arXiv subjects

V. A. Karmanov

Publications and source records attributed to V. A. Karmanov.

At least 55 records · Page 3Linked to original sources

arXiv2010

Proton Timelike Form Factors Near Threshold via Antiproton-Nucleus Electromagnetic Annihilation

In the reaction of the antiproton-deuteron electromagnetic annihilation pbar + d --> e+e-n the value of the invariant mass M of the (e+e-) pair can be near or below the (pbar p) mass even for enough high momentum of incident antiproton. This allows to access the proton electromagnetic form factors in the time-like region of q^2 near the (pbar p) threshold. We estimate the cross section dsigma(pbar + d --> e+e-n)/dM for an antiproton beam momentum of 1.5 GeV/c. We find that near the (pbar p) threshold this cross section is about 1 pb/MeV. The case of heavy nuclei target is also discussed. Elements of experimental feasibility are presented for the process pbar + d --> e+e-n in the context of the Panda project. We conclude that this process has a chance to be measurable at Panda.

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arXiv2010

Nonperturbative renormalization in light-front dynamics and applications

We present a general framework to calculate the properties of relativistic compound systems from the knowledge of an elementary Hamiltonian. Our framework provides a well-controlled nonperturbative calculational scheme which can be systematically improved. The state vector of a physical system is calculated in light-front dynamics. From the general properties of this form of dynamics, the state vector can be further decomposed in well-defined Fock components. In order to control the convergence of this expansion, we advocate the use of the covariant formulation of light-front dynamics. In this formulation, the state vector is projected on an arbitrary light-front plane $ω\cd x=0$ defined by a light-like four-vector $ω$. This enables us to control any violation of rotational invariance due to the truncation of the Fock expansion. We then present a general nonperturbative renormalization scheme in order to avoid field-theoretical divergences which may remain uncancelled due to this truncation. This general framework has been applied to a large variety of models. As a starting point, we consider QED for the two-body Fock space truncation and calculate the anomalous magnetic moment of the electron. We show that it coincides, in this approximation, with the well-known Schwinger term. Then we investigate the properties of a purely scalar system in the three-body approximation, where we highlight the role of antiparticle degrees of freedom. As a non-trivial example of our framework, we calculate the structure of a physical fermion in the Yukawa model, for the three-body Fock space truncation (but still without antifermion contributions). We finally show why our approach is also well-suited to describe effective field theories like chiral perturbation theory in the baryonic sector.

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arXiv2010

Solution of the Bethe-Salpeter equation in Minkowski space for a two fermion system

The method of solving the Bethe-Salpeter equation in Minkowski space, developed previously for spinless particles, is extended to a system of two fermions. The method is based on the Nakanishi integral representation of the amplitude and on projecting the equation on the light-front plane. The singularities in the projected two-fermion kernel are regularized without modifying the original BS amplitudes. The numerical solutions for the J=0 bound state with the scalar, pseudoscalar and massless vector exchange kernels are found. Binding energies are in close agreement with the Euclidean results. Corresponding amplitudes in Minkowski space are obtained.

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arXiv2010

Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model within truncated Fock space

Within the covariant formulation of light-front dynamics, we calculate the state vector of a physical fermion in the Yukawa model. The state vector is decomposed in Fock sectors and we consider the first three ones: the single constituent fermion, the constituent fermion coupled to one scalar boson, and the constituent fermion coupled to two scalar bosons. This last three-body sector generates nontrivial and nonperturbative contributions to the state vector, which are calculated numerically. Field-theoretical divergences are regularized using Pauli-Villars fermion and boson fields. Physical observables can be unambiguously deduced using a systematic renormalization scheme we have developed previously. As a first application, we consider the anomalous magnetic moment of the physical fermion.

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arXiv2008

Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model

Within the covariant formulation of light-front dynamics, we calculate the state vector of a fermion coupled to identical scalar bosons (the Yukawa model). The state vector is decomposed in Fock sectors and we consider the first three ones: a single fermion, a fermion coupled to one boson, and a fermion coupled to two bosons. This last three-body sector generates nontrivial and nonperturbative contributions to the state vector, and these contributions are calculated with no approximations. The divergences of the amplitudes are regularized using Pauli-Villars fermion and boson fields. Physical observables can be unambiguously deduced using a systematic renormalization scheme we developed. This renormalization scheme is a necessary condition in order to avoid uncancelled divergences when Fock space is truncated. As an example, we present preliminary numerical results for the anomalous magnetic moment of a fermion in the Yukawa model.

