THE KOBAYASHI-MASKAWA MIXING MATRIX
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Gilman, F.↗
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The Kobayashi-Maskawa Mixing Matrix
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Gilman, F.↗
Rephasing invariants of the Cabibbo-Kobayashi- Maskawa matrix
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.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Quark and lepton mixing as manifestations of violated mirror symmetry
The existence of heavy mirror analogs of ordinary fermions would provide deeper insight into the gedanken paradox appearing in the Standard Model upon direct parity violation and consisting in a physical distinguishability of left- and right-hand coordinate frames. Arguments are presented in support of the statement that such mirror states may also be involved in the formation of observed properties of the system of Standard Model quarks and leptons—that is, their mass spectra and their weak-mixing matrices: (i) In the case of the involvement of mirror generations, the quark mixing matrix assumes the experimentally observed form. It is determined by the constraints imposed by weak SU(2) symmetry and by the quark-mass hierarchy. (ii) Under the same conditions and upon the involvement of mirror particles, the lepton mixing matrix (neutrino mixing) may become drastically different from its quark analog—the Cabibbo-Kobayashi-Maskawa matrix; that is, it may acquire properties suggested by experimental data. This character of mixing is also indicative of an inverse mass spectrum of Standard Model neutrinos and their Dirac (not Majorana) nature.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Status of |V{sub cb}| and |V{sub ub}| CKM matrix elements
We summarize the status of |V{sub cb}| and |V{sub ub}| determinations, including the long standing tension among exclusive and inclusive determinations. We also discuss B meson semi-leptonic decays to excited states of the charm meson spectrum and leptonic and semileptonic B decays into final states which include τ leptons.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Correlation measurements in nuclear {beta}-decay using traps and polarized low energy beams
Precision measurements in nuclear {beta}-decay provide sensitive means to test discrete symmetries in the weak interaction and to determine some of the fundamental constants in semi-leptonic decays, like the coupling of the lightest quarks to charged weak bosons. The main motivation of such measurements is to find deviations from Standard Model predictions as possible indications of new physics. In this contribution I will focus on two topics related to precision measurements in nuclear {beta}-decay: i) the determination of the V{sub ud} element of the Cabibbo-Kobayashi-Maskawa quark mixing matrix from nuclear mirror transitions and ii) the search for exotic scalar or tensor contributions from {beta}{nu} angular correlations. The purpose is to underline the role being played by experimental techniques based on the confinement of radioactive species with atom and ion traps as well as the plans to use low energy polarized beams.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
The influence of pairing correlations on the isospin symmetry breaking corrections of superallowed Fermi beta decays
Within the framework of quasi-particle random phase approximation, the isospin breaking correction of superallowed 0{sup +} {yields} 0{sup +} beta decay and unitarity of Cabibbo-Kobayashi-Maskawa mixing matrix have been investigated. The broken isotopic symmetry of nuclear part of Hamiltonian has been restored by Pyatov's method. The isospin symmetry breaking correction with pairing correlations has been compared with the previous results without pairing. The effect of pairing interactions has been examined for nine superallowed Fermi beta decays; their parent nuclei are {sup 26}Al, {sup 34}Cl, {sup 38}K, {sup 42}Sc, {sup 46}V, {sup 50}Mn, {sup 54}Co, {sup 62}Ga, {sup 74}Rb.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Superallowed nuclear beta decay: Precision measurements for basic physics
