Tomoya Akiba

Hierarchic Chiral Condensate

Abstract Using the Schwinger-Dyson gap equation a chiral condensate is discussed in theories having a slowly varying running-coupling constant. It is shown that if the coupling strength λ remains close to a certain critical value λc up to a large scale Λ, a chiral condensate may occur with the hierarchic nature σ(0)/Λ ≈ exp[ − π/(λ − λ c ) 1 2 ] , σ(0) being the fermion d ynamical mass at zero-momentum. It is pointed out that such a condensate provides a possible solution to the flavor-changing neutral-current problem in the technicolor theory.

Z1=0 and the conditions from theN/D method

SummaryZ1=0 as a condition for a particle being composite is compared with the conditionD(m2)=0 from theN/D method. Previously, Leeet al. proved the equivalence between the composite particle defined as theZ3=0 limit of an elementary particle and the one defined by the condition (N(s)/(dD(s)/ds))s−m2=−g2 in theN/D method. Here we restrict further the compositeness of a particle byZ1=0 andD(m2)=0, respectively, and prove the equivalence between the composite particles defined by Salam’s conditionsZ3=Z1=0 and by the unsubtractedN/D equations. The equivalence is proved for a particle in theS-state composed of two spin-zero particles in the approximation of considering only two-particle intermediate states and under the assumptions: i) The scattering amplitudes have at most one particle pole below the threshold of scattering. ii) The Levinson theorem in its original sense is satisfied. iii) The generalized potential is such that there exists an amplitudet(s) determined through the unsubtractedN/D equations, andt(s) has a pole. For the proof we obtain by the method of Blanckenbecleret al. a general form of scattering amplitudes which have the given discontinuity on the left-hand cut and satisfy i), ii) and iii). Also, we are led to investigate nonuniqueness of the propagation function and the vertex function as well asZ3 andZ1 in detail.RiassuntoSi confrontaZ1=0, qua’e condizione perchè una particella sia composta, con la condizioneD(m2)=0 del metodoN/D. Precedentemente Leeet al. hanno dimostrato l’equivalenza tra la particella composta definita come il limite perZ3=0 di una particella elementare e quella definita dalla condizione (N(s)/(dD(s)/(ds))s−m2=−g2 nel metodoN/D. Qui restringiamo ulteriormente la condizione per cui una particella risulta composta conZ1=0 eD(m2)=0, rispettivamente, e dimostriamo l’equivalenza fra le particelle composte definite con le condizioni di SalamZ3=Z1=0 e con le equazioniN/D non sottratte. L’equivalenza è dimostrata per una particella nello statoS composta di due particelle di spin zero facendo l’approssimazione di considerare solo stati intermedi di due particelle, e nelle seguenti ipotesi: i) Le ampiezze di scattering hanno al massimo un polo della particella al di sotto della soglia dello scattering. ii) È soddisfatto il teorema di Levinson nel suo senso originario. iii) Il potenziale generalizzato è tale che esiste un’ampiezzat(s) determinata tramite le equazioniN/D non sottratte, et(s) ha un polo. Per la prova si ottiene col metodo di Blankenbecleret al. una forma generale di ampiezze di scattering che hanno la data discontinuità sul taglio sinistro e soddisfano i), ii) e iii). Inoltre si è condotti a studiare in dettaglio la non unicità della funzione di propagazione e la funzione di vertice ed ancheZ3 eZ1.

Finite-temperature effect on broken UA(1) symmetry and the η′ mass

Abstract The U A (1) symmetry-breaking effective lagrangian mediated by the instanton is calculated in the semiclassical approximation at finite temperature. It is found that the strength of the effective vertex decreases with increasing temperature up to the QCD scale. Also, we discuss the possible variation of the η′ and other pseudoscalar meson masses.

The Dispersion Relations for the Scattering of Photons from Proton

The dispersion relations are derived for the nonforward amplitudes for photon-proton scattering. By expanding these relations in momentum transfer and retaining first few terms, the dispersion relations for six independent combinstions of the partial wave amplitudes are obtained. Contributions of the nonphysical region are calculated to the first order in the fine structure constant, and are found to be consistent with the low-energy theorem. Using these relations and photopion production data, the differential cross sections are calculated. in doing this, the amplitudes for the mixtures of dipolse and quadrupole waves are taken into account in addition to electric dipole, electric quadrupole, and magnetic dipole amplitudes. The results turn out to be fairly improved compared with the dipole model, and roughly explain experiments. (auth)

Bootstrap Particles and Elementary Particles in the Z3=0 Limit Discussion in a Soluble Model

Some exactly soluble models, such as the Leeand Zachariasen-models, have been used to show the equivalence between composite particles defined by the ND1 method and the condition of vanishing wave function renormalization constant imposed upon elementary particles. These models, however, do not allow to discuss composite particles produced through the bootstrap mechanism. IIere a soluble moclel obtained by an extension of the Lee model is shown to allow such discussion, and the equivalence between one of the bootstrap conditions and the condition Z:; =0 is explicitly proved. The argument is supplemented by a general remark which shows the equivalence for more general cases, at least, formally.

A small bag model for the nucleon and the R ratio

Abstract In connection with a possible large primordial pT of partons inside a nucleon a small bag model for the nucleon substructure is proposed, which incorporates both the long standing constituent-quark picture and some salient features of the MIT bag model. It is applied to the ratio R = σ L σ T in deep inelastic e(μ)N scattering.

Unified treatment of photon and massive vector-meson scattering process by helicity amplitudes

Abstract A formalism to treat virtual photons and massive vector mesons on the essentially same footing is developed to include the scattering of a massless and massive spin-1 particle by a spin - 1 2 particle . It is explicitly shown that a smooth limit of the massive case amplitudes to the Compton amplitudes can be realized within the framework of helicity amplitudes and that the zero-mass limit satisfies all the requirements of gauge invariance. Such a formalism is advantageous to incorporate the vector-dominance hypothesis and yields a convenient parametrization of helicity amplitudes for the Regge-pole analysis of real and virtual photon processes.

Two-Nucleon Potentials from Dispersion Relations*)

Dispersion relations are applied to obtain the two-pionexchange nuclear potentials including the first order nonstatic effects. Calculation is made within the approximation in which only the contribution from the single nucleon intermediate state is considered for pion-nucleon scattering, though the S-wave suppression is considered. All the potentials are expressed in a spectral representation. It is shown that this form is suitable to distinguish the effects of low-energy pion exchange from those of high-energy exchange. The former can be reliably estimated; the latter are subjected to a cutoff and substituted by adjustable parameters. The potentials obtained are compared with phenomenological ones in terms of the spectral distributions of exchanged pions. Comparison of the method with the others for potential construction is made in relation to the problem of the coupling type between pions and nucleons. (auth)

A variational approach to bag formation and the quark-antiquark potential

Abstract A variational approach is used to the Adler problem which is to obtain the color confinement region and the q- q static potential from approximate effective potentials of quantum chromodynamics. It yields fairly good fits to the Adler-Piran numerical results.

Limiting fragmentation and Bjorken scaling in a baryon exchange model

The target fragmentation in an inclusive reaction is studied in a baryon exchange model. The invariant distribution function expressed by the total cross section of hadron-hadron scattering shows scaling behavior. The calculation is compared with the data. The formalism is also applied to the inclusive reaction by electrons. Possible connection of Bjorken scaling to the limiting fragmentation is discussed. (auth)