The Mean Lifetime of V-Particles Citation Alford, William Lumpkin (1953) The Mean Lifetime of V-Particles. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7EDY-K211. https://resolver.caltech.edu/CaltechETD:etd-04212003-085844 Abstract A maximum-likelihood procedure for determining mean lifetimes of V-particles from cloud chamber data is discussed and applied to samples taken from a group of 134 neutral V-particle decays. For 74 events which were consistent with a decay into a proton and a negative pi meson, a lifetime of (2.5 ± 0.7) x 10 -10 sec is obtained. Dividing the data into "low-Q" and "high-Q" groups on the basis of the calculated energy release in the decay, a value of Τ L = (2.9 ± 0.8) x 10 -10 sec is found for those cases with 0 < Q ≤ 50 Mev and a value of Τ H = (1.6 ± 0.5) x 10 -10 sec is found for those cases with 50 < Q < 150 Mev. While no significant difference exists between these two values, the difference is greater than for other plausible division schemes which are considered. A qualitative discussion of lifetimes is given for the case of 23 charged V-particle decays. For the charged V-particles these data suggest either a lifetime less than that of the neutral V-particles, provided the sample is homogeneous, or a more likely an apparent average lifetime less than that of the neutral V-particles, if the sample is a mixture of two or more types of particles. The possibility of kappa mesons making up a part of these decays is considered and data indicating lifetimes approximately equal to or longer than 10 -9 sec for both the kappa and tau mesons are briefly discussed. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics and Mathematics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Minor Option: Mathematics Thesis Availability: Public (worldwide access) Research Advisor(s): Anderson, Carl D. (advisor) Leighton, Robert B. (advisor) Thesis Committee: Unknown, Unknown Defense Date: 1 January 1953 Record Number: CaltechETD:etd-04212003-085844 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-04212003-085844 DOI: 10.7907/7EDY-K211 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 1429 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 21 Apr 2003 Last Modified: 17 May 2023 18:47 Thesis Files Preview PDF (Alford_wl_1953.pdf) - Final Version See Usage Policy. 3MB Repository Staff Only: item control page

THE MEAN LIFETIME OF V-PARTICLES Thesis by William Lumpkin Alford In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1953 ACKNOWLEVGMENT'S For taeir surervision of this tnesis and for their active narticiration in tne related expverinent, I would like to express my appreciation to rrofessor Carl Anderson, wio offered many nelpful suggestions in eacn pnase of tue work, and to lrofessor Nobert Leignton, wno suggested this topic and wno snared nis many ideas on tne procedure for making Lifetime determinations, would also iilke to express my aporeciation to mr. ht ean sanlass and mr. rank Shelton Yor their rriendly cooperation in tne experimental work and to Dr. Carl York and scrofessor Sugene Cowan for tneir helpful criticism of tnis thesis. ARSTHAGT A maximum-Likelinood vrocedure for determining mean life- tines of V-varticles from cloud cnamber data is discussed and applied to samples taken from a group of 13), neutral V- particie decays. Hor (Ly avents whieh were consistent with a decay into a nroton and a negative pi meson, a lifetime of oy wo . a wes . (2.5 * 0.7) x 10 sec is obtained. Dividing tne data into ‘ow-C" and "high-¢" croups on the basis of tne calculated energy release in tne decay, a value of TF (2.9% u.8) x 10714 sec is found tor tnose cases with 0 <G@ $50 nev and “10 see is found for tnose a value of UT, = (1.0 0.5) x 10 cases witn 50 <6 < 150 mev. wnile no significant difference exists between tnese two values, the difference is sreater tean for otner plausible division schemes which are considered. £ A qualitative discussion of lifetimes is given for tne GO case of 23 cnarged V-particle decays. for the cnarged V- particlss cnese data suggest elther a lifeline Less tuan tnat of tne neubreal V-narticles, provided tne samrle is nomosene- ous, or more likely an apparent average lifetime less than tnat of the neutral V-particles, if tne sample is a mixture of two or more tyves of varticles. Tre possibility of kappa mesons making un a vart of tnese decays is considered and data indicating Lifetimes approximately equai to or longer tnan 10°” sec for botn tne Keppa and tau mesons are briefly discussede PART I. It. Il. IV. Ve VI. VII. VIII. TABLE OF CONTENTS Introduction The Apparatus and Fiducial Surfaces The Data Discussion of the Data Method of Calculating the Mean Lifetime A. The Maximum-Likelihood Procedure B. Errors The Mean Lifetime of Neutral V-Particles The Mean Lifetime of Charged V-Particles Conclusion References PAGE 13 20 20 22 26 33 38 ho i. INTRODUCTION Since the first report of tne discovery of neutral and charged V-particles by Rochester and Butler (4) in 19147 and the subsequent confirmation of the discovery by Seriff et ai. (2) in 1950, a number of cloud chamber experiments (3-8) have boon porformed to make furtnor studics of those parti- cles. Although the findings have been more complex than one might have expected and the need for a great deal more work hes hecome apparent, certain definite conclusions have been reached and other possible results have been suggested. (758) All of these experiments point to the existence of two or more different types of neutral V-particles and one or