Gauge invariance and renormalization

The renormalization of Abelian and non-Abelian local gauge theories is discussed. It is recalled that whereas Abelian gauge theories are invariant to local c-number gauge transformations δA_μ(x) = ?_μ,…, with □Λ = 0, and to the operator gauge transformation δA_μ(x) = ?_μφ(x), …, δφ(x) = α^?1?·A(x), with □φ = 0, non-Abelian gauge theories are invariant only to the operator gauge transformations $\text{δA}{}_{\mathrm{\mu }}\text{(x) ～}\textcolor{red}{}{}_{\mathrm{\mu }}\text{C(x)}$, …, introduced by Becchi, Rouet and Stora, where

_μ is the covariant derivative matrix and C is the vector of ghost fields. The renormalization of these gauge transformation is discussed in a formal way, assuming that a gauge-invariant regularization is present. The naive renormalized local non-Abelian c-number gauge transformation $\text{δA}{}_{\mathrm{\mu }}\text{(x) = (Z}{}_1\text{/Z}{}_3\text{)gA}{}_{\mathrm{\mu }}\text{(x) ×}\text{Λ}\text{(x)+?}{}_{\mathrm{\mu }}\text{Λ}\text{(x)}$, …, is never a symmetry transformation and is never finite in perturbation theory. Only for $\text{Λ}\text{(x) = (Z}{}_3\text{/Z}{}_1\text{)L}$ with L finite constants or for $\text{Λ}\text{(x) = Ω}\text{z}\text{?}{}_3\text{C(x)}$ with Ω a finite constant does it become a finite symmetry transformation, where $\text{z}\text{?}{}_3$ is the ghost field renormalization constant. The renormalized non-Abelian Ward-Takahashi (Slavnov-Taylor) identities are consequences of the invariance of the renormalized gauge theory to this formation. It is also shown how the symmetry generators are renormalized, how photons appear as Goldstone bosons, how the (non-multiplicatively renormalizable) composite operator A_μ × C is renormalized, and how an Abelian c-number gauge symmetry may be reinstated in the exact solution of many asymptotically fr ee non-Abelian gauge theories.     

On the renormalization and short-distance properties of hadronic operators in QCD

We discuss the renormalization of the contour-dependent gauge-invariant composite bilocal or string operator $\text{q}\text{(2)}\text{exp}\text{|g ∫}{}_1{}^2\text{A}\text{d}\text{z|q(1)}$ in QCD, which one would naturally associated with the hadronic bound states. We then discuss the short-distance expansion of this operator as the end points merge. We argue that some functional average overall possible paths between x₁ and x₂ may be the appropriate operator to describe the mesonic modes in QCD and that the short-distance expansion may provide a valuable insight into the nature of this functional average. Most of our considerations are for smooth contours; however, we propose a simple way of treating on the same footing the additional divergences pointed out by Polyakov due to sharp bends in the contour. This latter confirms the conclusions reached for smooth contours.     

Singular perturbation potentials

This is a perturbative analysis of the eigenvalues and eigenfunctions of Schrödinger operators of the form ?Δ + A + λV, defined on the Hilbert space L²(Rⁿ), where $\text{Δ = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{n}}\text{?}{}^2\text{?X}{}_{\mathrm{i}}{}^2$, A is a potential function and V is a positive perturbative potential function which diverges at some finite point, conventionally the origin. λ is a small real or complex parameter. The emphasis is on one-dimensional or separable problems, and in particular the typical example is the “spiked harmonic oscillator” Hamiltonian, $\text{?d}{}^2\text{dx}{}^2\text{+ x}{}^2\text{+}\text{l(l + 1)}\text{x}{}^2\text{+ λ|x|}{}^{\mathrm{?\alpha }}$, where α is a positive constant. When this kind of perturbation is very singular, the first-order Rayleigh-Schrödinger perturbative correction, (u₀, Vu₀), where u₀ is the unperturbed eigenfunction, diverges. This analysis constructs explicitly calculable terms in a modified perturbation series to a finite order, by using linear operator theory in concert with approximation methods for differential equations. Along the way a connection between a W-K-B type approximation and Bessel functions is exploited.     