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arXiv2008

Electromagnetic form factor via Bethe-Salpeter amplitude in Minkowski space

For a relativistic system of two scalar particles, we find the Bethe-Salpeter amplitude in Minkowski space and use it to compute the electromagnetic form factor. The comparison with Euclidean space calculation shows that the Wick rotation in the form factor integral induces errors which increase with the momentum transfer Q^2. At JLab domain (Q^2=10 GeV^2/c^2), they are about 30%. Static approximation results in an additional and more significant error. On the contrary, the form factor calculated in light-front dynamics is almost indistinguishable from the Minkowski space one.

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arXiv2008

Three-body forces in Bethe-Salpeter and light-front equations

In relativistic frameworks, given by the Bethe-Salpeter and light-front bound state equations, the binding energies of system of three scalar particles interacting by scalar exchange particles are calculated. In contrast to two-body systems, the three-body binding energies obtained in these two approaches differ significantly from each other: the ladder kernel in light-front dynamics underbinds by approximately a factor of two compared to the ladder Bethe-Salpeter equation. By taking into account three-body forces in the light-front approach, generated by two exchange particles in flight, we find that most of this difference disappears; for small exchange masses, the obtained binding energies coincide with each other.

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arXiv2008

Manifestation of three-body forces in three-body Bethe-Salpeter and light-front equations

Bethe-Salpeter and light-front bound state equations for three scalar particles interacting by scalar exchange-bosons are solved in ladder truncation. In contrast to two-body systems, the three-body binding energies obtained in these two approaches differ significantly from each other: the ladder kernel in light-front dynamics underbinds by approximately a factor of two compared to the ladder Bethe-Salpeter equation. By taking into account three-body forces in the light-front approach, generated by two exchange-bosons in flight, we find that most of this difference disappears; for small exchange masses, the obtained binding energies coincide with each other.

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arXiv2008

Systematic renormalization scheme in light-front dynamics with Fock space truncation

Within the framework of the covariant formulation of light-front dynamics, we develop a general non-perturbative renormalization scheme based on the Fock decomposition of the state vector and its truncation. The counterterms and bare parameters needed to renormalize the theory depend on the Fock sectors. We present a general strategy in order to calculate these quantities, as well as state vectors of physical systems, in a truncated Fock space. The explicit dependence of our formalism on the orientation of the light front plane is essential in order to analyze the structure of the counterterms. We apply our formalism to the two-body (one fermion and one boson) truncation in the Yukawa model and in QED, and to the three-body truncation in a scalar model. In QED, we recover analytically, without any perturbative expansion, the renormalization of the electric charge, according to the requirements of the Ward identity.

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arXiv2007

Electromagnetic form factor via Minkowski and Euclidean Bethe-Salpeter amplitudes

The electromagnetic form factors calculated through Euclidean Bethe-Salpeter amplitude and through the light-front wave function are compared with the one found using the Bethe-Salpeter amplitude in Minkowski space. The form factor expressed through the Euclidean Bethe-Salpeter amplitude (both within and without static approximation) considerably differs from the Minkowski one, whereas form factor found in the light-front approach is almost indistinguishable from it.

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arXiv2007

Regularization of fermion self-energy and electromagnetic vertex in Yukawa model within light-front dynamics

