The effect of 1Q2 and αs corrections on tests of QCD

We discuss in detail the use of the structure function F₃(x, Q²) of deep-inelastic neutrino scattering for testing quantum chromodynamics. QCD is entirely consistent with all data. However, we show that higher-twist (order $\text{1}\text{Q}{}^2$) contributions, which are commonly neglected, can have a dramatic impact on interpretation of this result. At present the data are not accurate enough to determine the magnitudes of these $\text{1}\text{Q}{}^2$ contributions within the context of QCD. Furthermore, the possible presence of higher-twist terms makes it impossible to unambiguously detect the logarithmic Q² dependence and anomalous dimensions which distinguish QCD from hypothetical alternative theories. As a result, more precise data with higher Q² are needed to provide definitive tests of QCD. The corrections of second-order in α_s introduce fewer complications for testing QCD, and provide a useful context for understanding critical ambiguities in the definitions of α_s and Λ.     

Event shapes in deep inelastic lepton-hadron scattering

The structure of hadronic final states in deep inelastic scattering expected from QCD is analyzed in terms of the shape parameters H_l and C_l. We find that the effects of the fragmentation of quarks and gluons into hadrons are typically governed by $\text{√s = [Q}{}^2\text{(1/x?1)]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. For √s?30 GeV, the distributions of events in H₂ and C₂ should allow a test of the perturbative QCD prediction of three-jet events.     

A valence quark model for large pT pion production

A hard scattering mechanism for the production of large p_T hadrons is suggested which only involves valence quarks. The corresponding $\text{π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}$ ratio and the ratios of the away side charged pion correlations are in satisfactory agreement with data.     

A new proof of the invariance principle in scattering theory

For free and interacting Hamiltonians, H₀ and H = H₀ + V(r) acting in L²(R³, dx) with V(r) a radial potential satisfying certain technical conditions, and for ? a real function on R with ?′ > 0 except on a discrete set, we prove that the Moller wave operators

exist and are independent of ?. The scattering operator

$\text{S = (Ω}{}^{\mathrm{+}}\text{)1Ω}{}^{\mathrm{?}}$

is shown to be unitary. Our proof utilizes time independent methods (eigenfunction expansions) and is effective in cases not previously analyzed, e.g. $\text{V(r) =}\text{sin}\text{r}\text{r}$ and many others.     

Simple Z01 model

A model for isoscalar KN scattering near the K¹N threshold is constructed, and solved analytically in the approximation of retaining only pion exchange terms. Basic features of phenomenological phase shits are reproduced, including a wide $\text{J}{}^{\mathrm{P}}\text{=}\text{1}\text{2}{}^{\mathrm{+}}$ exotic resonance, Z₀¹(1800).     

Light-cone expansions,the parton model and virtual γγ scattering

It is shown that it is sufficient to use the light-cone algebra of currents and the algebra of bilocal operators to find the asymptotic behaviour of the γγ scattering amplitude when one (or two) of the photon masses q_1,2² is large, and for an arbitrary value of the energy squared s = (q₁+q₂)². A general form of this asymptotic behaviour is obtained. The box-diagram is dominant over the wide region in $\text{s(μ}{}^2\text{« s « q}{}_1{}^2\text{q}{}_2{}^2\text{/μ}{}^2\text{,μ ～ 1}\text{GeV}\text{)}$ and so the asymptotic amplitude is known completely. It is shown that the parton model of the type of ref.[8] gives the same predictions for the asymptotic behaviour of the γγ amplitude.     

Stereoelectronic properties of photosynthetic and related systems: Ab initio configuration interaction calculations on the ground and lower excited singlet and triplet states of magnesium chlorin and chlorin

