Search

We study the kaon-pole diagrams which involve the nonvanishing tadpole transition {l_angle}0{vert_bar}O{sub 6+i7}{vert_bar}{bar K}{sup 0}{r_angle} , where the operator O belongs to the (3{sup {asterisk}},3) representation of chiral SU(3){times}SU(3). As is well known, the pole contribution exactly cancels the direct contribution to K-2{pi} and s-wave nonleptonic hyperon decay in the SU(3) and chiral limits. It is shown that there are additional contributions which vanish in the SU(3) limit, these being of order (m{sub K}{sup 2}{minus}m{sub {pi}}{sup 2})/m{sub K}{sup 2} or (m{sub B{sup {prime}}}{minus}m{sub B})/m{sub K}{sup 2}. The contribution of such corrections to direct CP violation in K{r_arrow}2{pi} and hyperon decays is calculated, which could in some cases be a substantial fraction of the standard model predictions for direct CP violation in these transitions. {copyright} {ital 1997} {ital The American Physical Society}

The nonleptonic decays ${\ensuremath{\Lambda}}_{c}^{+}\ensuremath{\rightarrow}{\ensuremath{\Delta}}^{++}{K}^{\ensuremath{-}},{\ensuremath{\Sigma}}^{*0}{\ensuremath{\pi}}^{+}$, and ${\ensuremath{\Xi}}^{*0}{K}^{+}$ and ${\ensuremath{\Omega}}_{c}^{0}\ensuremath{\rightarrow}{\ensuremath{\Xi}}^{0}{\overline{K}}^{0}$, ${\ensuremath{\Omega}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$, and ${\ensuremath{\Xi}}^{*0}{\overline{K}}^{0}$ are studied. The dominant contribution for the former decays comes from the $W$ exchange and for the latter decays the $W$ emission gives the dominant contribution. These decays are especially suitable to determine directly the scale of $W$ exchange and $W$ emission from the experimental data. We obtain $\ensuremath{\alpha}({\ensuremath{\Omega}}_{c}^{0}\ensuremath{\rightarrow}{\ensuremath{\Xi}}^{0}{\overline{K}}^{0}\ensuremath{\approx}0.35$.

Second-class weak currents can in the standard model be induced by chiral-symmetry breaking. In the specific case of the decay $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\pi}{\ensuremath{\nu}}_{\ensuremath{\tau}}$, dominated by the first-class vector current with the $\ensuremath{\rho}$ quantum numbers, such effects would manifest themselves by small axial vector (or, generally, nonvector) contributions to the decay rate. We present an attempt to estimate such effects, based on a vector and axial-vector dominance model of the relevant matrix elements supplemented by $\ensuremath{\omega}\mathrm{\text{\ensuremath{-}}}\ensuremath{\rho}$ mixing. We also give an indication on the amplitude directly mediated by ${b}_{1}(1235)\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\pi}$, in principle also allowed in the standard model by isotopic spin violation.

The semileptonic decays of the type $B\ensuremath{\rightarrow}\ensuremath{\pi}l\ensuremath{\nu}$ are discussed. The form factor describing this decay is calculated and is compared with the experimental data on $D\ensuremath{\rightarrow}\mathrm{Kl}\ensuremath{\nu}$ decay. The $D({J}^{+})\ensuremath{\rightarrow}{D}^{*}(D)\ensuremath{\pi}$ decays are also discussed. The parameters in the form factor for the semileptonic decays are correlated with ${D}^{*}\ensuremath{\rightarrow}D\ensuremath{\pi}$ and ${D}_{0}\ensuremath{\rightarrow}D\ensuremath{\pi}$ decays. We also derive the relation $\frac{{f}_{{B}_{0}}}{{f}_{B}}=\frac{{m}_{{B}_{0}}}{{m}_{B}}$.

