Scaling violation,the Callan Gross relation,and color excitation in electroproduction

The Callan-Gross relation is shown to be consistent with MIT-SLAC data for $\text{σ}{}_{\mathrm{<mtext>L</mtext>}}\text{(Q}{}^2\text{)}\text{σ}{}_{\mathrm{<mtext>T</mtext>}}\text{(Q}{}^2\text{)}$ for x ? 0.33 in deep inelastic eN scattering, despite the fact that these data are taken in the large Q² region where F₁ and F₂ individually exhibit scaling violation. Comparison is made with asymptotic freedom predictions, and color excitation is proposed to explain large values of $\text{σ}{}_{\mathrm{<mtext>L</mtext>}}\text{σ}{}_{\mathrm{<mtext>T</mtext>}}$ at small x.     

Connections between thermodynamic quantities and vacancy and diffusion characteristics in binary metallic solid solutions

With the use of the similarity of interatomic potentials relations concerning vacancy and diffusion characteristics in disordered regular solid solutions have been derived. It has been shown that the vacancy concentration is constant along ifT_c(x) = T_A + (T_B ? T_A)x + 2ΔT_x(1?x), (T_A and T_B are the melting points of pure components A and B respectively, and ΔT is proportional to the excess enthalpy of mixing, x is the concentration of the atoms B) which is proportional to the binding energy of the crystal. The validity conditions of several empirical rules known in the literature are also analyzed. It has been found that the generalization of the well-known rule for self- and impurity diffusion in pure metals has the following form In $\text{D}{}_0{}^{\mathrm{z}}\text{(x) ～ p}\text{Q}{}^{\mathrm{z}}\text{(x)}\text{T}{}_{\mathrm{c}}\text{(x)}$ (Z = AorB) where p is a constant for alloys having identical structures (D₀^z(x) and Q^z(x) denote the preexponential factors and the activation energies respectively). The results calculated from the relations derived were compared with experimental data for tracer diffusion in the systems AgAu, CuNi (having slight deviation from regularity), Pb-Tl (showing ordering phenomena) and AlZn (clustering effects) and a good agreement was found.     

Inclusive pion distributions in e+e− annihilation from sum rules and duality

The threshold behaviour of pion production presented in our earlier work is successfully compared with the new SPEAR data. By using duality and sum rules we derive F_T^(π+)(x) ≈ F_L^(π+)(x) ≈ F_T^(π0)(x) ? F_L^(π0)(x) for x near 1. An accompanying results is $\text{σ}{}_{\mathrm{<mtext>\pi </mtext><mtext>A</mtext>}}{}_2\text{(s) ≈ 2σ}{}_{\mathrm{\pi \omega }}\text{(s) ≈ 4σ}{}_{\mathrm{\pi \pi }}\text{(s) ≈ 9(m}{}_{\mathrm{?}}{}^2\text{/s)}{}^3\text{σ}{}_{\mathrm{<mtext>\mu </mtext><mtext>\mu </mtext>}}$ for large s.     

Dynamical rescaling and universality of hadron structure functions

We argue that pion and nucleon structure functions differ principally due to their different numbers of quarks and different scales of confinement. The former generates an x rescaling while the latter, in QCD, gives rise to a Q² rescaling. Together these lead to the relation

with $\text{ξ}{}_{\mathrm{<mtext>N</mtext><mtext>\pi </mtext>}}\text{? 0.16}$, for x values away from the end points. This relation is in good agreement with data.     

Comments on the three-photon structure function

Using the simple quark parton model, estimates for the three-photon structure function, V(x), of the proton are given. This function, which is proportional to the interference between inelastic Compton scattering and wide angle bremsstrahlung, is shown to have an upper bound of $\text{2}\text{3}\text{vW}{}_2\text{(x)/x}$. Using SLAC inelastic electron scattering data from the proton this implies that V(x) is not dominated by a quasielastic peak, and therefore the sum rule, $\text{∝}{}_0{}^1\text{V(x)}\text{d}\text{x =}\text{5}\text{9}$, will be difficult to check at SLAC energies. Using electron scattering data from both the neutron and the proton, a more restrictive upper limit on V(x) is given which, at intermediate and large values of x, is nearly the same as values determined from two different sets of quark distributions. We conclude that the experiment still provides a new test of the proton model and a method for determining the quark charge.     

