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Amit Roy
Symmetry principles are very dear to physicists in their quest for the understanding of nature. T hese reflect the regularities that are present in nature and help in understanding the law s govern- ing them. A good definition of symmetry in a physical system w as given by H erman W eyl as:ìA thing is symmetrical if there is something w e can do to it so that after w e have done it,it looks the same as it did before.î In other w ords the system is invariant under the operation w e performed. A few examples of such operations for a physical system are:translation in space or time, rotation through a fixed angle,uniform velocity in a straight line,reversal of time,reflection in space,interchange of identi- cal particles and change of matter to antimatter.T hey arise from our basic perceptions about the nature of space and time and usually lead to conservation law s.T he invariance under transla- tions in space and time lead to conservation of linear momentum and energy,respectively.Invariance under rotation leads to the law of conservation of angular momentum and invariance under mirror reflection,i.e.symmetry betw een left and right,leads to conservation of parity (see Box 1).
T he question of sym m etry betw een left and right belongs to a category,w hich isnotapparentfrom ourdaily life. W eappearto m ove and act differently than our im ages in a m irror. In biologicalphenom ena,itw asknow n from L ouisPasteurísw ork in 1848 thatorganic com poundsappearoften in the form ofonly one oftw o kinds. T hese m olecules rotate polarised lightto the leftand are called laevo (left)-rotatory. H ow ever,both leftand right rotating m olecules occur in inorganic processes and are m irrorim agesofeach other. In fact,Pasteurhad considered for a tim e the idea that the ability to produce only one of the tw o form sofm oleculesw asthe very prerogative oflife. H ow ever,if
D iscovery of Parity V iolation
Breakdown of a Symmetry Principle
Amit Roy
Amit Roy is at the Nuclear Science C entre,New D elhi,building a supercon- ducting linac booster for the pelletron accelerator. H e spent over tw o decades at the T ata Institute of Fundamental Research, M umbai investigating nuclei using accelerators and probing symmetries in physics.H is hobbies are books and music.
“A thing is sy m m e tric a l if the re is so m e thing w e c a n d o to it so tha t a fte r w e ha v e d o ne it, it lo o k s the sa m e a s it d id b e fo re .”
Appeared in Vol.6, No.8, pp.32-43, 2001
Discovery of Parity Violation
Box 1. Symmetries, Parity, Interactions
Among the symmetry principles, some are continuous and others are discrete symmetries. Translations in space and time are ex amples of continuous symmetries, w hereas mirror ref lection is an ex ample of discrete symmetry. The continuous symmetries alw ays lead to conserv ation law s in classical physics; the discrete symmetry does not. H ow ev er, in q uantum mechanics the discrete symmetries also lead to conserv ation law s. The lef t- right mirror symmetry then leads to the conserv ation of parity. There are also a numb er of symmetries, w hich appear only in q uantum mechanics w ithout any classical analogue. The concept of parity can b e understood considering the simple case of one- dimensional time- independent S chrö dinger eq uation
- h^2 /2m d 2 Ψ(x)/d x^2 + V(x) Ψ(x) = E Ψ(x). (1 ) I f w e n o w c h a n g e x → – x , w e g e t th e e q u a tio n f o r th e m ir r o r im a g e p o s itio n ,
- h^2 /2m d 2 Ψ(– x)/d x^2 + V(– x) Ψ( – x) = E Ψ(– x). (2) I f th e p o te n tia l e n e r g y is s y m m e tr ic a b o u t x = 0 , th e n V(– x) = V(x) a n d th e e q u a tio n b e c o m e s ,
- h^2 /2m d 2 Ψ(– x)/d x^2 + V(x) Ψ(– x) = E Ψ(– x). (3 ) C o m p a r in g (1 ) a n d (3 ), w e f in d th a t f o r th e s a m e p o te n tia l V, th e r e a r e tw o s o lu tio n s , Ψ(x) a n d Ψ(– x). T h e s e s o lu tio n s c a n o n ly d if f e r b y a m u ltip lic a tiv e c o n s ta n t P, i.e ., Ψ(– x) = P Ψ(x).
N o w , c h a n g in g s ig n o f x in th e a b o v e w e g e t, Ψ(x) = P Ψ(– x) T h e r e f o r e , P^2 = 1 o r P = ± 1. S o th e s o lu tio n s o f th e S c h r ö d in g e r e q u a tio n a r e e ith e r e v e n o r o d d u n d e r a c h a n g e o f s ig n in th e s p a c e c o - o r d in a te s if th e p o te n tia l f u n c tio n is u n c h a n g e d b y th e p a r ity tr a n s f o r m a tio n. T h e e v e n s o lu tio n s h a v e e v e n p a r ity a n d th e o d d s o lu tio n s h a v e o d d p a r ity.
