Two different decays were found for charged strange mesons into pions:
Decay
θ+
→
π+
+
π0
Parity
+1
=
−1
×
−1
Decay
τ+
→
π+
+
π+
+
π−
Parity
−1
=
−1
×
−1
×
−1
The intrinsic parity of the pion is P = −1 (since the pion is a bound state of a quark and an antiquark, which have opposite parities, with zero angular momentum), and parity is a multiplicative quantum number. Therefore, assuming the parent particle has zero spin, the two-pion and the three-pion final states have different parities (P = +1 and P = −1, respectively). It was thought that the initial states should also have different parities, and hence be two distinct particles. However, with increasingly precise measurements, no difference was found between the masses and lifetimes of each, respectively, indicating that they are the same particle. This was known as the τ–θ puzzle.<ref name="Laymon-2022">Template:Cite book</ref> It was resolved only by the discovery of parity violation in the weak interaction (most significantly, by the Wu experiment). Since the mesons decay through weak interactions, parity is not conserved, and the two decays are actually decays of the same particle,<ref name="Lee 1956">Template:Cite journal</ref> now called the Template:SubatomicParticle.
The discovery of hadrons with the internal quantum number "strangeness" marks the beginning of a most exciting epoch in particle physics that even now, fifty years later, has not yet found its conclusion ... by and large experiments have driven the development, and that major discoveries came unexpectedly or even against expectations expressed by theorists. — Bigi & Sanda (2016)<ref>Template:Cite book</ref>
In 1947, G.D. Rochester and C.C. Butler of the University of Manchester published two cloud chamber photographs of cosmic ray-induced events, one showing what appeared to be a neutral particle decaying into two charged pions, and one that appeared to be a charged particle decaying into a charged pion and something neutral. The estimated mass of the new particles was very rough, about half a proton's mass. More examples of these "V-particles" were slow in coming.
In 1949, Rosemary Brown (later Rosemary Fowler), a research student of Cecil Powell of the University of Bristol, spotted her 'k' track, made by a particle of very similar mass that decayed to three pions.<ref name=":2">{{#invoke:citation/CS1|citation
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I knew at once that it was new and would be very important. We were seeing things that hadn't been seen before – that's what research in particle physics was. It was very exciting. — Fowler (2024)<ref name=":2" />
This led to the so-called 'tau–theta' problem:<ref name="Sheehy2024">Template:Cite journal</ref> what seemed to be the same particle (now called Template:SubatomicParticle) decayed in two different modes, Theta to two pions (parity +1), Tau to three pions (parity −1).<ref name="Brown-Camerini-etal-1949">Template:Cite journal Note same issue: Template:Cite journal</ref> The solution to this puzzle turned out to be that weak interactions do not conserve parity.<ref name="Lee 1956" />
The first breakthrough was obtained at Caltech, where a cloud chamber was taken up Mount Wilson, for greater cosmic ray exposure. In 1950, 30 charged and 4 neutral "V-particles" were reported. Inspired by this, numerous mountaintop observations were made over the next several years, and by 1953, the following terminology was being used: "L meson" for either a muon or charged pion; "K meson" meant a particle intermediate in mass between the pion and nucleon.
Leprince-Ringuet coined the still-used term "hyperon" to mean any particle heavier than a nucleon.<ref name=":0"/><ref name=":1"/> The Leprince-Ringuet particle turned out to be the K+ meson.<ref name=":0"/><ref name=":1"/>
Initially it was thought that although parity was violated, CP (charge parity) symmetry was conserved. In order to understand the discovery of CP violation, it is necessary to understand the mixing of neutral kaons; this phenomenon does not require CP violation, but it is the context in which CP violation was first observed.
Neutral kaon mixing
File:Kaon-box-diagram-with-bar.svgTwo different neutral K mesons, carrying different strangeness, can turn from one into another through the weak interactions, since these interactions do not conserve strangeness. The strange quark in the anti-Template:SubatomicParticle turns into a down quark by successively absorbing two W-bosons of opposite charge. The down antiquark in the anti-Template:SubatomicParticle turns into a strange antiquark by emitting them.
Since neutral kaons carry strangeness, they cannot be their own antiparticles. There must be then two different neutral kaons, differing by two units of strangeness. The question was then how to establish the presence of these two mesons. The solution used a phenomenon called neutral particle oscillations, by which these two kinds of mesons can turn from one into another through the weak interactions, which cause them to decay into pions (see the adjacent figure).
These oscillations were first investigated by Murray Gell-Mann and Abraham Pais together. They considered the CP-invariant time evolution of states with opposite strangeness. In matrix notation one can write
where ψ is a quantum state of the system specified by the amplitudes of being in each of the two basis states (which are a and b at time t = 0). The diagonal elements (M) of the Hamiltonian are due to strong interaction physics, which conserves strangeness. The two diagonal elements must be equal, since the particle and antiparticle have equal masses in the absence of the weak interactions. The off-diagonal elements, which mix opposite strangeness particles, are due to weak interactions; CP symmetry requires them to be real.
The consequence of the matrix H being real is that the probabilities of the two states will forever oscillate back and forth. However, if any part of the matrix were imaginary, as is forbidden by CP symmetry, then part of the combination will diminish over time. The diminishing part can be either one component (a) or the other (b), or a mixture of the two.
Mixing
The eigenstates are obtained by diagonalizing this matrix. This gives new eigenvectors, which we can call K1, which is the difference of the two states of opposite strangeness, and K2, which is the sum. The two are eigenstates of CP with opposite eigenvalues; K1 has CP = +1, and K2 has CP = −1 Since the two-pion final state also has CP = +1, only the K1 can decay this way. The K2 must decay into three pions.<ref>* Template:Cite book</ref>
Since the mass of K2 is just a little larger than the sum of the masses of three pions, this decay proceeds very slowly, about 600 times slower than the decay of K1 into two pions. These two different modes of decay were observed by Leon Lederman and his coworkers in 1956, establishing the existence of the two weak eigenstates (states with definite lifetimes under decays via the weak force) of the neutral kaons.
It turns out that although the Template:SubatomicParticle and Template:SubatomicParticle are weak eigenstates (because they have definite lifetimes for decay by way of the weak force), they are not quite CP eigenstates. Instead, for small ε (and up to normalization),
and similarly for Template:SubatomicParticle. Thus occasionally the Template:SubatomicParticle decays as a K1 with CP = +1, and likewise the Template:SubatomicParticle can decay with CP = −1. This is known as indirect CP violation, CP violation due to mixing of Template:SubatomicParticle and its antiparticle. There is also a direct CP violation effect, in which the CP violation occurs during the decay itself. Both are present, because both mixing and decay arise from the same interaction with the W boson and thus have CP violation predicted by the CKM matrix. Direct CP violation was discovered in the kaon decays in the early 2000s by the NA48 and KTeV experiments at CERN and Fermilab.<ref>
Template:Cite book</ref>
