The CKM Matrix (Non Technical Description)

The Nobel Prize for Physics in 2008 was split between three theoretical particle physicists. Two of the recipients, Makoto Kobayashi and Toshihide Maskawa were awarded the prize for their work on

"the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature".
Quarks are a sub-set of the fundamental particles that exist in nature. The significance of the work by Kobayashi and Maskawa was that by introducing additional quarks which had not been experimentally observed at that time, they were able to introduce a tiny difference between matter and antimatter to theory that was known to exist in nature. This tiny difference is called CP Violation and is related to how the early universe evolved into its present matter dominated state. The BaBar experiment at the Stanford Linear Accelerator Center is one of two experiments that confirmed the theory of Kobayashi and Maskawa (called the CKM mechanism). Physicists from QMUL's Particle Physics Research Center who work on the BaBar experiment have spent many years performing tests of the CKM mechanism. The work led by Dr A Bevan has resulted in the two most precise direct independent tests, and the work led by Dr F Di Lodovico has produced one of the most precise indirect tests of this theory. A more technical description of the tests performed by the QMUL BaBar group is given below.

The CKM Matrix (Technical Description)

It was recently announced that the theoretical physicists Makoto Kobayashi and Toshihide Maskawa share half of the Nobel Prize for Physics in 2008. Their work [1] built on that of the Italian Physicist Nicola Cabibbo [2] to extend the concept of quark mixing from two to three generations of quarks. This resulted in the Cabibbo-Kobayashi-Maskawa quark mixing matrix, a three by three unitary matrix that relates u, c, and t type quarks to d, s, and b type quarks via Higgs Yukawa couplings in the Standard Model of Particle Physics. The CKM matrix is given by

The CKM matrix can be written in terms of four parameters A, Lambda, rho and eta. The latter two parameters rho and eta describe how matter and antimatter differ. In the theory proposed by Kobayashi and Maskawa these parameters can be related to apex of the unitarity triangle:

where we can write the angles alpha, beta and gamma in terms of the elements of the CKM matrix:

Only two of the sides or angles are needed to make a self-consistent test of the CKM mechanism. We can do this using neutral B mesons. Physicists working at QMUL on the BaBar experiment (group web page) at the Stanford Linear Accelerator Center have measured alpha to 7 degrees [3], and beta to 1 degree [4] to test the CKM mechanism. These two measurements provide the most precise set of self consistent tests of matter-antimatter symmetries related to the CKM matrix. The experimental constraint on the unitarity triangle from these alpha and beta measurements is shown in the following:
where the black, brown and grey contours correspond to 68, 90 and 95% confidence levels, respectively. The solution to the right of this plot is excluded by measurements of cos(2beta) through studies of decays like B0->J/Psi K*0.

Indirect constraints on matter-antimatter symmetries are given by measurements of the sides of the unitarity triangle. Physicists from QMUL have measured the magnitude of Vub [5], which is an element of the CKM matrix related to one of the sides of the triange, with an 8% relative uncertainty. By making this third test of the measurement of Vub, we are able to overconstrain our picture of the unitarity triangle to see that CKM matrix really works.

The UT Fit and CKM Fitter groups compile up-to-date world averages of measurements of parameters and constraints on the CKM matrix, except for Vub and Vcb where the averages are compiled by the Selmi-Leptonic sub-group of the Heavy Flavor Averaging Group.

Popular Press Articles

Popular science press articles on the 2008 Nobel Prize are available in Nature, Science, Symmetry Magazine and was also reported in Slac Today.

Scientific References

[1] M. Kobayashi and T. Maskawa, Prog. Theor. Phys 49, 652 (1973).

[2] N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963).

[3] alpha measurement: B. Aubert et al., Phys. Rev. D. 76, 052007 (2007).  
    Dr A Bevan and Dr K A George of QMUL's Particle Physics Research Centre collaborated with scientists, 
    CEA Saclay and SLAC on this analysis. 

[4] beta measurement: B. Aubert et al., [hep-ex] arXiv:0808.1903 (2008).
    Dr A Bevan of QMUL's Particle Physics Research Centre collaborated with scientists from Caltech, 
    UC Irvine, Maryland on this analysis.

[5] Vub measurement: B. Aubert et al., PRL 100 171802 (2008).
    Dr di Lodovico, Dr R. Sacco and Mr C. Clarke of QMUL's Particle Physics Research Centre collaborated 
    with scientists from Ferrara, LBNL, and Valencia on this analysis.