Non affinity of Fe2+ for B sites in iron thiochromites and compared band structures of oxides and sulfides spinels

Departure from stoichiometry in vapor grown FeCr₂S₄ was studied using Mössbauer spectroscopy. The paramagnetic Mössbauer spectra give evidence of two singlets and two doublets which correspond respectively to A site Fe²⁺ ? Fe³⁺, Fe^II in T_d symmetry and in symmetry lower than T_d. The following ionic distribution has been deduced:

$\text{(Fe}{}^{\mathrm{2+}}{}_{\mathrm{1?y}}\text{Fe}{}^{\mathrm{3+}}{}_{\mathrm{y}}\text{)|Cr}{}^{\mathrm{3+}}{}_{\mathrm{2?x}}\text{□}{}_{\mathrm{x}}\text{|S}{}_{\mathrm{4?z}}\text{□}{}_{\mathrm{z}}$

Compounds in the system Fe_1+xCr_2?xS₄ have been studied for 0 ? x ? 0.1. The spectra are solved assuming Fe^II in A site with T_d symmetry, A site Fe^II with lower symmetry and B site Fe³⁺. No Fe²⁺ appears in B site. These features are discussed in terms of schematic band structures implying single electron narrow bands. The non-affinity of Fe²⁺ for B sites of iron thiochromites is discussed in relation with B site Cr²⁺ level.     

Evaluation of charged current neutrino–nucleon interaction differential cross section

The charged current neutrino–nucleon interaction differential cross section are evaluated in the kinematical range 30<Eν<300 GeV$30<E_{\nu }<300\text{GeV}$, 0.1<x<0.8$0.1<x<0.8$ and 0<y<1$0<y<1$ using QCD inspired Thermodynamic Bag Model (TBM). We also discuss the x   and Q²$Q^2$ dependence of nucleon structure functions F₂(x,Q²)$F_2(x,Q^2)$ and xF₃(x,Q²)$x{F}_3(x,Q^2)$ estimated with statistical approach. The contribution of strange quark distribution function to the cross section is explored and the results obtained have been compared with relevant data from NuTeV and CHORUS experiments.     

On the ratio Σ0/Λ in electroproduction off protons

Recent experimental results on electroproduction off protons show that the ratio σ(ep → eK⁺Σ⁰)/σ(ep → eK⁺Λ) decreases strongly with increasing Q². A simple argument is given in the framework of the quark parton model which could provide a qualitative understanding of this fact. The decrease of the Σ⁰/Λ ratio is related to the decrease of the ratio $\text{F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>n</mtext>}}\text{/F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>p</mtext>}}$ as Q² increases, where $\text{F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>p</mtext>}}\text{and F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>n</mtext>}}$ are the usual structure functions for deep inelastic electron-nucleon scattering.     

Large perturbative corrections to the Drell-Yan process in QCD

The total cross section $\text{d}\text{σ}\text{d}\text{Q}{}^2$ for the production of a muon pair of invariant mass Q²via the Drell-Yan mechanism and the Feynman x_F differential cross section $\text{d}{}^2\text{σ}\text{d}\text{Q}{}^2\text{d}\text{x}{}_{\mathrm{<mtext>F</mtext>}}$ are calculated in QCD retaining all terms up to order α_s(Q². The calculations are performed using dimensional regularisation of the intermediary infrared and collinear singularities, but we present our results in a form independent of such details. The corrections to both these cross sections coming from radiative corrections to the lowest-order $\text{q}\text{q}$ annihilation diagram are found to be large at present values of Q² and S when the cross section is expressed in terms of parton densities derived from leptonproduction, for all Drell-Yan processes of practical interest. Numerical calculations are presented which show, for any reasonable parametrisation of the parton densities, that the neglect of higher-order terms in α_s(Q²) is not justifiable. The quark-gluon diagrams on the other hand give small corrections in this order and are only important for PP scattering.     

Electron exchange between Fe2+ and Fe3+ ions on octahedral sites in spinels studied by means of paramagnetic Mössbauer spectra and susceptibility measurements

