Features of dynamically broken gauge theories

We discuss several features of dynamical symmetry breaking in gauge theories of strong, weak and electromagnetic interactions. We speculate that in some such theories the fine structure constant calculable. A possible solution of the strong P and T violation problem in QCD by dynamical symmetry breaking is indicated. Self-energy divergences are absent in such models and we compute the finite electromagnetic self-energy of a quark in QCD. The mass hierarchy problem is examined. We find models in which the fermion-gauge boson mass ratio is $\text{M}{}_{\mathrm{<mtext>F</mtext>}}{}^2\text{M}{}_{\mathrm{<mtext>B</mtext>}}{}^2\text{～}\text{exp}$ ($\text{?1}\text{g}{}^2$), where g is a gauge boson coupling, which could account for the origin of weak interactions.     

The ′T Hooft-Polyakov monopole near the Prasad-Sommerfield limit

A perturbative classical monopole solution for the SO(3) gauge theory is constructed in the limit of small but non-vanishing Higgs potential. This corresponds to the limit $\text{μ}{}^2\text{2M}{}_{\mathrm{W}}{}^2\text{=}\text{λ}\text{? 1}$, where μ equals the mass of the scalar particle and M_W equals the mass of the intermediate vector particles. The monopole solution and mass are found to involve non-analytic functions of λ: $\text{γ}$ and λ ln λ. The monopole mass M_m is calculated to order $\text{μ}{}^2\text{M}{}_{\mathrm{W}}$ as

$\text{M}{}_{\mathrm{m}}\text{=}\text{4π}\text{e}{}^2\text{M}{}_{\mathrm{w}}\text{1+}\text{1}\text{2}\text{μ}\text{M}{}_{\mathrm{w}}\text{+}\text{1}\text{2}\text{μ}{}^2\text{M}{}^2{}_{\mathrm{w}}\text{ln}\text{μ}\text{M}{}_{\mathrm{w}}\text{+0.7071}\text{μ}{}^2\text{M}{}^2{}_{\mathrm{w}}$

.     

Quark masses

In quark gluon theory with very small bare masses, -$\text{ψ}$$\text{M}$ψ, spontaneous breakdown of chiral symmetry generates sizable masses M_u, M_d, M_s, … We find ($\text{M}{}_{\mathrm{<mtext>u</mtext>}}\text{+ M}{}_{\mathrm{<mtext>d</mtext>}}\text{) /2 ≈ m}\text{p}\text{/ √6 ≈ 312}\text{MeV}\text{,}\text{and}\text{M}{}_{\mathrm{<mtext>s</mtext>}}\text{≈ 432}\text{MeV}$. Scalar densities have well determined non-zero vaccum expectations $\text{〈0|u}{}^{\mathrm{a}}\text{|0〉 ≡ 〈0|ψ(x) (λ}{}^{\mathrm{a}}\text{/2)ψ(x)/0〉 ≈ ?}{}_{\mathrm{\pi }}{}^2\text{M}{}^{\mathrm{a}}\text{,}\text{i.e}\text{〈0? u}{}^{\mathrm{o}}\text{/vb0〉 ≈ 8 × 10}{}^{\mathrm{?3}}\text{(}\text{GeV}\text{)}{}^3$ at an SU(3) breaking of the vacuum c′ ≡ 〈0|u⁸|〉/〈0|u^o|0〉 ≈ ? 16%     

Higgs particle production by Z→Hγ

The rate for the decay of a Z-boson into a Higgs boson and monochromatic photon is computed to leading order in the standard SU(2) × U(1) gauge theory. The coupling has contributions from fermion and W-boson loops. The W-boson loop dominates unless the number of heavy fermion generations exceeds six. The branching ratio computed from the W-boson loop contribution, B(Z→Hγ), is approximately 2 × 10^?6$\text{(1?(}\text{M}{}_{\mathrm{<mtext>H</mtext>}}{}^2\text{M}{}_{\mathrm{<mtext>Z</mtext>}}{}^2\text{))}{}^3$.     