For 60 years, superallowed 0{sup +}{yields}0{sup +} nuclear beta decay has been used to probe the weak interaction, currently verifying the conservation of the vector current (CVC) to high precision ({+-}0.01%) and anchoring the most demanding available test of the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix ({+-}0.06%), a fundamental pillar of the electroweak standard model. Each superallowed transition is characterized by its ft-value, a result obtained from three measured quantities: the total decay energy of the transition, its branching ratio, and the half-life of the parent state. Today's data set is composed of some 150 independent measurements of 13 separate superallowed transitions covering a wide range of parent nuclei from {sup 10}C to {sup 74}Rb. Excellent consistency among the average results for all 13 transitions - a prediction of CVC - also confirms the validity of the small transition-dependent theoretical corrections that have been applied to account for isospin symmetry breaking. With CVC consistency established, the value of the vector coupling constant, G{sub V}, has been extracted from the data and used to determine the top left element of the CKM matrix, V{sub ud}. With this result the top-row unitarity test of the CKM matrix yields the value 0.99995(61), a result that sets a tight limit on possible new physics beyond the standard model. To have any impact on these fundamental weak-interaction tests, any measurement must be made with a precision of 0.1% or better - a substantial experimental challenge well beyond the requirements of most nuclear physics measurements. I overview the current state of the field and outline some of the requirements that need to be met by experimentalists if they aim to make measurements with this high level of precision.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Constraining astrophysical neutrino flavor composition from leptonic unitarity
The recent IceCube observation of ultra-high-energy astrophysical neutrinos has begun the era of neutrino astronomy. In this work, using the unitarity of leptonic mixing matrix, we derive nontrivial unitarity constraints on the flavor composition of astrophysical neutrinos detected by IceCube. Applying leptonic unitarity triangles, we deduce these unitarity bounds from geometrical conditions, such as triangular inequalities. These new bounds generally hold for three flavor neutrinos, and are independent of any experimental input or the pattern of lepton mixing. We apply our unitarity bounds to derive general constraints on the flavor compositions for three types of astrophysical neutrino sources (and their general mixture), and compare them with the IceCube measurements. Furthermore, we prove that for any sources without ν{sub τ} neutrinos, a detected ν{sub μ} flux ratio < 1/4 will require the initial flavor composition with more ν{sub e} neutrinos than ν{sub μ} neutrinos.
79 ASTRONOMY AND ASTROPHYSICS↗
B decays into a scalar/tensor meson: In pursuit of determining the CKM angle {gamma}
In this work, I suggest a new way for determining the CKM angle {gamma} via B decays into a scalar/tensor meson without any hadronic uncertainty. The proposed idea makes profits of the two triangles formed by the B{sup {+-}}{yields}(D{sup 0},D{sup 0},D{sub CP}{sup 0})K*{sub 0(2)}{sup {+-}} (1430) decay amplitudes. The advantages in it are large CP asymmetries and the avoidance of the use of doubly Cabibbo-suppressed D decays. Branching ratios of B{sup {+-}}{yields}(D{sup 0},D{sup 0},D{sub CP}{sup 0})K*{sub 0(2)}{sup {+-}} (1430) are estimated to have the order 10{sup -6}- 10{sup -5} and therefore measurable on the ongoing LHCb experiment and future experimental facilities. The usefulness of other related channels, for instance the neutral B{sub d} decays into DK*{sub 0(2)} (1430) and B{sub s}{yields}(D{sup 0},D{sup 0})M(M f{sub 0}(980),f{sub 0}(1370),f Prime {sub 2}(1525),f{sub 1}(1285),f{sub 1}(1420),h{sub 1}(1180)), the B{yields}D{sup {+-}}a{sub 0,2}{sup {+-}} for the extraction of {gamma}+ 2{beta} and the B{sub s}{yields}D{sup {+-}}K*{sub 0,2}{sup {+-}} to access {gamma}+ 2{beta}{sub s}, is also discussed in brevity.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
50 years of CP violation — What have we learned?
Early after the discovery of CP violation, the explanation of how the Standard Model of particle physics could allow CP violation was quickly given, but it took many years for the original observation to be unequivocally explained on that basis. It was also proposed that this observation opened up the possibility that we could now explain the fact that the universe is made of matter. Remarkably, 50 years later we have no evidence in particle physics that there is any CP violation except that of the Kobayashi Maskawa mechanism of the standard model. Yet we fail completely to explain the baryon asymmetry of the Universe through that mechanism. After reviewing the main points in the history I describe the present experimental attempts to find CP violation beyond the standard model, and explain the theoretical attempts to explain the matter in the Universe.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