Regge Slope Research Articles

On the structure of baryons

A structure of baryons is proposed in which the quarks are attached to each other by flux tube links in conformity with triality. The properties of the links are lifted frorm the corresponding mesons. The latter are modelled from considerations of QCD, chiral symmetry and the principle of quantized intercepts ( m 2 2 − m 1 2 = m ϱ 2 = 1 2 (α′) −1 where α′ is the Regge slope of the ϱ and the indices 2 and 1 refer to states which transform one into the other by soft pion emission). Our principal quantitative results are m N = √ 3 2 m ϱ = 943 MeV, g A = 1.22 ; the ratios of mass splittings between strange baryons are in excellent agreement with experiment, but to get good absolute values it is necessary to adjust the mass of the strange link by some 15%. Reasonable results are obtained for the magnetic moments and the width of the Δ.

Baryon masses in relativistic potential models

We study the spectrum of a semi relativistic three-body hamiltonian. The hyperspherical method proves to be very efficient. We show that the ground states of baryons can be calculated with good accuracy. However, when using the meson potential, together with the colour assumption $$Vqq = \tfrac{1}{2}Vq\bar q$$ , baryon Regge slopes come out noticeably too small. We analyze this problem and show that a quarkdiquark structure for baryons cures this defect. Altogether the construction of a global unified potential model for mesons and baryons seems quite hopeful.

Inter-Flavor Consistency Resulting from Universal Potential Inspired by QCD

The potential model has so far systematized various quantites of quarkonium belonging to particular flavor, but it was not enough to say that the consistency between the quarkonia with different flavors was proved. Further careful analyses were made by using the potential restricted by the asymptotic behavior of QCD and some stringent experimental constraints. This potential contains only two parameters Λ (scale parameter) and k(cofining parameter) which have been loosely limited by the deep inelastic scattering and the Regge slope. In this note, we further restrict them by using fine structure of quarkonium. Λ and k are severely restricted in almost the same regions in spite of the difference of flavors. This reflects the adequacy of potential form. This form of potential is extensively applied to lighter quarkonia only by sliding mQ. The Ψ data including fine- and hyperfine-splitting are fairly well reproduced. Unexpectedly, even lighter mesons, which have been considered to be outside of the semirelativistic treatment (e.g., Breit-Fermi), have the qualitative tendency expected by sliding mQ from heavy quarkonia. The predictions related to toponium are also given to corroborate this potential.

Successes and difficulties of unified quark-antiquark potential models

We study the qualitative and quantitative properties of the spectrum of a two-body hamiltonian with relativistic kinematics. We show that this kinematics leads in a natural way to the observed features of light flavour (u, d, s) spectroscopy. After having established the basic properties of the operator (p2+m2)1/2+V(r) in the cases of linear or logarithmic potentials, we show that, to first approximation, all\(q_1 \bar q_2\) meson states can be reproduced with a very simple universal flavour-independent potential whose parameters are directly related to basic physical quantities: the Regge slopes of light flavours and the quasi-logarithmic coupling strength of heavy quarks. We can derive equivalent effective non-relativistic hamiltonians which justify the successes of N.R. approaches. The main difficulties encountered, in particular in incorporating spin effects, appear to be due to the fact that, in phenomenological potential models, chiral symmetry and the ensuing Goldstone nature of the pion cannot be implemented in a natural way. Hence, such an approach can take its full predictive power only if it is based on a deeper field-theoretic level.

Semi-relativistic quark-antiquark potential models

We study the qualitative and quantitative properties of the spectrum of a two-body hamiltonian with relativistic kinematics. We show that this kinematics leads in a natural way to the observed features of light flavour (u, d, s) spectroscopy. After having established the basic properties of the operator √ p2 + m2 + V(r) in the cases of linear or logarithmic potentials, we show that, to first approximation, all q1 q2 meson states can be reproduced with a very simple universal flavour-independent potential whose parameters are directly related to basic physical quantities : the Regge slopes of light flavours and the quasi-logarithmic coupling strength of heavy quarks. We can derive equivalent effective non-relativistic hamiltonians which justify the successes of NR approaches. The main difficulties encountered, in particular in incorporating spin effects, appear to be due to the fact that, in phenomenological potential models, chiral symmetry and the ensuing Goldstone nature of the pion cannot be implemented in a natural way. Hence, such an approach can take its full predictive power only if it is based on a deeper field-theoretic level.

Casimir effects in superstring theories

Compactification of the space in superstring theories is studied by calculating the one-loop effective potential provided that the supersymmetry is softly broken by some mechanism. The Casimir energy of closed string modes is shown to compactify the ten-dimensional Minkowski space M 10 into a stable M d ×T 10− d (1⩽ d<10) with a i= α′ R i =1 , where α′ and R i are the Regge slope and the ith radius of the torus T 10− d , respectively. In the SST-I model, although the closed string (gravity) sector decouples from the open string (Yang-Mills) sector in α′ → 0 limit, the former functions as an initiator as well as a stabilizer of the compactification.