We present an assessment of the standard model expectations for the branching ratio of the isotopic spin and G-parity violating decay tau --> eta' pi nu_tau. The estimate is based on a vector and scalar meson dominance parametrization of the relevant form factors, that explicitly accounts for pi^0-eta-eta' mixing. The numerical results obtained in this framework indicate a branching ratio one order of magnitude (or more) below the current experimental limit, and suggest the possibility of evidencing some novel interaction in high statistics studies of this decay.

The implications of heavy-quark spin symmetry for [ital P]-state mesons with one heavy quark are discussed. In particular, we have derived the mass relation [ital m][sub [ital D]1][sup *][minus][ital m][sub [ital D]0]=5/2([ital m][sub [ital D]2][sup *][minus][ital m][sub [ital D]1]) for the four [ital P]-state mesons. We have shown that the [ital E]1 transition decay [ital D][sub 1](2420)[r arrow][ital D]+[gamma] is a prediction of the above symmetry and as such should be tested experimentally. We predict [ital m][sub [ital D]1][sup *]=2.29 GeV and [ital m][sub [ital D]0]=2.19 GeV in the model in which the spin-dependent potential is taken to be a one-gluon-exchange potential. In the second model, with the Cornell potential in the Dirac Hamiltonian, we obtain [ital m][sub [ital D]1][sup *]=2.01 GeV and [ital m][sub [ital D]0]=1.91 GeV.

Motivated by recent estimates of the isospin-violating process $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\eta}\ensuremath{\pi}{\ensuremath{\nu}}_{\ensuremath{\tau}}$, mostly relying on the $\ensuremath{\rho}$ and ${a}_{0}$ dominance of the relevant form factors near threshold, we present an assessment for the branching ratio that accounts for additional, potential effects from the lowest radial excitations ${\ensuremath{\rho}}^{\ensuremath{'}}\ensuremath{\equiv}\ensuremath{\rho}(1450)$ and ${a}_{0}^{\ensuremath{'}}\ensuremath{\equiv}{a}_{0}(1450)$, respectively, also lying in the decay phase space.

The degenerate leptogenesis is studied when the degeneracy in two of the heavy right-handed neutrinos [the third one is irrelevant if $\ensuremath{\mu}\ensuremath{-}\ensuremath{\tau}$ symmetry is assumed] is due to $\overline{L}\ensuremath{\equiv}({L}_{e}\ensuremath{-}{L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}})$ discrete symmetry. It is shown that a sizable leptogenesis asymmetry ($\ensuremath{\epsilon}\ensuremath{\ge}{10}^{\ensuremath{-}6}$) is possible. The level of degeneracy required also predicts the Majorana phase needed for the asymmetry and this prediction is testable since it is the same phase, which appears in the double $\ensuremath{\beta}$ decay. Implications of nonzero reactor angle ${\ensuremath{\theta}}_{13}$ are discussed. It is shown that the contribution from ${sin }^{2}{\ensuremath{\theta}}_{13}$ to the leptogenesis asymmetry parameter may even dominate. An accurate measurement of ${sin }^{2}{\ensuremath{\theta}}_{13}$ would have important implications for the mass degeneracy of heavy right-handed neutrinos.

Leptogenesis is studied in a seesaw model with $\ensuremath{\mu}\ensuremath{-}\ensuremath{\tau}$ symmetry for $S{U}_{L}(2)$-singlet right-handed neutrinos. It is shown that lepton asymmetry is not zero and is given by the square of the solar neutrino mass difference and can be of the right order of magnitude. Further it involves the same Majorana phase which appears in the neutrinoless double $\ensuremath{\beta}$-decay. In this framework one of the right-handed seesaw partners of light neutrinos can be made massless. This can be identified with a sterile neutrino, once it acquires a tiny mass ($\ensuremath{\approx}1\text{ }\text{ }\mathrm{eV}$) when $\ensuremath{\mu}\ensuremath{-}\ensuremath{\tau}$ symmetry is broken in the right-handed neutrino sector. The above mentioned sterile neutrino together with another one can be identified to explain the MiniBooNE and LSND results. The light $5\ifmmode\times\else\texttimes\fi{}5$ neutrino mass matrix is completely fixed if $CP$ is conserved and so is the effective mass for neutrinoless double $\ensuremath{\beta}$-decay.

