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Discovery of Parity Violation Discovery of Parity Violation Gregoria Rizzardelli (n° 86888) July 26, 2010 Simmetry Besides, Ψ is an Eigenfunction of P 1 and so −! −! Symmetries have long played a crucial role in Ψ(− r ) = λΨ( r ) ; physics. The conservation laws of the past had more fundamental roots within the symmetry of the Uni- where λ is the Eigenvalue; consequently it is clear that verse. However, sometimes scientic reasoning lead if we do this twice we have to get back to our starting Tsung-Dao Lee and Chen Ning Yang to reconsider one 1For a Hamiltonian of this kind [2]: of the most successful and long believed symmetries of 2 nature, that of parity. H = − ~ r2 + V 2m the energy eigenfunctions are of the form (r) = R (r) Y m (#; ') : Parity nlm nl l Under the operation of mirror inversion in the origin, which in spherical polar coordinates is represented by: In this report we will talk about the simmetry of 8 r −! r space inversion [1], which although applicable to classi- <> cal systems, only gains its full signicance in the study # −! π − # :> of systems described by quantum mechanics. Parity is ' −! ' + π a Quantum Mechanical concept and the term parity is used in two ways, rst, as the operation P of spa- tial inversion (it is also known as mirror symmetry, or left-right symmetry, hence invariance under space in- version is equivalent to the indistinguishability of left and right), second, as a numerical quantity associated with the system. Parity in the rst sense is an ope- rator P for a wavefunction Ψ(−!r ) which reverses the coordinate −!r to −−!r : P Ψ(−!r ) −! Ψ(−−!r ) we nd from the properties of the spherical harmonics s (2l + 1) (l − jmj)! Y m (#; ') = eim'P m (cos#) ; l 4π (l + jmj)! l where ( (−1)m se m ≥ 0 = 1 se m ≤ 0 and jmj jmj=2 d P m (x) = 1 − x2 P (x) l dx l with l 1 d l P (x) = x2 − 1 ; l 2ll! dx that m l m , so that Yl (π − #; ' + π) = (−1) Yl (#; ') l nlm (r) = (−1) nlm (r) : (−1)l is called parity of the state and in this case is determined by the orbital angular momentum. 1 point: into two pions is just (−1)l and that of a particle of spin l decaying into three pions equals (−1)l+1. So, 2 −! −! 2 −! P Ψ( r ) −! Ψ( r ) = λ Ψ( r ) ; if the parity were conserved in weak interactions, the parity of τ + is (−1)l+1 = − (−1)l, whereas the parity therefore λ = ±1. If the Eigenvalue of Ψ is +1 we say of + is l. Therefore these two particles looked that is even or positive, otherwise odd or negative. θ (−1) Ψ the same, except for parity. The nagging thing, of Parity in the second sense is a multiplicative quantum course, is that apart from this parity dierence, the tau number which could be or . The total parity of +1 −1 and theta particles are identical and despite searching a system of particles is the product of their intrinsic for tiny dierences, no experiment could detect any parities and the spatial parity given by l, where (−1) l variation. The parity conservation law implied that denotes angular momentum of the wave function. such particles could decay into either an even or into an Basically, parity conservation in quantum mechanics odd number of pions, but not into both. Consequently means that two physical systems, one of which is a it was believed that tau and theta were dierent. mirror image of the other, must behave in identical fashion. In other words, parity conservation implies In 1954, R.H. Dalitz ([4], [5] and [6]) looked at the that Nature is symmetrical and makes no distinction decays of the tau into three pions and in doing so intro- 3 between right and left-handed rotations or between op- duced the Dalitz plot into physics. The rst use of the posite sides of a subatomic particle. Thus, for example, Dalitz plot revealed that the theta particle appeared two similar radioactive particles spinning in opposite to be the same as the tau, which was paradoxical. The directions about a vertical axis should emit their decay puzzle persisted for two years: Dalitz mused his col- products with the same intensity upwards and down- leagues that perhaps the law of odds and evens was wards. not true, even though all the evidence said otherwise [7]. The solution to this puzzle emerged rapidly. Two The τ-θ puzzle theorists, Tsung-Dao Lee and Chen Ning Yang publi- Two particles have all the same properties ex- shed a landmark paper [8] in which they showed that cept that they are of opposite intrinsic parity there was actually not a shred of evidence available that the weak interactions conserved parity. For over Prior to 1956 it was assumed that