Scaling violations and perturbative quantum chromodynamics

We try to understand the meaning of the recent data on scaling violations of the moments of the structure function F₃ measured in ν and $\text{ν}$ deep inelastic scattering, and their relevance as a test of QCD. We do this by reducing to the minimum the theoretical machinery and prejudices and stressing the perturbative nature of the problem. We are led to a definition of the perturbation coupling constant σ_S(Q = 2.5 GeV) = 0.61 ± 0.06, in termas of which the corrective terms for all quantities computed so far turn out to be relatively small.     

Generating heavy quarkonia in a perturbative QCD cascade

We present an implementation of heavy quarkonium production within a perturbative QCD cascade based on the Color Dipole Cascade model. We consider the processes most relevant in the context of the ψ′ surplus at the Tevatron; g → ψ′ and c → ψ′ in the color-singlet model and g → ψ′ through the color-octet mechanism. Our implementation is, however, easily extendible to other quarkonia and other production mechanisms. Where comparison is possible we find good agreement with analytical calculations. We present some suggestions for measurements at the Tevatron that would be sensitive to the shape of the fragmentation functions. Our calculations indicate that such measurements could be used to test the color-octet mechanism solution to the ψ′ surplus at the Tevatron.     

Higher order corrections in perturbative quantum chromodynamics

We present some techniques which have been developed recently or in the recent past to compute Feynman graphs beyond one-loop order. These techniques are useful to compute the three-loop splitting functions in QCD and to obtain the complete second order QED corrections to Bhabha scattering.     

On gauge invariance and perturbative calculations in quantum chromodynamics

It is possible to regularize infra-red divergences of QCD by giving a mass to the gluon in such a way that the Becchi-Rouet-Stora invariance of the action is preserved. This regularization allows straightforward extension of dispersive techniques to the computation of radiative corrections to on-shell processes in QCD. Problems of gauge dependence, however, exist: care must be taken in the choice of the expansion parameter and only physically meaningful processes are gauge independent, e.g., cross sections summed over all final degenerate states.     

Decoupling of heavy quarks in quantum chromodynamics

Decoupling of heavy quarks in quantum chromodynamics (QCD) defined by mass-independent renormalization is investigated. The structure of the relations between the parameters of f flavour QCD and the parameters of the effective f ? 1 flavour QCD below a heavy-quark threshold is discussed to all orders in the loop expansion, and the relations are computed to two-loop approximation for the minimal subtraction schemes (MS) and to one-loop approximation for some Weinberg schemes. These matching relations can be used to systematically determine the renormalization group (RG)-invariant parameters of the effective theory in terms of the RG-invariant parameters of the theory which includes the heavy quark, or vice versa. For the $\text{MS}$ scheme the connection between Λ_{f ? 1} nad Λ_f to two and three loops is given as well as the two-loop connection between the RG-invariant mass parameters of the f ? 1 and f flavour theory. The effect of heavy quarks on the evolution of the QCD coupling is of significance for present QCD phenomenology based on next-to-leading-order perturbation theory. This is illustrated with a few examples within the $\text{MS}$ scheme.     

Isospin violations in largeP T pion inclusive processes in perturbative quantum chromodynamics

We investigate the asymmetries arising due to electromagnetic interactions in largeP _T pion inclusive processes. The hardqcd processes that contribute to such asymmetries areq+g→q+γ,q+q→g+γ etc. which are suspected to be substantial, as indicated by theqcd predictions for a significant and increasingγ/π ^o ratio at largeP _T. We calculate the expected isospin related asymmetries and propose tests that might detect them. Our estimates indicate that the effects are much smaller than may be naively expected. We also observe a remarkable scaling of asymmetries in the variableP _T/(s)^1/2.     

Fine- and hyperfine structure of quarkonia

It is pointed out that the flux tube picture of electric confinement, which led to the “Coulomb plus linear” potential model, also predicts the structure of spin-dependent forces in heavy quark systems for large and small distances. The corresponding hamiltonian is obtained from a semiclassical argument and applied to the fine structure of the ψ and υ families.     

