Regge Slope Research Articles

Baryonium and nonexotic hadron trajectories from a color-dependent potential

A natural explanation is presented for the apparent increase in Regge slope with the number of quarks in a bound state. The framework used is that of a nonrelativistic harmonic-oscillator potential with a color dependence suggested by quantum chromodynamics. Ratios of modes of orbital excitations in baryonium, baryon, and meson states which are in good agreement with experiment are derived, and the modes of excitation within the baryonium states are discussed.

String interaction in quantum chromodynamics

The effective string lagrangian for hadron interaction in QCD with no adjustable parameters is obtained. The Regge slope is evaluated: L′ = 1.1 GeV −2 . Some problems of this approach and the connection with the charmonium potential model for the lowest bound states of heavy quarks are discussed.

Chiral symmetry breaking in quark confining theories

We exhibit a mechanism which breaks chiral symmetry in a confining theory. The ingredients are the postulated existence of chirally invariant confining forces and the Pauli principle. The qualitative structure of the fermion vacuum is outlined and the chiral parameters (〈 ψψ〉, m constituent) are related to the strength of the confining force (essentially the Regge slope). The suggested mechanism is anlogous to the BCS phenomenon and the counterpart of the Cooper instability is proved.

Semiclassical approach to the quark-string model and the hadron spectrum. II. Baryons and exotic hadrons

Leading Regge trajectories of baryons and exotic hadrons are studied in the quark-string model. Boundary conditions at the string end point and the junction provide a simple topological rule on the configuration of hadron structure and also provide a relationship between the asymptotic Regge slope and the hadron structure. The center of mass of the string is shown to play a special role in classical solutions. The quark-diquark type of the baryon is absent in our formalism.

Factorisation of Regge slopes for multi-quark hadrons

Using duality and the factorisation relationships between residues, the authors present general rules for expressing the Regge slopes of multi-quark hadrons without string loops in terms of those of the standard three-quark baryons and two-quark mesons.

Quark sea and stringlike non-Abelian gauge field contribution to Hadron states

I t is desirable to construct the dynamical model of hadrons based on their intrinsic structure. Recently, NAMBU (~) gave very instructive talks on his idea of quark confinement by way of proving the equivalence of string model (2,3) and non-Abclian gauge theory (4,6). In this approach it is essential to consider the vacuum as the matter (e). His efforts were devoted to the development of earlier ideas of electric confinement (7,s). IGI (9) has succeeded in including the new particle family (10) in the dynamical model of Veneziano type by relaxing the duali ty requirement in the resonance region, assuming its recovery at infinite energies (Ii). The purpose of this paper is to explain at first the apparent discrepancy of observed Regge slopes for different hadron families by reinterpreting the BCS-like gap in the coloured quark level. The many degrees of freedom associated with the coloured gauge gluons may also play the fundamental role in this mechanism. In the second place we show that the relative probability of quark seas (~2) in the hadron bags of each Regge family may be related to the Regge slopes. In this t reatment the stringlike nature of non-Abelian gauge gluons is essential in the statistical mechanical sense. In what follows the apparent dismateh of Regge slopes may be reduced to the structure of associated quark sea of the relevant hadron. The parameters specifying that probability and Reggc slope are determined by making use of available information.

High-spin meson decays in the dual resonance model with nondegenerate Regge trajectories

We discuss the decays of high-spin natural-parity resonances lying on a leading Regge trajectory. We do this by studying the reaction $\mathrm{VP}\ensuremath{\rightarrow}\mathrm{PP}$ in a dual resonance model with trajectories which are nondegenerate in the resonance region. This allows for SU(4)-symmetry breaking in meson decay rates. Owing to the factorization property of Regge slopes and to the equal-spacing rule, we find rates which depend only on an overall normalization (and the low $s \ensuremath{\rho}$ trajectory slope ${\ensuremath{\alpha}}_{\ensuremath{\rho}}^{\ensuremath{'}}$). Agreement with data is good.

