THE BEHAVIOURS OF F2ep(X,Q2)-F2en(X,Q2) AND THE SCALE-BREAKING PARAMETER

The scale-breaking parameter F₂^ep(x, Q²) of non-singlet component F₂^ep-F₂^en and some other quantities in the electro-production process are discussed by usinb the analytic expression for the distribution function of valence quarks in ha.drons up to leading log approximation given by a, previous paper^[1]. Comparisons with data are also given.

     

FURTHER DISCUSSION ON THE EQUATION AND ITS SOLUTIONS FOR THE BOUND STATES OF MESONS

We continue the investigation of the equation and its solutions for the bound states of mesons discussed previously, emphasizing on large values of v, a parameter characterizing the shape of the potential. The results show that the dependence of the eigenvalues λ and some related physical quantities upon the potential parameters v and E is approximately the same as in our previous work. But the average radii of the bound mesons cease increasing as v increases. For each value of v, there exists a maximum average radius√<R²>_max, and all these √<R²>_max are approximately equal to 12.6 M^-1 （M being the mass of the straton）, which is much smaller than the experimental value of the radius of the π meson. However, if we assume, in addition to the attractive potential, there exists, for the straton-anti-straton superstrong interactions, also a repulsive potential, and, in particular, if we introduce a differencetype potential V_D（r） corresponding to the potential V_v（r） in our previous work, the calculated radii of the bound mesons do approach the experimental value.     

SOME CONJECTURES ON THE MASS FORMULA OF CHARGED LEPTONS

In this note we propose that the electromagnetic self energy of lepton may beconnected with quantum number n by（ （δm）/m）=（1/（2π））n^-b ,in which b is a constant.Wefnrther propose that the cut-off value of momentum M is connected with gravitationalconstant κ and fine structure constant α by M=（1/√κ）αe^-1-b.So we obtainthe mass formula of charged leptons M=（1/√κ）α exp{-3/4-b-(1/3α)n^-b}.By using the masses of e^- and μ^- and the value of a as in put,we get the calculatedvalues of κ=（6.67231±0.00026）×10^-8cm³g^-1sec^-2and m_r=（1782.306±0.078）MeVwhich agree very well with experimental values κ=（6.6720±0.0041）×10^-8cm³g^-1sec^-2 and m_τ=(1782_-4⁺³)MeV respectively.The mass of the fourth charged leptonpredicted by the formula should be m=（11725.47±0.51）MeV,which can be checkedby experiments in the near future.We also discuss briefly the proposed formula andthe obtained results.     

THE BEHAVIOR OF THE PHASE-SHIFT IN THE BAKAMJIAN-THOMAS THEORY

The behavior of the phase-shift of the Bakamjian-Thomas theory and its relationwith the phenomenological nuclear force V=V_RiV_I at high energy are explored.Two limits are obtained:It is found that the repulsive core with a sharp outer edge may induce a characteris-tic oscillation of Re δ₁,and Im δ₁ is sensitive to V₁.The conclusion is that the analy-sis of the phase-shift extending to higher energy is relevant in determining therepulsive core and the imaginary part of the nuclear force.     

MICROSCOPIC CALCULATION OF THE INERTIA IN HEAVY NUCLEI

A realistic calculation of the inertia for ²³⁶U fisson based on the linear response theory is presented, in which the single particle states are provided by Nilsson model. The dependence of the nuclear inertia M_δiδi on the collective variables δ₂, δ₄ is studied at the range of certain nuclear temperature (0—1 MeV). The pairing effect and the shell effect on the nuclear inertia are discussed. The calculated results show a very prominent structure at level crossing points and when acrossing the critical temperature.     

TESTING GLUON DISTRIBUTION FUNCTION OF HADRONS IN LARGE PT PROCESS WITH DIRECT PHOTON EMISSION

In this paper we disscuse disscuse the physicsical aspect of cross-section differences Δ_AB^cγ=dσ(AB→cγX)-dσ(AB→cγX) and give the simple rules to select the elementary subprocesses which contribute to cross-section differences.
We bind a way to test the gluon distribution functions of hadrons through the measurement of cross-section difference or combination of cross-section differences in the large P_T process with direct photon emission. Moreover we obtain simple relations between each combination of cross-sections and the corresponding gluon distribution functions of proton, neutron, pion and daon:
G_p⁸(x)/(Δ_pp^hγ－Δ_pp^hγ)=G_n⁸(x)/(Δ_pp^hγ)=G_π⁸(x)/(Δ_π+p^hγ+Δ_π－p^hγ=G_K⁸(x)/(Δ_K+p^hγ+Δ_K－p^hγ)which are expected to be test in experiment.     

