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.     

Non-perturbative QCD effects at large momentum transfers

We calculate the simplest one-instanton correction to the perturbative QCD prediction for e⁺e^? annihilation to hadrons. At high centre-of-mass energies Q we find a contribution to the total cross section from a simple fermion loop of the form

$\text{δR}\text{R}\text{∝}\text{Q}{}^2\text{→∞}\text{Q}{}^{\mathrm{<mtext>?11?</mtext><mtext>Nf</mtext><mtext>3</mtext>}}\text{(1n Q}{}^2\text{)}{}^{\mathrm{<mtext>6(33?4Nf)</mtext><mtext>(33?2Nf)</mtext><mtext>or</mtext>}}\text{(1n Q}{}^2\text{)}{}^{\mathrm{<mtext>6(33?4Nf)</mtext><mtext>(33?2Nf)?1</mtext>}}$

where N_f is the number of quark flavours. The numerical value of this contribution is O(1) for Q ～ 1 to 2 GeV.     

Phase transition in the lattice gross-neveu model

The confining properties of the leading logarithm approximation to the effective lagrangian $\text{L}\text{= F}{}^2\text{/2g}{}^2\text{(t)}$ [ with g(t) a running coupling function of t = log(F²/μ⁴)] are seen to disappear when the second and the third approximations of the β-function power series expansion are considered.     

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.     

Perturbative QCD corrections in Drell-Yan processes

The influence of lowest-order QCD corrections on the Drell-Yan cross section $\text{Q}{}^4\text{(}\text{dσ}\text{dQ}{}^2\text{)(τ, Q}{}^2\text{)}$ is determined and compared with the asymptotic freedom (AF) corrections. The perturbative calculation exhibits the AF-characteristics of a (strongly) rising Q²-dependence for √τ?0.1 (qg-scattering) and falling for √τ?0.2 (qq?-annihilation). Qualitative agreement between the two calculation methods in the entire √τ-range is obtained with α_s = 0.3.     

On the super symmetry charges in the theory of scalar and spinor free fields

It is shown that for spinorial charges Q^(L))_α (α = 1, 2, L = 1, …, S) satisfying the commutation relations

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)}}{}_{\mathrm{\beta }}\text{} = ε}{}_{\mathrm{\alpha }}\text{βa}{}^{\mathrm{LM}}\text{Q,}$

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)+}}{}_{\mathrm{\beta }}\text{} = cσ}{}^{\mathrm{\mu }}{}_{\mathrm{\alpha \beta }}\text{P}{}_{\mathrm{\mu }}\text{δ}{}^{\mathrm{LM}}\text{,}$

$\text{[Q}{}^{\mathrm{(L)}}\text{)}{}_{\mathrm{\alpha }}\text{, P}{}^{\mathrm{\mu }}\text{] = 0,}$

where Q is a scalar charge commuting with the spinor charges as well aswith the energy- momentum vector Pμ, there can exist several different multiplets for free massive scalar and spinor fields.     

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.     

Preliminary evidence for UA(1) breaking in QCD from lattice calculations

We suggest a simple definition of the topological charge density Q(x) in the lattice Yang-Mills theory and evaluate A≡∝d⁴x〈Q(x)Q(0)〉 in SU(2) by Monte Carlo simulation. The “data” interpolate well between the strong and weak coupling expansions, which we compute to order g^?12 and g⁶, respectively. After subtraction of the perturbative tail, our points exhibit the expected asymptotic freedom behaviour giving $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{≌(0.11±0.02)K}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, K being the SU(2) quarkless string tension. Although a larger value for $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{K}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ would be preferable, we are led to conclude (at least tentatively) that the U_A(1) problem of QCD is indeed solved perturbatively in the quark loop expansion.     

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 $\text{V}{}_{\mathrm{<mtext>Fe</mtext>}}\text{V}{}_{\mathrm{<mtext>D</mtext>}}\text{≈ 1.3}$.     

