Hadronic Sector Research Articles

The standard model at low energies

The hadronic sector of the standard model at low energies is described by a non--decoupling effective field theory, chiral perturbation theory. An introduction is given to the construction of effective chiral Lagrangians, both in the purely mesonic sector and with inclusion of baryons. The connection between the relativistic formulation and the heavy baryon approach to chiral perturbation theory with baryons is reviewed.

Flavor violations in no-scale flipped SU(5)×U(1)

We study lepton-number violations in the flipped SU(5) × U(1) model in the context of no-scale supergravity. We find that the experimental limits on μ → eγ, μ → ee e , and μ conversion in nuclei generally imply an upper bound on the top quark mass and a lower bound on the gaugino mass. We conclude that the seed of supersymmetry breaking in no-scale models (gaugino masses) radically changes some results obtained in “minimal” N = 1 supergravity in the leptonic sector, while results in the hadronic sector (e.g. K− K , B− B mixings, and b→s γ) remain essentially unchanged.

Hadron spectroscopy and form factors at quark level

The theoretical status of hadrons as quark composites is examined from the point of view of a simultaneous understanding of their on-shell (mass spectra) and off-shell (form factors, transition amplitudes) properties. To that end we first offer a perspective view of the emerging scenario in quark physics since the seventies, preceded by a quick overview of some important ideas and models in the pre-QCD phase that were to determine the shape of the subsequent (post-QCD) developments. The primary emphasis is on theoretical approaches to effective confinement (pending a formal resolution of the confinement problem within a QCD-Lagrangian framework, Lattice or otherwise), in providing a fuller perspective from high to low energy physics or vice-versa. To that end greater stress is laid on light quark systems which are more sensitive to the confinement regime, and more prone to relativistic effects than on heavy quarkonia (on which many reviews exist). Two broad theoretical approaches obeying Lorentz and gauge invariance are identified: (i) QCD sum rules as a means of extrapolation from high to low energies; and (ii) dynamical equations for providing a microcausal link in the opposite direction (from low to high energies). The latter represents the major focus of attention in this article, with the Bethe-Salpeter Equation (BSE) providing a formal plank for a comparative assessment of several models. The Null-plane ansatz which facilitates the reduction of the 4-D BSE to a covariant 3-D form also provides the language for its comparison with other covariant 3-D equations. In particular, attention is drawn to the interesting possibility of reconstructing the 4-D BS wave function from its 3-D form (in a two-tier fashion) as a practical tool for generating higher Fock-space components ( q q effects) in the BS wave function, and (more interestingly) for a clean separation between soft and hard QCD effects. To illustrate one such practical tool for an integrated view of different hadronic sectors within a single framework, the results of a two-tier BS model are presented in respect of q q , qqq, gg, ggg, gq q states and compared with experiment as well as with the results of other contemporary models. The N.R Resonating Group Method, which becomes necessary for bigger (six-quark) systems is briefly discussed from the point of view of its compatibility with a relativistic form of quark dynamics motivated from the BSE.

Fritzsch-Stech model in SO(10).

The combined Fritzsch-Stech model for quarks is consistent with our present knowledge of quark masses and mixing angles. A possible way to extend it to leptons---by using an SO(10) framework---has been suggested by Bottino, Kim, Nishiura, and Sze. We investigate this model further and find some new features. It is first noted that the allowed quark masses are somewhat sensitive to the experimental uncertainties in the input parameters. This is carefully analyzed and we find that the original Stech Ansatz for the hadron sector is consistent. However, if the top-quark mass is greater than about 45 GeV, this Ansatz must be slightly modified. It is found that in a model of the present type the seesaw mechanism for neutrino masses may be drastically modified. This occurs because in SO(10) it is likely that the matrix of heavy ``right-handed'' neutrinos is close to a singular matrix. This feature is analyzed both analytically and numerically. Various patterns involving two extremely light neutrinos and one intermediate-mass (order of several MeV) neutrino which may arise are compared with experiment. More orthodox and perhaps more probable patterns for neutrino masses are also discussed. The lepton-mixing matrices are predicted and the results support recent explanations of the solar-neutrino paradox.

Kobayashi-Maskawa type of hard-CP-violation model with three-generation Majorana neutrinos.

Within the framework of the Kobayashi-Maskawa (KM) type of hard CP-violation model with three-generation Majorana neutrinos, we point out that on-shell CP-violation phenomena (i.e., CP-violating effects taking place in on-shell processes), which are characteristic of Majorana neutrinos, can only occur in total-lepton-number-conserving reactions, and are unobservably small. Off-shell CP-nonconserving effects which arise from gauge bosons are undetectable, but those which are mediated by Higgs bosons could be seen in certain rare decays. It is emphasized that CP-odd effects intrinsic to Majorana behavior depend not only on the two CP-violating Majorana phases but also on the KM phase. We then demonstrate why the KM model, which has rich implications in the hadronic sector, leads to no observable CP-violating effects in leptonic processes (except in neutrino oscillations) directly related to the CP-odd KM phase.

