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Lawrence Berkeley National Laboratory Recent Work Lawrence Berkeley National Laboratory Recent Work Title SIGN OF THE K^0 - Kq| MASS DIFFERENCE Permalink https://escholarship.org/uc/item/01d5v3dm Author Meisner, Gerald Warren. Publication Date 1966-07-22 eScholarship.org Powered by the California Digital Library University of California UCRL-17007 University of California Ernest 0. Lawrence Radiation Laboratory SIGN OF THE K K O MASS DIFFERENCE 1 ° - 2 TWO-WEEK LOAN COPY This is a Ubrar~ Circulating Copy which ma~ be borrowed for two weeks. For a personal retention copy. call Tech. Info. Dioision, Ext. 5545 Berkeley, California DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California. Special Thesis "•iii! UCRL-17007 ·'""· J~ UNIVERSITY OF CALIFORNIA Lawrence Radiation Laboratory Berkeley, California AEC Contract No. W -7405 -eng -48 SIGN.OF THE K O - K O MASS DIFFERENCE 1 2 Gerald Warren 1v1eisner (Ph. D. Thesis) July 22, 1966 I' .J.... : ' ' { ______ &______ -~·-- --- ... -iii- \r' SIGN OF THE K O - K O MASS DIFFERENCE • 1 2 ',· · Contents Abstract v I. Introduction 1. II. Theory. 2 III. Experimental Procedure A. The Beam 9 B. Scanning . 9 0 1. AK Production 1.1 0 0 . 2. ::E K Production .l .. 11. C. Data Processing 11. IV. Analysis and Results A. Scattering Amplitudes 18 1.. General Remarks 18 2. Restrictions on KN Amplitudes 20 3. Comparison of Observed and Predicted Counts 24 B. Time Distribution, Likelihood Function, and Monte Carlo Results 33 v. Discussion 44 Acknowledgments 45 Footnotes and References 46 ... -v- ( SIGN OF THE K o'- K MASS DIFFERENCE 1 2° Gerald Warren Meisner Lawrence Radiation Laboratory University of California Berkeley, California July 22, 1966 ABSTRACT We have performed an experiment to measure the sign of m - m by following the time development of K t -p elastic scat- . 1 2 neu ra1 ters. We find K to be heavier than K Our statistical confidence 2 ° 1 °. level depends on the unresolved Fermi-Yang~typ.e. {F-Y) ambiguity that exists at present in the KN {strangeness S = +1) phase shifts in isotopic-spin state I= 0. If the F solution {large positive p / phase 3 2 shift) is correct, we obtain Monte Carlo betting odds of 45 to 1 for -1 . m > m , assuming I m ,... m 1 0.5 7 T . If 1nstead the Y solution 2 1 1 2 = 1 {large positive p ; phase shift) is correct, our betting odds for 1 2 m >m are 5 to 1. We have not resolved the F-Y ambiguity. 2 1 !· 11. I~ -i- I. INTRODUCTION The magnitude of the K 1 °- K 2 ° -·7ass difference,j m 1. -· m 2.1, hasbeenestablishedtobeabout0.6·r (Ref. 1)(~3Xt0 eV/c2. or 1 -11 -38 . -10 ::::: 10 me or :::::10 grams!), with the assumptlon that 7' = 0.88X10 1 sec. Few experiments ha-ve been de signed to measure the sign of the difference, although several methods have been proposed. Kobzarov and Okun' suggested measu1·ing the K amplitude re­ 1° generated by a K beam passing througb. two regenerators of different 2° ·materials separated by a fixed gap, and then reversing the relative 2 position of the two slabs and repeating the measurements ; J ·:wanovich 3 et al. tried this method and found evidence that K °is heavier than 0 . 2 K . A different method, utilizing interference effects .between the 1 final state of the original and regenerated K °, was proposed by 4 1 Piccioni et al -, who recently used the 1nethod and presented evidence that K is heavier thanK A third method,_ and the one "\VC used, 2 ° 1°. was advanced by Camerini, Fry, and Gaidos. 5 In this method, one starts with neutral K's o£ known strangeness and detects the time de­ 6 velopment of elastic scatters followed by K decays. Since we per­ 1 ° formed our experiment in a hydrogen bubble chamber, we must rely on 'l knowledge of elastic scattering amplitudes in the KN and KN channels. 7 Unfortunately, there is a Fermi-Yang-type ambiguity in the KN phase shifts in isotopic -spin state ·I = 0 at the momentum. of the kaons (0< PK< 600 MeV/c) used in this experiment. We discuss consequences of this ambiguity in Sec. IV. In Sec. II we present son1e theoretical consequences of the 0-~ . 