The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting... more The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting are briefly discussed. A striking feature of the BLM approach is rather weak Q^2-dependence of the Pomeron intercept, which might indicate an approximate conformal symmetry of the equation. An application of the NLO BFKL resummation for the virtual gamma-gamma total cross section shows a good agreement with recent L3 data at CERN LEP2 energies.
The high-energy behaviour of the total cross section for highly virtual photons, as predicted by ... more The high-energy behaviour of the total cross section for highly virtual photons, as predicted by the BFKL equation at next-to-leading order in QCD, is presented. The NLO BFKL predictions, improved by BLM optimal scale setting, are in excellent agreement with recent OPAL and L3 data at CERN LEP2.
The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting... more The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting are briefly discussed. A striking feature of the BLM approach is rather weak Q^2-dependence of the Pomeron intercept, which might indicate an approximate conformal symmetry of the equation. An application of the NLO BFKL resummation for the virtual gamma-gamma total cross section shows a good agreement with recent L3 data at the CERN LEP2.
It is shown that the next-to-leading order (NLO) corrections to the QCD Pomeron intercept obtaine... more It is shown that the next-to-leading order (NLO) corrections to the QCD Pomeron intercept obtained from the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation, when evaluated in non-Abelian physical renormalization schemes with Brodsky-Lepage-Mackenzie (BLM) optimal scale setting, do not exhibit the serious problems encountered in the $\overline {MS} $ scheme. A striking feature of the NLO BFKL Pomeron intercept in the BLM approach is that it yields an important approximate conformal invariance.
The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting... more The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting are briefly discussed. A striking feature of the BLM approach is rather weak Q^2-dependence of the Pomeron intercept, which might indicate an approximate conformal symmetry of the equation. An application of the NLO BFKL resummation for the virtual gamma-gamma total cross section shows a good agreement with recent L3 data at the CERN LEP2.
The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting... more The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting are briefly discussed. A striking feature of the BLM approach is rather weak Q^2-dependence of the Pomeron intercept, which might indicate an approximate conformal symmetry of the equation. An application of the NLO BFKL resummation for the virtual gamma-gamma total cross section shows a good agreement with recent L3 data at CERN LEP2 energies.
) are used to obtain full asymptotic expansions of Feynman diagrams renormalized within the MS-sc... more ) are used to obtain full asymptotic expansions of Feynman diagrams renormalized within the MS-scheme in the regimes when some of the masses and external momenta are large with respect to the others. The large momenta are Euclidean, and the expanded diagrams are regarded as distributions with respect to them. The small masses may be equal to zero. The asymptotic operation for integrals is defined and a simple combinatorial techniques is developed to study its exponentiation. The asymptotic operation is used to obtain the corresponding expansions of arbitrary Green functions. Such expansions generalize and improve upon the well-known short-distance operator-product expansions, the decoupling theorem etc.; e.g. the low-energy effective Lagrangians are obtained to all orders of the inverse heavy mass. The obtained expansions possess the property of perfect factorization of large and small parameters, which is essential for meaningful applications to phenomenology. As an auxiliary tool, the inversion of the R-operation is constructed. The results are valid for arbitrary QFT models.
We consider SU(2) gauge potentials over a space with a compactified dimension. A non-Abelian Four... more We consider SU(2) gauge potentials over a space with a compactified dimension. A non-Abelian Fourier transform of the gauge potential in the compactified dimension is defined in such a way that the Fourier coefficients are (almost) gauge invariant. The functional measure and the gauge field strengths are expressed in terms of these Fourier coefficients. The emerging formulation of the non-Abelian gauge theory turns out to be an Abelian gauge theory of a set of fields defined over the initial space with the compactified dimension excluded. The Abelian theory contains an Abelian gauge field, a scalar field, and an infinite tower of vector matter fields, some of which carry Abelian charges. Possible applications of this formalism are discussed briefly.
Inclusive single jet production in hadron collisions is considered. It is shown that the QCD part... more Inclusive single jet production in hadron collisions is considered. It is shown that the QCD parton model predicts a nonmonotonic dependence of the inclusive cross section on the fraction of the energy deposited in the jet registered, if it is normalized on the same cross section measured at another collision energy. Specifically, if the cross section is normalized by the one measured at a higher collision energy, it possesses a minimum which depends on jet rapidity. This prediction can be tested at the Fermilab Tevatron, at the CERN LHC, and at the Very Large Hadron Collider under discussion.