Ab initio configuration interaction wavefunctions and energies are reported for the ground state and many low-lying singlet and triplet states of magnesium chlorin and chlorin, and are employed in an analysis of the electronic absorption spectra of these systems.In chlorin, the calculated visible spectrum consists of two ${}^1\text{(π, π}{}^1\text{)}$ states, the lower energy, y-polarized state exhibiting moderate absorption intensity in contrast to the very weak absorption of the higher energy x-polarized state. The configurational composition of both states is well described by the four-orbital model. Five ${}^1\text{(π, π}{}^1\text{)}$ states are responsible for the Soret band envelope. A moderately intense y-state lies under the low energy edge of the band envelope, while two x-polarized states of moderate and strong intensity, respectively, are responsible for the band maximum. The final two ${}^1\text{(π, π}{}^1\text{)}$ states lie at the high energy edge of the Soret band and introduce a measure of asymmetry into the band envelope. Two ${}^1\text{(n, π}{}^1\text{)}$ states of very weak oscillator strength are also found in this region of the spectrum. All the Soret states are of complex configurational composition, and several of the higher lying states contain contributions from doubly excited configurations.The calculated visible spectrum of magnesium chlorin also consists of two ${}^1\text{(π, π}{}^1\text{)}$ states, with the weakly absorbing x-polarized state lying approximately 200 cm^?1 lower in energy than the moderately intense y-polarized state. The configurational composition of both states is well described by the four-orbital model. Four ${}^1\text{(π, π}{}^1\text{)}$ states constitute the bulk of the intensity in the Soret band envelope. In distinction to chlorin, the moderately intense ${}^1\text{(π, π}{}^1\text{)}$ state at the low energy edge of the band envelope is x-polarized. Two intense ${}^1\text{(π, π}{}^1\text{)}$ states of y- and x-polarization, respectively, constitute the band maximum region, and a single x-polarized state of moderately strong intensity can be assigned to the high energy shoulder of the band envelope. Two other weakly absorbing ${}^1\text{(π, π}{}^1\text{)}$ states are also found in this region, along with another weakly absorbing state of mixed in-plane and out-of-plane polarization. No clearly defined ${}^1\text{(n, π}{}^1\text{)}$ states are observed. As was the case for chlorin, all the Soret states are of complex configurational composition, and some of the higher energy states contain significant contributions from doubly excited configurations.Chlorin and magnesium chlorin both possess three ${}^3\text{(π, π}{}^1\text{)}$ states which lie below S₁ and a single ${}^3\text{(π, π}{}^1\text{)}$ which lies slightly above S₂. All four of the low-lying ${}^3\text{(π, π}{}^1\text{)}$ states in each molecule are well described by the four-orbital model, with T₁ being essentially a single configuration in each case. The remainder of the ${}^3\text{(π, π}{}^1\text{)}$ states are clustered in the same energetic region as the comparable ${}^1\text{(π, π}{}^1\text{)}$ Soret states, with comparably complex configurational compositions.Dipole moments and charge distributions for low-lying singlet and triplet states are also reported, and are used to rationalize chemical reactivity characteristics.     

Measurement of Debye-Waller factors by Raman scattering from inter-term excitons and exciton-multiphonon states in FeF2

We have observed inter-term Raman scattering from ⁵T_2g→⁵E_g Frenkel excitons in antiferromagnetic FeF₂. It differs qualitatively from previously observed intra-term scattering in a sharply reduced zero-phonon cross section and the appearance of relatively strong exciton-phonon scattering. Since the Raman process is fully allowed, it is possible to measure excited state Debye-Waller factors, D, and we find $\text{D(Λ}{}_3{}^{\mathrm{+}}\text{+ Λ}{}_4{}^{\mathrm{+}}\text{,}{}^5\text{E}{}_{\mathrm{g}}\text{) = 0.04}$ and $\text{D(Λ}{}_1{}^{\mathrm{+}}\text{,}{}^5\text{E}{}_{\mathrm{g}}\text{) = 0.03}$.     

On the 1g2 corrections to hadron masses

The strong coupling limit of lattice QCD is reviewed and the important corrections of order $\text{1}\text{g}{}^2$ to the pion, rho, nucleon and delta masses are computed with Wilson's fermion method. The nucleon-delta mass difference is obtained by decomposing the baryon field into independent fields transforming in irreducible representations of the rotation-flavor group.     

Neutron-proton radius differences and isovector deformations from π+ and π− inelastic scattering from 18O

π⁺ and π^? elastic and inelastic scattering from ¹⁸O have been measured at T(π)=164 MeV. Consistent with the results at 230 MeV, it is found that the ratio $\text{σ(π}{}^{\mathrm{?}}\text{)}\text{σ(π}{}^{\mathrm{+}}\text{)}$ for the 2₁⁺ state is 1.86(16), while for the 3₁^? state it is 0.89(6). These results are interpreted as indicating differences in neutron and proton deformations characterizing the 2₁⁺ transition and partial neutron blocking for the 3₁^? transition. Optical model analysis of elastic scattering leads to the conclusion that $\text{〈r}{}_{\mathrm{<mtext>n</mtext>}}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{?〈r}{}_{\mathrm{<mtext>p</mtext>}}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{=0.03(3)}\text{fm}$.     

Super-cosmology

By using the jet calculus technique, the size of the colour singlet clusters of emitted partons of mass Q₀ is estimated. For $\text{α(Q}{}^2{}_0\text{)}\text{π}\text{?1}$, the average mass of these clusters turns out to be a few GeV, thus suggesting phenomenological applications of preconfinement in pertubbative QCD. This result is very sensitive to the correct treatment of infrared singularities.     