8 K -K mixing scheme postulated by Gell-Mann and Pais ; in Sec. III we discuss the beam set-up, scanning procedures, and data processing; in Sec. IV we present results from the analysis of our data; and in ·Sec. V we discuss our conclusions . .., -2- II. THEORY 8 0 -0 In 1955 Gell-Mann and Pais postulated that the K - K system . ,. was not to be thought of as two one -component systems; rather, the 0 -0 . K and K should be considered as two components of a single system. Thus, one should write the probability amplitude tjJK of the neutral K 0 system as a superposition of amplitudes of K and ~. eigenstates of the strong-interaction Hamiltonian: 0 0 llJlK) = aiK ) + biK ) 2 2 0 0 where I a 1 and I b 1 are the probabilities of observing a K and a K 0 0 respectively. Sinc.e the K and K are each other's antiparticles, they must have identical masses and lifetimes. 9 However, experimenters 10 have measured two distinct lifetimes for the neutral K system and a 1 distinct mass difference between the two decay eigenstates. Labeling the two eigenstates K and K adopting a conventional choice of 1 ° 2 °, 5 phase, and neglecting CP non-conservation, we can write these decay 0 -0 eigenstates as ·linear combinations of the degenerate K and K : ) (1) Ass·uming that the time development of the decay eigenstates is gov- 11 erned by the factor exp(-imt-A..t/2) in the particles rest frame, where m is the mass of the particle and A. is the decay rate, we can write the probability amplitude ljl~ for the neutral K system at time t, which at t = 0 was pure K , as .JllJlK= IK exp(-im t- A.. t/2) +IK exp(-im trA.. t/2). (2) 1 °) 1 1 2°) 2 2 0 --0 Using Eq. (2} and projecting out the K and K components, we have 12 their time -dependent amplitudes (3a) (3b) The absolute squares of Eq. (3) give the unnormalized counting rates of -3- .... 0 K 0 and K interactions; these rates are a function of the magnitude of the mass difference. To get information on the sign of the mass differ­ ence, one can observe neutral K elastic scatters followed by a K orK 1 2 0 0 decay. If A and A are amplitudes for elastic K -p and K -p scatter-· ing, we can write the amplitude of the neutral K system immediately 12 following an elastic scatter at time t as ( 2)3/2 ~( t) =[(A.+A) e -im1 t->..1 t/2 + (A-A) e -im2 t:.:}..2 t/l] K 10 { 4) + [(A-A) e -im1 t-\1 t/2 + (A+A.) e -im2 t-\2 t/2] K2 0" If T' is the potential proper time of the K from the position of the 1 ° elastic scatter to the edge of the fiducial volume, the probability of their being an elastic scatter at time t followed by a K decay v,;ithin 1° the fiducial volume is proportional to [1 - exp( -\ T')]I , where 1 1 (5) This simple but daring application of the principle of super­ position, a cornerstone of quanturn mechanics, leads to unusual results, some of which are contained in Eqs. (3) and (5). For example, the absolute square of Eq. (3b) tells us that even though at t =0 the prob­ 0 ability of observing a K interaction is zero, at some later time the probability is finite and varies sinusoidally with a period inversely proportional to I m -m !. 1 2 Since there appear to be no .6.S( strangeness) = 2 transitions al ~ 0 0 lowed, this increase and decrease of the K and K amplitudes with time can take place only because there are intermediate states comrrwn 0 0 to b()th particles, the dominant one being 2-rr. That is, K and K. both appear to decay into two pions with an equal rate (more precisely, 0 -0 the z,. decay rates from K and K production are consistent with one another); therefore, since there must be son'le amplitude for the -~~;~;..;: ·-'!' ... L :.~-l !'"!'!-~"<: -4- '"' 0 0 -0 virtual process 2'11"- K , there exists the virtual process K -2'11"-K , which can account for the transfer of probability between the two eigenstate s. The phenomenon of energy exchange in a coupled system is not unusual in physics.
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