arXiv subjects

Dmitri Melikhov

Publications and source records attributed to Dmitri Melikhov.

143 records · Page 8Linked to original sources

arXiv2006

Dispersion representations and anomalous singularities of the triangle diagram

We discuss dispersion representations for the triangle diagram $F(p_1^2,p_2^2,q^2)$, the single dispersion representation in $q^2$ and the double dispersion representation in $p_1^2$ and $p_2^2$, with special emphasis on the appearance of the anomalous singularities and the anomalous cuts in these representations. For the double dispersion representation in $p_1^2$ and $p_2^2$, the appearance of the anomalous cut in the region $q^2>0$ is demonstrated, and a new derivation of the anomalous double spectral density is given. We point out that the double spectral representation is particularly suitable for applications in the region of $p_1^2$ and/or $p_2^2$ above the two-particle thresholds. The dispersion representations for the triangle diagram in the nonrelativistic limit are studied and compared with the triangle diagram of the nonrelativistic field theory.

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arXiv2006

Chiral properties of the constituent quark model

We show that, in a model based exclusively on constituent-quark degrees of freedom interacting via a potential, the full axial current is conserved if the spectrum of \bar QQ states contains a massless pseudoscalar. The current conservation emerges nonperturbatively if the model satisfies certain constraints on (i) the axial coupling g_A of the constituent quark and (ii) the \bar QQ potential at large distances. We define the chiral point of the constituent quark model as that set of values of the parameters (such as the masses of the constituent quarks and the couplings in the \bar QQ potential) for which the mass of the lowest pseudoscalar \bar QQ bound state vanishes. At the chiral point the main signatures of the spontaneously broken chiral symmetry are shown to be present, namely: the axial current is conserved, the decay constants of the excited pseudoscalar bound states vanish, and the pion decay constant has a nonzero value.

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arXiv2006

Constituent quarks, chiral symmetry, and chiral point of the constituent quark model

We construct the full axial current of the constituent quarks by a summation of the infinite number of diagrams describing constituent-quark soft interactions. By requiring that the conservation of this current is violated only by terms of order $O(M_π^2)$, where $M_π$ is the mass of the lowest pseudoscalar $\bar QQ$ bound state, we derive important constraints on (i) the axial coupling $g_A$ of the constituent quark and (ii) the $\bar QQ$ potential at large distances. We define the chiral point of the constituent quark model as those values of the parameters, such as the masses of the constituent quarks and the couplings in the $\bar QQ$ potential, for which $M_π$ vanishes. At the chiral point the main signatures of the spontaneously broken chiral symmetry are shown to be present, namely: the axial current of the constituent quarks is conserved, the leptonic decay constants of the excited pseudoscalar bound states vanish, and the pion decay constant has a nonzero value.

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arXiv2006

Fall-apart decays of polyquark hadrons

We analyse fall-apart decays of poliquark (tetra, penta and molecule type) hadrons within the constituent quark picture. For processes in which a poliquark hadron goes to final states containing a light pseudoscalar meson the constraints given by chiral symmetry are implemented. As an application of the approach developed, fall-apart decays of $a(980)$ and X(3872) are studied, assuming these mesons are poliquark hadrons. Two extreme options - confined diquark-diquark states and molecular states - are considered. For $a^0(980)$, the observed width can be obtained assuming that this meson is a diquark-diquark composite with a relatively large size of around $1÷1.5$ fm. The pure $K \bar K $ molecular-type state, however, can be excluded. For the X(3872), a sufficiently small width can be obtained if it is a dominantly isospin-0 diquark-diquark composite with a very large size of $\ge 2.5$ fm. The pure molecular option appears possible if the binding energy is tiny, $E_b\lesssim 0.2$ MeV, corresponding to a huge size.

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arXiv2005

A narrow "peanut" pentaquark

We analyse the decay $Θ_s(1/2^+)\to NK$ in a non-relativistic Fock space description using three and five constituent quarks for the nucleon and the pentaquark, respectively. Following Jaffe and Wilczek \cite{jw}, we assume that quark-quark correlations in spin-zero state play an important role for the pentaquark internal structure. Within this scenario, a strong dynamical suppression of the decay width is shown to be possible only if the pentaquark has an asymmetric "peanut" structure with the strange antiquark in the center and the two extended composite diquarks rotating around. In this case a decay width of $\simeq$ 1 MeV may be a natural possibility.

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arXiv2005

Can Chiral Symmetry Explain the Small Pentaquark Width?