T h e s y m m e tr ie s a n d th e ir c o n s e q u e n t c o n s e r v a tio n la w s c a n b e c la s s if ie d in tw o c a te g o r ie s , ‘ a b s o lu te ’ a n d ‘ r e s tr ic te d ’. A b s o lu te c o n s e r v a tio n la w s a r e th o s e th a t a r e o b e y e d in a ll s itu a tio n s b y a ll th e k n o w n in te r a c tio n s , w h e r e a s th e r e s tr ic te d s y m m e tr ie s a r e th o s e w h ic h a r e v io la te d b y o n ly s o m e in te r a c tio n s. P a r ity is th e s y m m e tr y o f m ir r o r r e f le c tio n a n d is a r e s tr ic te d s y m m e tr y. T h e in te r a c tio n s a r e o f f o u r ty p e s , v iz ., s tr o n g , e le c tr o m a g n e tic , w e a k a n d g r a v ita tio n. T h e s tr e n g th s o f th e s e in te r a c tio n s , d e f in e d b y h o w th e y c o u p le to m a tte r a r e : 1 (n o r m a lis e d ) f o r s tr o n g , 1 /1 3 7 f o r e le c tr o m a g n e tic , 1 0 – 1 4^ f o r w e a k a n d 1 0 – 3 8 f o r g r a v ita tio n. T h e s tr o n g a n d w e a k in te r a c tio n s h a v e v e r y s h o r t r a n g e s a n d m a n if e s t th e m s e lv e s o n ly in th e s u b - a to m ic w o r ld. T h e e le c tr o m a g n e tic a n d g r a v ita tio n a r e lo n g - r a n g e d a n d th e ir m a n if e s ta tio n s a r e a p p a r e n t in th e m a c r o s c o p ic w o r ld. T h e id e a th a t a ll th e s e f o u r in te r a c tio n s a r e e s s e n tia lly o n e a t s o m e le v e l h a s d r iv e n th e e f f o r ts f o r u n if y in g a ll th e in te r a c tio n s th r o u g h th e a g e s , le a d in g to th e c u r r e n t g r a n d u n if ie d th e o r y w h ic h u n ite s e le c tr o m a g n e tic , w e a k a n d s tr o n g in te r a c tio n s. G r a v ity s till w a its f o r th e r ig h t th e o r y o f u n if ic a tio n a n d s o m e c u r r e n t r e s e a r c h e r s h o p e th a t s tr in g th e o r y w ill b e a b le to p r o v id e th e u n if ic a tio n o f a ll f o u r in te r a c tio n s.
Discovery of Parity Violation
existing literature and did not come up with any information on the validity of the principle of left-right symmetry in the realm of weak interactions. T hey claimed that the tau and theta were the same particle (it is now known as the K meson)and that left- right symmetry was violated in weak interactions. It became then absolutely essential to gather independent experimental evidence for establishing the breakdown of parity symmetry. T hey proposed experimental tests for this principle in weak- interaction processes like beta-decay of nuclei, π ñ μ (mu) meson decays and decays ofstrange particles.
T he essence ofthe experimentinvolving beta-decay w as to line up the spins ofthe beta emitting nucleialong a given axis and observe w hether the beta particles (electrons or positrons) w ere emitted preferentially in one direction or the other along the axis. T he tw o positions ofthe beta counter w ith respectto the axis are mirror images of each other as show n in Figure 1. A positive resultw ould confirm the violation ofparity. T D L ee approached hisexperim entalcolleague atthe Colum bia U niver- sity, C S W u, w ho had w orked extensively on beta-decay of nuclei. She im m ediately realised the significance ofthe experi-
Figure 1. Sketches show- in g con cep tua lly p a rity v io- la tion in b eta d eca y. T he v ertica l a rrow d ep icts the d irection of p ola risa tion of the 6 0^ C o n ucleus. T he situ- a tion d ep icted in (I) a n d (II) a re m irror sy m m etric to ea ch other. T he d ifferen ce in coun tin g ra tes in d etec- tors 1 a n d 2 in a rra n ge- m en ts (I) a n d (II) would in d i- ca te p a rity v iola tion.
They claimed that the tau an d theta w ere the s ame p article (it is n o w k n o w n as the K mes o n ) an d that left-rig ht s ymmetry w as v io lated in w eak in teractio n s.
Amit Roy
ment and thought about using a 60 Co beta-source polarised by the demagnetisation method.