The effects of a second heavier {ital Z}{prime} gauge boson predicted in a model of unification of electroweak and strong interactions without grand unification are studied on the properties of {ital Z}. It is shown that future measurements of such effects can distinguish the model from the other extended gauge models which also have an extra {ital Z}{prime}.

The branching ratio for $B\ensuremath{\rightarrow}{K}_{1}\ensuremath{\gamma}$ at next-to-leading order of ${\ensuremath{\alpha}}_{s}$ has been calculated in large energy effective theory. By incorporating higher twist effects in the light-cone decay amplitude for the axial $K$ meson, it is shown that the form factor is not sensitive to these twists.

The newly observed resonances ${D}_{{s}_{1}}^{*}$ and ${D}_{{s}_{0}}$ are discussed in a potential model. The relationship between the mass difference between the p states ${D}_{{s}_{1}}^{*}{(1}^{+}{),D}_{{s}_{0}}{(0}^{+})$ and the s states ${D}_{s}^{*}{(1}^{\ensuremath{-}}{),D}_{s}{(0}^{\ensuremath{-}})$ is also examined. Some remarks about the states ${D}_{{}_{1}}^{*}{(1}^{+})$ and ${D}_{{}_{0}}{(0}^{+})$ in the nonstrange sectors are also made.

The aim of the work is to study LFV in a newly proposed Seesaw model of neutrino mass and to see whether it could explain LSND excess. The motivation of this Seesaw model was that there was no new physics beyond the TeV scale. By studying \mu \to 3e in this model, it is shown that the upper bound on the branching ratio requires Higgs mass m_{h} of a new scalar doublet with lepton number L=-1 needed in the model has to be about 9 TeV. The predicted branching ratio for \mu \to e\nu_{l}\bar{\nu}_{l} is too small to explain the LSND. PACS: 11.30.Hv, 14.60.Pq

The decay process $B\to D^+ D^- \pi^0$ is an interesting channel for the investigation of CP violating effects in the $b-$ sector. We write down a decay amplitude constrained by a low-energy theorem, which also includes the contribution of resonant $S-$ and $P-$wave beauty and charmed mesons, and we determine the relevant matrix elements in the infinite heavy quark mass limit, assuming the factorization ansatz. We estimate the rate of the decay: ${\cal B}(B \to D^+ D^- \pi^0)\simeq 1 \times 10^{-3}$. We also analyze the time-independent and time-dependent differential decay distributions, concluding that a signal for this process should be observed at the B-factories. Finally, we give an estimate of the decay rate of the Cabibbo-favoured process $B\to D^+ D^- K_S$.

An estimate of the gluon contribution {Delta}{ital G} to the target-proton spin arising due to the anomaly in the singlet axial-vector current is made by using the axial-vector-current divergence equations. A particular combination of these divergences allows the above estimate without any detailed assumptions about proton matrix elements of pseudoscalar densities or of current quark masses. This estimate indicates that {Delta}{ital {tilde G}} (the SU(3)-singlet part of the gluon contribution {Delta}{ital G}) is negative but small. Further it is shown that the quark content of the proton spin is zero irrespective of the value of {Delta}{ital {tilde G}}.

The two body nonleptonic ${\ensuremath{\Lambda}}_{b}$ decays are analyzed in the factorization approximation, using the quark model, treating $\ensuremath{\xi}{=1/N}_{c}$ as a free parameter. It is shown that the experimental branching ratio for ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}J/\ensuremath{\psi}$ restricts $\ensuremath{\xi}$ and this ratio can be understood for a value of $\ensuremath{\xi}$ which lies in the range $0l~\ensuremath{\xi}l~0.5$ suggested by two body $B$ meson decays. The branching ratios for ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}{\ensuremath{\Lambda}}_{c}{D}_{s}^{*}{(D}_{s})$ are predicted to be larger than the previous estimates. Finally it is pointed that the CKM-Wolfenstein parameter ${\ensuremath{\rho}}^{2}+{\ensuremath{\eta}}^{2}$, where $\ensuremath{\eta}$ is the $\mathrm{CP}$ phase, can be determined from the ratio of widths of ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}\overline{D}$ and ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}\ensuremath{\Lambda}J/\ensuremath{\psi}$ or that of ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}p{D}_{s}$ and ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}{\ensuremath{\Lambda}}_{c}{D}_{s},$ independent of the parameter $\ensuremath{\xi}$.

