage of thefollowing considerations may be to bring a certainamount of clarity in a field in which a great deal ofconfusion exists. 'The more or less standard position seems to be that

every elementary particle must have a definite "in-trinsic parity" factor, which can be determined un-ambiguously from experiment' (at least in principle).In order to understand the limitations of this view-

point, it will be useful to recall first some simple pointsabout the formalism.The transformation properties (in our case, the parity)' The origin of the present article is an address which was pre-

sented by the last author at the International Conference onNuclear Physics and the Physics of Elementary Particles in Sep-tember 1951 in Chicago and which was based on a review articlewhich the last two authors are preparing together with V. Barg-mann. In view of several inquiries concerning the above-mentionedaddress, the authors feel that a preliminary publication of some ofthe main points in the present paper is justified, even though theymust refer the reader to the review article to appear later for amore exhaustive and consistent presentation of the whole subject.' This is no doubt an oversimplified version even of "current"belief, especially in the case of spin ~ particles. This case, however,will be discussed later in greater detail.

of a certain kind of particles can be described in twoways; it will be useful to keep both in mind. One canstate the transformation law of the quantized field.One will say, for instance, that a certain kind of spin-less particles are the quanta of a "pseudoscalar" field,i.e., a.field y such that the transformation law for aninversion at the origin is

y'(x, y, s) =—p(—x, —y, —s). (~)

Alternatively, one can state the transformation law forthe state vector or Schrodinger function F, which givesthe quantum-mechanical description of the state of thefield, ' i.e., one can find the unitary operator I such that

F'= IF (2)

describes the state which is the mirror image of thestate described by F.The two alternative descriptions of the transforma-

tion law are, of course, very simply related, for inquantum mechanics the "observables" or operatorquantities, such as the field p(x, y, s) above, transformaccording to the law

&'=I&I—',when the state vector transforms according to (2).Thus the unitary operator I determines completely

the transformation law for the field quantities, andconversely, the transformation law for the latter issufhcient to determine the operator I. Thus, for in-stance, if one states that y is a pseudoscalar, thismeans that

Iy(x, y, z)I '=—s(—x, —y, ——s), (4)

and from this equation one may infer that I is of theform:

IP ~( l)&0+&2+N4+" P (5)where S~ is the number of particles (of the kind de-scribed by &p) with angular momentum / while a& is anarbitrary factor of modulus unity, which remains

' In this particular kind of discussion it seems to be a good ideato avoid the chameleon-like term wave function. We shall adherestrictly to state-vector in one case and field function in the other.

ioi

• Parityisamultiplicativequantumnumber• Quarkshaveintrinsicparity+1• Thelighterbaryons(qqq)havepositiveintrinsicparity.Whataboutlight

antibaryons?• Whataboutmesons?

In1954,Chinowsky andSteinbergerdemonstratedthatthepionhasnegativeparity(isapseudoscalar particle)

P12 = P1P2(�1)L12

Charge conjugationC - interchangesparticles&antiparticles

Itreversesalltheinternalquantumnumberssuchascharge,leptonnumber,baryonnumber,andstrangeness.Itdoesnotaffectmass,energy,momentumorspin.

Whataretheeigenstates ofchargeconjugation?

• MaxwellequationsareinvariantunderC• C reversestheelectricfield• PhotonhaschargeparityhC=-1

• Isthefollowingdecaypossible?

C-parityorchargeparity

⇒ photon,neutralpion…Whataboutpositronium,neutrino?

http://pdg.lbl.gov/2016/tables/contents_tables.html

Other Symmetries

CP - violatedinK0 decay(1964Cronin&Fitchexperiment)

CPT - followsfromrelativisticinvariance

SinceCP isviolated,T hastobeviolatedaswell!

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)

PLAN VIEW

I root

VFEEEPEEEEPz

57 Ft. to =internal target

Cerenkov

FIG. 1. Plan view of the detector arrangement.