It is shown that the decay amplitude for the Jaffe-Wilczek type pentaquarks is not suppressed by chiral symmetry. On the other hand, pentaquarks of positive or negative parity built up of an antiquark and two chirally different diquarks in an $S$-state are stable in the limit of a strictly unbroken chiral symmetry. These states can decay only via the spontaneous breaking of chiral symmetry. However, this breaking is strong because of the sizeable magnitude of the quark condensate. Thus, chiral symmetry cannot be the cause of a tiny decay amplitude, even for pentaquarks which are stable in the strict chiral symmetry limit.

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arXiv2004

Pentaquarks in the Chiral Symmetry Limit

We demonstrate that a five quark state of positive parity with an internal P-wave structure - usually pictured as a composite of an antiquark and two diquarks in a P-wave state - can couple to nucleons and Goldstone particles in a chirally invariant way. The corresponding decay width is generally not suppressed. A pentaquark of positive or negative parity with an internal S-wave structure, which may be viewed as a composite of an antiquark and two chirally different diquarks in an S-state, does not couple to nucleons and light mesons in the limit of an unbroken chiral symmetry. It is stable in this limit. However, such states can decay via the effect of the spontaneous breaking of chiral symmetry. This breaking is strong because of the sizeable magnitude of the quark condensate. Thus, chiral symmetry cannot be the cause of a tiny decay amplitude, even for pentaquarks stable in a strict chiral symmetry limit.

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arXiv2004

Rare radiative leptonic decays B_{d,s}-> l^+l^-γ

Long-distance QCD effects in $B_{d,s}\to\ell^+\ell^-γ$ decays are analyzed. We show that the contribution of the light vector-meson resonances related to the virtual photon emission from valence quarks of the $B$-meson, which was not considered in previous analyses, strongly influences the dilepton differential distrubution. Taking into account photon emission from the $b$-quark loop, weak annihilation, and Bremsstrahlung from leptons in the final state, we give predictions for dilepton spectrum in $B_{d, s}\to \ell^+\ell^-γ$ decays within the Standard model.

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arXiv2004

Correspondence between QCD sum rules and constituent quark models

We compare two widely used approaches to the description of hadron properties: QCD sum rules and constituent quark models. Making use of the dispersion formulation of the quark model, we show that both approaches lead to similar spectral representations for hadron observables with an important difference that quark model is based on Feynman diagrams with massive quarks, whereas QCD sum rules are based on the same Feynman diagrams for current quarks with the additional condensate contributions for light quarks and gluons. We give arguments for a similarity of the smearing function in sum rules and the hadron wave function of the quark model. Analyzing the sum rule for the leptonic decay constant of the heavy pseudoscalar meson containing a light $u$ or $s$ quark, we find that the quark condensates at the chiral symmetry-breaking scale $μ_χ\simeq 1$ GeV, $<\bar u u > = - (230 \pm 15 {\rm MeV})^3$ and $<\bar s s > = - (220 \pm 15 {\rm MeV})^3$ correspond to constituent quark masses $m_u\simeq 220$ MeV and $m_s \simeq 350$ MeV, respectively. We also obtain the running of the quark model parameters above the chiral scale $μ_χ$. The observed correspondence between constituent quark models and QCD sum rules allows a deeper understanding of both methods and their parameters. It also provides a QCD basis for constituent quark models, extending their applicability above the scale of chiral symmetry breaking.

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arXiv2003

Gauge invariance and form factors for the decay B --> gamma l^+l^-

We analyse the form factors for the B --> gamma l^+l^- weak transition. We show that making use of the gauge invariance of the B --> gamma l^+l^- amplitude, the structure of the form factors in the resonance region, and their relations at large values of the photon energy results in efficient constraints on the behavior of the form factors. Based on these constraints, we propose a simple parametrization of the form factors and apply it to the lepton forward-backward (FB) asymmetry in the B --> gamma l^+l^- decay. We find that the behavior of the FB asymmetry as a function of the photon energy, as well as the location of its zero, depend only weakly on the B --> gamma l^+l^- form factors, and thus constitutes a powerful tool for testing the standard model.

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arXiv2001

Dispersion approach to quark-binding effects in weak decays of heavy mesons

Dispersion approach based on the constituent quark picture and its applications to weak decays of heavy mesons are reviewed. Meson interaction amplitudes are represented within this approach as relativistic spectral integrals over the mass variables in terms of the meson wave functions and spectral densities of the corresponding Feynman diagrams. Various applications of this approach are discussed: Relativistic spectral representations for meson elastic and transition form factors at spacelike momentum transfers are constructed. Form factors at $q^2>0$ are obtained by the analytical continuation. As a result of this procedure, form factors are given in the full $q^2$ range of the weak decay in terms of the wave functions of the participating mesons. The 1/m_Q expansion of the obtained spectral representations for the form factors for the particular limits of the heavy-to-heavy and heavy-to-light transitions are analysed. Their full consistency with the constraints provided by long-distance QCD for these limits is demonstrated. Predictions for form factors for B, B(s), D, and D(s) decays to light mesons are given. The B\toγlνdecay and the weak annihilation in rare radiative decays are considered. Nonfactorizable corrections to the B^0-\bar B^0 mixing are calculated. Inclusive weak B-decays are analysed and the differential distributions are obtained in terms of the B-meson wave function.