N ow lining up nuclei is not an easy task, as the only w ay to manipulate nuclei is w ith their magnetic moment. T he mag- neticfields required forthis purpose are too large (~ 10^6 gauss)to be generated in a laboratory even today,and only w ithin atoms themselves do such large fields exist. So specialatoms are first lined up to produce a field (this requires only a few hundred gauss field),w hich in turn lines up the magnetic nuclei. T he aligning force is,how ever,not strong enough to maintain the orderly alignment at room temperature. T he thermalagitation of the atoms must be reduced to a minimum and this can obviously be done only at very low temperatures, near a few millikelvin above absolute zero. Such low temperatures can be produced by the principle ofadiabatic demagnetisation(see Box
- of a paramagnetic salt. But once the temperatures are pro- duced,it needs to be maintained for a sufficient length of time for the experiments to be performed. Specially designed vacuum bottles know n as cryostats are used w here an object can be maintained at these low temperatures.
T his made the experiment considerably complicated, as the electron detector had to function inside a liquid helium cryostat (the electrons w ould be stopped in the cryostat w alls) and this had not been done before. T he electron detector usually w as a scintillator crystal,w hich produces light pulses w hen radiation impinges on it. T hese light pulses are then detected by photo- multipliers, w hich convert the light falling upon them to an electrical pulse suitable for handling,by further electronic cir- cuits. T he then available photomultipliers w ould not w ork at the low temperatures and hence the light from the scintillators had to be brought out of the cryostat,so that the photomultiplier could be placed in room temperature environment. T he beta- source had to be located in a thin surface layer (otherw ise the electrons w ould get absorbed in the material) and polarised for a period long enough to obtain sufficient number of counts. W u enlisted the help of the team of E A mbler,R W H ayw ard,D D
Aligning the m a gnetic m o m ents o f nu c lei req u ires ex tra o rd ina rily c lev er tec hniq u es.
Amit Roy
Hoppes and R P Hudson of the National Bureau of Standards at W ashington D C,w ho w ere equipped to do nuclear orientation experim ents. T heir collaboration resulted in the m easurem ent set-up sketched in Figure 2. The set-up took about six months to design,prepare,test and get ready forthe experiment. W u made the 60 Co specimen for the beta-ray measurement by taking a good single crystalofthe paramagnetic salt cerium magnesium nitrate (CM N )and grow ing on the upper surface only an addi- tional crystalline layer containing 60 Co. The thickness of the radioactive layerw as about 0.05 mm and contained a few micro- curies (= 10ñ6^ Curie,1 Curie = 3.7× 1010 decays/sec) ofactivity. She prepared another specim en w ith the 60 Co activity spread evenly throughouta CM N crystalfor the study ofanisotropy of gam m a rays. T he beta particles w ere detected in a thin an- thracene crystal3/8''diam eterand 1/16''thick located inside the cryostatvacuum cham berabout2 cm abovethe 60 Co source.T he scintillation lightproduced in theanthracenecrystalw eretrans- m itted outside the cryostatthrough a glass w indow and carried to a photom ultiplier at the top of the cryostat through a 1"
Figure 2. Schematic dia- gram o f the ap p aratus us ed b y C S W u an d o thers. (R ep ro duced fro m P hy s ical R ev iew L etters , V o l. 1 0 5 , p p. 1 4 1 3 -1 4 1 4 , 1 9 5 7 w ith p ermis s io n fro m A merican P hy s ical So ciety ).
Discovery of Parity Violation
diameter Lucite pipe 4 feet long. The Lucite head was machined to a logarithmic spiral shape for maximum light collection. The stability of the beta counter was carefully checked for any magnetic or temperature effects and none were found. The effect of backscattering of the beta particles from the CM N crystal was also thoroughly investigated as this could interfere with the asymmetry effect. Two additional sodium iodide scintillation detectors were installed,one in the equatorial plane and one near the top of the cryostat,to measure the gamma rays emitted in the decay of 60 Co. The observed gamma ray anisot- ropy was used as a measure of polarisation and effectively, temperature. The temperature reached in the experiment was ~ 0.01 K.
A fter demagnetisation,the magnet was opened and a vertical solenoid was raised around the lower part of the cryostat,the solenoid providing the polarising field. This polarising field was applied in the direction of minimum susceptibility of the CM N crystal to minimise the heating of the crystal. This process took about 20 sec,after which beta and gamma counting were started. The measurements were then taken by reversing the polarising field. This ensured that beta particles emitted in directions both parallel to the magnetic field and anti-parallel to the magnetic field were measured without disturbing the source and the counter.