more types of charged V-particles. Tnis thesis will be concerned principally with that type of neutral V-particle which decays with an energy release, @, in a manner consistent with the scheme Vo P+ T+ Q There is no assurance tnat additional neutral particles as light as the pi meson are not among the decay products. Nevertheless, for the purpose of the lifetime determinations to which this thesis is devoted, tnis decay scheme will be assumed to hold for tnoso cases in which tne visible decay products are consistent with a proton and a negative pl meson. This procedure is justified by tne fact that the numepicai results are not greatly changed if other decay scnemes, consistent with the chserved data, are assumed. Tnose events whicen are discussed as enarged Veparticle decays are cases in whicn a charged particle decays into a single cnarged particle plus one or more neutral particies. Only those events which can be shown to be inconsistent with known processes such as the decay of a pi meson into a mu meson are included in the group of cnarged V's, The average lifetime of Veparticles is one cnaracteristic quantity for wnich estimates nave been made from tne above experiments. '2s9) Altnougn tne cloud cnamber can be used for lifetime determinations in principle, tne cifficulty of ob- taining a large unbiased sample of V-particie decays of a single type nas pronibited accurate results. TYnis difficulty is still apparent in tne vresent work, which treats the decay “ a) of 134 neutral V-particles and 23 cnarged V-particles, How- ever, tne information now available on tne decay of neutral V-particles is more extensive than in the previously revorted experiments. Tnus an attempt is made here to determine the best value of tne mean lifetime ootainabie from this still ratner meager set of data. Tne method used is a maximum-likelinood procedure, which essentially involves finding that vaiue of the mean lifetime wh * <A ratbner complete analysis of tnese same events nas been made by other workers whose findings are given in refer- ences 8, 10 and ll. ‘Tnese reports describe the experiment al tecnnioues and discuss tne exmerimental errors in more detail than will be done here. waen information such as tne masa of the neutral V-particle, decay schemes, etc. is needed for tne purpose of a lifetime determination, the results given by these workers will be used. oe 3 ‘nee woich maximizes the probability of obtaining the observed “ ~ distribution of decay points in tne chamber.” This procedure is applied to tne case of the neutral V-particle decays. Since it is apparent from the data that no significant treat- ment of the charged decays can be made, only a qualitative discussion of the mean lifetime is given in this case. * Tne maximum-likelihood procedure was used at tne suggestion of vrofessor Leverett Davis, Jr. iI. TH ArPANATUS AND FIDUCIAL SURFACES The apparavus used in this exreriment (8,10) was a counter- controlled double cloud chamber operated in a masnetic field of approximately 5,000 gauss. The experimental arrangement is shown in figure 1. The lead blocks acove and between the two chambers served to filter out tne soft radiation and pro- vided a region in which the production of V-particles could taxe place near the tops of the chambers. The trays of counters above and scelow tne double chamber were used to select penetrating showers. The chambers, lead and counters were inclosecd in a thermostatically controlled coprer box placed between te pole pieces of an electromagnet. Upon each expansion, stereoscopic photographs were taken of the chambers, which were illuminated by the discuarge of a con- denser cank through a gas-filled flash tube. Additional information on the apparatus and its operstion is given in reference 10. Also shown in figure 1 are fiducial surfaces which are used in the measurement of certain geometrical quantities needed for the lifetime determination. These surfaces were drawn to include only well-illuminated reszions of the cloud chamber within which all V-particle decays would be almost equally likely to be detected. They were located at dis- vances ranging from 3 cm to 5 cm from each of the inner walls of the chambers. One misht wish to make this seperation of the fiducial surfaces from the inner walls much greater so Ny TIS ID EI TITS TIO LEAD v IIT IT TT LLL Va Wh C COUNTERS Cy “ LL a. 4 ) ne memes amen rumen ents te oe my ea CHAMBER ett I ey ) LYLE - a a | — ome —_— oo om ~~ oo ee eae ny CUAMBER enellbeedi COUNTERS VIEN FRONT t Lane e) 1¢ a tT Fieare 1. ‘The ee ee ane counters an 73 : i 4 RS FRO Ment be bes oy ae n S AS a Ne 2 US 2 Dhue 2 5 10) 35 CRN TIMETERS arranvement of the iead, = 4 ny ate . ro i "t oy mes RR ¢ i cloud cvtambers, The dashed boi fiducial surfaces. ~6- that any track originating within these surfaces would have sufficient visible lensth within the chamber to allow all necessary measuresents to be made; nowever, the already critically small size of the cnambers srohibits such a restric- tion on the usable volume. Although tracks and V-narticle decays were often clearly visible in much of the region between the fiducial surfaces and the walls of the chambers, the terms "visible" or "illuminated" region will be used to efer to the volume within the fiducial surfaces. -~ 7 Tift. THE DATA The experimental data which were used in the determina- tion of the lifetime of the neutral V-particle are given in table I. The quantities tabuleted sre described briefly below with a more detailed description immediately following