Rephasing invariants of the Cabibbo-Kobayashi- Maskawa matrix

Journal Article · Tue Mar 15 04:00:00 EDT 2016 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4944427· OSTI ID:22597049

Pérez R, H.

The paper is motivated by the importance of the rephasing invariance of the CKM (Cabibbo-Kobayashi-Maskawa) matrix observables. These observables appear in the discussion of the CP violation in the standard model (Jarlskog invariant) and also in the renormalization group equations for the quark Yukawa couplings. Our discussion is based on the general phase invariant monomials built out of the CKM matrix elements and their conjugates. We show that there exist 30 fundamental phase invariant monomials and 18 of them are a product of 4 CKM matrix elements and 12 are a product of 6 CKM matrix elements. In the main theorem we show that a general rephasing invariant monomial can be expressed as a product of at most five factors: four of them are fundamental phase invariant monomials and the fifth factor consists of powers of squares of absolute values of the CKM matrix elements. We also show that the imaginary part of any rephasing invariant monomial is proportional to the Jarlskog’s invariant J or is 0.

• OSTI ID: 22597049
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 3 Vol. 57; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CP INVARIANCE
KOBAYASHI-MASKAWA MATRIX
MATRIX ELEMENTS
QUARKS
RENORMALIZATION
STANDARD MODEL
YUKAWA POTENTIAL