Quark-antiquark interaction at all momentum transfers

The running coupling constant of quantum chromodynamics ${\ensuremath{\alpha}}_{s}({q}^{2})$ is obtained for all ${q}^{2}$ by integrating the renormalization-group equation. The $\ensuremath{\beta}$ function in the asymptotic- freedom region is given by perturbation theory through order ${g}^{5}$ and at large coupling by the string model with string tension related to the Regge slope ${\ensuremath{\alpha}}^{\ensuremath{'}}$. We incorporate these features into a Pad\'e approximant to the $\ensuremath{\beta}$ function thereby obtaining it for all $g$. The constant of integration $\ensuremath{\Lambda}$ of the renormalization-group equation is chosen to be about 500 MeV, as required by deep-inelastic phenomenology. ${\ensuremath{\alpha}}_{s}$ is thus completely determined by ${\ensuremath{\alpha}}^{\ensuremath{'}}$, $\ensuremath{\Lambda}$, and the first two terms of the $\ensuremath{\beta}$ function. The resulting charmonium and $\ensuremath{\Upsilon}$ spectroscopy is in excellent agreement with experiment. In particular the ${\ensuremath{\Upsilon}}^{\ensuremath{'}}\ensuremath{-}\ensuremath{\Upsilon}$ mass difference is forced to be nearly equal to the ${\ensuremath{\psi}}^{\ensuremath{'}}\ensuremath{-}\ensuremath{\psi}$ mass difference. In addition, it is shown that the structure of ${\ensuremath{\alpha}}_{s}(q)$ signals the presence of instantons.

A Closed String as a Source of the Yang-Mills Field

A closed string as a source of the Yang-Mills field is discussed in the range of the classical theory. It is shown that under certain conditions, the Yang-Mills field can be expressed in a non-linear combination of two Abelian gauge fields produced by the string and its center of mass and that the field from the string forms a singular flux with quantized magnitude. Discussions for the massive Yang-Mills field are also given and the effective action of the string is derived from the action of the field in the presence of its source. The Regge slope parameter associated with the string is shown to be proportional to the effective coupling constant of the interaction which is obtained by approximating the interaction via the massive Yang-Mills field as a direct one.

Bounds for Regge slopes and intercepts for ordinary and new hadrons

We have derived a constraint 2α i j (0) + α i i (0) + α j j (0) form the einequality for he unitarity relation. This constraint, combined with slope factorization leads to bounds for Regge slopes and intercepts. Bottom cases are also argued.

Factorization of Regge slopes for ordinary and new hadrons and their spectroscopy

We discuss in detail a factorization property of Regge slopes between ordinary and new hadrons proposed earlier. This is supported experimentally in a known case, and the (tensor) ${D}^{**}$ mass in this scheme is predicted to be 2.43 GeV. In addition, we obtain relations between boson slopes and baryon slopes with four flavors. By combining these with the slope-factorization property, we can predict all of the baryon slopes. Predictions for both boson and baryon spectra are also given.

Regge spectra, symmetry-breaking effects, and decays of old and new mesons in dual resonance amplitudes

Single-term Veneziano dual amplitudes with nondegenerate Regge slopes are examined in detail. Factorization of parent resonance residues and the equal-spacing rule extracted from the universal-slope case are used to determine all the leading-meson-trajectory parameters in terms of that of the $\ensuremath{\rho}$. Relations between nondegenerate slopes and SU(4)-symmetry-breaking effects are discussed. The predicted meson mass spectra and the partial decay widths into two pseudoscalars are shown to agree well with data for the cases in which data exist.

Estimate of the Pseudoscalar Decay Constant

We calculate the weak decay constant of paracharmonium (eta/sub c/) using a linear potential model. The result is somewhat larger than, but of the order of, F/sub ..pi../ and depends on the universal Regge slope ..cap alpha..'. A number of amusing features are noted.