Spectroscopic information on ground-state Ar2, Kr2, and Xe2 from interatomic potentials

Calculations of vibrational and rotational level spacings of homonuclear inert gas diatomic molecules by numerical integration of the radial Schrödinger equation are presented. The potentials which were used for the ground states of Ar₂, Kr₂, and Xe₂ were obtained from accurate fits to the molecular beam scattering data. From the calculated $\text{Δ}\text{G}{}_{\mathrm{<mtext>v+</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{'}\text{s}$ and B_v's, the following spectroscopic constants (in cm^?1) were fitted: for Ar₂ω_e = 31.92, ω_ex_e = 3.31, ω_ey_e = 0.11, B_e = 0.060, α_e = 0.004; for $\text{Kr}{}_2\text{ω}{}_{\mathrm{e}}\text{? 23.99}$, $\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}\text{? 1.30}$, $\text{ω}{}_{\mathrm{e}}\text{y}{}_{\mathrm{e}}\text{? 0.021}$, $\text{B}{}_{\mathrm{e}}\text{? 0.024}$, $\text{α}{}_{\mathrm{e}}\text{? 0.001}$; for $\text{Xe}{}_2\text{ω}{}_{\mathrm{e}}\text{? 21.26}$, $\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}\text{? 0.75}$, $\text{ω}{}_{\mathrm{e}}\text{y}{}_{\mathrm{e}}\text{? 0.008}$, $\text{B}{}_{\mathrm{e}}\text{? 0.013}$, $\text{α}{}_{\mathrm{e}}\text{? 0.0004}$.     

Phenomenological predictions of the SO(10) supersymmetric grand unified model

The phenomenological predictions of the SO(10) supersymmetric grand unified model (SO(10) SGUM) for the mass scales M₁, M₂, weak angle ifsin²θ_w, quark-leptons mass ratios $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, $\text{m}{}_{\mathrm{t}}\text{m}{}_{\mathrm{<mtext>b</mtext>}}$, $\text{m}{}_{\mathrm{\tau }}\text{m}{}_{\mathrm{\nu }}{}_{\mathrm{\tau }}$ and proton lifetime τ_p are estimated by using renormalization group analysis at one-loop level. In contrast with SU(5) SGUM, we find that the SO(10) SGUM still has problems with τ_p but not with sin²θ_w and $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, which may suggest that supersymmetry would be bro at a mass scale $\text{?10}{}^7\text{GeV}$.     

Predissociation and Λ-doubling in the even-parity Rydberg states of the nitrogen molecule

Predissociations in the y¹Π_g and $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ Rydberg states of N₂ (configurations $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{4pσ}$ and $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{3pπ}$, respectively) and their likely causes, are discussed. Peaking of rotational intensity at unusually low J values, without sharp breaking off, is interpreted as due to case c^? or case cⁱ predissociation. Λ doubling in the y state, attributed to interactions with the $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state and with another, ¹Σ⁺, state of the same electron configuration as x, is analyzed. From this analysis the location of the (unobserved) ${}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ state, here labeled x′, is obtained. It is concluded that the predissociation in the Π⁺ levels of the y state is an indirect one mediated by the interaction with x′ coupled with predissociation of x′ by a ${}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state dissociating to ${}^4\text{S +}{}^2\text{P}$ atoms: combined, however, with perturbation of the y state by the k¹Π_g Rydberg state (configuration $\text{3σ}{}_{\mathrm{g}}{}^{\mathrm{?1}}\text{4dπ}$), whose Π⁺ levels are completely predissociated.     

The uniform and the strong topology on realizations of the algebra of polynomials

It is shown that under quite general assumptions on the operators A₁,…,A_n (unbounded, symmetric) and on the domain $\text{D}$ on the realization $\text{P}\text{(A}{}_1\text{,…,A}{}_{\mathrm{n}}\text{)}$ of the algebra of polynomials $\text{P}\text{(x}{}_1\text{,…,x}{}_{\mathrm{n}}\text{)}$, the strongest locally convex topology τ_st coincides with the uniform topology τ_$\text{D}$ as well as with the strong operator topology τ_s. In the case n = 2 some conditions are given, under which these general assumptions are fulfilled.     

