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H. Sazdjian

Publications and source records attributed to H. Sazdjian.

At least 37 records · Page 2Linked to original sources
arXiv2004

Quarkonium bound state equation in the Wilson loop approach with minimal surfaces

Wilson loop averages are evaluated for large contours and in the large N limit by means of minimal surfaces. This allows the study of the quark-antiquark gauge invariant Green function through its dependence on Wilson loops. A covariant bound state equation is derived which in the center-of-mass frame and at equal-times takes the form of a Breit-Salpeter type equation. The interaction potentials reduce in the static case to a confining linear vector potential. For moving quarks, flux tube like contributions are present. The nonrelativistic limit is considered.

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arXiv2004

Relevance of the strange quark sector in chiral perturbation theory

Results obtained in recent years in the strange quark sector of chiral perturbation theory are reviewed and the theoretical relevance of this sector for probing the phase structure of QCD at zero temperature with respect to the variation of the number of massless quarks is emphasized.

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arXiv2003

Bound state equation in the Wilson loop approach with minimal surfaces

The large-distance dynamics in quarkonium systems is investigated, in the large N limit, through the saturation of Wilson loop averages by minimal surfaces. Using a representation for the quark propagator in the presence of the external gluon field based on the use of path-ordered phase factors, a covariant three-dimensional bound state equation of the Breit-Salpeter type is derived, in which the interaction potentials are provided by the energy-momentum vector of the straight segment joining the quark to the antiquark and carrying a constant linear energy density, equal to the string tension. The interaction potentials are confining and reduce to the linear vector potential in the static case and receive, for moving quarks, contributions from the moments of inertia of the straight segment. The self-energy parts of the quark propagators induce spontaneous breakdown of chiral symmetry with a mechanism identical to that of the exchange of one Coulomb-gluon. The nonrelativistic and ultrarelativistic properties of the bound state spectrum are studied.

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arXiv2000

Relationship of pionium lifetime with pion scattering lengths in generalized chiral perturbation theory

The pionium lifetime is calculated in the framework of the quasipotential-constraint theory approach, including the sizable electromagnetic corrections. The framework of generalized chiral perturbation theory allows then an analysis of the lifetime value as a function of the pion S-wave scattering lengths with isospins I=0,2, the latter being dependent on the quark condensate value.

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arXiv2000

The pionium lifetime in generalized chiral perturbation theory

Pionium lifetime corrections to the nonrelativistic formula are calculated in the framework of the quasipotential-constraint theory approach. The calculation extends an earlier evaluation, made in the scheme of standard chiral perturbation theory, to the scheme of generalized chiral perturbation theory, in which the quark condensate is left as a free parameter. The pionium lifetime is calculated as a function of the combination $(a_0^0-a_0^2)$ of the $ππ$ S-wave scattering lengths with isospin I=0,2.

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arXiv1999

Pionium lifetime and ππscattering lengths in generalized chiral perurbation theory

The relationship between the pionium lifetime and the $ππ$ scattering lengths is established, including the sizable electromagnetic corrections. The bound state formalism that is used is that of constraint theory which provides a covariant three-dimensional reduction of the Bethe--Salpeter equation. The framework of generalized chiral perturbation theory allows then an analysis of the lifetime value as a function of the $ππ$ scattering lengths, the latter being dependent on the quark condensate value.

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arXiv1998

Pionium lifetime corrections

Pionium lifetime corrections are evaluated in the frameworks of constrained Bethe-Salpeter equation and chiral perturbation theory. Corrections of order $O(α)$ are calculated with respect to the conventional lowest-order formula, in which the strong interaction amplitude has been calculated to two-loop order with charged pion masses. The total correction is found to be of the order of $(6.1\pm 2.0)%$.