We discuss the radiative decays of ψ in the charmonium model. We find the main radiative decay of ψ is ψ→ηc+γ provided ηc is at 2.8 GeV. We also discuss the hadronic decay width of ηc. We estimate the branching ratio Γ(ηc→pp¯)Γ(ηc→hadrons).

Intermediate mass scales $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{m}$ and ${m}_{R}$ associated, respectively, with the violation of electron\char22{}muon\char22{}tau-lepton universality and the parity restoration within the framework of Pati-Salam groups $\mathrm{S}{\mathrm{U}}_{L}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{S}{\mathrm{U}}_{R}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{S}{\mathrm{U}}_{C}(4)$ and $\mathrm{S}{\mathrm{U}}_{L}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{S}{\mathrm{U}}_{R}(2)\ifmmode\times\else\texttimes\fi{}{[\mathrm{S}{\mathrm{U}}_{C}(4)]}^{4}$ are discussed, assuming that $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{m}\ensuremath{\le}{m}_{R}\ensuremath{\le}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{m}}_{X}$, where ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{m}}_{X}$ is the usual partial-unification mass scale for Pati-Salam groups. It is shown that, with $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{m}\ensuremath{\simeq}8\ifmmode\times\else\texttimes\fi{}{10}^{5}$ GeV (a lower limit from the ${K}_{L}\ensuremath{-}{K}_{S}$ mass difference), ${m}_{R}\ensuremath{\approx}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{m}}_{X}=8\ifmmode\times\else\texttimes\fi{}{10}^{9}$ GeV for the first case and ${m}_{R}\ensuremath{\simeq}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{m}}_{X}\ensuremath{\approx}9\ifmmode\times\else\texttimes\fi{}{10}^{7}$ GeV or ${m}_{R}\ensuremath{\simeq}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{m}=8\ifmmode\times\else\texttimes\fi{}{10}^{5}$ GeV, ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{m}}_{X}={10}^{11}$ GeV for the second case.

Partial-unification mass scales for the group (SU/sub c/ (4))/sup 2/ x SU/sub L/(2) x SU/sub R/(2) are studied. We show that for this group the intermediate mass scale m/sub R/ is given by 300 or =M/sub X/> or =3 x 10/sup 10/ GeV. This is in contrast to other models for which m/sub R/> or =10/sup 9/ GeV.

Within the framework of light-cone algebra, it is shown that a logarithmic divergence in the electromagnetic mass shift of a hadron arises precisely due to a mass term in the quark propagator. This divergence, therefore, can be removed by mass renormalization, The coefficient of this divergence is a scalar density which transform as S/sub 3/ for the case of a nucleon. In our analysis, the gauge invariance to order l/q/sup 2/ is explicitly used. (auth)

The light-cone algebra is used to estimate the inclusive cross section for charmed-particle production by high-energy neutrinos. The results obtained are compatible with the recent experimental results on dimuon events. (AIP)

Partial-unification mass scales for the groups SU/sub L/(2)xSU/sub R/(2)xSU/sub C/(4) and SU/sub L/(2)xU/sub R/(1)xSU/sub C/(4) are studied by means of renormalization-group equations. A partial-unification mass scale of 4 x 10/sup 6/ GeV is found for both the groups when these groups are broken down directly to SU/sub L/(2)xU(1)xSU/sub C/(3). Mass relations between the leptons and quarks are also discussed.