The microwave spectrum of 2,4-dioxabicyclo[3.1.0]hexan-3-one

The R band (26.5–40 GHz) microwave spectrum of 2,4-dioxabicyclo[3.1.0]hexan-3-one is reported. Rotational constants for the ground vibrational state of the common ¹²C₄¹H₄¹⁶O₃ and ¹³C₁, ¹³C₆ isotopically substituted species (the latter observed in natural abundance) have been evaluated. In addition rotational constants of the V_B = 1 to V_B = 5 quanta associated with the bending vibration of the five membered ring have been determined. A partial r_s structure has been calculated:

$\text{r(}\text{C}{}_1\text{?}\text{C}{}_5\text{) = 1.497± 0.016}\text{A}\text{?}\text{, r(}\text{C}{}_1\text{?}\text{C}{}_6\text{) = r(}\text{C}{}_6\text{?}\text{C}{}_5\text{) = 1.522 ± 0.015}\text{A}\text{?}$

,

$\text{∠}\text{C}{}_6\text{C}{}_1\text{C}{}_5\text{= ∠}\text{C}{}_1\text{C}{}_5\text{C}{}_6\text{= 60°32′ ± 1°36′, ∠}\text{C}{}_1\text{C}{}_6\text{C}{}_5\text{= 58°′ ± 1°47′}$

. With certain assumed molecular information a least squares fit yields the following parameters:

$\text{β = 68.5 ± 0.02°, r(}\text{C}{}_1\text{O}{}_2\text{= 1.408 ± 0.004}\text{A}\text{?}$

,

$\text{∠}\text{C}{}_5\text{C}{}_1\text{O}{}_2\text{= 105.8 ± 0.02°, ∠}\text{C}{}_1\text{O}{}_2\text{C}{}_3\text{= 108.10 ± 0.03°}$

,

$\text{∠}\text{O}{}_2\text{C}{}_3\text{O}{}_4\text{= 112.8 ± 0.02°}$

.     

Bounded diffusion in solid solution electrode powder compacts. Part II. The simultaneous measurement of the chemical diffusion coefficient and the thermodynamic factor in LixTiS2 and LixCoO2

Two electrochemical methods - involving the application of a long-time galvanostatic current pulse and a small potentiostatic voltage step to a M/M_xSSE cell - are presented. From the overvoltage, respectively current response the chemical diffusion coefficient ($\text{D}{}_{\mathrm{M}}{}^{\mathrm{+}}$) and the thermodynamic factor (? ln a/? ln c) are obtained. The methods have been applied to the cells: Li/1M·LiClO₄ in propylenecarbonate/Li_xTi_1.03S₂ 0.05 < x < 0.95, T = 20°C; and Li_xCoO₂ 0.10 < × < 1, T = 20°C. From the application of the current pulse/voltage decay method it followed: $\text{D}{}_{\mathrm{<mtext>Li</mtext>}}{}^{\mathrm{+}}\text{(}\text{Li}{}_{\mathrm{x}}\text{Ti}{}_{1.03}\text{S}{}_2\text{) = 1?4 × 10}{}^{\mathrm{?8}}\text{cm}{}^2\text{s}{}^{\mathrm{?1}}$, with a slight tendency to increase with decreasing x; $\text{D}{}_{\mathrm{<mtext>Li</mtext>}}\text{C}\text{(}\text{Li}{}_{\mathrm{x}}\text{CoO}{}_2\text{) = 2?40 × 10}{}^{\mathrm{?9}}\text{cm}{}^2\text{s}{}^{\mathrm{?1}}$, decreasing with decreasing x. These values are among the highest found for solid state Li⁺-ion diffusion, and will be closely evaluated and compared with data reported by other workers. The x-dependence of the thermodynamic factor, determined from kinetic data, for Li_xTi_1.03S₂ (x = 0.05-0.95) and Li_xCoO₂ (x = 0.60-1.00) is in accordance with a simple thermodynamic model. Unlike for Li_xTi_1.03S₂, the thermodynamic factor for Li_xCoO₂, determined from the EMF-x relation, cannot be accounted for by this model. Furthermore, a fast, but crude method to determine the average chemical diffusion coefficient in Li_xTi_1.03S₂ and Li_xCoO₂ is discussed.     

CLL = (L,L; 0, 0) measurements and a structure due to a P partial wave in the pp system

Measurements of C_LL of pp elastic scattering near θ_c.m. = 90° at thirteen energies between 300 and 800 MeV are reported. These, together with previous values of C_NN, are used to extract values of two quantities, $\text{?}{}_{\mathrm{<mtext>s</mtext>}}$ and $\text{?}{}_{\mathrm{<mtext>t</mtext>}}$, which contain only spin-singlet and only coupled spin-triplet partial waves, respectively. The $\text{?}{}_{\mathrm{<mtext>s</mtext>}}$ curve, which is not dependent on C_LL, exhibits the behavior expected for the previously conjectured ¹D₂ resonance. The $\text{?}{}_{\mathrm{<mtext>t</mtext>}}$ curve also exhibits a resonance-like behavior, which could be due either to the ³P₀ or the ³P₂ partial wave.     