Mössbauer spectra were obtained of the paramagnetic spinels $\text{Zn}{}^{\mathrm{2+}}\text{|}\text{Zn}{}^{\mathrm{2+}}{}_{\mathrm{<mtext>(1?x)</mtext><mtext>2</mtext>}}\text{Ti}{}^{\mathrm{4+}}{}_{\mathrm{<mtext>(1+x)</mtext><mtext>2</mtext>}}\text{Fe}{}^{\mathrm{3+}}{}_{\mathrm{<mtext>(1?</mtext><mtext>x)</mtext>}}\text{Fe}{}^{\mathrm{2+}}{}_{\mathrm{x}}\text{|}\text{O}{}_4$ and susceptibilities were measured. The strong difference between the paramagnetic Fe²⁺ and Fe³⁺ spectrum, due to the different quadrupole splitting, is used for the distinction between the two species. At 300 K a superposition of the Fe³⁺ and the Fe²⁺ spectra is found for most of the iron and, in addition, some continuous absorption. The latter is strongest for equal Fe³⁺ and Fe²⁺ concentration $\text{(x =}\text{1}\text{2}\text{)}$ while it disappears towards the end members (Fe³⁺ only or Fe²⁺ only) as well as with decreasing temperature (between 78 and 200 K). From this it is concluded that it arises from thermally activated electron exchange, the frequency of which passes a “critical” value of ～10⁸ sec^?1 for increasing temperature. Paramagnetic susceptibilities are found to obey a Curie-Weiss law down to low temperatures. From the dependence of the asymptotic Curie temperature on the composition the magnetic interaction parameters J₁₁ = ?1.4 K, J₂₂ = ?3.3 K and J₁₂ = + 1.6 K for the Fe³⁺Fe³⁺, Fe²⁺Fe²⁺ and Fe³⁺Fe²⁺ interactions are derived. The experimental results are discussed in terms of a hopping model with an activation energy q ～- 0.12eV and a non-equivalence of the octahedral sites expressed by a varying potential energy difference U₀ between neighbouring sites. The continuous absorption at 300 K for $\text{x =}\text{1}\text{2}$ is attributed to about 17% of the iron on sites with U₀ running from 0 to ??0.06 eV. The ferromagnetic Fe³⁺, Fe²⁺ interaction (J₁₂) is attributed to electron transfer from localized Fe²⁺ ions to Fe³⁺ neighbours via a transfer integral b of the order of 0.05 eV. The magnitudes of J₁₂ and b are tentatively explained.     

Right-handed weak currents in neutrino scattering

We investigate transition strengths of right-handed weak charged currents in deep inelastic neutrino scattering, exploiting the dominance of p, n valence quarks in the nucleon. The energy dependence of σ_t and the average quantities 〈y〉 and 〈Q²〉 are shown to provide sensitive measures of new quark production thresholds and right-handed currents in $\text{ν}\text{N}$ scattering. With our analysis, the present data give an upper bound on the right to left hand structure function ratio of $\text{F}{}_{\mathrm{<mtext>R</mtext>}}{}^{\mathrm{<mtext>\nu </mtext><mtext>N</mtext>}}\text{F}{}_{\mathrm{<mtext>L</mtext>}}{}^{\mathrm{<mtext>\nu </mtext><mtext>N</mtext>}}\text{≈}\text{1}\text{2}$, above a threshold of W≈7.5 GeV.     

How to continue the predictions of perturbative QCD from the spacelike region where they are derived to the timelike regime where experiments are performed

The predictions of perturbative QCD are derived in the deep euclidean region, whereas the physical region for most observables is timelike. The confrontation of these predictions with experiment thus necessitates an analytic continuation. This we find introduces large higher order corrections in terms of α_s(|Q²|), the usual choice ofperturbative expansion parameter. These corrections are naturally absorbed by changing to the expansion parameter $\text{a}\text{(Q}{}^2\text{) = |α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|(}\text{Re}\text{α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)/|α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|)}{}^{\mathrm{<mtext>(n?2)</mtext><mtext>3</mtext>}}$, where α_s(Q²)ⁿ is the leading term in the spacelike region. For the intermediate range of Q² experimentally accessible at present, where $\text{a}\text{(Q}{}^2\text{)}$ is significantly smaller than α_s(|Q²|), we find the resulting phenomenology is improved. In particular, we demonstrate how the values of $\text{Λ}{}_{\mathrm{<mtext>MS</mtext>}}$ obtained from analyses of quarkonium decays become consistent.     

On the transverse spread of QCD jets

Recent QCD results on two-particle longitudinal spectra inside quark and gluon jets are extended to the case of a fixed relative transverse momentum q_T with Λ ≈ 0.5 GeV ? 2|q_T| ? √Q². Broad q_T distributions, especially for gluon jets, are obtained which smooth out automatically the perturbative result and whose integrated versions scale in η_Max ≡ $\text{log}\text{(}\text{2q}{}_{\mathrm{<mtext>T</mtext>}}{}^{\mathrm{<mtext>Max</mtext>}}\text{Λ}\text{)/}\text{log}\text{(}\text{Q}\text{Λ}\text{)}$.     

α(Q2) corrections to particle multiplicity ratios in gluon and quark jets

The order $\text{α(Q}{}^2\text{)}$ correction to the particle multiplicity ratio in gluon and quark jets is calculated in QCD. We find

$\text{r=}\text{9}\text{4}\text{1?}\text{αC}{}_{\mathrm{<mtext>A</mtext>}}\text{2π}\text{1}\text{3}\text{+}\text{N}{}_{\mathrm{?}}\text{3C}{}_{\mathrm{<mtext>A</mtext>}}\text{?}\text{2N}{}_{\mathrm{?}}\text{C}{}_{\mathrm{<mtext>F</mtext>}}\text{3C}{}^2{}_{\mathrm{<mtext>A</mtext>}}$

with r=〈n〉_{gluon jet}/〈n〉_{quark jet}. The method used is systematic and could be used for an order α(Q²) calculation.     