A sum rule is derived for the deep-inelastic scattering of polarized and unpolarized electrons from polarized protons: ${\mathcal{F}}_{0}^{1}$ [4g${\ifmmode \tilde{}\else \~{}\fi{}}_{1}^{\mathrm{ep}}$(x,${q}^{2}$) -${c}_{W}$${g}_{1}^{\mathrm{ep}}$(x,${q}^{2}$)]dx =(1/6(F-D)[1-${\mathrm{\ensuremath{\alpha}}}_{\mathrm{s}}$/B (${q}^{2}$)/\ensuremath{\pi}], where ${g}_{1}^{\mathrm{ep}}$ is the usual spin-dependent structure function for electroproduction, g${\ifmmode \tilde{}\else \~{}\fi{}}_{1}^{\mathrm{ep}}$ is the spin-dependent structure function arising from the interference of the electromagnetic and weak neutral currents, and ${c}_{W}$=(3\char21{}8 ${\mathrm{sin}}^{2}$${\mathrm{\ensuremath{\theta}}}_{\mathrm{W}}$). The structure function g\ifmmode \tilde{}\else \~{}\fi{} $_{1}^{\mathrm{ep}}$, in principle, can be extracted from deep-inelastic scattering of unpolarized electrons from polarized protons.

We postulate a concept of isospin in purely leptonic space. In particular, we consider a group $G\ensuremath{\equiv}[{\mathrm{SU}}_{L}(2)\ensuremath{\bigotimes}\mathrm{U}(1)][{\mathrm{SU}}_{\mathrm{lL}}(2)\ensuremath{\bigotimes}{\mathrm{SU}}_{\mathrm{lR}}(2)\ensuremath{\bigotimes}{\mathrm{U}}_{l}(1)]$ for leptons. The first group is the group introduced by Salam and Weinberg and generates ordinary weak and electromagnetic interactions. The second group is in leptonic space only such that the leptonic multiplet $L=\frac{1}{2}(1+{\ensuremath{\gamma}}_{5})(_{\ensuremath{\mu}}^{\ensuremath{\nu}}\ensuremath{\mu} _{e}^{\ensuremath{\nu}}e)$ belongs to a representation ${T}_{\mathrm{lL}}=\frac{1}{2}$, ${T}_{\mathrm{lR}}=0$, ${Y}_{l}=1$ of this group and a representation ${T}_{L}=\frac{1}{2}$, $Y=\ensuremath{-}1$ for the group ${\mathrm{SU}}_{L}(2)\ensuremath{\bigotimes}\mathrm{U}(1)$. The multiplet $R=\frac{1}{2}(1\ensuremath{-}{\ensuremath{\gamma}}_{5})(\ensuremath{\mu},e)$ has ${T}_{L}=0$, $Y=\ensuremath{-}2$ for the group ${\mathrm{SU}}_{L}(2)\ensuremath{\bigotimes}\mathrm{U}(1)$ and has ${T}_{\mathrm{lL}}=0$, ${T}_{\mathrm{lR}}=\frac{1}{2}$, ${Y}_{l}=1$ for the other group. ${T}_{\mathrm{lL}}$ and ${T}_{\mathrm{lR}}$ are left-handed and right-handed isospins, and ${Y}_{l}$ is the hypercharge for the leptonic group. The leptonic charge ${Q}_{l}={T}_{\mathrm{lL}3}+{T}_{\mathrm{lR}3}+\frac{1}{2}{Y}_{l}$. Thus for the muon ${Q}_{l}=1$ and for the electron ${Q}_{l}=0$ so that muonic number acquires a group-theoretic meaning. We consider the spontaneously broken gauge symmetry based on the group $G$ such that in zeroth order only the muon acquires a mass and the electron remains massless. We calculate the electron self-mass due to radiative corrections in second order of the gauge coupling constant $f$ of the leptonic group. Our conclusion is that for the electron mass to be calculable, the electron remains massless even in second order so that the electron mass may arise in fourth order of $f$.