“Forbidden” rotational spectra of symmetric-top molecules: PH3 and PD3

A millimeter-wave spectrometer having a sensitivity of 4 × 10^?10 cm^?1 in the 2-mm region has been constructed for observation of extremely weak millimeter-wave spectra of gases. It has been used to measure J → J, K = 0 ← 3 transitions in PH₃ and J → J, K = 0 ← 3 as well as K = ±1 ← ±4 transitions in PD₃. The B₀ and C₀ spectral constants (in MHz) are: for PH₃, B₀ = 133 480.15 ± 0.12 and C₀ = 117 488.85 ± 0.16; for PD₃, B₀ = 69 471.10 ± 0.03 and C₀ = 58 974.37 ± 0.05. The effective ground-state values obtained for the bond angle and bond length are: for PH₃, $\text{r}{}_0\text{(}\text{A}\text{?}\text{) = 1.420}{}_0$ and $\text{α}{}_0\text{(}{}^{\mathrm{o}}\text{) = 93.34}{}_5$; for PD₃, $\text{r}{}_0\text{(}\text{A}\text{?}\text{) = 1.417}{}_6$ and $\text{α}{}_0\text{(}{}^{\mathrm{o}}\text{) = 93.35}{}_9$. The corresponding zero-point-average values were calculated to be: for PH₃, $\text{r}{}_{\mathrm{z}}\text{(}\text{A}\text{?}\text{) = 1.4269}{}_9\text{± 0.0002}$ and $\text{α}{}_{\mathrm{z}}\text{(}{}^{\mathrm{o}}\text{) = 93.228}{}_7$; for PD₃, $\text{r}{}_{\mathrm{z}}\text{(}\text{A}\text{?}\text{) = 1.4226}{}_5\text{± 0.0001}$ and $\text{α}{}_{\mathrm{z}}\text{(}{}^{\mathrm{o}}\text{) = 93.256}{}_7\text{± 0.004}$. For both species, the equilibrium values are $\text{r}{}_{\mathrm{e}}\text{(}\text{A}\text{?}\text{) = 1.4115}{}_9\text{± 0.0006}$ and $\text{α}{}_{\mathrm{e}}\text{(}{}^{\mathrm{o}}\text{) = 93.32}{}_8\text{± 0.02}$.     

Microwave spectrum and structure of cyanamide: Semirigid bender treatment

An extensive study of the microwave spectrum of cyanamide has been undertaken, the analysis being based in part on semirigidbender calculations by the methods of Bunker and Szalay. Inversion lines of NH₂CN, $\text{K}{}_{\mathrm{?1}}\text{= 2}{}^{\mathrm{a}}\text{Q}$ branches and a number of vibrational satellites of the J = 2?1 transition were observed. A two-vibrational-state Hamiltonian was used to fit simultaneously the 0⁺ and 0^? microwave data and yielded rotational constants X, Y, Z, D_J, D_JK, d₁, H_JK as well as the inversion splitting and the μ_yz-connecting matrix element. Vibrational satellite data of seven isotopic species and infrared frequencies of NH₂CN were included in the semirigid bender calculations: The NCN spine is nonlinear by ca. 5° in the equilibrium structure of the molecule. Also, $\text{r}{}_{\mathrm{<mtext>NH</mtext>}}\text{A}\text{?}\text{= 0.9994 + 0.0144?}{}^2$; <HNH/2 = 60.39° ? 0.1134?²; $\text{r}{}_{\mathrm{<mtext>NC</mtext>}}\text{A}\text{?}\text{= 1.3301 + 0.0327?}{}^2$ (? is the inversion angle in rad); $\text{r}{}_{\mathrm{<mtext>CN</mtext>}}\text{= 1.1645}\text{A}\text{?}$ fixed. The inclusion of the NC bond flexing was necessary in order to reproduce the observed vibrational satellite patterns of NH₂CN, NHDCN, and ND₂CN. The barrier to inversion of the amino group is 510 ± 6 cm^?1 with minima at ±45.0 ±0.2°. The inversion dipole moment is 0.91 ± 0.02 Debye.     