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arXiv1997

Relativistic effects in the pionium lifetime

The pionium decay width is evaluated in the framework of chiral perturbation theory and the relativistic bound state formalism of constraint theory. Corrections of order O(α) are calculated with respect to the conventional lowest-order formula, in which the strong interaction amplitude has been calculated to two-loop order with charged pion masses. Strong interaction corrections from second-order perturbation theory of the bound state wave equation are found to be of the order of 0.4%. Electromagnetic radiative corrections, due to pion-photon interactions, are estimated to be of the order of -0.1%. Electromagnetic mass shift insertions in internal propagators produce a correction of the order of 0.3%. The correction due to the passage from the strong interaction scattering amplitude evaluated with the mass parameter fixed at the charged pion mass to the amplitude evaluated with the mass parameter fixed at the neutral pion mass is found to be of the order of 6.4%.

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arXiv1997

The infinite mass limit of the two-particle Green's function in QED

The behavior of the two-particle Green's function in QED is analyzed in the limit when one of the particles becomes infinitely massive. It is found that the dependences of the Green's function on the relative times of the ingoing and outgoing particles factorize and that the bound state spectrum is the same as that of the Dirac equation with the static potential created by the heavy particle. The Bethe-Salpeter wave function is also determined in terms of the Dirac wave function. The present result excludes the existence, in the above limit, of abnormal solutions due to relative time excitations as predicted by the Bethe-Salpeter equation in the ladder approximation.

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arXiv1996

Gauge transformations in relativistic two-particle constraint theory

Using connection with quantum field theory, the infinitesimal covariant abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding wave equations shown. Because of the three-dimensional projection operation, these transformation laws are interaction dependent. Simplifications occur for local potentials, which result, in each formal order of perturbation theory, from the infra-red leading effects of multiphoton exchange diagrams. In this case, the finite gauge transformation can explicitly be represented, with a suitable approximation and up to a multiplicative factor, by a momentum dependent unitary operator that acts in $x$-space as a local dilatation operator. The latter is utilized to reconstruct from the Feynman gauge the potentials in other linear covariant gauges. The resulting effective potential of the final Pauli-Schrödinger type eigenvalue equation has the gauge invariant attractive singularity $α^2/r^2$, leading to a gauge invariant critical coupling constant $α_c =1/2$.

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arXiv1996

Incorporation of anomalous magnetic moments in the two-body relativistic wave equations of constraint theory

Using a Dirac-matrix substitution rule, applied to the electric charge, the anomalous magnetic moments of fermions are incorporated in local form in the two-body relativistic wave equations of constraint theory. The structure of the resulting potential is entirely determined, up to magnetic type form factors, from that of the initial potential descibing the mutual interaction in the absence of anomalous magnetic moments. The wave equations are reduced to a single eigenvalue equation in the sectors of pseudoscalar and scalar states ($j=0$). The requirement of a smooth introduction of the anomalous magnetic moments imposes restrictions on the behavior of the form factors near the origin, in $x$-space. The nonrelativistic limit of the eigenvalue equation is also studied.

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arXiv1996

The relativistic two-body potentials of constraint theory from summation of Feynman diagrams

The relativistic two-body potentials of constraint theory for systems composed of two spin-0 or two spin-1/2 particles are calculated, in perturbation theory, by means of the Lippmann-Schwinger type equation that relates them to the scattering amplitude. The cases of scalar and vector interactions with massless photons are considered. The two-photon exchange contributions, calculated with covariant propagators,are globally free of spurious infra-red singularities and produce at leading order O(α^4) effects that can be represented in three-dimensional x-space by local potentials proportional to (α/r)^2. Leading contributions of n-photon exchange diagrams produce terms proportional to (α/r)^n. The series of leading contributions are summed. The resulting potentials are functions, in the c.m. frame, of r and of the total energy. Their forms are compatible with Todorov's minimal substitution rules proposed in the quasipotential approach.