It is shown that it is possible to obtain the neutral-current weak interaction as the third component of the SU(2) group without electroweak unification, provided that fundamental doublets contain in general a mixture of left-handed and right-handed fields. The main experimental consequence is the relation m/sub W//sub 3/approx. =..sqrt..2m/sub W/, with the further possibility that m/sub W/ could be lower than that predicted by the standard model.

We analyze the breaking of grand unification group SU/sub W/(4) x SU/sub C/(4) and group G = SU/sub L/(3) x SU/sub R/(3) x SU/sub C/(3) into the electroweak group with an extra U(1) factor. Several patterns of symmetry breaking are considered and their experimental consequences in terms of an extra neutral vector boson Z' are discussed.

Unification of electroweak and strong interactions based on SU/sub L/(2) x U(1) x SU/sub c/(4) is obtained. Leptons and quarks are treated symmetrically with respect to weak interactions; color distinguishes electric charges of quarks from leptons. The unification mass scale could be as low as a few times that of electroweak unification and is in any case

We demonstrate that in the effective Hamiltonian for the process s+u..-->..u+d+..gamma.., one can identify two types of local four-quark operators; type I operators violate Hara's theorem and type II respect it. By an explicit calculation we demonstrate that the quark-quark bremsstrahlung process generates both types of operators but only type I survive in the SU(3) limit.

Tests based on neutrinoless double-..beta.. decay and rare muon processes are proposed for the detection of a heavy Majorana neutrino with a mass of approx.100 GeV. Existence of such a neutrino would distinguish between the standard and left-right-symmetric electroweak gauge models with U(1) in the latter identified with (B-L). The sensitivity of these processes to the mass of the heavy Majorana neutrino is discussed.

By a simple extension of the standard electroweak gauge group to SU/sub L/(2) x U/sub e/(1) x U/sub ..mu../(1) x U/sub tau/(1), it is shown that it is possible to get light-neutrino masses in the range of a few electron volts. For this purpose it is necessary that M/sub R/, the mass scale associated with the masses of superheavy neutrinos which carries U/sub i/(1) quantum numbers and which is related to the scale at which e-..mu..-tau universality is broken, is to be greater than 10/sup 9/ GeV. However, for the solar-neutrino problem M/sub R/ should be in the range of 10/sup 11/--10/sup 12/ GeV. In particular, we obtain two Majorana neutrinos of almost equal mass and one Majorana neutrino (predominantly an electron neutrino) of almost zero mass.

A good understanding of the decays V ..-->.. e/sup -/e/sup +/, V ..-->.. P..gamma.., and P ..-->.. 2..gamma.., including the suppression of psi ..-->.. eta/sub c/..gamma.., has been obtained in a dispersion-theoretic approach, by assuming that the unitarity relation for the absorptive part in the dispersion integral is dominated by the quark-antiquark state near the threshold of quark-antiquark production. Moreover, it is assumed that the scaling mass in the dispersion integral as well as the coupling constants of vector and pseudoscalar mesons with quarks satisfy some simple scaling relations.

It is shown that K/sub 2pi/ decay amplitudes vanish up to first order in the chiral-SU(3) x SU(3)-symmetry breaking in the standard model even when the contribution from penguin diagrams is included.

Electroweak unification is obtained in an SU(4) model with SU/sub L/(2) x SU/sub R/(2) x U(1) as its subgroup and sin/sup 2/theta/sub W//sup 0/ = (1/4) in the symmetry limit. The unification mass scale is 3.3 x 10/sup 4/> or =m/sub X/> or =6.4 x 10/sup 3/ GeV for 240< or =m/sub R/< or =6.4 x 10/sup 3/ GeV. Some consequences of the model are discussed.