Quantum spin model for Reggeon field theory

We study the Hamiltonian form of Reggeon field theory on a lattice in the two-dimensional $D = 2$ transverse or impact-parameter space. The Hamiltonian formalism allows naturally for the privileged character of the longitudinal variable or rapidity, which is kept continuous. Based on recent results for the one-dimensional theory, we argue that we may truncate the single-site basis of the Hamiltonian by retaining the lowest two states only, and we arrive at a lattice spin model. In terms of Pauli spin matrices ${\ensuremath{\sigma}}_{k}^{\stackrel{\ensuremath{\rightarrow}}{n}}$ at each site $\stackrel{\ensuremath{\rightarrow}}{n} = ({n}_{1},{n}_{2})$, our Reggeon quantum spin model has the Hamiltonian $H=\ensuremath{\Sigma}{\stackrel{\ensuremath{\rightarrow}}{n}}^{}(\frac{\ensuremath{\delta}}{2})(1\ensuremath{-}{\ensuremath{\sigma}}_{x}^{\stackrel{\ensuremath{\rightarrow}}{n}})+\ensuremath{\Sigma}{\stackrel{\ensuremath{\rightarrow}}{n}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{^}{i}}^{}A[1\ensuremath{-}2{\ensuremath{\sigma}}_{+}^{\stackrel{\ensuremath{\rightarrow}}{n}+\stackrel{^}{i}})(1\ensuremath{-}2{\ensuremath{\sigma}}_{+}^{\stackrel{\ensuremath{\rightarrow}}{n}})\ensuremath{-}{\ensuremath{\sigma}}_{z}^{\stackrel{\ensuremath{\rightarrow}}{n}+\stackrel{^}{i}}{\ensuremath{\sigma}}_{z}^{\stackrel{\ensuremath{\rightarrow}}{n}}]$, where $\stackrel{^}{i}$ represents the lattice unit vectors (1,0) and (0,1). The parameters $\ensuremath{\delta}$ and $A$ are related to those of the original field theory. All the approximations are valid for small Regge slope ${\ensuremath{\alpha}}_{0}^{\ensuremath{'}}$ in the region of the phase transition at output Regge intercept $\ensuremath{\alpha}(0)=1$. The critical exponents of the original system can be determined by the properties of the low-energy states of $H$ in strict analogy with the established relation between the ${\ensuremath{\varphi}}^{4}$ theory in $d = 2$ and the ground state of the quantum Ising model with a transverse magnetic field in $D=d\ensuremath{-}1=1$ dimension. The general properties of the Reggeon quantum spin model are exhibited, and several new approximation schemes for Reggeon field-theoretic calculations are suggested. While the above Hamiltonian is adequate, by universality, to describe the critical Pomeron, systematic improvements can be made to study the theory away from criticality by retaining more states in the single-site basis of the Hamiltonian.

Factorization of Regge slopes for ordinary and new hadrons

We propose a factorization property of Regge slopes between ordinary and new hadrons. We derive three (six) relations for bosons (baryons). This is supported experimentally in a known case and several predictions are made. The D ∗∗ mass is predicted to be 2.36 GeV.

A Dual String Model with Quantized Regge Slope

A Dual String Model with Quantized Regge Slope

Classical solutions for the relativistic three-string baryon problem

The dynamical system consisting of three relativistic massless strings, self coupled at a common junction, is investigated classically. The equations of motion are generated from the fundamental action used to describe the single string. An essentially non-linear free boundary problem is recognised in the orthogonal transverse gauge and a large class of solutions is obtained. The leading Regge slopes associated with some of these solutions are calculated and their implications for a viable model of a baryon discussed.

Soft dilatons and scale renormalization in dual theories

In this paper we study in some detail the divergences arising in the dual loops. They are a consequence of the existence of a massless and spinless particle of the pomeron sector, which can make an on-shell transition into the vacuum. Using the fact that this particle is a “dilaton” (i.e. it couples to the trace of the energy momentum tensor of the string) we can prove that the sum over the divergent parts of the dual loops provides a renormalization of the Regge slope α' and the coupling constant g. In particular the procedure of renormalization preserves the relation between the coupling constants of the pomeron and the reggeon sector.

Quantization for Regge Slopes and -Particles

1 (n) =a'(l)/n (In! =1, 2,-··) in the vortex model of the dual string, where n is the quantum number of the flux quantization. We propose a model that the newly discovered 4'-particles have n=2 whereas ordinary hadrons have n=l.

Dilatation Transformation in the String Model

Dilatation transformation is discussed in the string model. We show that it becomes meaningful in the infinite slope limit of Regge trajectories for the motion of a free string. It turns out to. be equivalent to the high energy limit of the dual amplitudes, with the Regge slope kept finite, in the case of interacting strings. The scaling phenomenon is ex­ plained from this point of view.