Anomalous mass dependence of glueball exclusive decay rates

Exclusive decays such as G → ππ are studied in the framework ofperturbative QCD. We discuss the possibility of the constituent gluons' virtualness scaling as the glueball mass M_G, which is a picture equivalent to a glueball containing a few slow-moving, heavy gluons. In this case, the decay rate exhibits a pinch singularity which enhances it by a factor of order (M_G²/m_q²)² over the dimensional scaling expectation. This singularity is partially suppressed by Sudakov effects which reduce the enhancement factor to $\text{(M}{}_{\mathrm{<mtext>G</mtext>}}{}^2\text{/m}{}_{\mathrm{<mtext>q</mtext>}}{}^2\text{)}{}^{\mathrm{2n}}\text{,}\text{where}\text{n ? 0.4}$.     

From high energy supersymmetry breaking to low energy physics through decoupling

We reconsider a realistic model of electroweak and strong interactions with calculable mass spectrum at the tree level in which supersymmetry and an extra gauge group factor ?(1) beyond SU(3) × SU(2) × U(1) are both broken at very high energies: $\text{M}{}_{\mathrm{<mtext>SUSY</mtext>}}\text{?(M}{}_{\mathrm{<mtext>W</mtext>}}\text{M)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{M}{}_{\mathrm{<mtext>U</mtext><mtext>?</mtext><mtext>(1)</mtext>}}\text{?M}\text{with}\text{M?M}{}_{\mathrm{<mtext>W</mtext>}}$. In spite of these high-energy scales, especially the large scale of supersymmetry breaking, the low energy spectrum - including the relevant Higgs boson - is decoupled from the heavy degrees of freedom. Due to the “non-renormalization” theorems this decoupling persists to all orders in perturbation theory.     

Parity violation in atoms in SO(3) gauge models

We have evaluated the parity-violation contribution in atoms in the framework of SO(3) gauge theory. Various hadronic models have been used: first, for simplicity, the unrealistic five-quark one, next, others involving three ordinary SU(3) triplets for which all unwanted strangeness-changing processes are suppressed, up to order $\text{Gα}\text{or}\text{GαΔM}{}^2\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}^2$. In the free quark approximation, we obtain quite similar parity-violation effects which are proportional to $\text{GαΔM}{}^2\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}^2$ (ΔM² is the difference of squared masses of leptons (M_X0² ? M_ν² = M_X0²), or of quarks (ΔM_q²)). Namely, in large atoms (Z ? 1) the electronic contribution which is proportional to

gives the largest effect ($\text{σ}{}_{\mathrm{?}}\text{,}\text{p}{}_{\mathrm{?}}\text{and}\text{m}{}_{\mathrm{?}}$are the spin, momentum operators and mass of the lepton). Parity-violating effects in SO(3) gauge models are ?10^?4 smaller than those evaluated in the Weinberg theory with a neutral parity-violating current and will remain undetectable in the near future.     

Studies of interface phonons

The vibrational modes localized at the interface between two distinct crystals have been studied for a simple crystal model obeying all of the invariance conditions required for models used in studies of dynamical properties of crystal surfaces, and giving rise to Rayleigh surface waves. The two crystals are assumed to be semi-infinite simple cubic and to have the same lattice parameter a. They differ by their mass (M and M_A) and the central force interactions between first (K and K_a) and second nearest neighbors $\text{1}\text{2}\text{K}$ and $\text{1}\text{2}\text{K}{}_{\mathrm{A}}$. The interface is obtained by coupling the (001) free surfaces of these distinct crystals by central force intractions (K^'). We find that the variation of the interaction conditions (K^') at the interface and of the $\text{(}\text{K}\text{M}\text{)}\text{(}\text{K}{}_{\mathrm{A}}\text{M}{}_{\mathrm{A}}\text{)}$ parameter has the following qualitative effects on the properties of surface and bulk phonons. When (K^') increases from zero to a finite value, the frequencies of the surface phonons increase and are splitted in the case of two identical crystals. One can say that the surface phonons are transformed into interface modes. For some values of $\text{K}{}^{\mathrm{\text{'}}}\text{K}$ and $\text{(}\text{K}\text{M}\text{)}\text{(}\text{K}{}_{\mathrm{<mtext>A</mtext>}}\text{M}{}_{\mathrm{<mtext>A</mtext>}}\text{)}$ parameters these interface phonons may be admixed with bulk phonons and thus become virtual interface states.     