In light-front dynamics, the regularization of amplitudes by traditional cutoffs imposed on the transverse and longitudinal components of particle momenta corresponds to restricting the integration volume by a non-rotationally invariant domain. The result depends not only on the size of this domain (i.e., on the cutoff values), but also on its orientation determined by the position of the light-front plane. Explicitly covariant formulation of light front dynamics allows us to parameterize the latter dependence in a very transparent form. If we decompose the regularized amplitude in terms of independent invariant amplitudes, extra (non-physical) terms should appear, with spin structures which explicitly depend on the orientation of the light front plane. The number of form factors, i.e., the coefficients of this decomposition, therefore also increases. The spin-1/2 fermion self-energy is determined by three scalar functions, instead of the two standard ones, while for the elastic electromagnetic vertex the number of form factors increases from two to five. In the present paper we calculate perturbatively all these form factors in the Yukawa model. Then we compare the results obtained in the two following ways: (i) by using the light front dynamics graph technique rules directly; (ii) by integrating the corresponding Feynman amplitudes in terms of the light front variables. For each of these methods, we use two types of regularization: the transverse and longitudinal cutoffs, and the Pauli-Villars regularization. In the latter case, the dependence of amplitudes on the light front plane orientation vanishes completely provided enough Pauli-Villars subtractions are made.

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arXiv2006

Bethe-Salpeter equation with cross-ladder kernel in Minkowski and Euclidean spaces

Some results obtained by a new method for solving the Bethe-Salpeter equation are presented. The method is valid for any kernel given by irreducible Feynman graphs. The Bethe-Salpeter amplitude, both in Minkowski and in Euclidean spaces, and the binding energy for ladder + cross-ladder kernel are found. We calculate also the corresponding electromagnetic form factor.

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arXiv2006

Solving Bethe-Salpeter equation in Minkowski space

We develop a new method of solving Bethe-Salpeter (BS) equation in Minkowski space. It is based on projecting the BS equation on the light-front (LF) plane and on the Nakanishi integral representation of the BS amplitude. This method is valid for any kernel given by the irreducible Feynman graphs. For massless ladder exchange, our approach reproduces analytically the Wick-Cutkosky equation. For massive ladder exchange, the numerical results coincide with the ones obtained by Wick rotation.

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arXiv2006

Cross-ladder effects in Bethe-Salpeter and Light-Front equations

Bethe-Salpeter (BS) equation in Minkowski space for scalar particles is solved for a kernel given by a sum of ladder and cross-ladder exchanges. The solution of corresponding Light-Front (LF) equation, where we add the time-ordered stretched boxes, is also obtained. Cross-ladder contributions are found to be very large and attractive, whereas the influence of stretched boxes is negligible. Both approaches -- BS and LF -- give very close results.

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arXiv2005

Non-perturbative renormalization in Light Front Dynamics with Fock space truncation

Within the framework of the Covariant formulation of Light-Front Dynamics, we develop a general non-perturbative renormalization scheme based on the Fock decomposition of the state vector and its truncation. The explicit dependence of our formalism on the orientation of the light front is essential in order to analyze the structure of the counterterms and bare parameters needed to renormalize the theory. We present here a general strategy to determine the dependence of these quantities on the Fock sectors. We apply our formalism to QED for the two-body (one fermion and one boson) truncation and recover analytically, without any perturbative expansion, the renormalization of the electric charge according to the requirements of the Ward Identity.

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arXiv2005

Bethe-Salpeter equation in Minkowski space with cross-ladder kernel

A new method for solving the Bethe-Salpeter equation is developed. It allows to find the Bethe-Salpeter amplitudes both in Minkowski and in Euclidean spaces and, as a by product, the light-front wave function. The method is valid for any kernel given by irreducible Feynman graphs. Bethe-Salpeter and Light-Front equations for scalar particles with ladder + cross-ladder kernel are solved.

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arXiv2004

Recent developments in light-front dynamics

Recent results on relativistic few body systems, obtained in the framework of light-front dynamics, are briefly reviewed. The following subjects are discussed: two scalar bosons with ladder and cross ladder kernel; two fermions with OBE kernel; relativistic scattering (elastic and inelastic); three bosons and fermions with zero-range interaction; many-body contributions.

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arXiv2004

Higher Fock sectors in Wick-Cutkosky model

In the Wick-Cutkosky model we analyze nonperturbatively, in light-front dynamics, the contributions of two-body and higher Fock sectors to the total norm and electromagnetic form factor. It turns out that two- and three-body sectors always dominate. For maximal value of coupling constant $α=2π$, corresponding to zero bound state mass M=0, they contribute 90% to the norm. With decrease of $α$ the two-body contribution increases up to 100%. The form factor asymptotic is always determined by two-body sector.

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