the table. When a knowledge cf the decay scheme of the neutral V-particle was required in order to determine some . of the quantities given, a two-body decay into a proton plus a negative pi meson was assumed. x © is the distance between the voint of entrance of the V-particle into the visible region of the chamber and the point of decaye is the distance between the point of entrance of the V-particle into the visible region and the point at which it would have left this region if it had not decayed. The term "gate length" or "potential path length" will be used to refer to this quantity. is the momentum of the V-particle. is the time taken to traverse the distance x. This time is given in the rest system of the V-particle. is the time, measured in the rest system of the V-particle, taken to traverse the distance d. is the angle between the paths of the two charged decay products of the neutral V-particle. is the calculated energy release as given in refer- ence 10. ~§- No. serves to identify the photograch on which the decay was recorded, TABLE I O72, 65 152.0 712 8.1 14.1 h.2 Tolt 9200 == 22,0 (2200) 10.3 15.6 1.8 2.7 $285 -- 21.5 (2306) 6.2 15.0 ) 2h S89 bh S5h.5 OT U.0 L5.h. U.d 12.3 10876 28 72.0 WSs 1.2 13.7 1.0 11.2 11326 76 2h.c 1600 0.8 99.1 0.2 21 113723 37 132.0 310 14 17.8 1.7 21.6 12717 63 71.0 850 O.1l 16.1 0 Tel 13231 33 41.6 868 «896. 13.8 2.8 5.9 1h228 ahS $85.0 850 2.7 lil 1.2 5.0 w3b5 86 28.0 706 3.8 = 20.3 2.0 10.9 11539 33 5.0 508 1.8 19.2 1.3 wed 15011 35 ho9.o 1080 $9.7 ik.o 3.3 4.8 15181 20 15.0 1250 6.0 13.2 1.8 3.9 15543 $1 28.0 922 2.1 10.5 0.9 1.3 10631 -- ho.ag (90¢) 13.5 1.8 5.6 6.1 17078 -- 15.0 (3206) 11.2 ik. 1.3 1.7 17407 BL BYU 938 Vel LO. 0 3 175€2 26 26.0 878 9.5 12.2 hee 5.2 17596 80 2.5 1390 O.1 17.0 @) h.6 * The values of F shown in parenthesis were estimated from a Knowledgeof Gas described in tne next section. - 10 - TABLE I (Continued) aya No. & 9 p* x d t T (luev) (Deg) (iiev/e) (em) (em) (10719 gece) (10719 sec) 17685 lb 22,0 900 10.5 l1h.2 ody 5.9 16075 ~- ih.o (1000) Oe7T 1h.0 Oe3 5.2 19063R 3k, (| s 3. 0 woo be? ibe. 1.2 347 19063C 42 -151.0 3u8 9.0 23.0 9.7 aed 19063L 51 51.0 O72 5.3 0622.2 2.0 8.5 19286 18 16.0 1l2ho 2.7 13.3 0.8 20 19267 79 39.0 1570 1.1 16.4 0.3 3.9 19955 72 19.0 830 0.2 16.3 0.1 7.3 19960 -- 3h.0 (1400) 2.h 10.6 0.6 2.8 20019 -- 31.0 (1500) 5.3 1.8 1.3 3.7 21301 -- 47.0 (900) 1.9 lS 0.8 1.9 2128 -- 15.0 (2800) 6.8 16. 0.9 2.2 21910 10 19.0 1590 6.3 «1h.5 1.5 3. 22578 25 2.0 608 1.6 8.1 1.0 5.0 22895 57 32.0 880 3.6 11.0 1.5 Le? 23159 2 37.2 880 5.2 16.2 2.2 6.9 23865 33 32.9 1186 4.0 13.3 1.3 2 39,27 -- 35.0 (1300) O.1 14.2 0G hed 2391428 37 65.0 291 3.5 9.8 ed 12.6 21026 3h 5.0 802 0.7 Le 0.3 2.1 2hihi 35 72.0 hil 1.8 34h 1.6 361 2u358 73 Bleit 1300 3.1 11.2 0.9 3.2 TASLE I {(Gontinued) No. Q 8 ~ x a c Pp t Tt (Mev) (Deg) (sev/e) (om) {em} (1071° sec) (10719 sec) 24390 22 28.0 1072 5.4 13.0 1.9 1.5 e550, 32 1.8 816 5.1 14.6 2.3 5.7 25587 31 he. 853 1.9 8.5 0.8 367 25686 10 52.7 Loe S.l 13.4 4.7 12.5 20585 32 37.1 Leko 5.3 18.5 1.9 6.7 26655 75 65.0 1074) 411.2 15.7 3.9 5.5 267609 50 2.0 62h, 3.6 15.3 2.2 9.2 26867 32 S52 188 3670 eS 2.8 1.2 20912 29 10.4 5580 u.5 1.3 0.3 1.0 27529 60 62.0 693 O.1l 14.0 0 765 27875 97 78.5 1030 2.7 13.2 1.0 1.8 281c7 79 11.0 770 0.4 13.3 0.2 64h 28225 -= 16.0 (3000) 5.3 10.1 0.8 1.3 28569 37 27.8 1970 3.2 18.1 0.6 3elt 21s -- = 32.4 (970) 0.81.6 0.3 5.6 29637 97 2.8 750 bel 15.9 2.0 79 30045 59 30.3 1160 2.8 12.7 0.9 hel 30047 33 42.8 790 Le 15.3 0.7 722 30095 Lo ib.o 1250 5.1 15.8 1.5 Le? 30117 -- 12.3 (3500) 3.2 11.8 0.3 1.3 30129 3h 67.0 552 0.7 17.0 0.5 11.5 3033) o7 13.5 1900 12.8 14.6 2.5 2.9 -12- TABLE I (Continued) Nee Gey) (Dee) (aiev /e) (ein) (Sm) (10720 sec) (10°10 sec) 30770 28 28.0 882 0.8 11.7 0-3 5.0 30803 h6 39.0 1350 5.9 1.0 1.6 3.9 3084, 81 0.0 990 0.2 15.7 O.1 5.9 _ 30925 -- 90.0 (340) 6.5 11.7 Tel 12.8 3096, li 31.0 1600 6.1 1.8 1.9 3.5 30986 -- 22.0 (2200) 5.0 16.1 0.8 2.7 3104, 36 32.0 82 1.0 10.0 Oo.) bel, 31200 Ib 29.0 12h0 0.8 16.1 0.2 1.8 31216 -- 13.0 (3800) 7.3 1.6 0.7 Le 31337 -- 1.0 (3600) 7.6 11.3 0.9 1.2 -13- ‘ IV. DISCUSSION OF THE DATA™ oe x and d were measured from the predetermined fiducial fo supfaces which were shown in figure 1 and discussed in part Ii. The values of x and dad were obtained from the two stereo- scopic photograpns of the cnamber. The two views were projected through a lens system identical to that of the camera onto a single screen following the srocedure described in reference 8. The projection was such that points lying the chamber were suverimc-osed upon the ry on the back plate o screen, while points which were forward in the chamber were ad by an amount dependent on their distance from the o separat back plate. Figure 2 illustrates this for a V-particle which was produced in the lead vlate between the two chambers. The particle had an origin determined from 0' and 0", a point of entrance through the top fiducial surface determined from A! and A", a decay roint determined from Bt and B", and a "notential point of exit" from tne illuminated region at the back fiducial surface determined from ¢' and C", The point D, at which the sevareblion becomes sero, lles in the back plate. Figure 3 is a photograph showing one view of a decay in which the V-particle was following a trajectory of this Kind. PF, the momentum of the V-particle, was determined in % Mueh of the vrocedure used in collecting data and in making lifetime determinations is due to Professor Robert Leighton. Although developed indevendently, the