Measurement of the isospin amplitude ∣M012∣ in the reaction γn → ϱ0(pπ−) at 7.5 GeV

The cross-channel isospin amplitude $\text{∣M}{}_0{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{∣}$ is measured in the single reaction γn → ?⁰(pπ^?) at 7.5 GeV assuming the ?⁰ dominance model. A low-mass enhancement is found for $\text{∣M}{}_0{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{∣}{}^2$ in the range of m(pπ^?) of ～1.2 to ～1.7 GeV. The reaction strongly violates s-channel helicity conservation but is consistent with t-channel helicity conservation. The $\text{∣M}{}_0{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{∣}$ features are found to be very similar to those obtained in previous analyses of πp → π(Nπ) reactions.     

On the oscillatory modes of quarks in baryons

The color bond structure of a quark-antiquark system is extended, in the long-range approximation, self-consistently to the baryonic three-quark bond structure for SU(3)_c and generally to the N-quark bond structure for SU(N)_c. The universal (N-independent) mass square eigenvalues for massless quarks are

$\text{M}{}^2\text{=(H}{}_{\mathrm{N}}\text{)}{}^2\text{?2m}{}_{\mathrm{\rho }}{}^2\text{∑}\text{α=1}\text{3N?3}\text{ν}{}_{\mathrm{\alpha }}\text{+}\text{constant}\text{, ν}{}_{\mathrm{\alpha }}\text{=0,1,2,…}$

.     

Brillouin study of acoustic phonon softening and optical absorption coefficients of ultraheavily doped n-Si

The self-energies of acoustic phonons in ion implanted and laser annealed ultraheavily doped n-type Si have been measured by Brillouin scattering. The corresponding softening of the elastic constants has been estimated from the observed phonon softening and compared it with theory. At high doping levels ($\text{N}{}_{\mathrm{e}}\text{≧ 10}{}^{21}\text{cm}{}^{-3}$) the effect of the increase in atomic mass on the phonon frequency is observed in the case of doping with As. From the increase in the linewidths of the Brillouin lines with doping, the optical absorption coefficients for $\text{λ = 5145}\text{A}\text{?}$ as a function of doping are determined.     

Coupling supersymmetric Yang-Mills theories to supergravity

We extend the technique of Cremmer et al. to couple arbitrary chiral multiplets with supersymmetric Yang-Mills interactions to N = 1 supergravity. We present the general form of the lagrangian and the detailed form of the scalar potential is spelled out. In the case of N chiral multiplets, “minimally” coupled to supergravity, we derive, in the absence of gauge interactions, a model-independent mass formula Supertrace $\text{M}{}^2\text{= Σ}{}_{\mathrm{J}}\text{(?)}{}^{\mathrm{2J}}\text{(2J + 1)m}{}_{\mathrm{J}}{}^2\text{= 2(N ? 1)m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^2$, where $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is the gravitino mass. A concrete example of the super Higgs effect involving N chiral multiplets is exhibited.     

Multiplicities in lepton-hadron processes

The average multiplicity in deep inelastic electro- and neutrinoproduction at large ω(ω～s/Q² + 1) is related in Feynman's version of the parton model to the average multiplicities in high-energy electron-positron annihilation and hadron-hadron scattering. The relation is: , where C_e⁺e^? and C_h are, respectively, the coefficients of ln(s/M_1⊥²) in the multiplicities from e⁺-e^? and P-P in to hadrons, and M_1⊥ is an average transverse mass.     

