P. Kielanowski

The beta decay of hyperons

Hyperon semileptonic decays.- Low statistics experiments.- The Cabibbo theory.- Radiative corrections.- Other corrections.- Comparison between theory and experiment.- A Revision of postulates: Symmetry breaking and other possibilities.- Spectrum generating SU(3).- High statistics experiments.- Conclusion.- Numerical Formulas for the Transition Rates and Angular Coefficients.- Addendum.

A quantum mechanical arrow of time and the semigroup time evolution of Gamow vectors

The exponential decay (or growth) of resonances provides an arrow of time which is described as the semigroup time evolution of Gamow vector in a new formulation of quantum mechanics. Another direction of time follows from the fact that a state must first be prepared before observables can be measured in it. Applied to scattering experiments, this produces another quantum mechanical arrow of time. The mathematical statements of these two arrows of time are shown to be equivalent. If the semigroup arrow is interpreted as microphysical irreversibility and if the arrow of time from the prepared in‐state to its effect on the detector of a scattering experiment is interpreted as causality, then the equivalence of their mathematical statements implies that causality and irreversibility are interrelated.

The preparation-registration arrow of time in quantum mechanics

Abstract A part from the “collapse of the wave function” axiom, there is a quantum mechanical arrow of time expressing the fact that a state needs to be first prepared before observables can be measured in it. We show that this preparation-registration arrow of time is identical to the arrow for exponential decay (or growth) of resonance by Gamow vectors.

Theorems on the renormalization group evolution of quark Yukawa couplings and CKM matrix

Abstract We analyze the two loop renormalization group equations in the standard model and its extensions for the coupling constants and the quark Yukawa couplings. The key point of our analysis is the observed hierarchy of the quark masses and the CKM matrix. For the one loop evolution we find the explicit solution for the evolution of the Yukawa couplings and show the following: 1. the CKM matrix depends on the energy on only one function of energy; 2. the ratios of the down quark masses depend on the energy through the same function as the CKM matrix; 3. the diagonalizing matrices of the biunitary transformation of the up quarks are energy independent. Next we give the explicit form of the two loop corrections to the evolution of the quark Yukawa couplings and show that the relative corrections are of the order λ 4 for the quark Yukawa couplings and of the order λ 5 for the CKM matrix. Finally we give the equations of the one loop evolution of the squares of the matrix elements of the CKM matrix and their explicit solution.

Semigroup representations of the Poincare group and relativistic Gamow vectors.

Abstract Gamow vectors are generalized eigenvectors (kets) of self-adjoint Hamiltonians with complex eigenvalues ( E R ∓ iΓ /2) describing quasistable states. In the relativistic domain this leads to Poincare semigroup representations which are characterized by spin j and by complex invariant mass square s = s R = M R − i 2 Γ R 2 . Relativistic Gamow kets have all the properties required to describe relativistic resonances and quasistable particles with resonance mass M R and lifetime ℏ/ Γ R .

Scale dependence of the quark masses and mixings: Leading order

We consider the renormalization group equations (RGE) for the couplings of the standard model and its extensions. Using the hierarchy of the quark masses and of the Cabibbo-Kobayashi-Maskawa (CKM) matrix our argument is that a consistent approximation for the RGE should be based on the parameter

Multipole expansion in magnetostatics

\ensuremath{\lambda}=|{V}_{\mathrm{us}}|\ensuremath{\approx}0.22.

Time Asymmetric Quantum Mechanics

We consider the RGE in the approximation where we neglect all the relative terms of the order

A highly significant deviation from the Cabibbo theory in hyperon leptonic decays

\ensuremath{\sim}{\ensuremath{\lambda}}^{4}

Unstable quantum oscillator

and higher. Within this approximation we find the exact solution of the evolution equations of the quark Yukawa couplings and of the vacuum expectation value of the Higgs field. Then we derive the evolution of the observables: quark masses, CKM matrix, Jarlskog invariant, Wolfenstein parameters of the CKM matrix and the unitarity triangle. We show that the angles of the unitarity triangle remain constant. This property may restrict the possibility of new symmetries or textures at the grand unification scale.