A thermodynamic study of nonstoichiometric cerium dioxide

Thermogravimetric measurements were performed on nonstoichiometric CeO_2?x in the temperature range 750–1500°C and from oxygen pressures of 10^?2 to 10^?26 atm. From this data the deviation from stoichiometry x = x(T, P_o2) was determined. The thermodynamic quantities Δ$\text{H}$_o2 and Δ$\text{S}$_o2 were calculated in the region 0.001? x ? 0.3 and found to be independent of temperature.In the composition region 0.001< x < 0.006, the variation of Δ$\text{S}$_o2 with x is consistent with a defect model involving randomly distributed doubly ionized oxygen vacancies. The experimental dependence of x and σ (electrical conductivity) is shown to be consistent with this model as Δ$\text{H}$_o2 (≈ -10 eV) exhibits a slight dependence on x. It is postulated that the variation in Δ$\text{H}$_o2 may result from lattice parameter increases with x, while the defects remain essentially randomly distributed.In the composition region 0.006 < x < 0.1, x ∝ with 1 < n < 5, and in the region 0.1 < x < 0.3, x ∝ with n increasing rapidly with x to n? 30. This behavior is believed to result from increasing defect interaction with increasing departures from stoichiometry. It is interesting to note that the ordered phase observed by Bevan and Kordis between CeO_1·72 and CeO_1·70 was not observed in this study at temperatures between 1300° and 1500°C.     

Analysis of the (ν1 + ν2) and (ν2 + ν3) combination bands of ozone

The fine structures of the (ν₁ + ν₂) and (ν₂ + ν₃) combination bands of ozone in the 5.7-μm region have been recorded and analyzed. The two vibrational states are coupled through Coriolis and second-order distortion terms. The interaction has been treated by the numerical diagonalization of the secular determinant for the two coupled states. With the centrifugal distortion parameters fixed to the ground state values, the following constants have been obtained: ν₁ + ν₂ = 1796.26₆, A₁₁₀ = 3.610₄, B₁₁₀ = 0.4414₅, $\text{C}{}^1{}_{110}\text{= 0.3902}{}_9$, ν₂ + ν₃ = 1726.52₆, A₀₁₁ = 3.553₇, B₀₁₁ = 0.4398₂, $\text{C}{}^1{}_{011}\text{= 0.3884}{}_4$, Y₁₃ = ?0.46₆, and X₁₃ = ?0.01₀ cm^?1. In addition, the following anharmonic constants have been obtained: x₁₂ = ?7.82₁ and x₂₃ = ?16.49₄ cm^?1. The value of the dipole moment ratio, $\text{R =}\text{〈011|μ}{}_{\mathrm{z}}\text{|0〉}\text{〈110|μ}{}_{\mathrm{x}}\text{|0〉}$, is 1.30 ± 0.10.     

Partial summation of gradient expansion of canonical density matrix

The canonical density matrix $\text{C(}\text{rr}{}_0\text{β)=C}{}_0\text{(}\text{rr}{}_0\text{β)}\text{exp}\text{{-βU(}\text{rr}{}_0\text{β)}}$, where C₀ is the free particle matrix, can be developed by expanding U to second-order in the potential V. Bhaduri's suggested form of C is thereby transcended.     

Stokes parameters representation of the light propagation equations in inhomogeneous anisotropic,optically active media

A simple expression is obtained by using the Stokes parameters and transforming the light propagation equations derived by the authors in a weakly inhomogeneous anisotropic active medium. By applying the transformation to photoelasticity it is shown that Aben's equations reduce to $\text{?S/?x}{}_3\text{= Ω × S}$, where S is the polarization vector propagating through the photoelastic medium, x₃ is the distance traveled along the propagation direction and $\text{Ω = (C(σ}{}_{11}\text{? σ}{}_{22}\text{) 2Cσ}{}_{12}\text{0)(σ}{}_{\mathrm{jp}}$, stress tensor components: C, constant), Ω is a vector representing the stress-induced optical properties of the medium which influence the polarization vector. On the basis of the expression obtained it will be convenient to evaluate a stress tensor field in a photoelastic model by measuring the Stokes parameters.     