Semileptonic decays of heavy quarks in quantum chromodynamics

We investigate the semileptonic decays of heavy quarks in the leading non-trivial order in quantum chromodynamics. Effects of gluon corrections and the initial quark Fermi motion on the semileptonic rates and decay distributions are calculated. The resulting lepton energy spectrum for the charm semileptonic decay is compared with data to extract the mass of the charm quark. This is combined with the semileptonic branching ratio to predict the charm-quark lifetime. We find the lepton energy spectrum very stable with respect to gluon corrections. Expected spectra from the semileptonic decays of bottom and top quarks are presented. We also study the semileptonic decay process Q → q?v_? + G, involving the emission of a single hard non-collinear gluon. This process should be observable with a branching ratio of a few percent in the decays of top (and heavier) quarks.     

Relativistic quark model with quantum chromodynamics, P-states of quarkonia and scalar-vector confinement

In this paper we try to understand several phenomenological issues related to the mass spectra of P-states quarkonia in a relativistic quark model. We give particular emphasis on understanding the most recent experimental data within a relativized scalar-vector confining potential. In this paper we extend the previous works on the studies of quark confinement in non-relativistic QCD, using a formalism which uses a covariant Hamiltonian in the centre of mass frame. The spin-structure of the potential is obtained from the reduction of Bethe-Salpeter equation into Breit-interaction. Printed as S Chakrabarty in several papers published earlier e.g. References [1,11] etc. of this paper.     

The hyperfine splittings in heavy-light mesons and quarkonia

Hyperfine splittings (HFS) are calculated within the Field Correlator Method, taking into account relativistic corrections. The HFS in bottomonium and the B _q (q = n, s) mesons are shown to be in full agreement with experiment if a universal coupling α _HF = 0.310 is taken in perturbative spinspin potential. It gives M(B*) −M(B) = 45.7(3) MeV, M(B _s ^* ) − M(B _s ) = 46.7(3) MeV (n _f = 4), while in bottomonium Δ_HF(b $ \bar b $ \bar b ) = M(Υ(9460)) − M(η _b (1S)) = 63.4 MeV for n _f = 4 and 71.1 MeV for n _f = 5 are obtained; just the latter agrees with recent BaBar data. For unobserved excited states we predict M(Υ(2S))−M(η _b (2S)) = 36(2)MeV,M(Υ(3S))−M(η _b (3S)) = 28(2)MeV, and also M(B _c ^*) = 6334(4) MeV, M(B _c (2S)) = 6868(4) MeV, M(B _c ^* (2S)) = 6905(4) MeV. The mass splittings between D(2³ S ₁) − D(2¹ S ₀), D _s (2³ S ₁) − D _s (2¹ S ₀) are predicted to be ∼75 MeV, which are significantly smaller than in several other studies but agree with the mass splitting between recently observed D(2533) and D*(2610).     

Direct decays of heavy quarkonia

The branching ratios are evaluated of the ψ (3770) and (4S) decays into ππ, , ωπ⁰, ωη, ωη ′, π, η, η′, , . They arise due to the transition through the real intermediate states and , respectively. It is shown that some branching ratios exceed the three-gluon one by an order of magnitude. The rates of the decays ,

Full-size image

and are evaluated also. τ-C and B factories coul be good tools for studying all decays mentioned.     

Heavy meson spectra for heavy quark potential in quantum chromodynamics with dilaton

For heavy meson systems, we study the heavy quark potential, which emerges from the effective dilaton－gluon coupling inspired from the superstring theory. We put emphasis on the new confinement generating mechanism of this potential through the investigation of the spin-averaged energy levels of the heavy meson systems. By using a unified approach to the solutions of the Schr?dinger and the spinless Salpeter equations, we can examine in a realistic way the effects of using a relativistic kinetic energy. The obtained results agree favourably with other predictions, and the relativistic equation can better account for the observed energy levels.     

Hadronic decays of excited heavy quarkonia

We construct an effective Lagrangian for the hadronic decays of a heavy excited s-wave-spin-one quarkonium Ψ′ into a lower s-wave-spin-one state Ψ. We show that reasonable fits to the measured invariant mass spectra in the charmonium and bottomonium systems can be obtained within this framework. The mass dependence of the various terms in the Lagrangian is discussed on the basis of a quark model.