seneral procedure is pi gilar to that suggested by J. G. Wilson and Gc. ©. Batier, 12) Flegure 2. A senematic dlasram showing the sursrnesitionof tne two steransconic 3 wf acre ss , Wy fa views of a neutral V-particle decay. ~ Tp Pigure 3. Two examples of the decay of a neutral V- particle. The decay products are consistent with a proton and a negative pi meson. The trajectory of the V-par ticle in the lower chamber is describedin part IV. ~ 16 « one of two ways depending on the information which was avail- able. If the momenta of the two decay nroducts could he determined, P was calculated as the vector sum of these mo- menta. If the momenta of the decay vroducts could not be determined, P was found from @ under the assumptions: (1) that the energy release in the assumed two body decay was 50 Mev and (2) that the decay products were emitted at right angles to the line of flight of the V-particle, in the center- of-mass system. Fisure l. shows that, if the decay oroducts have a panudum aivular distribution in the Ch system of the Veparticle, the second of the above assumptions could lead to considerable error in any one case but statistically should be a Pair wroceduro. Also, it might be noted thal PF was quite large for most of the cases for which this procedure was used and, as shown later, such cases have very little weight in the determination of the lifetime. The times, t and T, are given in the rest systems of the V-particles and are relatei to the distances, x and d, by the equations t = (x/e) (M/Fe) and T = (a/c) (M/Pc). Kya ae M" and Pe are given in Mev so that Fe*/i is she product of the velccity of the V-particle and the time diletion factor. in addition to tne quantities given in table I, one may feel that a knowledge of the time interval between the * The value of the mass of the neutral yparticle used in forming table I was taken tv be 1120 mev‘t , @ (Degrees) E po ant ~ 5 ] ! qT ] | | ] | I 180 i000 590 10 5 i L I “1.0 -0.8 -0.6 -0.4 -O02 O 02 04 0.6 08 1.0 oe t : ; : ° Fieure i. A two-body decay of a neutral Verarticle into a rroton and a negative pi meson with an enor-~ Ur release of 50 Mev is assumed, 6] is the anzle, neasured in the CM system of the V-narticle, whi wee proton saves with the line of flifht of the V~ particle. P and 6 are defined in vart III. - 16 - production of the V-particle and its entrance into the visible region of the chamber is necessary for a lifetime determination. However, it is assumed that the probability of decay follows an exponential law, and this assumotion implies that the decay is spontaneous and is independent of the past history of the V-particle. Thus one is justified in treating each particle as if it were created at its point of entrance into the visible region and in measuring t and T from the time at which the particle passed this point. This procedure has advantages in that: (1) it allows the use of many cases for which approximate points of entry into the Chamber can be obtained, but for which no clearly identifi- able origin can be found in the lead above the chamher, and (2) it eliminates the necessity for considering the unknown number of particles which decay before reaching the visible region. ‘the only use which was made of the origins that were identified was in the determination of the direction along whieh to measure x and d. For those V-particles which had no identifiable origin, x and d were measured along the line determined by the vector sum of the momenta of the two decay particles. For fifteen per cent of the events, for which neitner an origin could be identified nor a momentum measure- ment made, the direction of Plight of the neutral V-particle was taken to be along the line bisecting the angle between the paths of the two decay products. For most of the cases included in this last category the general direction of travel of the V-particle was clearly from the top of the chamber -~ 19 - toward the bottom, and the angle between the paths of the decay products was amall. These two conditions made the resulting error in x, d, and x/d quite small. Such would not be the case if the V-particle were traveling obliquely across the chamber or if the angle between the paths of the decay products were large. -~ 20 — Ve. (@STHOD CR CALSULATING THE MEAN LIFETIME In treating methods of determining the sean lifetime of radioactive substances, Peieris (13) in 1935, Bartistt (tt) in 1936 and Hole >) in 191.7 nave discussed the application of the maximum-likelihood vrocedu re (10) to counter experi- ments. The results riven by these workers are almost immediately applicable to the rresent sibuation with th principal exception that each of these has treaved the problem in which the sate time, T, is a constant, whereas the data obtained by use of tne cloud chamber contain U's which vary cover a rather wide rance. From table I it is seen thet the range in values of T is due to a difference in both the potential rath lengths and tne velocities of the v°-particles. in sprite of this difference the proesdure with eonstant T is readily extended to cover the case in which T varies over a range of values. A. The wtaximum-Likelihood Frocedure An unstabie particie, which follows an exnonential decay law with mean lifetime tT and which is known to be alive at time t = 0, has the probability (dp =(1/T) enti/Tat (1) of decaying at time t, in the time interval ct. If the decay is known to nave taxen place within the time Ty, the proba- - 21 - wn ee bility of decay in that time can be normalized to unity