We formulate a gauge model for basic interactions based on the symmetry group G = G/sub wk/ x G/sub c/, where G/sub c/ is the chiral symmetry group (SU(3) x SU(3))/sub c/ in color space. G/sub wk/ is taken to be the left-right-symmetric model SU/sub L/(2) x SU/sub R/(2) x U(1). The chiral color symmetry is spontaneously broken in such a way that quarks acquire a common mass and an octet of axial-vector gluons become massive but an octet of vector gluons remain massless. In this way quark mass arises from spontaneous color-chiral-symmetry breaking. The experimental consequences of the left-right-symmetric model are discussed and it is shown that one version of this model gives results similar to the Salam-Weinberg model for the currently available energies. There is also another version, where the results are again similar to the Salam-Weinberg model except that the y dependence for the asymmetry parameter for the deep-inelastic scattering of polarized electrons is completely different although its value at y = 0.21 is compatible with experiment.

The K 1 0 -K 2 0 mass difference is calculated exactly from some recently suggested nonleptonic decay models by use of the techniques of the algebra of currents. We find M(K 2 0 )-M(K 1 0 )=0.49/τ(K 1 0 ), which agrees in both sign and magnitude with the recent experiments.

The question of cancellation of the logarithmic divergence appearing in the proton-neutron mass difference is studied in a unified theory of weak and electromagnetic interactions. It is concluded that the contribution from weak hadronic currents in an extension of the Salam-Weinberg model for leptons to hadrons does not cancel the logarithmic divergence arising from purely electromagnetic interactions.

A symmetry-breaking mechanism is used to derive a sum rule between ${f}_{K}$, ${f}_{\ensuremath{\pi}}$, and ${f}_{\ensuremath{\kappa}}$, the decay constants for $K$, $\ensuremath{\pi}$, $\ensuremath{\kappa}\ensuremath{\rightarrow}l+\ensuremath{\nu}$. By means of the sum rule $\frac{{f}_{K}}{{f}_{\ensuremath{\pi}}}$, $\frac{{f}_{\ensuremath{\kappa}}}{{f}_{\ensuremath{\pi}}}$ and ${f}_{+}(0)$ (the form factor which enters in ${K}_{l3}$ decay) are expressed in terms of the $\ensuremath{\kappa}$-meson mass and the experimentally known number $\frac{{f}_{K}}{{f}_{\ensuremath{\pi}}{f}_{+}(0)}$. The second-order $\mathrm{SU}(3)$-symmetry-breaking corrections to ${f}_{+}(0)$ are found to be small. The ${K}_{l3}$ form factors are determined. The $\ensuremath{\kappa}\ensuremath{\rightarrow}K\ensuremath{\pi}$ width is determined and in certain cases is found to be the same as in the Veneziano model.

Nucleon-nucleon dispersion relations have been used to discriminate among various sets of solutions given by MacGregor for low-energy proton-proton scattering. This has greatly reduced the ambiguity existing in the phase-shift analysis at low energy.

We apply the $\mathrm{SU}(6)$ algebra of Gell-Mann to nonleptonic decays of hadrons. We assume that the weak-interaction Hamiltonian for $s$-wave decays transforms like $S_{7}^{}{}_{}{}^{5}$ (the seventh component of the space integral of the pseudoscalar quark density). Using the Fubini-Furlan-Adler-Weisberger technique and the partially conserved axial-vector current, we express the $s$-wave decay amplitudes in terms of the reduced matrix elements, which are the same as the ones that appear in the expression for mass splittings if one assumes that the symmetry-breaking part of the mass operator transforms like ${S}_{8}$ (the eighth component of the space integral of the scalar quark density). Making use of the fact that the mass-splitting parameter is universal, and assuming that the $s$-wave coupling constant ${G}_{s}$ is also universal, we predict a ratio $\frac{(K_{1}^{}{}_{}{}^{0}\ensuremath{\rightarrow}2\ensuremath{\pi})}{A(\ensuremath{\Sigma}_{\ensuremath{-}}^{}{}_{}{}^{\ensuremath{-}})}$ which is in excellent agreement with experiment. Knowing any one of the hyperon $s$-way decay amplitudes we can predict the others. Also we get $A(\ensuremath{\Sigma}_{+}^{}{}_{}{}^{+})=0$. The implications of these results are discussed.