Centrifugal distortion effects in the hyperfine spectrum of KCl

The hyperfine spectrum of KCl has been examined at near-zero electric field and zero magnetic field using a molecular beam electric resonance spectrometer. Rotational as well as vibrational shifts have been observed in both nuclear quadrupole interactions. With $\text{eqQ = Q}{}_{00}\text{+ Q}{}_{10}\text{(v +}\text{1}\text{2}\text{) + Q}{}_{20}\text{(v +}\text{1}\text{2}\text{)}{}^2\text{+ Q}{}_{01}\text{J(J + 1)}$, we find (all in units of kHz) for K in ³⁹K³⁵Cl: Q₀₀ = ?5691.47 ± 0.04, Q₁₀ = 51.32 ± 0.06, Q₂₀ = ?0.205 ± 0.020, Q₀₁ = 0.014 ± 0.007, Q₀₀(K³⁷Cl) ? Q₀₀(K³⁵Cl) = ?0.03 ± 0.07; for Cl in ³⁹K³⁵Cl: Q₀₀ = 137.0 ± 0.3, Q₁₀ = ?163.2 ± 0.5, Q₂₀ = 1.57 ± 0.15, Q₀₁ = 0.07 ± 0.03, $\text{[}\text{Q(}{}^{35}\text{Cl}\text{)}\text{Q(}{}^{37}\text{Cl}\text{)}\text{]Q}{}_{00}\text{(}\text{K}{}^{37}\text{Cl}\text{) ? Q}{}_{00}\text{(}\text{K}{}^{35}\text{Cl}\text{) = ?0.5 ± 0.6}$; and magnetic constants c_K = 0.154 ± 0.007, c_Cl = 0.435 ± 0.010, c₃ = 0.035 ± 0.012, and c₄ = 0.009 ± 0.006. These have been used to provide a mapping of the field gradients at both nuclear sites to fourth order in $\text{ξ =}\text{(r ? r}{}_{\mathrm{e}}\text{)}\text{r}{}_{\mathrm{e}}$. We find eQq_K(ξ) = (?5692.5 ± 2.5) + (1.7 ± 0.8) × 10⁴ξ + (?2. ± 4.) × 10⁴ξ² + (?8. ± 18.) × 10⁵ξ³ + (8. ± 15.) × 10⁶ξ⁴ and eQq_Cl(ξ) = (120. ± 22.) + (8. ± 4.) × 10⁴ξ + (?5.8 ± 2.0) × 10⁵ξ² + (?1.1 ± 1.6) × 10⁷ξ³ + (1.1 ± 1.3) × 10⁸ξ⁴.     

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.     

The spectrum of HeNe+

Discharges through mixtures of helium and neon show two band groups near 4250 and 4100 Å as first observed by Druyvesteyn. These bands, assigned to the HeNe⁺ ion by Tanaka, Yoshino, and Freeman, have been studied under high resolution and have been fairly completely analyzed. The upper state of the transition is a very weakly bound state resulting from $\text{He}{}^{\mathrm{+}}\text{(}{}^2\text{S) +}\text{Ne}\text{(}{}^1\text{S}{}_0\text{)}$. There are two lower states resulting from the two components of $\text{Ne}{}^{\mathrm{+}}\text{(}{}^2\text{P) +}\text{He}\text{(}{}^1\text{S}{}_0\text{)}$. The upper of these two (${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$) is also very weakly bound while the lower of the two, the ²Σ⁺ ground state, has a dissociation energy of 0.69 eV and an r_e value of 1.30 Å. All bands in both band groups show four branches designated R_ff, Q_ef, Q_fe, and P_ee. From their analysis the rotational constants in the various vibrational levels of the three electronic states have been determined. While no spin splitting in the B²Σ⁺ state has been found the ground state X²Σ shows a very large spin splitting and the $\text{A}{}_2{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ state a very large $\text{Ω-type}$ doubling. The vibrational numberings in all these states were established by the study of the spectrum of ³HeNe⁺. At the same time the hyperfine structure observed in all lines of ³HeNe⁺ confirmed the nature of the upper state B²Σ⁺ as resulting from He⁺ + Ne, i.e., by charge exchange from the ground state. The ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ component of the ²Π state has not been observed, presumably because of low intensity.     

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.     

Determination of the spectroscopic quadrupole moments of 131Cs, 132Cs and 136Cs

Nuclear spectroscopic quadrupole moments of the radioactive isotopes ¹³¹Cs, ¹³²Cs, and ¹³⁶Cs have been determined from the hyperfine structure of the $\text{6}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ state by the level crossing method. The results including a Sternheimer correction are: $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{131}\text{Cs}\text{) = ?0.625(6)}\text{b}$, $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{132}\text{Cs}\text{) = +0.508(7)}\text{b}$, $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{136}\text{Cs}\text{) = +0.225(10)}\text{b}$. The quadrupole moments of all the Cs isotopes from A = 131 to A = 137 are recalculated. It is shown, that nuclear quadrupole moments of a specific isotope obtained from different atomic P-states only agree within the limits of error after application of the Sternheimer correction. The increase of Q_s with decreasing neutron number conforms with other observations and theoretical calculations stating that for elements around Z = 55 nuclear deformation develops below N = 82. The staggering of the sign of Q_s may be interpreted as consequence of an oblate-prolate degeneracy of the nuclear energy surface. Some magnetic moments have been slightly improved: $\text{μ}{}_{\mathrm{<mtext>I</mtext>}}\text{(}{}^{132}\text{Cs}\text{) = 2.219(7) μ}{}_{\mathrm{<mtext>N</mtext>}}$, $\text{μ}{}_{\mathrm{<mtext>I</mtext>}}\text{(}{}^{136}\text{Cs}\text{) = 3.705(15)μ}{}_{\mathrm{<mtext>N</mtext>}}$ (corrected for diamagnetism).     