so that e7ti/t — eats (2) (i-e7Fi/T) (dP), =(1/7) For a set of N independent decays which follow the probability law of equation (2), the probability of having obtained the varticular set of excerimental data is propor- tional to WN -t;/T L = 1 /y—2—4. . (3) IT ett tLe L will be referred to as the likelihood function. The maximum-likelihood procedure is based upon the assumption, much used in statistical methods, that the best value of a parameter on which the likelihood function depends is that value of the parameter which makes this function a maximum. Hence one wishes to find that value of T for which L, or more conveniently inl, is a maximum: ginb =o, Ch) at + Carrying out tne differentiation of In one obtains for the best value of the mean Lifetime 24. % This normalization to unity essentially corrects for those particles which passed through the chamber and decayed after time T;. Peieris(13) does not proceed in this way but rather uses a procedure which requires assumptions as to the a orlori probability of having had a given total number of decays for each particle which decayed in time T;. a al 1! fre Hj fe 1a ). (5) 1 3 a4 N D (t+ Pr e Hence, in principle, the mean lifetime can be determined from data octained in cloud chamber exveriments. Given a set of ts and T; such as table I conbains for the yo-narticle, egaation (5) ean be solved by tteration toa find the best value of T. The actual worth of sucn a determination will depend of course on the statistical and systematic errors involved. The next section will be devoted to a discussion of these errors. B. Errors Following Eartlett's discussion of the maximum-likeli- nood nrocedure, one is led to tne statistical error in @ given by AT - . in which I is defined by the equation N in, 2 ; T =~9%int = 1 S |i wi eMi/T | (7) ate te 4, te (6TI/ V3 )2 Equation (0) is derived on the assumption that the estimates of tne parameter, T , are normally distributed as the f= variance of ging (1) | Although this cond oTv mately met in the present exceriment because of tne small tion is only approxi- - 23 - sample available, this equation probably furnishes the best means of arriving at somo ostimate of tho statistical orror. To gain some feeling for the effect of the finite gate time, it is interesting to consider the case for which all of the Ty are the same and to look at the quantity, n, which is given by ~7—_2-y/1- 2 _ef/T n=It sala (0/0)? foe (8) and which is the number of decays with an infinite gate reguired to produce the same statistical accuracy as N cases with a given finite gate, I. ‘the quantity N/n is plotted versus T/T in figure 5." As an example, if T/T is equal to unity, N/n is found to be 12.5; so that 10 decays observed with T infinite would yield a lifetime with the same statis- tical accuracy as 125 decays for which T/T was unity. Since one assumes a knowledge of tT in using the quan- tity T/T discussed above, the ratio t/T, which can be found directly from the experimental data, is more readily given as a measure of significance. For gate times which are small compared with T one expects the decay points to be uniformly distributed throughout the chamber so that t/T would be equal to one-half. Thus, one can hope to use the cloud chamber to measure mean lifetimes only if the ratio t/f = x/d is significantly less than one-half, *% This granh was also quite useful in evaluating the terms in equation (7) to find the statistical error when T WaS allowed blo bake on muny different valuese 190 | | | | [Or ivure 5. The retio “/n, as aAePir: . he os - a s-d)o* rr en miation (Gj,is plosted varsus the tre cate time to the mean OO PaO} -~ 25 - Further uncertainty in the lifetime is due to the limita- tions of the experimental technique and to a lack of know- ledge of the decay process or processes which are taking place. In each of the lifetime determinations which are given later, it is quite possible that the samples contain a mix- cure of varticles of different lifetimes so that the “lifetime” calculated is actually some sort of an average value of two or more characberistic lifetimes. Efforts which were made to seperate such possible mixtures will be discussed. Apart from the fact that the errors in tho measurements of momentum prevent an accurate classification of the V-particle decays into homogeneous groups and may thereby prevent us from making a proper calculation, the errors in the quantities FP, KX, and d do not contribute very large errors to the mean life, UT. For most cases x and d can be measured with suffi- client accuracy that the error can be neglected, and if selec- tion criteria are used such that the momentum of each V- particle in the sample is measurable Lo within twenty or thirty per cent, the resulting probable error in the mean lifetime should be small compared with the statistical error given by equation (6)* * since such a selection might tend to discriminate against the decay of long lived particles near the walls of the chamber, care must be taken that bias is not introduced into the sample. = 26 = Vil. TEE MEAN LIFETINE OF NEUTRAL V-PARTICLES In a series of 23,000 cloud chamber photographs taken at Pasadena and on Mount Wilson, 13) examples of the decay of neutral V-particles have been obtained. Data on 7 of these examples which were consistent with the decay scheme + - : VO—>P™ + 17 + @ (9) were given in table I. The remaining 60 decays have been eliminated from consideration for at least one of the following reasons? (1) the decay occurred outside the fiducial