Symmetries of Nonrelativistic Phase Space and the Structure of Quark-Lepton Generation

According to the Hamiltonian formalism, nonrelativistic phase space may be considered as an arena of physics, with momentum and position treated as independent variables. Invariance of x^2+p^2 constitutes then a natural generalization of ordinary rotational invariance. We consider Dirac-like linearization of this form, with position and momentum satisfying standard commutation relations. This leads to the identification of a quantum-level structure from which some phase space properties might emerge. Genuine rotations and reflections in phase space are tied to the existence of new quantum numbers, unrelated to ordinary 3D space. Their properties allow their identification with the internal quantum numbers characterising the structure of a single quark-lepton generation in the Standard Model. In particular, the algebraic structure of the Harari-Shupe preon model of fundamental particles is reproduced exactly and without invoking any subparticles. Analysis of the Clifford algebra of nonrelativistic phase space singles out an element which might be associated with the concept of lepton mass. This element is transformed into a corresponding element for a single coloured quark, leading to a generalization of the concept of mass and a different starting point for the discussion of quark unobservability.Comment: Proceedings of DICE2008, Castiglioncello, Italy, 22nd-26th September 200

Nonleptonic charmed meson decays: Quark diagrams and final-state interactions

Effects of final-state interactions in nonleptonic decays of charmed mesons are studied in the framework of quark-diagram approach. For the case of u-d-s flavour symmetry we discuss how the inelastic coupled-channel rescattering effects (and, in particular, resonance formation in the final state) modify the input quark-diagram weak amplitudes. It is shown that such inelastic effects lead to the appearance of nonzero relative phases between various quark diagrams, thus invalidating some of the conclusions drawn in the past within the diagrammatical approach. The case of SU(3) symmetry-breaking in Cabibbo once-forbidden $D^0$ decays is also studied in some detail.Comment: 29 pages, LaTe

Weak radiative hyperon decays

The problem of weak radiative hyperon decays (WRHD) is reviewed. With the recent measurement of the $\Xi ^0 \to \Lambda \gamma$ asymmetry confirming Hara's theorem, implications from its violation in low-energy theoretical approaches are discussed. It is shown how an underlying symmetry link should be formulated for a successful description of both nonleptonic and radiative weak hyperon decays. The sign of the $\Xi ^0 \to \Lambda \gamma$ asymmetry and the overall size of parity-violating WRHD amplitudes together lead to the resolution of the old S:P problem in nonleptonic decays.Comment: 5 pages, uses espcrc2.sty; invited talk at the 5th International Conference on Hyperons, Charm and Beauty Hadrons (BEACH2002), University of british Columbia, Vancouver, June 25-29,200

Weak Radiative Decays of Hyperons: Quark Model and Nonlocality

It is proved that symmetry structure of the parity-viol. (p.v.) amplitudes of weak radiative hyperon decays in the VMD approach, and the violation of Hara's theorem in particular, are also obtained when direct coupling e_q \bar{q}\gamma_{\mu}q A^{\mu} of photon to quarks is used in place of VMD. Thus, violation of Hara's theorem in VMD-based models does not result from the lack of gauge invariance. It is further shown that, in the static limit of the quark model, the CA commutator term in the p.v. amplitudes of nonleptonic hyperon decays (NLHD) and the parity-violating \Sigma ^+ \to p \gamma decay amplitude are proportional to each other. As a result, Hara's theorem may be satisfied in this limit if and only if the contribution from the CA commutator in NLHD is zero. Violation of Hara's theorem is traced back to the nonlocality of quark model states in the static limit. It is argued that the ensuing intrinsic baryon nonlocality does not have to be unphysical. It is stressed that the \Xi ^0 \to \Lambda \gamma asymmetry will provide very important information concerning the presence or absence of nonlocal features in p.v. photon coupling to baryons at vanishing photon momentum. If the \Xi ^0 \to \Lambda \gamma asymmetry is found negative, Hara's theorem is satisfied but the gauge-invariant quark model machinery predicting its violation must miss some contribution, or be modified. If experiment confirms positive \Xi ^0 \to \Lambda \gamma asymmetry, then, most likely, Hara's theorem is violated. Although positive \Xi ^0 \to \Lambda \gamma asymmetry admits of the possibility that Hara's theorem is satisfied, this alternative is in disagreement with hints suggested by the similarity of photon and vector-meson couplings and the observed size of p.v. nuclear forces.Comment: Revised with minor changes; 31 LaTeX pages, 1 .ps figure; to appear in Acta Phys. Pol.

