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L. Micu

Publications and source records attributed to L. Micu.

15 recordsLinked to original sources
arXiv2008

Suppressing the spurious states of the centre of mass

Following Dirac's ideas concerning the quantization of constrained systems, we suggest to replace the free centre of mass Hamiltonian H_{CM} by another operator which commutes with all the elements of the algebra generated via the commutation relations by H_{CM} and the constraints which fix the centre of mass position. We show that the new Hamiltonian is a multiple of the identity operator and, as a result, its unique effect is to raise the internal energy levels by a constant amount.

quant-ph↗
arXiv2006

Comments on a bound state model for a two body system

We show that in classical mechanics, as well as in nonrelativistic quantum mechanics the equation of the relative motion for a two-body bound system at rest can be replaced by individual dynamical equations of the same kind as the first one, but with different parameters. We assume that in relativistic quantum mechanics the individual equations are Dirac equations with modified parameters in agreement with the individual Schrödinger equations. We find that products of solutions to the individual equations with correlated arguments are the quantum analogues of the classical representation of a bound system and represent suitable models for the bound state wave functions. As validity test for the new representation of bound states we suggest to use some observable differences between this one and the representation in terms of relative coordinates.

quant-ph↗
arXiv2004

A Lorentz covariant representation of bound state wave functions

We present a method enabling us to write in relativistic manner the wave function of some particular two particle bound state models in quantum mechanics. The idea is to expand the bound state wave function in terms of free states and to introduce the potential energy of the bound system by mens of the 4-momentum of an additional constituent, supposed to represent in a global way some hidden degrees of freedom. The procedure is applied to the solutions of the Dirac equation with confining potentials which are used to describe the quark antiquark bound states representing a given meson state.

hep-ph↗
arXiv2002

Dispersion relations and Omnès representations for $K \to ππ$ decay amplitudes

We derive dispersion relations for $K\toππ$ decay, using the Lehmann-Symanzik-Zimmermann formalism, which allows the analytic continuation of the amplitudes with respect to the momenta of the external particles. No off-shell extrapolation of the field operators is assumed. We obtain generalized Omnès representations, which incorporate the $ππ$ and $πK$ $S$-wave phase shifts in the elastic region of the direct and crossed channels, according to Watson theorem. The contribution of the inelastic final-state and initial-state interactions is parametrized by the technique of conformal mappings. We compare our results with previous dispersive treatments and indicate how the formalism can be combined with lattice calculations to yield physical predictions.

hep-ph↗
arXiv2002

A stationary relativistic representation of the bound state

We show that a bound system in momentum space can be treated like a gas of free elementary constituents and a collective excitation of a background field which represents the countless quantum fluctuations generating the binding potential. The distribution function of the internal momenta in the bound system at rest is given by the projection of the solution of a relativistic bound state equation on the free wave functions of the elementary constituents. The 4-momentum carried by the collective excitation is the difference between the bound state 4-momentum and the sum of the free 4-momenta. This definiton ensures the explicit fulfilment of Lorentz covariance, mass-shell constraints and single particle normalizability of the bound state function. The discussion is made for a two particle bound state and can be easily generalized to the case of three or more particles.

hep-ph↗
arXiv2001

Relativistic covariance and the bound state wave function

We establish a relation between the solution of a relativistic bound state equation in quantum mechanics and the field representation of a bound state with the aid of creation and annihilation operators. We show that a bound system can be represented by a gas of free constituents and a classical effective field representing the countless quantum fluctuations generating the binding potential. The distribution function of the internal momenta is given by the projection of the free states on the solution of a relativistic bound state equation in the rest frame of the bound system. In this approach Lorentz covariance, mass-shell constraints and single particle normalizability of the bound state function are simultaneously and explicitly satisfied. The discussion is made for a two particle bound state and can be easily generalized to the case of three or more particles.

hep-ph↗
arXiv2001

Quark-Hadron Duality, Factorization and Strong Phases in $B^0_d \to π^+π^-$ Decay

We consider the hadronic description of the $B^0_d\to π^+π^-$ decay, with the aim to investigate the strong phases generated by the final state interactions. The derivation of the dispersion relations using the Lehmann-Symanzik-Zimmermann formalism and the Goldberger-Treiman method to include inelastic effects in the spectral function are presented. We discuss the problem of quark-hadron duality and estimate in the hadronic formalism the corrections to the factorized amplitude in the heavy quark limit.

hep-ph↗
arXiv2000

A Lorentz covariant approach to the bound state problem

The relativistic equivalent of the Schrödinger equation for a two particle bound state having the total angular momentum $S$ is written in the form of a Lorentz covariant set of equations (p_1^mu+p_2^mu+Omega^mu)Psi(p_1,p_2;P) chi_S(\vec{p}_1,\vec{p}_2)=P^mu Psi(p_1,p_2;P) chi_S(\vec{p}_1,\vec{p}_2) where the operators Omega^mu are the components of a 4-vector quasipotential. The solution of this set is a stationary function representing the distribution of spins and internal momenta in a reference frame where the momentum of the bound system is P^μ. The contribution of the operators Omega^mu to the bound state momentum is assumed to be the 4-momentum of a vacuum-like effective field entering the bound system as an independent component. It is shown that a state made of free quarks and of the effective field has definite mass and can be normalized like a single particle state. The generalization to the case of three or more particles is immediate.