Demythification of electroproduction local duality and precocious scaling

In an effort to develop a quantitative check of asymptotically free color-gauge theories, we analyze the logarithmic corrections to ξ-scaling coming from anomalous dimensions and coefficient functions of twist-two operators and compare with electroproduction data for 1 ? Q² ? 16 GeV². Excellent agreement is obtained using $\text{g}{}^2\text{(2}\text{GeV}\text{)}\text{4π}{}^2\text{= 0.17}$ for the effective quark-gluon coupling in the color-gauge theory. Effects of higher-twist operators are suppressed by powers of $\text{M}{}_0{}^2\text{Q}{}^2$. We use data from the resonance region to show $\text{M}{}_0\text{? 400}\text{MeV}$, in agreement with theoretical expectations. Our fit to νW₂ in the scaling region also describes the resonance region in the sense of Bloom-gilman local duality. We show that local duality is a consequence of the moment predictions obtained from the operator-product expansion in quantum chromodynamics. We resolve a paradox associated with local duality and spin-zero targets. Present measurements of $\text{R =}\text{σ}{}_{\mathrm{L}}\text{σ}{}_{\mathrm{T}}$ at large x and Q² are systematically higher than our predictions.     

Isospin analysis of NN → NNπ reactions at 5.7 GeV/c

A cross-channel isospin analysis has been performed on the channels $\text{p}\text{N}\text{→}\text{N}\text{(}\text{N}\text{π)}\text{and}\text{p}\text{N}\text{→}\text{N}\text{(}\text{N}\text{π)}$ in terms of three isospin amplitudes $\text{M}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^0\text{, M}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^1$, and $\text{M}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^1$ where the upper index is the isospin of the exchanged “object” in the t-channel and the lower index is the isospin of the $\text{(}\text{N}\text{π)}\text{or}\text{(}\text{N}\text{π)}$ system. Enhancements are observed in the low Nπ) invariant mass region for an $\text{I =}\text{1}\text{2}$ final state when the isospin of the exchanged object in cross channel is I_E = 0 and 1.     

Higher order correction to the sine-Gordon soliton mass

We calculate in the 2-dimensional sine-Gordon theory

$\text{L}{}_{\mathrm{GC}}\text{=}\text{1}\text{2}\text{(?}{}^{\mathrm{\mu }}\text{φ)}{}^2\text{?(}\text{m}{}_4\text{λ}\text{)[1?cos(}\text{λ}\text{φ}\text{m}\text{)]}$

the soliton mass M_sol to order λ and compare it to the meson mass. We find

$\text{M}{}_{\mathrm{sol}}\text{m}{}_{\mathrm{menson}}\text{=}\text{8m}{}^2\text{λ}\text{?}\text{1}\text{π}\text{+}\text{λ}\text{192m}{}^2\text{+O(λ}{}^2\text{)}$

This supports the belief that the field-theoretic WKB approximation of Dashen, Hasslacher and Neveu gives the correct answer for the sine-Gordon problem.     

Deviation from scaling in the triple-regge region of pp→ pX and fP universality

By generalizing $\text{f}\text{P}$ universality to Regge-particle “scattering” we obtain $\text{s}\text{d}\text{σ}\text{d}\text{t}\text{d}\text{M}{}^2\text{= F(}\text{s}\text{M}{}^2\text{,t)}$$\text{[1 +}\text{M}{}^{\mathrm{?1}}\text{b}{}_{\mathrm{<mtext>f</mtext>}}\text{(0)}\text{b}{}_{\mathrm{<mtext>P</mtext>}}\text{(0)}\text{]}$ for pp → pX, where b_f(t) and b_P(t) are the f and P Regge residues for, say, pp → pp. This agrees with the recent NAL data.