In their first ëruní,W u and her collaborators found that the thick (^60) Co source was easily polarised,whereas for the thin surface
source,the polarisation effect lasted only for a few seconds and then completely disappeared. They identified the cause of this correctly as due to the warming up of the surface layer caused by radiation,conduction or condensation of the H e-exchange gas. They grew ten large size (> 1"diameter)CM N crystals and these formed a housing surrounding the CM N crystal with the thin Co source, providing better thermal isolation. W ith this set-up, they observed for the first time a genuine asymmetry effect in the emission of beta particles. M ore beta particles were observed when the magnetic field was pointing in the direction of the
The observed g a m m a ra y a n isotrop y w a s u sed a s a m ea su re of p ola risa tion a n d effec tively , tem p era tu re.
Discovery of Parity Violation
if the emission of electron was measured with respect to the direction of polarisation of the mu meson. T he π±^ m eson is produced by bom barding high energy protons on a target. T he π±^ decaysin a few nanosecsinto a μ±^ m eson and a neutrino.T he μ±,in turn decays in about2 m icroseconds into an e±^ and tw o neutrinos (or anti-neutrinos). L ederm an and G arw in realised thaton thebasisofL eeand Y angíssuggestion,m uonsm oving in the forw ard direction in the decay of pions w ould already be polarised ifparity violation occurred. So,allthey had to do w as to m easuretheasym m etry oftheem itted electrons(orpositrons) reliably.Form easuring theelectron asym m etry they had to stop the m uons. T hey w ere w orried that the m uon spin m ight not retain its initialdirection during the stopping process,or that the m uonsm ightbe depolarised in the tw o m icrosecondsbefore decay.
T he experim ental arrangem ent is show n in Figure 3. The T- shaped carbon block of length 8" w as used to separate the μ+ from the π+^ beam as the m ean range of85 M eV pions from the cyclotron is ~ 5". T his arrangem entallow ed a m axim um num - ber of m uons to com e to rest in the one-inch carbon block
Figure 3. Sketch of the ex- p erim en ta l a rra n gem en t of G a rw in , L ed erm a n a n d W ein rich. (R ep rod uced from P hy s ica l R ev iew L et- ters , Vol. 105, pp.1415-1417, 19 57 w ith pe r m is s ion fr om A m e r ic a n P h y s ic a l S oc i- e ty ).
Amit Roy
Box 3. Coincidence Counting Using coincidence counting techniques, it is possible to establish experimentally if two events occurred within a finite interval of one another. S uppose the first event is identified in detector 1 producing an electronic pulse and the second event is identified by another pulse in detector 2. B oth these pulses are fed as inputs to the coincidence circuit and an output is produced only if these two pulses appear within a short time interval, termed the resolving time of the circuit. T raditionally, for fast coincidence circuits the resolving time is a few nanoseconds, whereas for slow- coincidence circuits it is about a few microseconds. I n a delayed coincidence, one of the pulses is intentionally delayed by a k nown time interval before it is fed to the coincidence circuit. I n modern parlance, the coincidence circuit is an A N D gate. S uch coincidence circuits were developed for studying nuclear decays and are now ubiquitous.
chosen as the stopping material. The stopping of a muon was signalled by a fast coincidence (see Box 3) between counters 1 and 2. T he subsequent beta decay ofthe m uon was detected by the electron telescope 3-4, which norm ally required electron energies above 25 M eV to register. A delayed coincidence between counters 1-2 and 3-4 ensured that the electrons were em itted by the stopped m uons. A t first they wound a uniform solenoid on a hollow cylindrical lucite shell to serve as the m agnet for producing a uniform m agnetic field over the carbon block. D uring the initial run the lucite shell overheated and m elted down. T hen they wound the wire in the form of a rectangular solenoid directly over the carbon block. A lthough neither the m uon spin nor its m agnetic m om ent was known at that tim e,they assum ed a value of one-half for the m uon spin and that the gyrom agnetic ratio had the value g = 2. The mag- nitude ofthe solenoid currentw ascalculated on thisbasis. The electronic coincidence circuit used for this experiment w as developed by G arw in earlier. They set about to measure the countrate in theirelectron counterasa function ofthe magnetic field in the solenoid and observed a sinusoidalvariation,w hich gave the value ofthe angular distribution parameter,a = ñ0. ± 0.03 for the decay of μ+. T hey checked the experim ental system by allow ing the end of range pions from the beam to com e to rest in the carbon target, thereby allow ing electrons em itted by m uonstravelling in alldirectionsto reach thecounter. T hetotalelectron counting ratein thiscasedid notvary w ith the
