Understanding CP-Violation in Physics

[shakeel]

What is Cp-violation

 

[selfAdjoint]

There are three important discrete symmetries in physics. Charge symmetry means that the total electric charge (algebraically added) on both side of a particle interaction should be the same. Parity symmetry means that the mirror image of an interaction should show the same physics as the original. And time symmetry means that physics running backwards should be as valid as physics running forward. (THis is elementary physics we're talking about, no questions of entropy here. Recall Boltzmann caused quite a stink claiming to derive t-asymmetric entropy from t-symmetric elementary physics.) These symmetries are denoted by the captal letters C, P, and T. CP symmetry would be one where failure of either charge symmetry or parity symmetry would be tolerated but not both at the same time. CP violation would be an observed case where they both were violated in the same interaction.

The CPT theorem says that CPT symmetry is never violated. Any one or any two can fail, but not all three at once.

Added: the multiple symmetry works by assigning each component symmetry the value 1, so the product of the components is 1, and then imagining each replaced by -1. So long as the product is unchanged, the multiple symmetry is not violated, but if the product becomes -1, it is violated. Thus a positron viewed as en electron moving backward in time (T=-1) with a positive charge (C=-1) is OK so long as it doesn't violate parity; CPT = (-1)(1)(-1)=1.


Back in the 1950s parity violation was discovered, and made its discoverers' careers. Physicsts working with B particles (mesons involving the bottom quark), are hot on the trail of CP violation.

They are looking for new instances of it. The first instance was discovered in the 1960s; see the posts after this one.[/color]

 

[reilly]

Christensen, Cronin, Fitch and Turlay demonstrated CP violation in the K meson system at Brookhaven, and published in Phys. Rev. in 1964.

Regards,
Reilly Atkinson

 

[dextercioby]

For the interested reader,the article is

J.H.Christenson et al. Phys.Rev.Lett. (sic!) 13 ,138(1964).

Daniel.


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Nice discussion in D.J.Griffiths "Introduction to Elementary Particles",Harper & Row,1987,p.130 pp.134.

 

[shakeel]

thanks
is it violated only in weak intractions only

 

[Chronos]

Correct, it has only been confirmed in weak interactions [and let's not forget kaons as well as mesons]. It's still a bit baffling [at least to me] why it does not show up in strong interactions.

 

[humanino]

People sometimes say :
"start with the required symmetries, and you'll see that you can add another term to the largrangian" :
$${ \cal L}=\bar{\psi}<br /> (\imath\gamma^\mu D_\mu-{m} \exp^{\imath \theta'\gamma_{5}})<br /> \psi<br /> +\frac{1}{4} F^a_{\,\mu\nu}F^{a\mu\nu} -n_f \frac{g^2 \theta}{32\pi^3}F^a_{\,\mu\nu}\tilde{F}^{a\mu\nu}$$
For the sake of completeness, I also have mentionned $$\theta'$$, but one can show that it is unphysical in a regularized theory. It is integrated out, and only the difference between $$\theta$$ and $$\theta'$$ remains. So let us concentrate on $$\theta$$.

For the data : first attempts to explain the vanishing of $$\theta$$ tried to introduce a new particule, known as the "axion" and definitely absent from experimental data.
Also, the electric dipole moment of the neutron is zero, ruling out CP-violation in QCD.

A first reaction could be to answer : so you want to add this $$Tr(F\tilde{F^*})$$. Fine, but why bother ! That pretty much amounts to adding CP-violation by hand. Besides, in terms of gauge connection $$Tr(FF^*)$$ is simply the curvature term, which provides an elegant geometrical interpretation of gluonic gauge fields. Adding $$Tr(F\tilde{F^*})$$ makes the geometrical interpretation much more complicated. And torsion is absent in GR as well !

The electroweak and strong sectors are rather different. Who needs gluons to couple to the axial part of the quark current ?
Why not admit that massless bosons couple only to the vector part of the currents ?

A second reaction : All this is good, but to be honnest, one must confess that it is quite complicated business, involving intantons and the non-perturbative chiral-symmetry breaking of QCD. And even admitting that one starts with a bare lagrangian without CP-violation, one can expect higher-order corrections contributing to CP-violation.


Soft Superweak CP Violation and the Strong CP Puzzle
by Howard Georgi & Sheldon L. Glashow

We discuss a class of models in which CP is violated softly in a heavy sector adjoined to the standard model. Heavy-sector loops produce the observed CP violation in kaon physics, yielding a tiny and probably undetectable value for $$\epsilon^\prime$$. All other CP-violating parameters in the effective low-energy standard model, including the area of the unitarity triangle and $$\bar\theta$$, are finite, calculable and can be made very small. The leading contribution to $$\bar\theta$$ comes from a four-loop graph. These models offer a natural realization of superweak CP violation and can resolve the strong CP puzzle. In one realization of this idea, CP is violated in the mass matrix of heavy majorana neutrinos.

and check as well, if you liked, later work they've done in the same spirit.

TASI Lectures on The Strong CP Problem
Michael Dine

These lectures discuss the $\theta$ parameter of QCD. After an introduction to anomalies in four and two dimensions, the parameter is introduced. That such topological parameters can have physical effects is illustrated with two dimensional models, and then explained in QCD using instantons and current algebra. Possible solutions including axions, a massless up quark, and spontaneous CP violation are discussed.