Adjoint representation admixture to weak nonleptonic decays in SU(4) and SU(8)

In order to remove some of the unsatisfactory features of the GIM model, we consider15-admixture in SU(4). ΔC=±ΔS decays remain unaffected. Lee-Sugawara sum-rule is obtained.15-admixture is extended then to63-admixture in SU(8). The most general Hamiltonian (H _w∼63⊕720⊕1232) in SU(8) is found to give Lee-Sugawara relation and Σ₊ ⁺=0 forS-wave decays of uncharmed baryons. Decay amplitude relations for ΔC=−1, ΔS=0 mode are obtained.     

Magnetic moments of baryons in broken SU(4)

Assuming that the anomalous magnetic moment interaction has the formaT ₁ ¹ +bT ₂ ² +cT ₄ ⁴ +sT _α ^α in SU(4), which may arise due to symmetry breaking or some other dynamical effects, we have obtained the magnetic moments and the transition moments of the ordinary and charmed baryons.     

Non-leptonic weak decays of charmed baryons

It is shown that the ΔC _h=ΔS decays of a baryon sextuplet, triplet and singlet of SU (3), into meson and baryon, can provide simple tests of the iscspin and SU (3) transformation properties of the ΔC _h=ΔS non-leptonic interaction in the Glashow Iliopoulos-Maiani scheme.     

Chiral SU(4) × SU(4) breaking: masses and decay constants of charmed hadrons

The (4, 4*) ⊕ (4*, 4) model of broken chiral SU (4) × SU (4) symmetry has been used to calculate the third-order coupling constants involving charmed and ordinary pseudoscalar mesons. These coupling constants are exploited to derive some interesting new relations among the masses and decay constants of these charmed particles. Using the known masses and decay constants as inputs, we exploit these relations to predict:F _D = −1·41F _π ,F _F = −1·13F _π ,F _D/F_F = 1·25,m(D _s) = 1·43 GeV,m(F _s) = 1·39 GeV andm(K _s) = 1·02 GeV.     

Non-leptonic weak charmed baryon decays in theSU(4) semidynamical scheme

We study here the Cabibbo enhanced charmed baryon decays in theSU(4) semidynamical model. The weak Hamiltonian 20″ + 15 + 45 + 45* can have the parity violating amplitude for charmed baryon decays. Decay width and α for some modes are also calculated.     

Magnetic moments ofb-quark baryons in broken SU(5) symmetry

The magnetic moments ofb-quark baryons within the framework of five quark models are derived. Also the transition magnetic moments of variousb-quark baryons are calculated.     

SU (8) mass relations amongJ P=1/2+ and 3/2+ baryons

Mass relations among charmed and uncharmed baryons belonging to20 and20′ multiplets of SU(4) are derived in the framework of SU(8) symmetry, Spin singlet mass breaking interaction is found to give unsatisfactory results. Second order effects and spin triplet mass breaking interactions are studied to improve the situation.     

SU(3) symmetry breaking in charmed baryon decays

We explore the breaking effects of the SU(3) flavor symmetry in the singly Cabibbo-suppressed anti-triplet charmed baryon decays of \(\mathbf{B}_c\rightarrow \mathbf{B}_n M\), with \(\mathbf{B}_c=(\Xi _c^0,\Xi _c^+,\Lambda _c^+)\) and \(\mathbf{B}_n(M)\) the baryon (pseudo-scalar) octets. We find that these breaking effects can be used to account for the experimental data on the decay branching ratios of \({\mathcal {B}}(\Lambda _c^+\rightarrow \Sigma ^{0} K^{+},\Lambda ^{0} K^{+})\) and \(R'_{K/\pi }={\mathcal {B}}(\Xi ^0_c \rightarrow \Xi ^- K^+)\)/\({\mathcal {B}}(\Xi ^0_c \rightarrow \Xi ^- \pi ^+)\). In addition, we obtain that \({\mathcal {B}}(\Xi _{c}^{0} \rightarrow \Xi ^{-} K^{+},\Sigma ^{-} \pi ^{+})=(4.6 \pm 1.7,12.8 \pm 3.1)\times 10^{-4}\), \({\mathcal {B}}(\Xi _c^0\rightarrow pK^-,\Sigma ^+\pi ^-)=(3.0 \pm 1.0, 5.2 \pm 1.6)\times 10^{-4}\) and \({\mathcal {B}}(\Xi _c^+\rightarrow \Sigma ^{0(+)} \pi ^{+(0)})=(10.3 \pm 1.7)\times 10^{-4}\), which all receive significant contributions from the breaking effects, and can be tested by the BESIII and LHCb experiments.     