We present nonperturbative light-front energy eigenstates in the broken phase of a two-dimensiona... more We present nonperturbative light-front energy eigenstates in the broken phase of a two-dimensional λ/4!ϕ quantum field theory using discrete light cone quantization and extrapolate the results to the continuum limit. We establish degeneracy in the even and odd particle sectors and extract the masses of the lowest two states and the vacuum energy density for λ=0.5 and 1.0. We present two novel results: the Fourier transform of the form factor of the lowest excitation as well as the number density of elementary constituents of that state. A coherent state with kink-antikink structure is revealed.
Without a gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined... more Without a gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined. The Gauss law is written in terms of the canonical variables. The system is qualified as a generalized dynamical system with first class constraints. Abeliazation is a specific feature of the formulation (most of the canonical variables transform nontrivially only under the action of an Abelian subgroup of the gauge transformations). At finite volume, a discrete spectrum of the light-front Hamiltonian $P_+$ is obtained in the sector of vanishing $P_-$. We obtain, therefore, a quantized form of the classical solutions previously known as non-Abelian plane waves. Then, considering the infinite volume limit, we find that the presence of the mass gap depends on the way the infinite volume limit is taken, which may suggest the presence of different ``phases'' of the infinite volume theory. We also check that the formulation obtained is in accord with the standard perturbation theory if the latter is taken in the covariant gauges.
We explain what is the challenge of light-front quantisation, and how we can now answer it becaus... more We explain what is the challenge of light-front quantisation, and how we can now answer it because of recent progress in solving the problem of zero modes in the case of non-Abelian gauge theories. We also give a description of the light-front Hamiltonian for SU(2) finite volume gluodynamics resulting from this recent solution to the problem of light-front zero modes.
Without gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined. ... more Without gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined. The Gauss law is written in terms of the canonical variables. The system is qualified as a generalized dynamical system with first class constraints. Abelianization is a specific feature of the formulation (most of the canonical variables transform nontrivially only under the action of an Abelian subgroup of the gauge transformations). At finite volume, a discrete spectrum of the light-front Hamiltonian P+ is obtained in the sector of vanishing P-. We obtain, therefore, a quantized form of the classical solutions previously known as non-Abelian plane waves. Then, considering the infinite volume limit, we find that the presence of the mass gap depends on the way the infinite volume limit is taken, which may suggest the presence of different phases of the infinite volume theory. We also check that the formulation obtained is in accord with the standard perturbation theory if the latter is taken in the covariant gauges.
The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting... more The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting are briefly discussed. A striking feature of the BLM approach is rather weak Q^2-dependence of the Pomeron intercept, which might indicate an approximate conformal symmetry of the equation. An application of the NLO BFKL resummation for the virtual gamma-gamma total cross section shows a good agreement with recent L3 data at CERN LEP2 energies.
The high-energy behaviour of the total cross section for highly virtual photons, as predicted by ... more The high-energy behaviour of the total cross section for highly virtual photons, as predicted by the BFKL equation at next-to-leading order in QCD, is presented. The NLO BFKL predictions, improved by BLM optimal scale setting, are in excellent agreement with recent OPAL and L3 data at CERN LEP2.
The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting... more The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting are briefly discussed. A striking feature of the BLM approach is rather weak Q^2-dependence of the Pomeron intercept, which might indicate an approximate conformal symmetry of the equation. An application of the NLO BFKL resummation for the virtual gamma-gamma total cross section shows a good agreement with recent L3 data at the CERN LEP2.
It is shown that the next-to-leading order (NLO) corrections to the QCD Pomeron intercept obtaine... more It is shown that the next-to-leading order (NLO) corrections to the QCD Pomeron intercept obtained from the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation, when evaluated in non-Abelian physical renormalization schemes with Brodsky-Lepage-Mackenzie (BLM) optimal scale setting, do not exhibit the serious problems encountered in the $\overline {MS} $ scheme. A striking feature of the NLO BFKL Pomeron intercept in the BLM approach is that it yields an important approximate conformal invariance.
The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting... more The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting are briefly discussed. A striking feature of the BLM approach is rather weak Q^2-dependence of the Pomeron intercept, which might indicate an approximate conformal symmetry of the equation. An application of the NLO BFKL resummation for the virtual gamma-gamma total cross section shows a good agreement with recent L3 data at the CERN LEP2.
The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting... more The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting are briefly discussed. A striking feature of the BLM approach is rather weak Q^2-dependence of the Pomeron intercept, which might indicate an approximate conformal symmetry of the equation. An application of the NLO BFKL resummation for the virtual gamma-gamma total cross section shows a good agreement with recent L3 data at CERN LEP2 energies.