the parity was twenty years people had just assumed without check- conserved in all the fundamental interactions2 and cer- ing it. Lee and Yang argued that the τ-θ puzzle was tainly in the case of electrodynamics, this fact had been an evidence that, perhaps, the weak interactions didn't tested, and found to hold. Without realizing it, most conserve parity after all. They found that while there physicists simply carried the assumption that the same was plenty of evidence for the validity of parity con- would be true in the weak interactions. It took an servation in electromagnetic and strong interactions, experimental anomaly to shake that assumption: the there was no experimental evidence4 whatsoever for original motivation for the experimets which led to the parity conservation in β-decay or the weak decays of discovery of parity violation came from the τ-θ puzzle. the mesons then known. They were proved to be right, In the early 1950's there were two particles called the tau (this is not the same as the tau lepton, discovered 3The Dalitz plot is a scatterplot (a type of mathematical dia- in 1975) and theta particle that were both discove- gram using Cartesian coordinates to display values for two va- red in cosmic rays and that appeared to be identical riables for a set of data) used to represent the relative frequency of various manners in which the products of certain three-body in every aspect: careful studies had shown that the decays may move apart. The axes of the plot are the squares masses, charges, spin and lifetimes of the two mesons of the invariant masses of two pairs of the decay products. For example, + decays to particles +, +, and −, a Dalitz plot were equal within experimental errors. However, they τ π1 π2 π3 for this decay could plot m2 on the x-axis and m2 on the had one striking dierence; they exhibited dierent de- 12 23 y-axis. cay modes, mediated by the weak interaction: tau de- 4A few weeks after the Sixth Rochester Conference, late April cayed into three pions, while theta turned into two. or early May (1956) Lee and Yang met in New York at the White Rose Cafe near 125th and Broadway and discussed the possibi- τ + −! π+ + π+ + π− lity that parity could be violated in weak processes. Afterwards Lee asked his colleague from Columbia, Chien Shiung Wu, an + + 0 θ −! π + π expert in β-decay, whether she knew of any experiments related to this question. Lee and Yang soon discovered that nobody has The intrinsic parity of the pion was estabilished to be ever proved that parity conservation was valid for weak inte- −1: thus the parity of a particle of spin l decaying ractions. They decided to analyze the problem thoroughly. On June 22 1956, their paper entitled Is Parity Conserved in Weak 2Since invariance under space reection is intuitively so ap- Interactions? was submitted to the Physical Review. The edi- pealing (why should a left and a right-handed system be dif- tor of that journal, Samuel Goudsmit, protested against using ferent?), conservation of parity quickly became a sacred cow the question mark in the title. The paper was nally published [3]. as Question of Parity Conservation in Weak Interactions [8]. 2 and in 1957 won a well-deserved Nobel Prize. To see why this is relevant to parity, we look at the The tau and theta particle today are known as the mirror image of the same system. In the mirror, the K strange meson [9]: electron ies out of the nucleus at the same angle to the positive z-axis; however, in the mirror the nucleus K+ = (us) is spinning the other way around, and so its magnetic Mass 493:677 ± 0:016 MeV moment is now in the negative z-direction. This means Charge +1 that the angle between the electron trajectory and the Mean life (1:2380 ± 0:0021) × 10−8 s magnetic moment of the nucleus has changed. Spin 1 2 Prity −1 Lee and Yang, prior to the publication of their paper, had relayed their ideas5to an experimentalist Chien-Shiung Wu. Following on this analysis Wu with her coworkers Ambler, Hayward, Hoppes and Hudson showed conclusively that parity is violated in β-dacay [10]. -decay Figure 2: β-decay in the mirror. In the mirror the nu- β cleus now spins in the opposite direction, as indicated by β-decay is mediated by the weak interaction and in- the looping arrow, and the direction of the magnetic mo- volves the transformation of a neutron into a proton, ment µ ips to the negative z-direction. Thus the angle or vice versa, and the creation of an electron and neu- between the electron trajectory and the magnetic moment trino.
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