First and second order hadron mass formulas in internal SU(6)

We use broken SU(6) internal symmetry to derive the mass formulas amongst hadrons (1/2⁺, 3/2⁺, 0⁻, 1⁻) including second order mass contributions from symmetric 405 representation. Some hybrid mass relations are also obtained by relating second order parameters.     

Tree-level breaking of SU(2)×U(1) in general SUGRA theories

It is shown that SU(2)×U(1) can be broken at the tree level, without the occurrence of global potential minima that break U(1)_e.m., in supergravity models that are more general than those proposed by Nilles, Srednicki and Wyler. The study comprises an analysis of models with a general soft supersymmetry-breaking structure as well as those of the Hall-Lykken-Weinberg type.     

A numerical study of SU(3) charge-two monopoles with minimal symmetry breaking

Charge-two SU(3) monopoles with minimal symmetry breaking can be generated via Nahm's equations. This paper investigates the detailed structure of such monopoles, through explicit calculation of the energy density, and the norm and discriminant of the Higgs field. Monopoles may be classified according to the maxima and minima of these quantities.     

A quark model study of semileptonic baryon decays in the electronic decay modes

A relativistic quark model based on Dirac equation with the independent-quark confining potential of the form (1 +γ ⁰)[a ln(r/b)] is used to compute the weak electric and magnetic form factors for semileptonic baryonic decays in the electronic decay modes. The values obtained for (g ₂/g ₁) agree with the non relativistic results and those for (f ₂/f ₁) agree with the MIT bag model values of Donoghue and Holstein. The SU(3) symmetry breaking does not generate appreciable departures in (f ₂/f ₁) values from corresponding Cabibbo values.     

Sterile neutrinos in lepton number and lepton flavor violating decays

We study the contribution of massive dominantly sterile neutrinos, N, to the lepton number and lepton flavor violating semileptonic decays of τ and B, D, K-mesons. We focus on special domains of sterile neutrino masses mN where it is close to its mass-shell. This leads to an enormous resonant enhancement of the decay rates of these processes. This allows us to derive stringent limits on the sterile neutrino mass mN and its mixing UαN with active flavors. We apply a joint analysis of the existing experimental bounds on the decay rates of the studied processes. In contrast to other approaches in the literature our limits are free from ad hoc assumptions on the relative size of the sterile neutrino mixing parameters. We analyze the impact of this sort of assumptions on the extraction of the limits on mN and UαN, and discuss the effect of finite detector size. Special attention was paid to the limits on meson decays with e^±e^± in final state, derived from non-observation of 0νββ-decay. We point out that observation of these decays may, in particular, shed light on the Majorana phases of the neutrino mixing matrix.     

SU (3) Chern-Simons field theory in three-manifolds

We present the solution of the non-Abelian SU (3) Chern-Simons field theory defined in a generic three-manifold which is closed, connected and orientable. The surgery rules, which permit us to solve the theory, are derived and several examples of vacuum expectation values of Wilson line operators are computed. The three-manifold invariant associated with the non-Abelian SU (3) Chern-Simons model is defined and its values are computed for various three-manifolds.     

Single particle SU(3) parentage coefficients

The single particle SU(3) parentage coefficients are calculated for the case of leading SU(3) representation in the highest orbital symmetry partition, using the method suggested by Hecht. Tabulations are given for all possible cases of identical nucleons in η=3 and η=4 shells.     

Weak decays of doubly heavy baryons: SU(3) analysis

Motivated by the recent LHCb observation of doubly charmed baryon \(\Xi _{cc}^{++}\) in the \(\Lambda _c^+ K^-\pi ^+\pi ^+\) final state, we analyze the weak decays of doubly heavy baryons \(\Xi _{cc}\), \(\Omega _{cc}\), \(\Xi _{bc}\), \(\Omega _{bc}\), \(\Xi _{bb}\) and \(\Omega _{bb}\) under the flavor SU(3) symmetry. The decay amplitudes for various semileptonic and nonleptonic decays are parametrized in terms of a few SU(3) irreducible amplitudes. We find a number of relations or sum rules between decay widths and CP asymmetries, which can be examined in future measurements at experimental facilities like LHC, Belle II and CEPC. Moreover, once a few decay branching fractions have been measured in the future, some of these relations may provide hints for exploration of new decay modes.