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arXiv2000

Weak form factors for heavy meson decays

We calculate the form factors for weak decays of $B_{(s)}$ and $D_{(s)}$ mesons to light pseudoscalar and vector mesons within a relativistic dispersion approach based on the constituent quark picture. This approach gives the form factors as relativistic double spectral representations in terms of the wave functions of the initial and final mesons. The form factors have the correct analytic properties and satisfy general requirements of nonperturbative QCD in the heavy quark limit. The effective quark masses and meson wave functions are determined by fitting the quark model parameters to lattice QCD results for the $B\to ρ$ transition form factors at large momentum transfers and to the measured $D\to (K,K^*)lν$ decay rates. This allows us to predict numerous form factors for all kinematically accessible $q^2$ values.

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arXiv2000

Non-factorizable effects in the $B-\bar B$ mixing

We analyse the corrections to factorization for the $B-\bar B$ mixing amplitude assuming that non-factorizable soft gluon exchanges can be described by the local gluon condensate. Within this approximation the $<α_s GG>$-correction to the mixing amplitude can be expressed through the $B$-meson transition form factors at zero momentum transfer. The correction is negative independent of the particular values of the form factors. As a next step, we study these form factors making use of the relativistic dispersion approach based on the constituent quark picture. We obtain spectral representations for the form factors in terms of the $B$-meson soft wave function and the propagator of the color-octet $b\bar q$ system. The $B$-meson wave function has been determined previously from weak exclusive B decays, so the main uncertainty in our estimates comes from the unknown details of the propagator in the nonperturbative region. We obtain $ΔB_{B_d}(m_b)=-0.06\pm 0.035 $ and $ΔB_{B_s}(m_b)=-0.05\pm 0.03 $.

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arXiv1997

Dispersion Quark Model of Heavy Meson Decays

We discuss applications of the dispersion quark model to exclusive semileptonic decays of heavy mesons. The transition form factors in this relativistic formulation of the quark model are given by double spectral representations through the wave functions of the initial and final mesons both in the scattering and the decay regions. An important feature of the model is that the form factors have the correct behavior in accordance with QCD in the case of meson decays induced by heavy parent quark transition both to heavy and light daughter quarks. We demonstrate that the dispersion quark model gives results compatible with the lattice calculations at large $q^2$ and thus provides reliable form factors in the whole decay region.

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arXiv1997

Heavy quark expansion and universal form factors in quark model

Meson transition amplitudes of the vector, axial-vector, and tensor quark currents are analyzed within dispersion formulation of the constituent quark model. The form factors in the decay region are given by relativistic double spectral representations through the wave functions of the inital and final mesons. We perform heavy quark expansion of the quark-model mesonic matrix elements with a next-to-leading order accuracy and demonstrate that matching this expansion to the heavy-quark expansion in QCD requires subtractions in the double spectral representations for the form factors and allows fixing the subtraction terms. The Isgur-Wise function and next-to-leading order universal form factors are calculated.

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arXiv1997

Long-distance contribution to exclusive rare decays of heavy mesons in quark model

Nonperturbative effects in exclusive reactions $B\to K^{(*)}ll$ are discussed. Form factors which describe the main long-distance contribution to the meson transition amplitude are calculated within the dispersion formulation of the quark model: namely, the form factors in the decay region are expressed as relativistic double spectral representations through the wave functions of the initial and final mesons. The dilepton forward-backward asymmetry and the lepton polarization turn out to be largely independent of the particular choice of the quark model parameters and can be predicted with high accuracy. At the same time, these asymmetries are sensitive to the short-distance structure of the theory and might be used as a test of the Standard Model and probe of new physics.

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arXiv1997

Exclusive semileptonic decays of heavy mesons in quark model

Semileptonic decays $D\to K,K^*,π,ρ$, $D_s\to η,η',ϕ$, and $B\to D,D^*,π,ρ$ are analyzed within the dispersion formulation of the quark model. The form factors at timelike $q$ are derived by the analytical continuation from spacelike $q$ in the form factors of the relativistic light--cone quark model. The resulting double spectral representations allow a direct calculation of the form factors in the timelike region. The results of the model are shown to be in good agreement with all available experimental data. From the analysis of the $B\to D,D^*$ decays we find $|V_{cb}|=0.037\pm 0.004$, and the $B\toπ,ρ$ decays give $|V_{ub}|=0.004\pm 0.001$.

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