Time-dependent correlation functions of the transverse Ising chain at the critical magnetic field

We study the correlation function 〈σ₀^x(t)σ_n^x(0)〉 of the transverse Ising model in a critical field whose hamiltonian is $\text{1}\text{2}\text{Σ}{}_{\mathrm{l}}\text{{σ}{}_{\mathrm{l}}{}^{\mathrm{x}}\text{σ}{}_{\mathrm{l+1}}{}^{\mathrm{x}}\text{?σ}{}_{\mathrm{l}}{}^{\mathrm{z}}\text{}}$. At an arbitrary temperature T we relate the autocorrelation to a Fredholm determinant. Moreover at T = 0 the correlations are given by a Painlevé V function for all n. The long-time asymptotic behavior of this function is found and the connection problem is studied. This result contains oscillatory terms which are related to the density of states at the Brillouin zone boundary.     

On Weinberg's model of CP violation in gauge theories

The consequences of the Weinberg model of CP violation in gauge theories (ref. [1]) are discussed in detail. It is shown (using the valence quark hypothesis) that the contribution of the induced superweak interaction to the experimentally measured quantities η+? and η₀₀ are ≈m_K²/m_π² times larger than that of the direct milliweak decay K₂⁰→2π. The correction to the relation |η+?|/|η₀₀|=1 is also calculated in the model. We estimate the neutron dipole moment $\text{(D}{}_{\mathrm{<mtext>n</mtext>}}\text{??2.8·10}{}^{\mathrm{?25}}\text{e.cm.}\text{)}$ and note that the dipole moments of particles with strange quark constituents should be about three orders of magnitude larger $\text{(}\text{e.g.}\text{D}{}_{\mathrm{\Lambda }}\text{??1.15·10}{}^{\mathrm{?22}}\text{e·}\text{cm}$. The CP violating vertex d?s + gluon is also discussed.All physical quantities appear to depend crucially on the values of quark masses, so that CP violating effects in the models of the type considered may elucidate the nature of quark masses. We argue that the bare (or “mechanical”) values should be used in the calculations and this leads to a considerable difference in the estimates of various effects as compared to those of ref. [1].     

Infrared-radio frequency double resonance observations of pure rotational Q-branch transitions of methane

The $\text{F}{}_2{}^{\mathrm{(2)}}\text{← F}{}_1{}^{\mathrm{(2)}}$ and $\text{F}{}_2{}^{\mathrm{(2)}}\text{← F}{}_1{}^{\mathrm{(1)}}$ transitions of the J = 7 levels of the ground state of CH₄ have been observed by infrared-radio frequency double resonance using the 3.39 μ HeNe laser line. The transition frequencies are 423.02 ± 0.02 MHz and 1246.55 ± 0.02 MHz, respectively. Using these frequencies and the splitting of the E and F₂ levels of the J = 2 state calculated from the molecular beam magnetic resonance spectra of Ozier, the centrifugal distortion constants are derived to be D_t = 132933 ± 10 Hz, H_4t = ? 16.65 ± 0.2 Hz, and H_6t = 10 ± 1 Hz. The J = 15 E⁽¹⁾ → E⁽²⁾ microwave transition is predicted as 14150 ± 9 MHz.     

The average transverse distance between partons as measured by nucleon form factors

The values of $\text{d}\text{F}{}_1\text{(q}{}^2\text{)}\text{d}\text{q}{}^2$ at q²=0 for the neutron and the proton provide a measure of the average transverse separations squared, 〈$\text{y}{}^2$〉, between a u or d quark and the rest of the partons in a nucleon. Using the measured values of the form factors (together with parton x-distributions), we find that 〈$\text{y}{}^2\text{= 17.4}\text{GeV}{}^{\mathrm{?2}}$ for u quarks and 16.4 GeV^?2 for d quarks in a proton. We speculate that the small difference between u and d quarks is caused by “quark pairing” and discuss other possible experimental signatures of quark pairing.     

Effects of composition on the upper critical field of V-Ga

Measurements of the temperature dependence of the upper critical field, H_c2(T), for a series of V_100?xGa_x materials are presented for 20.5 ≤ × ≤ 29.6. Fits of the data to conventional theory for a paramagnetically limited, dirty, type II superconductor show: 1) a maximum in T_c and H_c2(0) for x ? 25; 2) a constant ( for x ≤ 25; 3) a slowly increasing value of λ_so with increasing x up to x ～ 25; and 4) good agreement with stoichiometric ordered and thermally disordered V₃Ga. Above $\text{x ? 25}$ broader transitions are observed. For x = 25, T_c = 15.3 K, (, λ_so = 0.3 and H_c2(0) = 23.4 tesla. The effects of inclusion of strong-coupling in the theory are discussed briefly.