hep-ph↗
arXiv2000

Improvements to the Method of Dispersion Relations for B Nonleptonic Decays

We bring some clarifications and improvements to the method of dispersion relations in the external masses variables, that we proposed recently for investigating the final state interactions in the B nonleptonic decays. We first present arguments for the existence of an additional term in the dispersion representation, which arises from an equal-time commutator in the LSZ formalism and can be approximated by the conventional factorized amplitude. The reality properties of the spectral function and the Goldberger-Treiman procedure to perform the hadronic unitarity sum are analyzed in more detail. We also improve the treatment of the strong interaction part by including the contributions of both t and u-channel trajectories in the Regge amplitudes. Applications to the $B^0\to π^+π^-$ and $B^+\to π^0 K^+$ decays are presented.

hep-ph↗
arXiv1999

Space-like meson electromagnetic form factor in a relativistic quark model

The space-like electromagnetic form factor is expressed in terms of the overlap integral of the initial and final meson wave functions written as Lorentz covariant distributions of internal momenta. The meson constituents are assumed to be valence quarks and an effective vacuum-like field. The momentum of the latter represents a relativistic generalization of the potential energy of the quark system. The calculation is fully Lorentz covariant and the form factors of the charged mesons are normalized to unity at t=0. The numerical results have been obtained by freezing the transverse degrees of freedom. We found r_π^2=0.434 fm^2, r_{K^+}^2=0.333 fm^2, r_{K^0}^2=-0.069 fm^2 by taking m_{u,d}=430 MeV, m_s=700 MeV.

hep-ph↗
arXiv1999

Dispersion Relations and Rescattering Effects in B Nonleptonic Decays

Recently, the final state strong interactions in nonleptonic B decays were investigated in a formalism based on hadronic unitarity and dispersion relations in terms of the off-shell mass squared of the $B$ meson. We consider an heuristic derivation of the dispersion relations in the mass variables using the reduction LSZ formalism and find a discrepancy between the spectral function and the dispersive variable used in the recent works. The part of the unitarity sum which describes final state interactions is shown to appear as spectral function in a dispersion relation based on the analytic continuation in the mass squared of one final particles. As an application, by combining this formalism with Regge theory and SU(3) flavour symmetry we obtain constraints on the tree and the penguin amplitudes of the decay $B^0\to π^+π^-$.

hep-ph↗
arXiv1998

Meson electromagnetic form factors in a relativistic quark model

The main assumption of the model is that in soft processes mesons behave like systems made of valence quarks and an effective vacuum- like field. The 4-momentum of the latter represents the relativistic generalization of the potential energy. The electromagnetic form factors are expressed in terms of the overlap integral of the initial and final wave functions written under the form of Lorentz covariant distribution of quark momenta. The calculation is fully Lorentz covariant and the form factors of the charged mesons are normalized to unity at t=0.

hep-ph↗
arXiv1996

The decay constants of pseudoscalar mesons in a relativistic quark model

The decay constants of pseudoscalar mesons are calculated in a relativistic quark model which assumes that mesons are made of a valence quark antiquark pair and of an effective vacuum like component. The results are given in terms of quark masses and of some free parameters entering the expression of the internal wave functions of the mesons. By using the pion and kaon decay constants $F_{π^+}=130.7~MeV,~F_{K^+}=159.8~MeV$ to fix the parameters of the model one gets $60~MeV\leq F_{D^+}\leq 185~MeV,~95~MeV\leq F_{D_s}\leq230~MeV,~80~MeV\leq F_{B^+}\leq205~MeV$ for the light quark masses $m_u=5.1~MeV,~m_d=9.3~MeV,~m_s=175~MeV$ and the heavy quark masses in the range: $1.~GeV\leq m_c\leq1.6~GeV,~4.1~GeV\leq m_b\leq4.5~GeV$. In the case of light neutral mesons one obtains with the same set of parameters $F_{π^0}\approx 138~MeV,~F_η\approx~130~MeV,F_{η'} \approx~78~MeV$. The values are in agreement with the experimental data and other theoretical results.

hep-ph↗
arXiv1994

Structure Dependence in $π\to \bf\ellν, π to \ellνγ$ and $π^0\ to γγ$ Decays

The amplitudes of $π$-meson decays are calculated in a relativistic nonperturbative quark model which assumes that mesons are made of a quark antiquark pair and of a scalar neutral component representing the contribution of the nonelementary fluctuations of the quark gluonic field. The experimental data can be fitted in a satisfactory manner using current quark masses $m_u\approx1.5\ MeV, m_d\approx9\ MeV$.

hep-ph↗