surfaces, (2) the total angle between the paths of the two decay products was £10°, (3) the decay did not seem to fit the proton plus negative pi meson decay scheme. These criteria were established in an attempt to obtain an unbiased sample of events for which maximum information was available. Nineteen decays between the walls of the chambers and the fiducial surfaces were discarded because of the non- uniform illumination and the rerlections which made it doubt- ful that all of the V-decays in this region were detected. The arbitrary restriction on the total angle eliminated twenty-three cases for which the V-particle momentum was unmeasurably high and eliminated no case for which the V- particle momentum was accurately known. This restriction was chosen sines the angle measurements could be made almost - 27 - irrespective of tne track length availaole and of the posi- tion of the decay point in toe chamber. Thus there was no apparent discrimination against decays occurring near the bettom of the chamber. Such would not be the case if mo- mentum measurements were required in maxing the selection. More of the cases for which the momentum had to be estim- ated could have been eliminated by throwing out those cases with @ 20°; however, this mich greater restriction would have caused tne loss of several events with known V-particle momentum. Tne final group of sighteen decays was removed because of the apparent inconsistency with the decay scheme given by equation (9). This group included such cases as those in which the nositive dacay particle was definitely lighter than a croton or in which the calculated energy re- lease was greater than 150 Mev. Assuming that the remaining 7, examples follow the two- body decay scheme given above, a mean lifetime has been Calculated from the set of t, and tT in table I. The average value of tne ratio bs /Ty was 0.30, with a statistical error of approximately 0.05, so that there was at least an indica- tion of a result with some significance. Substituting from 2 table I into equation (5), the first term gives a value of 1.6 x 19710 sec. for the average value of ty. Since the second or correction term is always additive, this nlaces a lower limit on the mean lifetime, subject only to the ordinary statistical Pluctuations. Following an iterative vrocedure to solve equation (5), one obtains for ~ the value TT = (2.5% 0.7) x 10729 sec, (10) The statistical error has been computed by use of equations (6) and (7). Although the effect of additional errors in the experimentally determined quantities is difficult to estimate, an attempt has been made to determine the magnitude of the resulting error int. For three-fourths of the 7 cases the error in the V-particle momentum was approximately twenty per cent or less, while for the remaining cases there Was an apvreciable probability of errors as large as one hundred per cent in the momenta determined solely from the value of ©. The errors in x and d were small compared with these errors in P. A consideration of these facts leads to an estimated probable error of about * 0.2 x 10°+° sec. in the value of the lifetime. If this error is assumed to be independent of the statistical error given above, the com- bined error is still given approximately as £O.7 x 10720 sec. This leaves to be considered the uncertainty due to the possibilities that the sample of 7, cases is a mixture of two orp more types of particles with different lifetimes and that sources of bias are present in the data. Although it is impossible to reach any definite conclusions as to the actuality of these possibilities, the following checks were made in an effort to detect any such sources of error. (1) A procedure was used which in effect reduced the volume enclosed by the fiducial surfaces. ~ 29 - (2) A separate lifetime determination was made for 32 decays occurring in the upper chamber and for |\2 decays occurring in the lower chamber. (3) A separate lifetime determination was made for those V-particles with identifiable origins and for those without clearly identifiable origins. (,) A comparison of the lifetime calculated for cases with an energy release between 30 Wev and 1,0 Mev was made with the lifetime calculated for the remaining cases with @ either less than 30 Mev or greater than 0 Mev. (5) Lifetimes were calculated for the two groups formed by placing those cases with Q less than or equal to 50 Mev in one group and those cases with @ greater than 50 Mev in a second group. The first of these checks was aimed at testing whether or not the fiducial surfaces really eliminated bias due to observational difficulties in the region near the walls of the chamber. The method used was approximately equivalent to moving in the fiducial surfaces by reducing each gate time ‘, as by ten per cent. The mean lifetime was then redetermined and found to agree within ten per cent with the above value. The same result was found when each gate time was reduced by thirty-three per cent. The separate lifetime determinations for the 32 decays occurring in the upper chamber and for ],2 decays occurring *% Any event for which the decay time was then greater than the new gate time was removed fron the saumple.e - 30 ~ in the lower chamber were compared. Since the illumination improved slightly from top to bottom for the upper chamber and conversely for the lower chamber, it was felt that this check might indicate bias in the deta. However, the two values of the lifetime fell within ten per cent of the result given above for the combined