THE VERTICAL INTEGRATED MOMENTUM SPECTRUM OF THE MUON WITH MOMENTUM LARGER THAN 4 GeV/c AT 3220m ABOVE SEA-LEVEL

At an altitude of 3220 meters above sea level in Yunnan Province, we measured, by using a G-M counter-magnetic spectrometer, the vertical integratted momentum spectrum of the cosmic muon with momentum larger than 4 GeV/c. The spectrum obtained from this experiment is expressed by a power function in the form of I（>p）=Q （p+4）^-1.86±0.06(cm^-2·sr^-1·s^-1), where p is in GeV/c and Q is a constant. We also measured the charge ratio of muon in the 4—23 GeV/c momentum range. The result is N_μ/N_μ-=1.26±0.11. The error in the momentum measurement with spectrometer has been discussed and calculated.     

AN ANALYSIS OF FOUR-ELEMENT MODELS OF LEPTONS AND NON-DIAGONAL NEUTRAL CURRENTS

Due to the possible production of neutral and charge heavy leptons by v_μ, models consisting of four elements per "line", e.g. v_e, e^-, E⁰, E^- v_μ, μ^-, M^0, M^- v_τ, τ^-, T⁰, T^- ……are analysed. Non-diagonal neutral currents cannot be avoided. Nevertheless, a model is proposed within SU_（2）×U_（1） in which the process μ→eγ can still be suppressed by the Bjorken-Lane-Weinberg mechanism; various production cross-sections for heavy leptons are reasonable when compared with experiments. Models corresponding to SU_（3）×U（1） and still higher symmetries are discussed.     

A METHOD FOR FINDING POTENTIALS CORRESPONDING TO POLYNOMIAL-FACTOR EIGENFUNCTIONS IN QUANTUM MECHANICS

A method for finding potentials corresponding to polynomial-factor eigenfunc-tions is given for the Schr（?）dinger equation as an example.It is shown that theeigen-solutions for harmonic and Columb's potentials in quantum mechanics are the twoexamples which can be given by this method and some other examples are discovered.This method and some results of this paper may be useful for hadron structure mo-del theory.One of the examples is the equation in Ref.（4）which is derived fromBethe-Salpeter equation for the case that the straton is tightly bounded in certain po-tential well.When this method is applied to that equation for three dimensionalcentral symmetric potential V（r）=V₀—2（N+（1/2））β^-1（√V₆r²）+（V₆r⁶）, some resultsare obtained as shown in Fig. 2 in which λ′ must be considered as a linear function of m².The so called“quasic Regge trajectory”behavior is manifested.     

QCD PREDICTION FOR THE REACTION γ+p→2γ+X

In the framework of the perturbative QCD, the two-fold differential cross section d²σ/dx_Tdx_L of the reaction γ+p→2γ+X and its two backgrounds (γ+p→γ++X, γ+p→γ++X) are calculated in c.m.s.. The results show that, in a large range of (x_T, x_L), the calculated reaction cross section can be measured in current laboratory condition. And due to the properties of this reaction, i.e., large p_T photoproduction and direct photon pair emission, all of the backgrounds can be greatly suppressed.

     

THE TEST OF SLAC METHOD USING LEE MODEL

Treating Lee Model by Slac method,we find that,to state ||V> of one particle and state ||VN> of two particles,there corresponds a solution of Slac bag type re-spectively.The latter bears resemblance to the former in energy especially for ||V> state with the replacement of the interaction constants g by g/√e only.In addition,the“bag”corresponds precisely to the scalar field in ||V> and ||VN> states.However,for ψ_N^- and ψ_V^- field,we get δ-function type solutions by Slac method.They deviate greatly from the rigorous solutions.The“skin confinement”as statedby Bardeen et al.,and Rafelski is closely related to the δ-confinment in the one par-tiele state found here by coherent state approximation.Thus it may not representthe physical picture in the rigorous solution of a quantum field theory.     

FINE STRUCTURES OF INCLUSIVE SPECTRA(Ⅰ)——SUM RULES AND THE GENERALIZATION OF FEYNMAN-YANG SCALING

Important implications of the fine structure of inclusive spectra(to be calledinclusive and semi-inclusive spectra of nearby particles,which represent the local dis-tributions of nearby particles in three-dimensional phase space with rapidity y and transverse momenta P_⊥x, P_⊥z as independent coordinates are explained,and some basicfeatures of the fine stucture are found,namely,sum rules and the generalized formof the Feynman-Yang scaling.One of the sum rules,for example,is:where f_(1;k) denotes the normalized invariant inclusive cross section of k closely neigh-boring particles.It follows that the inclusive the spectra of nearby particles arequalitatively different from the usual ones.The generalized form of the Feynman-Yang scaling for the case of k closelyneighboring particles,for example,is:f_(1;k)(s,x₁,P_⊥1,…x_k,P_⊥k⁾∞,（s→∞,x₁≤x₂≤…≤x_k）.where‘∞’denotes‘approaches a definite limit’.For k=2,the existing experimentaldata for the rapidity gap-length distributions show that for FNAL energies,f_(1,k） isalready close to its limiting form.The inclusive（semi-inclusive）spectra of nearbyparticles way be able to reflect effectively short-range correlation effects.     

