# What is a CP number? In terms of CP-Symmetry and CP-Violation?

When researching the origins of CP-symmetry and CP-violation, and the Fitch-Cronin experiment demonstrating 'indirect' CP-violation, I came across these statements:

https://www2.lbl.gov/abc/wallchart/chapters/05/2.html

Until 1964 it was thought that the combination CP was a valid symmetry of the Universe. That year, Christenson, Cronin, Fitch and Turlay observed the decay of the long-lived neutral K meson, , to p + + p -. If CP were a good symmetry, the would have CP = -1 and could only decay to three pions, not two. Since the experiment observed the two pion decay, they showed that the symmetry CP could be violated. If CPT symmetry is to be preserved, the CP violation must be compensated by a violation of time reversal invariance. Indeed later experiments with K 0 systems showed direct T violations, in the sense that certain reaction processes involving K mesons have a different probability in the forward time direction (A + B Æ C + D) from that in the reverse time direction (C + D Æ A + B). Nuclear physicists have conducted many investigations searching for similar T violations in nuclear decays and reactions, but at this time none have been found.

And:

http://large.stanford.edu/courses/2008/ph204/coleman1/

The first experimental test of CP violation came in 1964 with the Fitch-Cronin experiment. The experiment involved particles called neutral K-mesons, which fortuitously have the properties needed to test CP. First, as mesons, they're a combination of a quark and an anti-quark, in this case down and antistrange, or anti-down and strange. Second, the two different particles have different CP values and different decay modes: K1 has CP = 1 and decays into two pions; K2 has CP = 1 and decays into three. Because decays with larger changes in mass occur more readily, the K1 decay happens 100 times faster than the K2 decay. This means that a sufficiently long beam of neutral Kaons will become arbitrarily pure K2 after a sufficient amount of time.

What does CP = 1 or CP = -1 mean, exactly?

• I hope cutting-and-pasting AND posting links is okay...... Mar 19 at 5:49
• if it is a quote , one inserts >before the quoted paragraph, or makes it into italics Mar 19 at 6:09
• What’s your question? Mar 19 at 17:13

Their eigenvalues are $$\pm 1$$, meaning some states/particles stay the same under these operations, except for an overall — sign in the second option. Before the mid 50s, it had been established that the strong and electromagnetic interactions preserved P and C, that is the left-hand side and the right-hand side of a reaction/decay, had the eigenvalues of C and P match across these sides.
But then it was discovered in weak interactions that the P and C eigenvalues of the left-hand side and the right-hand side did not match. P and C were thus said to be violated, or equivalently, the weak interactions are not P and C symmetric. Nevertheless, CP was still apparently preserved in these reactions, as formally proposed by Landau. This means that the product of the C and P eigenvalues, the eigenvalue of CP (which is therefore also $$\pm 1$$) stayed the same across a reaction, thereby restoring order.