This Letter reports the results of experimentalstudies designed to search for the 2m decay of theK, meson. Several previous experiments haveserved"~ to set an upper limit of 1/300 for thefraction of K2 's which decay into two charged pi-ons. The present experiment, using spark cham-ber techniques, proposed to extend this limit.In this measurement, K,' mesons were pro-

duced at the Brookhaven AGS in an internal Betarget bombarded by 30-BeV protons. A neutralbeam was defined at 30 degrees relative to the

1 1circulating protons by a 1&-in. x 12-in. x 48-in.collimator at an average distance of 14.5 ft. fromthe internal target. This collimator was followedby a sweeping magnet of 512 kG-in. at -20 ft. .and a 6-in. x 6-in. x 48-in. collimator at 55 ft. A1~-in. thickness of Pb was placed in front of thefirst collimator to attenuate the gamma rays inthe beam.The experimental layout is shown in relation to

the beam in Fig. 1. The detector for the decayproducts consisted of two spectrometers eachcomposed of two spark chambers for track delin-eation separated by a magnetic field of 178 kG-in.The axis of each spectrometer was in the hori-zontal plane and each subtended an average solidangle of 0.7&& 10 steradians. The squark cham-bers were triggered on a coincidence betweenwater Cherenkov and scintillation counters posi-tioned immediately behind the spectrometers.When coherent K,' regeneration in solid materialswas being studied, an anticoincidence counter wasplaced immediately behind the regenerator. Tominimize interactions K2' decays were observedfrom a volume of He gas at nearly STP.

Water

The analysis program computed the vector mo-mentum of each charged particle observed in thedecay and the invariant mass, m*, assumingeach charged particle had the mass of thecharged pion. In this detector the Ke3 decayleads to a distribution in m* ranging from 280MeV to -536 MeV; the K&3, from 280 to -516; andthe K&3, from 280 to 363 MeV. We emphasizethat m* equal to the E' mass is not a preferredresult when the three-body decays are analyzedin this way. In addition, the vector sum of thetwo momenta and the angle, |9, between it and thedirection of the K,' beam were determined. Thisangle should be zero for two-body decay and is,in general, different from zero for three-bodydecays.An important calibration of the apparatus and

data reduction system was afforded by observingthe decays of K,' mesons produced by coherentregeneration in 43 gm/cm' of tungsten. Since theK,' mesons produced by coherent regenerationhave the same momentum and direction as theK,' beam, the K,' decay simulates the direct de-cay of the K,' into two pions. The regeneratorwas successively placed at intervals of 11 in.along the region of the beam sensed by the detec-tor to approximate the spatial distribution of theK,"s. The K,' vector momenta peaked about theforward direction with a standard deviation of3.4+0.3 milliradians. The mass distribution ofthese events was fitted to a Gaussian with an av-erage mass 498.1+0.4 MeV and standard devia-tion of 3.6+ 0.2 MeV. The mean momentum ofthe K,o decays was found to be 1100 MeV/c. Atthis momentum the beam region sensed by thedetector was 300 K,' decay lengths from the tar-get.For the K,' decays in He gas, the experimental

distribution in m is shown in Fig. 2(a). It iscompared in the figure with the results of aMonte Carlo calculation which takes into accountthe nature of the interaction and the form factorsinvolved in the decay, coupled with the detectionefficiency of the apparatus. The computed curveshown in Fig. 2(a) is for a vector interaction,form-factor ratio f /f+= 0.5, and relative abun-dance 0.47, 0.37, and 0.16 for the Ke3, K&3, andEg3 respectively. The scalar interaction hasbeen computed as well as the vector interaction

138

TheCPTtheoremappearedforthefirsttimeintheworkofJulianSchwingerin1951toprovetheconnectionbetweenspinandstatistics.In1954,Lüders andPauliderivedmoreexplicitproofs.Ataboutthesametime,andindependently,thistheoremwasalsoprovedbyJohnStewartBell.TheseproofsarebasedontheprincipleofLorentzinvarianceandtheprincipleoflocalityintheinteractionofquantumfields.

HW3:UsinginformationfromPDG.lbl.gov andnndc.bnl.gov determinewhetherthefollowingdecays/reactionsareallowedbyfundamentalsymmetries:

a. p0⟶µ- + e+

b. e +e⟶gc. Gammadecayofexcitedstateof40Caat3353keVd. Decayofmeson h⟶g + p0e. Decayofmeson h⟶p0+p0+p0