The influence of excess oxygen on the elastic properties of non-stoichiometric SrO crystals

Measurements have been carried out of the elastic constants of SrO in the virgin undoped state and of the changes produced in them by equilibrium doping with oxygen at ? 1200°C and oxygen partial pressure of 0.95 atm. The method used was Papadakis' pulse-echo overlap technique in conjunction with thermogravimetric analysis (T.G.A.) to determine mass and density changes due to oxygen doping.The values obtained for C₁₁, C₁₂ and C₄₄ of the virgin crystal at 23°C are

$\text{C}{}_{11}\text{= 17.60 ± 0.03 × 10}{}^{11}\text{dynes/cm}{}^2$

;

$\text{C}{}_{12}\text{= 4.808 ± 0.007 × 10}{}^{11}\text{dynes/cm}{}^2$

;

$\text{C}{}_{44}\text{= 5.577 ± 0.008 × 10}{}^{11}\text{dynes/cm}{}^2$

.(These values are in very good agreement with those of Son and Bartels [2].)Values for $\text{δC}{}_{11}\text{C}{}_{11}$ and $\text{δC}{}_{44}\text{C}{}_{44}$ were found to be ?1.74% and ?0.86% respectively. Accurate valu $\text{δC}{}_{12}\text{C}{}_{12}$ could not be obtained because of sample size limitations after quenching. However, C₁₂ was shown to definitely increase due to doping.Analysis of the results indicate that the elastic modulus changes can only be attributed to the formation of cation vacancies during doping. Analysis of the T.G.A. behavior indicates that this cation vacancy formation is probably associated with the presence of various tripositive cation and uninegative anion species depending upon the impurity concentrations of the sample. This implied impurity-controlled cation vacancy concentration is consistent with the earlier observed extrinsic nature of cation diffusion in SrO at 1200°C.     

The B̃2Σ−g (Πu) ← X̃2A1 system of nitrogen dioxide in neon matrices

The $\text{B}\text{?}\text{←}\text{X}\text{?}$ band system of NO₂, ${}^2\text{Σ}{}^{\mathrm{?}}{}_{\mathrm{g}}\text{(π}{}_{\mathrm{u}}\text{) ←}{}^2\text{A}{}_1$, has been measured in absorption in a neon matrix at 6 K, using ¹⁵NO₂ and N¹⁸O₂ in addition to the normal isotope. The spectrum consists essentially of a single, long progression of bands terminating on successive levels of the bending mode in the upper state. Transitions to odd- and even-v₂′ states occur with a uniform intensity distribution indicating that the rotation of the bent ground state of NO₂ about its near-prolate axis is hindered in the matrix. The observations strongly suggest that the top axis of the molecule coincides with a C₂ axis of neon crystals in the polycrystalline matrix. Relative to the vapor absorption the matrix spectrum is red shifted by about 150 cm^?1, the crystal field parameter V₂ and principal constants of the $\text{B}\text{?}$ state of ¹⁴N¹⁶O₂ in neon being

$\text{T}{}_{010}\text{14 571 cm}{}^{\mathrm{?1}}\text{: x}{}_{22}\text{, ?0.3 cm}{}^{\mathrm{?1}}\text{;}$

$\text{w}{}_2\text{460.2 cm}{}^{\mathrm{?1}}\text{: V}{}_2\text{, 80 cm}{}^{\mathrm{?1}}\text{.}$

     

Charmed baryon pair production in e+e− annihilation

Cross sections for charmed baryon pair production near threshold in e⁺e^? annihilation are calculated using pole-dominated form factors modified to take intoccount continuum effects. When the C₀⁺$\text{C}$₀^? production cross section is normalized with the help of data for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{p}\text{X}$ it is found that the total charmed baryon production cross $\text{(}\text{C}{}_0\text{C}{}_0\text{,}\text{C}{}_1\text{C}{}_1\text{,}\text{C}{}_1\text{C}{}_1{}^1\text{+}\text{C}{}_1{}^1\text{C}{}_1\text{,}\text{C}{}_1{}^1\text{C}{}_1{}^1\text{)}$ reaches a peak value of approximately 2.7 nb at √s = 5 GeV.     

Thermodynamical analysis of the EMC effect

Assuming that the sea quark distribution vanishes for x > 0.3, we analyse the F₂^Fe(x, Q²) and F₂^D(x, Q²) structure functions measured by the European Muon Collaboration in the framework of a thermodynamical model of the valence quarks. The experimental ratio $\text{F}{}_2{}^{\mathrm{<mtext>Fe</mtext>}}\text{(x)}\text{F}{}_2{}^{\mathrm{<mtext>D</mtext>}}\text{(x)}$ is well reproduced over the whole x range by the ratio of two valence quark distributions at different temperatures T and confinement volumes V. We obtain T_D?T_Fe≈3 MeV and $\text{V}{}_{\mathrm{<mtext>Fe</mtext>}}\text{V}{}_{\mathrm{<mtext>D</mtext>}}\text{≈ 1.3}$.