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arXiv1995

The two-fermion vector potential of constraint theory from Feynman diagrams

The relativistic fermion-antifermion bound state vector potential of constraint theory is calculated, in perturbation theory, by means of the Lippmann-Schwinger type equation that relates it to the scattering amplitude. Leading contributions of n-photon exchange diagrams are calculated in an approximation scheme that adapts eikonal approximation to the bound state problem. They produce terms proportional, in three-dimensional x-space, to $(α/r)^n$. The series of leading contributions is summed.

hep-ph↗
arXiv1995

Strongly coupled positronium in a chiral phase

Strongly coupled positronium, considered in its pseudoscalar sector, is studied in the framework of relativistic quantum constraint dynamics. Case's method of self-adjoint extension of singular potentials, which avoids explicit introduction of regularization cut-offs, is adopted. It is found that, as the coupling constant αincreases, the bound state spectrum undergoes an abrupt change at the critical value α= α_c = 1/2. For α> α_c, the mass spectrum displays, in addition to the existing states for α< α_c, a new set of an infinite number of bound states concentrated in a narrow band starting at mass W=0. In the limit αgoing to α_c from above, these states shrink to a single massless state with a mass gap with the rest of the spectrum. This state has the required properties to represent a Goldstone boson and to signal a spontaneous breakdown of chiral symmetry. It is suggested that the critical coupling constant α_c be viewed as a possible candidate for an ultra- violet stable fixed point of QED, with a distinction between two phases, joined to each other by a first-order chiral phase transition.

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arXiv1994

How to obtain a covariant Breit type equation from relativistic Constraint Theory

It is shown that, by an appropriate modification of the structure of the interaction potential, the Breit equation can be incorporated into a set of two compatible manifestly covariant wave equations, derived from the general rules of Constraint Theory. The complementary equation to the covariant Breit type equation determines the evolution law in the relative time variable. The interaction potential can be systematically calculated in perturbation theory from Feynman diagrams. The normalization condition of the Breit wave function is determined. The wave equation is reduced, for general classes of potential, to a single Pauli-Schrödinger type equation. As an application of the covariant Breit type equation, we exhibit massless pseudoscalar bound state solutions, corresponding to a particular class of confining potentials.

hep-ph↗
arXiv1994

$SU_3$ coherent state operators and invariant correlation functions and their quantum group counterparts

Coherent state operators (CSO) are defined as operator valued functions on G=SL(n,C), homogeneous with respect to right multiplication by lower triangular matrices. They act on a model space containing all holomorphic finite dimensional representations of G with multiplicity 1. CSO provide an analytic tool for studying G invariant 2- and 3-point functions, which are written down in the case of $SU_3$. The quantum group deformation of the construction gives rise to a non-commutative coset space. We introduce a "standard" polynomial basis in this space (related to but not identical with the Lusztig canonical basis) which is appropriate for writing down $U_q(sl_3)$ invariant 2-point functions for representaions of the type $(λ,0)$ and $(0,λ)$. General invariant 2-point functions are written down in a mixed Poincaré-Birkhoff-Witt type basis.

hep-th↗
arXiv1994

The two-fermion relativistic wave equations of Constraint Theory in the Pauli-Schrödinger form

The two-fermion relativistic wave equations of Constraint Theory are reduced, after expressing the components of the $4\times 4$ matrix wave function in terms of one of the $2\times 2$ components, to a single equation of the Pauli-Schrödinger type, valid for all sectors of quantum numbers. The potentials that are present belong to the general classes of scalar, pseudoscalar and vector interactions and are calculable in perturbation theory from Feynman diagrams. In the limit when one of the masses becomes infinite, the equation reduces to the two-component form of the one-particle Dirac equation with external static potentials. The Hamiltonian, to order $1/c^2$, reproduces most of the known theoretical results obtained by other methods. The gauge invariance of the wave equation is checked, to that order, in the case of QED. The role of the c.m. energy dependence of the relativistic interquark confining potential is emphasized and the structure of the Hamiltonian, to order $1/c^2$, corresponding to confining scalar potentials, is displayed.

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