Semileptonic decays of pseudoscalar particles (M→M′+ℓ+νℓ) and short-distance behaviour of quantum chromodynamics

The form factors which govern the semileptonic decays of pseudoscalar particles (M→M′+?+ν_?) are constrained by the knowledge of the two-point function Π^μν(q) = i ∫ d⁴x e^iqx〈06TV^μ(x) V^ν+ (0)60〉 in the deep euclidean region, where V^μ(x) denotes the vector current responsible for the transition M→M′. We derive the precise constraints from a QCD calculation of Π^μν which includes perturbative contributions to two loops as well as leading non-perturbative contributions. Applications to π_?3, K_?3 and $\text{D}{}^{\mathrm{+}}\text{→}\text{K}{}^0\text{e}{}^{\mathrm{+}}\text{ν}{}_{\mathrm{<mtext>e</mtext>}}$ decays are discussed.     

Dielectric susceptibility and correlation length of one-dimensional CDW with impurties. II. weak disorder

Dependence of static dielectric susceptibility and correlation length of charge density waves (CDW) with weak defects on parameter of incommensurability with lattice is investigated. In almost commensurate phase (h?h_ch_c), $\text{χ ～ (h?h}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{In}{}^{\mathrm{<mtext>-4</mtext><mtext>3</mtext>}}\text{h}{}_{\mathrm{c}}\text{/h?h}{}_{\mathrm{c}}$ and R_c ～ (h ? h_c)^{$\text{2}\text{3}$}. In${}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{h}{}_{\mathrm{c}}\text{/h ? h}{}_{\mathrm{c}}$. Far from commensurability $\text{(h?h}{}_{\mathrm{c}}\text{) χ～ (a+h}{}^2{}_{\mathrm{c}}\text{/h}{}^2\text{)}{}^{\mathrm{<mtext>-2</mtext><mtext>3</mtext>}}$, $\text{R}{}_{\mathrm{c}}\text{～ (a + h}{}^2{}_{\mathrm{c}}\text{/h}{}^2\text{)}{}^{\mathrm{<mtext>-2</mtext><mtext>3</mtext>}}$, where a is the dimensionless ratio of random potential intensities, corresponding to backward and forward scattering impurities.     

Anomalous mass dependence of glueball exclusive decay rates

Exclusive decays such as G → ππ are studied in the framework ofperturbative QCD. We discuss the possibility of the constituent gluons' virtualness scaling as the glueball mass M_G, which is a picture equivalent to a glueball containing a few slow-moving, heavy gluons. In this case, the decay rate exhibits a pinch singularity which enhances it by a factor of order (M_G²/m_q²)² over the dimensional scaling expectation. This singularity is partially suppressed by Sudakov effects which reduce the enhancement factor to $\text{(M}{}_{\mathrm{<mtext>G</mtext>}}{}^2\text{/m}{}_{\mathrm{<mtext>q</mtext>}}{}^2\text{)}{}^{\mathrm{2n}}\text{,}\text{where}\text{n ? 0.4}$.     

A clear test of perturbative QCD in large-pT photoproduction

It is shown that measurement of the cross-section differences $\text{E}\text{d}\text{σ}\text{d}{}^3\text{p(γ}\text{p}\text{→}\text{h}{}^{\mathrm{+}}\text{X}\text{) ?}\text{E}\text{d}\text{σ}\text{d}{}^3\text{p (γ}\text{p}\text{→}\text{h}{}^{\mathrm{?}}\text{X}\text{)}$ at large transverse momentum provides a good test of perturbative QCD. Such differences are insensitive to the parton Fermi motion and to the poorly known sea-quark and gluon distribution functions. Moreover the hadronized photon component is shown to contribute little compared to the point-like one. Presently available photon beams at the CERN-SPS and FNAL are sufficient to test QCD in large-p_T photoproduction.     

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.     

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.     

Pion form factor from 480 MeV to 1100 MeV

The pion form factor is measured in the reaction e⁺e^? → π⁺π^? for center of mass energies in the range 480–1100 MeV. Our results are first analysed in terms of the conventional Vector Meson Dominance formalism, and then taking into account the ωπ inelastic channel. The result of this later formalism is a pion form factor (F_π) which fits quite well all the existing data on F_π both in the timelike and spacelike regions, and pion mean square radius of 〈r_π²〉 = 0.460 ± 0.011 fm² or $\text{〈r}{}_{\mathrm{\pi }}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 0.678 ± 0.008}\text{fm}$.     

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.