Hara's theorem, quark model, and gamma_5-dependent renormalization constants

We discuss the applicability of gamma_5-dependent field renormalization as a means of renormalizing away the apparent violation of Hara's theorem observed in the quark model. It is pointed out that a result totally analogous to the violation of Hara's theorem is predicted by the quark model also for neutral baryons. For neutral baryons, however, such a result cannot be renormalized away. This proves that gamma_5-dependent renormalization does not provide a proper way for a hadron-level understanding of the violation of Hara's theorem observed in the quark model.Comment: 8 pages, LaTe

On the Origin of the Violation of Hara's Theorem for Conserved Current

I elaborate on the argument that the violation of Hara's theorem for conserved current requires that the current is not sufficiently well localized. It is also stressed that whatever sign of asymmetry is measured in the $\Xi ^0 \to \Lambda \gamma$ decay, one of the following three statements must be incorrect: 1) Hara's theorem is satisfied, 2) vector meson dominance is applicable to weak radiative hyperon decays, and 3) basic structure of our quark-model description of nuclear parity-violation is correct.Comment: LaTeX, 14 pages, 1 ps figur

Remark on Koide's Z3-symmetric parametrization of quark masses

The charged lepton masses may be parametrized in a Z3-symmetric language appropriate to the discussions of Koide's formula. The phase parameter \delta_L appearing in this parametrization is experimentally indistinguishable from 2/9. We analyse Koide's parametrization for the up (U) and down (D) quarks and argue that the data are suggestive of the low-energy values \delta_U=\delta_L/3=2/27 and \delta_D=2\delta_L/3=4/27.Comment: 6 pages, 1 figure, minor improvements in wordin

The Harari-Shupe Observation without Preons - a Glimpse of Physics to Come?

We argue that one has to distinguish between the Harari-Shupe model (HSM) and the Harari-Shupe observation (HSO). The former - in which quarks and leptons are viewed as composite objects built from confined fermionic subparticles (`rishons') - is known to be beset with many difficulties. The latter may be roughly defined as this part of the HSM that really works. We recall that the phase-space Clifford-algebra approach leads to the HSO without any of the HSM problems and discuss in some detail how this is achieved. The light which the phase-space-based view sheds on the HSO sets then a new direction along which the connection between space and particle properties could be studied and offers a glimpse into weird physics that probably lurks much deeper than the field-theoretical approach of the Standard Model.Comment: 21 page

Weak Radiative Hyperon Decays: Questioning the Basics

Main theoretical approaches to weak radiative hyperon decays are briefly reviewed. It is emphasized that only approaches with great predictive power should be seriously considered when seeking a resolution of the puzzle presented by observed large negative asymmetry alpha (Sigma ^+ --> p gamma). In such cases, asymmetry in the Xi ^0 --> Lambda gamma decay is always large while its sign is positive (negative) if Hara's theorem is violated (satisfied). Measuring this asymmetry is therefore crucial for determining whether the large value of alpha (Sigma ^+ --> p gamma) is due to large SU(3) breaking or to some deeper reason. Some arguments suggesting that violation of Hara's theorem might be a feature of Nature, and hints as to its possible origin are also given.Comment: 8 LaTeX pages, uses hyperon99_paper.sty which is included; Talk given at Hyperon 99: Hyperon Physics Symposium, Batavia, IL, 27-29 Sep 199

Inelastic Final State Interactions in B→PPB \to PP Decays

A method parametrizing all inelastic final state interactions (FSI) in $B\to PP$ decays is presented ($P$ - pseudoscalar meson). The method explicitly shows how rescattering leads to the replacement of the short-distance amplitudes with the effective quark diagram amplitudes, and how it affects the extraction of the unitarity triangle angle $\gamma$ from the data. It is furthermore pointed out that the size of FSI effects cannot be determined from $B^0_d \to K^+ K^-$ decays in a satisfactory way. The case of SU(3)-violating FSI is also discussed. When fits to the branching ratios of all $B \to PP$ decays are performed with all inelastic FSI included, the extracted value of $\gamma$ is shifted down by some $20^o-30^o$ when compared to the no-FSI analyses, and becomes consistent with the Standard Model value of $65^o \pm 7^o$.Comment: Talk presented at the Sixth International Conference on Hyperons, Charm and Beauty Hadrons, IIT, Chicago, June 27--July 3 200