data. Because of the distances of tne principal source of V-particles in the lead above each chamber to the respective illuminated regions (fig. 1), it was thought that this test might also indicate the presence of a mixture of two different lifetime particles with the upper chamber favoring the detection of the longer-lived particles and the lower chamber favoring the detection of the shorter-lived ones, The negative result which was found could mean among many possibilities that the V's were all or almost all of one kind or that different kinds, if present in comparable numbors, were of very nearly the seme lifetime. There was no significant difference between the life- time calculated for the decays with identifiable origins and that calculated for those without clearly identifiable origins. The fourth point was checked because of the suggestion that part of the Vis which were observed might follow the decay scheme of equation (9) with @ near 35 Mev while the remainder followed the scheme fe) + - . Va P+ + vt e (11) with the apparent energy release calculated on the basis of the decay scheme of equations (9) varying over a range of values. Again the result was negative with no significant difference appearing in the two lifetimes. The final division of the data arose from the analysis of the 13h neutral Veparticle decays renorted in references 6 and 10. This analysis suggests the possible existence of two groups of V-particles which follow the decay scheme of equation (9), but with different values of the energy release, @, and with different lifetimes. There was a concentration ot a number of decays with © near 35 Mev and with @ near 75 ueve This suggested a division of the data such that 37 cases © with @ less than or equal to 50 Mev were placed in a low group and 20 cases with @ less than 150 Mev, but greater than 50 Mev, were placed in a high @ group. Substituting the data for the 37 low © cases into equation (5), a lifetime of T, = (2.9% 0.8) x 1071° was obtained. Again the error has been computed by using equations (6) and (7) and does not include an estimate of the bias due to the failure to consider the remaining 17 cases for which @ could not be determined. If the 17 cases were added to the low @ cases but weighted by the Yactor 31/815" the resulting lifetime was Yound to be c. = (3.0 + 0.8) x 10719 sec. A similar treatment of the high @ cases yielded a mean lifetime of Ty (1.3 % 0.5) x 1078 sece for the 20 cases of known & value anda mean lifetime of T= (1.6 0.5) x 10710 sec. when the 17 cases of unknown * This weighting factor divides the cases in proportion to the number of cases of known @ value in each group. - 32 - @ value are added in but weighted by the factor 20/57. Other possible division schemes were tried in the treatment of the 17 cases to determine the range of lifetime values which resulted from various ways of adding in these cases, If those divisions which give the greatest possible range of values consistent with the data are included, the values found in units of yo7 lo seconds were 1.35 °U_€ 2e3 and H 2.4. $ Ty < 3.5. Thus on the basis of these results and of the large statistical errors one would hesitate to place any real significance on tne difference between the lifetimes of the low @ and high @ groups. (17) - 33 - VIL, THE WEAN LIFETIME OF CHARGED V-PARTICLES In the same series of 23,000 photographs which contained the 13) examples of neutral V-particles, 23 examples of charged V-particle decay were observed. For most of those cases, both tne incident charged V-particle and the visible decay product had high momenta with the result that very few data could be obtained and no significant lifetime determination could be made. The distribution of doeays as shown in figure 7 is suggestive of the existence of at least two different types of carticles in the group. The events shown in the figure with a dot at the apex to indicate their production in the lead clate between the chambers were decays wnich occurred predominantly near the top of the lower cham- ber. A qualitative comparison of these events with the neutral V-decays shown in figure 6 indicates a somewhat shor- Bs “% ter mean free path for the charged V-particle. Since ioniza- Le tion estimates show that P/ii is, on the average, greater for the charged V's than for the neutral V's, a mean lifetime of less than 2.5 x 19710 sec, possibly by a factor of from 2 to lh, is indicated for this particular tyne of charged V-decay. Also in support of this short lifetime 1s a consideration of the ratio of the number of V-particles produced in the lead % The arguments based on this overall comparison of neutral and charged V's are weakened somewhat because of the unequal efficiency of observing the two types of decay. A small deflection in the track left by a very fast particle is often the only indication of a charged V-decay. Such a deflec- tion is much more difficult to detect than is the inverted V which characterizes the decays of the neutral variety. This is especially true of events near the walls of the chambers. 