Search results for "Matrix"
showing 10 items of 3205 documents
ΔF=2 effective Lagrangian in theories with vector-like fermions
1997
In this work we analyze a new piece present in the $\Delta F = 2$ effective Lagrangian in models with extra vector-like quarks. This piece, which was not taken into account previously, is required in order to preserve gauge invariance once the unitarity of the CKM matrix is lost. We illustrate the effects of this new piece in both, CP conserving and CP violating processes.
Follow-up on non-leptonic Kaon decays at large $N_c$
2018
We report on the status of our dynamical simulations of a $SU (N_c )$ gauge theory with $N_c=3-6$ and $N_f =4$ fundamental fermions. These ensembles can be used to study the Large $N_c$ scaling of weak matrix elements in the GIM limit $m_c=m_u$, that might shed some light on the origin of the $\Delta I=1/2$ rule. We present preliminary results for the $K \to \pi$ matrix elements in the $N_c=3$ dynamical simulations, where we observe a significant effect of the quark loops that goes in the direction of enhancing the ratio of $A_0/A_2$ amplitudes. Finally, we present the relevant NLO Chiral Perturbation Theory predictions for the relation between $K \to \pi $ and $K \to \pi \pi$ amplitudes in…
High-precision atomic mass measurements for a CKM unitarity test
2013
Abstract The Cabibbo–Kobayashi–Maskawa (CKM) quark-mixing matrix describes the transformation of quarks from weak-force eigenstates to mass eigenstates. The most contributing element in this matrix is the up-down matrix element V ud , derived in most precise way from the nuclear beta decays and in particular, from decays having superallowed 0 + → 0 + decay branch. What high-precision mass spectrometry community can offer are decay energies of such decays derived from parent–daughter mass differences, which are ideally, and in almost all cases, determined with Penning trap mass spectrometry directly from parent–daughter cyclotron frequency ratio. Typically frequency (and thus mass) ratios a…
Semileptonic decays of the lightJP=1/2+ground state baryon octet
2008
We calculate the semileptonic baryon octet-octet transition form factors using a manifestly Lorentz covariant quark model approach based on the factorization of the contribution of valence quarks and chiral effects. We perform a detailed analysis of SU(3)-breaking corrections to the hyperon semileptonic decay form factors. We present complete results on decay rates and asymmetry parameters including lepton mass effects for the rates.
Weak Quark Mixing and the CKM Matrix
2003
Weak quark mixing and the Cabibbo-Kobayashi-Maskawa (CKM) matrix are outlined in this chapter.
Experimental analysis of weak mixing angles between three or four quark generations
1987
New data on weak quark decays and on weak heavy quark production are used to obtain the allowed ranges of elements of the quark mixing matrix for three or four generations of sequential quarks. The analysis yields allowed ranges for the three mixing angles in the six-quark case and for the six mixing angles in the eight-quark case.
Teaching stable two-mirror resonators through the fractional Fourier transform
2009
We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation–lens–propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam q-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincid…
A Tutorial Approach to the Renormalization Group and the Smooth Feshbach Map
2006
2.1 Relative Bounds on the Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 The Feshbach Map and Pull-Through Formula . . . . . . . . . . . . . . . . . 4 2.3 Elimination of High-Energy Degrees of Freedom . . . . . . . . . . . . . . . . 5 2.4 Normal form of Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Banach Space of Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6 The Renormalization Map Rρ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Relativistic scattering theory of charged spinless particles
1986
In the context of a relativistic quantum mechanics we discuss the scattering of two and three charged spinless particles. The corresponding transition operators are shown to satisfy four-dimensional Lippmann-Schwinger and eight-dimensional Faddeev-type equations, respectively. A simplified model of two particles with Coulomb interaction can be solved exactly. We calculate: (i) The partial waveS-matrix from which we extract the bound state spectrum. The latter agrees with a fourth-order result of Schwinger, (ii) The full scattering amplitude which in the weakfield limit coincides with the expression derived by Fried et al. from eikonalized QED.
Definition of an appropriate free dynamics and the physical S-matrix in multichannel hyperradial adiabatic scattering
2010
In the hyperradial adiabatic (HA) treatment of the three-body problem the total wave function is i expanded as ΨHA(R, ξ, η) = R−5/2 ∑iχi(R)φi(R|ξ, η),where R denotes the hyperradius and (ξ , η) are internal hyperangles. Integration over ξ and η converts the Schrödinger equation into a system of coupled hyperradial equations. It is a well-known fact that, within the HA approach, the non-adiabatic corrections that couple channels converging to the same asymptotic configuration can show an unphysical long-range behavior ∼ 1/R. Though the latter is of purely kinematic origin and arises from the use of the hyperradius instead of the pertinent Jacobi variables, it is nevertheless the source of the…