The QCD effective coupling constant in e+e− annihilation

The QCD effective coupling constant α_s(Q²) is determined by comparing the O(α_s)² jet-distributions with the high-energy e⁺e^? data from PETRA. We get α_s(Q² = 1225 GeV²) = 0.125 ± 0.01, which corresponds to $\text{Λ}{}_{\mathrm{<mtext>MS</mtext>}}\text{= 110}{}^{\mathrm{+70}}{}_{\mathrm{?50}}\text{MeV}$ with five flavours.     

Coriolis intensity perturbations in the SO2 molecule: Experimental determination of the relative signs of (∂μ∂Qi)

The Coriolis interactions between ν₁ and ν₃, and between ν₂ and ν₃ in SO₂ have been analyzed to obtain the signs of the products $\text{ζ}{}_{3.1}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_1\text{)}$ and $\text{ζ}{}_{3.2}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_2\text{)}$. It has been found that both of the signs of these products are positive. Then, relative signs of ($\text{?μ}\text{?Q}{}_1$) have been determined using the calculated values of the Coriolis zeta constants for the present definition of the normal coordinates. The obtained sign combination of ($\text{?μ}\text{?Q}{}_{\mathrm{i}}$) is ±(+?+), which agrees with the one predicted by the molecular orbital calculations. Using the sign combination (+?+), the polar tensors of S and O atoms were also calculated.     

Polarization and polarization transfer in the 2H(d,n)3He reaction at 10 MeV

Angular distributions of six polarization transfer coefficients $\text{K}{}_{\mathrm{x}}{}^{\mathrm{x\prime }}\text{(θ), k}{}_{\mathrm{x}}{}^{\mathrm{z\prime }}\text{(θ), K}{}_{\mathrm{z}}{}^{\mathrm{<mtext>x</mtext><mtext>?</mtext>}}\text{(θ), K}{}_{\mathrm{z}}{}^{\mathrm{<mtext>z</mtext><mtext>?</mtext>}}\text{(θ),}\text{and}\text{K}{}_{\mathrm{yy}}{}^{\mathrm{<mtext>y</mtext><mtext>?</mtext>}}\text{(θ)}$; of the four analyzing powers A_y(θ), A_xx(θ), A_yy(θ), and A_zz(θ); and of the polarization function P^ý(θ), have been measured atE_d = 10.00 MeV for the reaction ²H(d, n)³He. Measurements were made for neutron lab angles between 0° and 80° in 10° steps. Additionally the y-axis associated quantities were measured at θ_1ab = 99°. Most of the measured coefficients are large at some angles and all show considerable variation with angle.     

Contributions of operators of twist two and higher in large n moments of structure functions

Though high twist terms are becoming important as x→1, or equivalently, in large n moments, their detection in this regime in deep inelastic lepton scattering needs special caution. The high order terms in the twist two component are strongly dependent on n; one finds that at $\text{Q}{}^2\text{?Q}{}^2{}_7\text{?Λ}{}^2\text{a}{}_{\mathrm{k}}\text{exp}\text{[α}{}_{\mathrm{k}}\text{(}\text{log}\text{n)}{}^{\mathrm{<mtext>2?1</mtext><mtext>k</mtext>}}\text{(}\text{1+b}{}_{\mathrm{k}}\text{log}\text{n}\text{)]}$ the perturbative expansion is invalid whereas higher twist terms are important at $\text{Q}{}^2\text{?Q}{}_1{}^2\text{= Λ}{}^2\text{nC}$. Since $\text{Q}{}_7{}^2$ grows very fast with n the necessary requirement for any deep inelastic phenomenological analysis, namely $\text{Q}{}_1{}^2\text{?Q}{}_7{}^2$, cannot hold for too large moments. The scheme dependence of a_k, α_k and b_k is also discussed.     

Elementary-particle treatment of the radiative muon capture in 12C

We consider radiative muon capture to a definite nuclear final state. The example chosen is the ${}^{12}\text{C}\text{(0}{}^{\mathrm{+}}\text{T = 0)(μ}{}^{\mathrm{?}}\text{, γν)}{}^{12}\text{B}\text{(1}{}^{\mathrm{+}}\text{T = 1)}$ transition. The elementary particle treatment adopted in this work discloses several aspects of the reaction mechanism, which remain hidden in the usual impulse approximation calculations. In particular, one sees a considerable enhancement of the capture rate when the q² dependence of the weak form factors F_A(q²) and F_P(q²) is taken into account. The branching ratio of the radiative capture in the region sensitive to the possibly non-zero mass m_νμ of the muon-neutrino is estimated to be ≈1.36 × 10^?10.