Model-independent access to the structure of quark flavor mixing

Abstract

We show that the observed pattern of quark flavor mixing, such as $|{V}_{us}|\ensuremath{\simeq}|{V}_{cd}|$, $|{V}_{cb}|\ensuremath{\simeq}|{V}_{ts}|$, $|{V}_{cd}/{V}_{td}|\ensuremath{\simeq}|{V}_{cs}/{V}_{ts}|\ensuremath{\simeq}|{V}_{tb}/{V}_{cb}|$, and $|{V}_{ub}/{V}_{cb}|<|{V}_{td}/{V}_{ts}|$, can essentially be understood in the chiral and heavy quark mass limits. In particular, the phenomenologically successful relations $|{V}_{ub}/{V}_{cb}|\ensuremath{\sim}\sqrt{{m}_{u}/{m}_{c}}$ and $|{V}_{td}/{V}_{ts}|\ensuremath{\simeq}\sqrt{{m}_{d}/{m}_{s}}$ can be reasonably conjectured in the ${m}_{b}\ensuremath{\rightarrow}\ensuremath{\infty}$ and ${m}_{t}\ensuremath{\rightarrow}\ensuremath{\infty}$ limits, respectively. We stress that the strength of weak $CP$ violation in the quark sector is determined by the moduli of the four corner elements of the Cabibbo-Kobayashi-Maskawa matrix. A comparison between strong and weak $CP$-violating effects in the standard model is also made.