7 . NA \ rs | i) A NA qa Ay en i | \ \ | A fA | 4 / KY f . va tf h s Ay AY \ 4 \ | A \ Figure 6, The distribution of the neutral V- particle decay points. A dot at the apex indicates production in the lead plate between the two cham- bers, A dashed track signifies a hidden apex. Figure 7. The distribution of the charged V-particle decay points. A dot at the apex indicates produc- tion in the lead nlate between the two chambers. between the two chambers to the number oroduced in the lead above the upper cnamber. For the cnarged V-particles with identifiable orisins this ratio is eprroximately 1 compared with 1/2 for the neutral Veoarticles. This comparison polos to a shorter averaze lifetime for the combined cases of charged V's tnan for the neutral V's. On the other hand, the decays shown in fiseure 7 without a dot ab the avex were apparently preduced in the lead above the upper chamber and were distributed more uniformly through- py O out the enambers. Several of the particles decaying in t lower chamber traversed completely tne uvper chamber indica- ting a long lifetime, provided P/ik is not too much greater for tnese marticles than for the neutral V's. In addition, two examples, in which a relatively slow varticle of estima- ted mass between that of the rroton ani the pi meson has been observed to decay into a particle consistent with a pi or ma mescen after a time greater than 1077 sec, also suggest tne presence of a comparatively long-lived narticle of such mass accompanying penetrating showers. Thus it is felt that at least some of the charged Vis are identical with these two (18.19) . 4 examples and are rrobably kavva mesons Wobli a pie lifetime of 1077 see or erpeater. In addition to those events which nave been described as charged V-deeayvs and which may in part be zanna mesons decaying into a mu meson clus one or more neutral particles, neat to) two examples have been obtain of a charged particle decaying into three charged particles. Hach of the three decay ~ 47 = products in these two events had a mass consistent with that of a pi meson and the primary particle appeared to be identi-~ cal with the tau mesons which had previously been observed in nuclear emulsions. (29) Although no good estimate of the lifetime of this particle can be made from only two cases, the relatively long paths of the tau's in the chamber before decay and the estimates of P/M indicate a mean lifetime grea- ter than that of the neutral V-particle. Just as for those particles which were thought to be kappa's, this mean life- Je ve time is probably 107% see or longer. * Approximately twice the amount of data discussed in this section is now available and these additional data lead to essentially the same conclusions as those given. - 38 - Vill. CONCLUSION In the present attempt to delermine Lhe mean lifeblime of V-particles, a worthwhile numerical analysis is permitted only for those cases in which the decay is consistent with equation (9). Although the accursey of this analysis is some- wnat limited because of the present state of knowledge con- cerning the exact type of decay involved, assuming any one of several alternative decay processes, which are consistent with the data, should not greatly alter the given results. For example, the results would be changed very little if a three- body decay proved to be the actual process rather than the assumed two-body decay. Considering apparatus which is soon to be in operation, it is quite possible that many of the difficulties encountered here will be overcome because of the larger chambers which are to be used, the stronger magnetic field which is available, and other improvements which have been made in the apparatus and in the experimental techniques, It is likely that further investigation of lifetimes ean be made, particularly for the neutral V treated here and for the short-lived charged V if additional evidence of its existence is found. There should also be an opportunity for investigation of the one or more additional types of neutral V's which have been proved to exist (7,5) put which have essentially been ignored in this thesis because of the small number of cases observed. For the appar- ently longer-lived tau and kappa mesons, the direct method here used in determining lifetimes is of doubtful value in obtaining good statistical accuracy since the gate times for useful events must be long and tne frequency of observation of such decays has been quite low. Perhaps however, even this aifficulty will be eliminated by the use of these larger chambers or oy the use of techniques which will increase the frequency of observing slow particles. 10. ll. 12. 13. lh. 15. 16. 17. 18. 19. 20 6 REFERENCES fad G. D. Rochester and G. C. Butler, Nature 160, 855 (1947). A. Seriff, R. B. Leighton, ©. Hsiao, #. Cowan and ©. D. Anderson, Phys. Rev. 78, 290 (1950). R. Armenteros, K. H. Barker, C. C. Butler, A. Cachon and A&A. H, Chapman, Nature 167, 501 (1951). R. W. Thompson, H. 0. Gohn and R. S. Flum, Phys. Rev. 83, 175 (1951). W. B. Fretter, Phys. Rev. 82, 29), (1951). R. B. Leighton, 5. D. Wanless and W. L. Alford, Phys. Rev. 83, 843 (1951). R. Armenteros, K. H. Barker, 0. G. Butler and A. Cachon, Phil. Mag. 4.2, 1113 (1951). R. B. Leighton, &S. D. Wanlass and C. D. Anderson (In press). K. H. Barker, ©. ©. Butler, M. G. Sowerby and ¢. Mi. York, Phil. Mag. 43, 1201 (1952). S. D. Wanlass, Ph.D. Thesis (1953). F. H. Shelton, Ph.D. Thesis (1953). J. G, Wilson and C. C. butler, Phil. Meg. 43, 993 (1952). R. Peierls, Proc. Roy. Soc. (London) 149, 167 (1935). li. S. Bartlett, Proc. Roy. Soc. (London) 154, 12, (1936). N. Hole, Arkiv f¥r Mathematik, Astronomi och Fysik, Band 34B, No. 12 (19l:7). R. A. Fisher, Phil. Trans. Roy. Soc. 222, 309 (1922). R. J. Finkelstein, Phys. Rev. 88, 555 (1952). R. Be Leighton and S. D. Wanlass, Phys Rev. 86, 1.26 (1952). Re Brown, U. Camerini, FP. H. Fowler, H. Muirhead, C. F. Powell and D. M. Ritson, Nature 163, 82 (191)9). C. O'Ceallaigh, Phil. Mag. 4.2, 1032 (1951).