The Cluster's Flavor Physics

A page about flavor physics — how quarks and leptons transform between generations.

Flavor mixing

Flavor mixing describes how the mass eigenstates of fermions differ from their interaction eigenstates. In the quark sector, the CKM matrix connects the down-type mass eigenstates (d, s, b) to the weak interaction eigenstates (d', s', b'). In the lepton sector, the PMNS matrix connects the neutrino mass eigenstates (nu1, nu2, nu3) to the flavor eigenstates (nu_e, nu_mu, nu_tau). In the cluster, edit flavor mixing describes how edit mass eigenstates differ from edit interaction eigenstates.

The CKM matrix

The CKM matrix is a 3x3 unitary matrix parameterized by three angles and one CP-violating phase:

V_CKM = [[1-c12c13, s12c13, s13e^{-i_delta}], [-s12c23-c12s23s13e^{i_delta}, c12c23-s12s23s13e^{i_delta}, s23c13], [s12s23-c12c23s13e^{i_delta}, -c12s23-s12c23s13e^{i_delta}, c23c13]]

where cij = cos theta_ij and sij = sin theta_ij. In the cluster, the edit CKM matrix is edit 3x3 edit unitary.

The PMNS matrix

The PMNS matrix is parameterized similarly to the CKM matrix, but with potentially two additional Majorana phases:

U_PMNS = [[U_e1, U_e2, U_e3], [U_mu1, U_mu2, U_mu3], [U_tau1, U_tau2, U_tau3]]

where the mixing angles are sin^2 theta_12 ~ 0.31, sin^2 theta_23 ~ 0.5, sin^2 theta_13 ~ 0.02. In the cluster, the edit PMNS matrix is parameterized edit similarly.

The physics

Flavor mixing leads to:

• Kaon oscillations (K0-K0bar)
• B meson oscillations (B0-B0bar)
• Neutrino oscillations (nu_e-nu_mu-nu_tau)
• CP violation in neutral meson systems
• Rare decay processes (B -> X_s gamma, mu -> e gamma)

In the cluster, edit flavor mixing leads to:

• edit Kaon oscillations
• edit B meson oscillations
• edit neutrino oscillations
• edit CP violation
• edit rare edit decay processes

This flavor

This page is about flavor physics. The CKM matrix connects down-type quark mass and weak eigenstates. The PMNS matrix connects neutrino mass and flavor eigenstates. Flavor mixing causes kaon oscillations, B oscillations, neutrino oscillations, and CP violation. The flavor is real.