Chiral symmetry breaking in QCD; Mesons as spin waves

The strong chiral symmetry breaking in Wilson's lattice version of QCD is discussed and interpreted as a necessary manifestation of the triangle anomaly. At strong coupling the effective hamiltonian acting in the s-wave hadron sector is found to describe a generalized antiferromagnet which is analyzed with the 1 2 S (= 1/N, N = N color ) expansion known in the theory of magnetism. Mesons emerge as spin waves: pseudoscalars as Nambu-Goldstone bosons, vectors as “dormant” Goldstone bosons. Current and dynamical quark masses are identified, such that m P 2 ∫ m(cur), m v≈2[ m(cur) + m(fyn)], and a fit to the particle spectrum gives m(dyn) = 390 MeV, m u,d(cur) = 5.4 MeV, m s(cur) = 140 MeV, m c(cur) = 1.07 GeV. Static baryons emerge with a mass m B = N[ m(dyn) + m(cur)] + a contribution which is argued to vanish in the continuum limit. Vector and axial vector currents are defined on the lattice and studied at strong coupling. The relations 1 = 3 5 g A γ ϱ(f π/m ϱ)(Z π/Z ϱ) 1 2 , Z π / Z ϱ = 3.0 are found to agree with experiment. The resolution of the U(1) problem at strong coupling is discussed.

Superweak CP violation mediated by neutral Higgs bosons

I t is known that the weak and electromagnetic interactions can be unified in the framework of gauge theories (~). Actually, the bulk of the experimental data, in various domains, included atomic physics (~) and neutrino physics are in very good agreement with the minimal model of W]~I~BERG and SALAM (3). Nevertheless some controversies still remain in the hadronic sector with regard to the AI ~ 89 rule (4) and to the CP violation (~). The main point is that CP violation has been only detected in the (K0, Ko) system, and that the upper experimental linlit of the electric-dipole moment of the neutron (EDM), becomes smaller and smaller so tha~ it appears that a gauge theory of weak interactions must describe CP violation in a superweak way (e), preserving at the same t ime the features of the WS model. We show in this note tha t this can be accomplished using a two-Higgs-doublet boson model (7). The key is that only one of the two doublets entering in the composition of the invariant scalar energy term and in the Yukawa flavour interaction, has a complex mixing. Then CP violation can be restricted to the Higgs potential , and can occur in Lhe theory if o~e chooses the set of parameters of the Higgs potential in such a way that spontaneous symmetry breaking (1) generates a tr iplet and a singlet of Higgs bosons of different masses. According to this scheme let

Hadronic wave equations from lattice gauge theories: The breathing modes on a restricted lattice

A continuum limit of the lattice gauge theory restricted to the hadron sector is proposed. Details of the appropriateness of formulating such a limit within a specific scheme of approximation are discussed for the quarkless hadron sector. The general method is then applied to the gauge fields, with the restriction that motions occur only along one spatial direction. This leads to a continuum eigenvalue equation for the spectrum of internal excitations associated with fluctuations in the length of the electric flux line. In addition, a nontrivial renormalization condition is encountered if one insists on a relativistic form for the spectrum. A speculative method for dealing with this condition is proposed---the method eliminates the lattice spacing and removes the coupling constant as a free parameter, as in dimensional transmutation. Alternative possibilities for restoring covariance in the hadronic sector of the theory are discussed.

Implications of parity violation in atoms for gauge theories

The knowledge to be gained on neutral currents from parity-violating observables in heavy atoms is studied. After isolating the relevant couplings, the major part of the analysis is done within the framework ofSU 2 ⊗U 1 unified gauge theories of weak and electromagnetic interactions. The leptonic and hadronic sectors of these models are studied separately, by means of the available information from neutrino physics, to impose restrictions on the mass of the neutral intermediate boson and on the unification angle. The observable in atoms, which provides a link between the two sectors, is found to be powerful in discriminating among models.

Leptonic octets and heavy-lepton decays in an SU(3) gauge theory

Unified weak-electromagnetic gauge theories based on the group SU(3) are discussed in some detail. In particular, the consequences of assigning the electron, the muon, and the newly discovered lepton of Perl et al. to an octet are explored. Almost uniquely, this leads to the prediction that the Perl particle decays preferentially into muons and neutrinos rather than into electrons and neutrinos. This means that in the ${e}^{+}{e}^{\ensuremath{-}}$ annihilation experiments there should be more ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ pairs than ${e}^{+}{e}^{\ensuremath{-}}$ pairs, after subtraction of background. Such a situation would be very difficult to achieve naturally in the framework of an SU(2) \ifmmode\times\else\texttimes\fi{} U(1) gauge theory. The hadron sector of the theory and neutral-current reactions are also discussed as well as some general considerations on the construction of weak-interaction gauge theories with large groups.

Incorporation ofCPviolation with a unified renormalizable gauge theory

A unified renormalizable gauge theory with $\mathrm{CP}$ violation is presented without having to introduce heavy leptons. The theory utilizes three triples of quarks and three charmed quarks. Models in the SU(2) \ifmmode\times\else\texttimes\fi{} U(1) and SU(2) \ifmmode\times\else\texttimes\fi{} SU(2) \ifmmode\times\else\texttimes\fi{} U(1) gauge groups are constructed. The $\mathrm{CP}$-violating phases are in the hadronic sector which is partly composed of a mixture of two triples. The lepton-hadron anomaly cancellation mechanism is adopted, and a superweak type of $\mathrm{CP}$ violation results from the model.

Properties of hadron states containing a condensed phase of quark-antiquark excitations

We analyze how one-particle states can arise in a field theory of (three) quark triplets with current-current interactions which does not produce asymptotic quark states. A condensed phase of quark-antiquark pairs resembling the corresponding phase in a superconductor is responsible for the lack of stable states in the sectors with triality different from zero, provided that stable one-particle states indeed exist in the triality zero sectors, corresponding to stable configurations of valence quarks in the presence ofthe condensed phase. The precise dynamics of valence quarks is beyond the scope of the present model which is meant to illustrate a mechanism which prevents the basic quanta of the underlying fields to become asymptotically isolated and still eventually generates stable states in the hadronic sectors without inconsistencies.