THE INTERACTION OF A HIGH ENERGETIC PROTON WITH A NUCLEUS—THE RELATION OF THE PRODUCED PARTICLES WITH THE NUCLEAR MASS NUMBER A

Suppose that a high energetic proton interacts with a cluster of m particles in anucleus the mean multiplicity of this interaction and that of PP interaction followthe same law: n=CS^k. Using the Glauber theory we get R(A)≡n_PA/n_PP1.26A ^1/3(A ^1/3+1) ^-2/3 This formula explains the current experimental result quite well.     

APPLICATION OF THE EIKONAL WAVE FUNCTION TO QUASIFREE SCATTERING

In this paper. we have used the Eikonal wave functionφ_E(r)=(2π)^-3/2 exp(ik.r)X(r)whereexp{-i/hv∫_-∞^zV(x,y,z,')dz'}and V=nk/m to investigate the quasifree scattering ⁶Li (p, pd)α with E_p=156 MeV,590MeV and 670 MeV. In V(x, y, z), the nuclear interaction and the Coulomb inte-raction are included. For the case of 156 MeV, the nuclear potential is taken to be the Woods-Saxon type.The result is shown in fig. 1. This result is compared with those obtained by themethod of partial waves. For the cases of 590MeV and 670MeV, a new method is used to describe thenuclear potential, and the results are showh in fig. 3 and fig. 4, respectively.     

APPROXIMATE B.S. WAVE FUNCTIONS FOR AN ELECTROMAGNETIC BOUND SYSTEM OF SPINS (1/2, 1/2) OR (1/2, 1/2) WITH UNEQUAL MASSES

The Bethe-Salpeter equation for an electromagnetic bound system of spins (1/2—1/2) or (1/2—1/2) with unequal masses are solved in this paper. The approximate B.S. wave functions for these systems are given. Utilising these wave functions, the decay rate and branching ratio for Ξ⁰→(Σ⁺μ^－)+v_μ are calculated with accuracy up to order O(α). The results are wΞ⁰→(Σ⁺μ^－)+v_μ1.12(1/sec) and R=[wΞ⁰→(Σ⁺μ^－)+v_μ]/[wΞ⁰→(Σ⁺μ^－)+v_μ]4.7×10^-7. Similarly, the process Λ→(pμ^－)+v_μ is also discussed.     

SYMMETRY OF THE ROTATION+VIBRATION SPECTRA FOR NUCLEAR MOLECULE 12C+12C

The rotation-vibration spectra of nuclear molecule ¹²C+¹²C is chassified by the irreducible representations of group U(5). It is shown that the symmetry of rotation-vibration levels of nuclear molecule ¹²C+¹²C are discribed by means of dynamical symmetry U(5)U(4)O(4)O(3).     

THE DIFFICULTY OF THE DECAY τ→πντ AND SPIN 3/2 HEAVY LEPTON

We discuss the suppression of the decay of heavy lepton τ into πv_τ,by assuming that τ and/or v_τ carry spin 3/2. For the case of spin 3/2 T and spin 1/2 v_τ, using the weak current ψ_μ^(τ)(a+b_^γ5)Ψ^(v_τ)we find that the πv_τ decay channel relative to the v_τv_ll^-channel is suppressed 12/5 times, while other decay channels are not changed appreciably. △R=σ（e⁺e^-→τ⁺τ^-）/σ（e⁺e^-→μ⁺μ^-） is also discussed.     

ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(III)

In this paper, using the method employed in two earlier papers: "On the Irredu-cible Representations of the Compact Simple Lie Groups of Rank 2(I) and (II)",theirreducible representations of the groups B₂ and G₂ are discussed. A method for cal-culating the irreducible representations of these groups is given. Moreover,some ofthe low dimensional representations of these groups are calculated.     

TRACELESS OPERATORS AND SO6 WAVE FUNCTIONS OF sd BOSONS

Traceless operators of sd bosons are introduced and used to construct the SU₆SO₆SO₅SO₃ wave functions of sd bosons according to the method of T.S.Yang     

THE SPECTRAL REPRESENTATION OF PROPAGATOR FOR FERMION FIELD AND QUARK CONFINEMENT

The properties of fermion causal Green's function is discussed according to the theory of spectral representation. The definition of effective mass is established from the view point of field theory, and the approximate expression of S_F' (p) as |p²|&#171;M² and the asymptotic formula of S_F' (p) as p²→+∞ is given. In terms of these result the problem of quark confinement is discussed. We find that: (ⅰ) Based on the theory of spectral re presentation the concept of relative confinement is allowed, and if renormalization effect is strong, the quarks can demonstrate definitely lighter effective mass when they are far away from the mass shell; (ⅱ) Based on the theory of spectral representation the concept of absolute confinement is unallowable, even the absolute confinement is taken as the limit of relative confinement. That is if the concept of absolute confinement is introduced, we must discard a part of elementary hypothesis of spectral representation theory.