) are used to obtain full asymptotic expansions of Feynman diagrams renormalized within the MS-sc... more ) are used to obtain full asymptotic expansions of Feynman diagrams renormalized within the MS-scheme in the regimes when some of the masses and external momenta are large with respect to the others. The large momenta are Euclidean, and the expanded diagrams are regarded as distributions with respect to them. The small masses may be equal to zero. The asymptotic operation for integrals is defined and a simple combinatorial techniques is developed to study its exponentiation. The asymptotic operation is used to obtain the corresponding expansions of arbitrary Green functions. Such expansions generalize and improve upon the well-known short-distance operator-product expansions, the decoupling theorem etc.; e.g. the low-energy effective Lagrangians are obtained to all orders of the inverse heavy mass. The obtained expansions possess the property of perfect factorization of large and small parameters, which is essential for meaningful applications to phenomenology. As an auxiliary tool, the inversion of the R-operation is constructed. The results are valid for arbitrary QFT models.
We consider SU(2) gauge potentials over a space with a compactified dimension. A non-Abelian Four... more We consider SU(2) gauge potentials over a space with a compactified dimension. A non-Abelian Fourier transform of the gauge potential in the compactified dimension is defined in such a way that the Fourier coefficients are (almost) gauge invariant. The functional measure and the gauge field strengths are expressed in terms of these Fourier coefficients. The emerging formulation of the non-Abelian gauge theory turns out to be an Abelian gauge theory of a set of fields defined over the initial space with the compactified dimension excluded. The Abelian theory contains an Abelian gauge field, a scalar field, and an infinite tower of vector matter fields, some of which carry Abelian charges. Possible applications of this formalism are discussed briefly.
Inclusive single jet production in hadron collisions is considered. It is shown that the QCD part... more Inclusive single jet production in hadron collisions is considered. It is shown that the QCD parton model predicts a nonmonotonic dependence of the inclusive cross section on the fraction of the energy deposited in the jet registered, if it is normalized on the same cross section measured at another collision energy. Specifically, if the cross section is normalized by the one measured at a higher collision energy, it possesses a minimum which depends on jet rapidity. This prediction can be tested at the Fermilab Tevatron, at the CERN LHC, and at the Very Large Hadron Collider under discussion.
We present nonperturbative light-front energy eigenstates in the broken phase of a two-dimensiona... more We present nonperturbative light-front energy eigenstates in the broken phase of a two-dimensional λ/4!ϕ quantum field theory using discrete light cone quantization and extrapolate the results to the continuum limit. We establish degeneracy in the even and odd particle sectors and extract the masses of the lowest two states and the vacuum energy density for λ=0.5 and 1.0. We present two novel results: the Fourier transform of the form factor of the lowest excitation as well as the number density of elementary constituents of that state. A coherent state with kink-antikink structure is revealed.
Without a gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined... more Without a gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined. The Gauss law is written in terms of the canonical variables. The system is qualified as a generalized dynamical system with first class constraints. Abeliazation is a specific feature of the formulation (most of the canonical variables transform nontrivially only under the action of an Abelian subgroup of the gauge transformations). At finite volume, a discrete spectrum of the light-front Hamiltonian $P_+$ is obtained in the sector of vanishing $P_-$. We obtain, therefore, a quantized form of the classical solutions previously known as non-Abelian plane waves. Then, considering the infinite volume limit, we find that the presence of the mass gap depends on the way the infinite volume limit is taken, which may suggest the presence of different ``phases'' of the infinite volume theory. We also check that the formulation obtained is in accord with the standard perturbation theory if the latter is taken in the covariant gauges.
We explain what is the challenge of light-front quantisation, and how we can now answer it becaus... more We explain what is the challenge of light-front quantisation, and how we can now answer it because of recent progress in solving the problem of zero modes in the case of non-Abelian gauge theories. We also give a description of the light-front Hamiltonian for SU(2) finite volume gluodynamics resulting from this recent solution to the problem of light-front zero modes.
Without gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined. ... more Without gauge fixing, canonical variables for the light-front SU(2) gluodynamics are determined. The Gauss law is written in terms of the canonical variables. The system is qualified as a generalized dynamical system with first class constraints. Abelianization is a specific feature of the formulation (most of the canonical variables transform nontrivially only under the action of an Abelian subgroup of the gauge transformations). At finite volume, a discrete spectrum of the light-front Hamiltonian P+ is obtained in the sector of vanishing P-. We obtain, therefore, a quantized form of the classical solutions previously known as non-Abelian plane waves. Then, considering the infinite volume limit, we find that the presence of the mass gap depends on the way the infinite volume limit is taken, which may suggest the presence of different phases of the infinite volume theory. We also check that the formulation obtained is in accord with the standard perturbation theory if the latter is taken in the covariant gauges.
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