Correspondances between the Symmetric Lund Model and the Dual Resonance Model

The Symmetric Lund Model is formulated in a manifestly forward-backward symmetric way and generalized to include transverse momenta and finite width resonances. It is shown to possess multiregge behaviour and inclusive-exclusive connection. It's characteristic exp (−area) damping factor is shown to occur also in dual amplitudes, if the Regge slope is given an imaginary part. The introduction of an infinite family of resonances described by a continuous mass spectrum is advocated; it realizes the synthesis of the Symmetric Lund Model with the Bowler and the Artru-Mennessier models, and improves the connection with the Dual Resonance Model.

Critical properties of a model of planar random surfaces

We describe results for a model of planar random surfaces which suggest that the model has a well-defined continuum limit from which a relativistic quantum theory of strings without tachyons can be reconstructed. The mean-field theory of that model is developed, and Osterwalder-Schrader positivity is exhibited. Some scaling relations and mean-field bounds for critical exponents and correlations are established. It is argued that, in dimension <6, our model may serve to calculate the leading O( N −2) correction to the two-glue-ball amplitude and that in high dimensions the Regge slope is infinite.

Abelian dominance and quark confinement in Yang-Mills theories. II. Oblique confinement andη′mass

Making a working hypothesis of Abelian dominance at a long-distance scale, we analyze the U(1) problem as well as the confinement problem in the $\mathrm{SU}(N)$ Yang-Mills theory with the vacuum angle $\ensuremath{\theta}$. We show that quarks are confined only when $\frac{\ensuremath{\theta}}{2\ensuremath{\pi}}$ is a rational number such that $\frac{\ensuremath{\theta}}{2\ensuremath{\pi}}\ensuremath{\ne}\frac{(1+nN)}{\mathrm{mN}}$, $n$ and $m$ being integers. We also calculate a correlation function of the topological charge density $Q(x)={(16{\ensuremath{\pi}}^{2})}^{\ensuremath{-}1}\mathrm{Tr}{F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}_{\ensuremath{\mu}\ensuremath{\nu}}^{*}(x)$ at $\ensuremath{\theta}=0$. We derive that $\ensuremath{\int}{d}^{4}x〈T{Q(x)Q(0)}〉=\frac{{N}^{2}}{128{\ensuremath{\pi}}^{4}(N\ensuremath{-}1){({\ensuremath{\alpha}}^{\ensuremath{'}})}^{2}}$, where ${\ensuremath{\alpha}}^{\ensuremath{'}}$ denotes the Regge slope of mesons. This formula yields \ensuremath{\sim}${(150\phantom{\rule{0ex}{0ex}}\mathrm{M}\mathrm{e}\mathrm{V})}^{4}$ in case of SU(3), which gives rise to a mass \ensuremath{\sim} 550 MeV to the ${\ensuremath{\eta}}^{\ensuremath{'}}$ meson through a chiral anomaly in QCD with massless quarks. This numerical result would explain the ${\ensuremath{\eta}}^{\ensuremath{'}}$ mass reasonably well in the approximation where pions are massless Goldstone bosons.

Saddle point analysis of pomeron singularities in Polyakov's string theory

A saddle-point analysis of Polyakov's string theory is carried out where the Liouville action is defined on surfaces with two disjoint boundaries, (the cylinder topology). This topology is appropriate for probing the closed string excitations. In a saddle point approach, a family of pomeron singularities having a Regge slope half of the ordinary particle trajectories is identified. However, a difficulty with the factorization property arises.

Abelian dominance and quark confinement in Yang-Mills theories

We define the Abelian component of the gauge field as a gauge-invariant object in the Yang-Mills theory. Then, by assuming that the Abelian component dominates in the theory at a long-distance scale, we demonstrate that quarks as well as gluons are confined by electric vortices. The vacuum structure is shown to depend on resolution $R$. That is, the vacuum has two phases in $R$ and monopole condensation occurs for $R\ensuremath{\ge}{R}_{c}$. The string tension of mesons is obtained as ${\ensuremath{\sigma}}_{q}=\frac{{{g}_{c}}^{2}}{3\ensuremath{\pi}{{R}_{c}}^{2}}$, where ${g}_{c}$ is the effective coupling constant at the critical resolution ${R}_{c}$. We estimate ${{R}_{c}}^{\ensuremath{-}1}$ to be 0.6 GeV in the presence of static quarks, and the bag constant ${B}^{\frac{1}{4}}$ to be 0.2-0.4 GeV. We also derive a relation ${\ensuremath{\alpha}}_{g}^{\ensuremath{'}}=\frac{1}{3}{\ensuremath{\alpha}}^{\ensuremath{'}}$ between Regge slopes of mesons (${\ensuremath{\alpha}}^{\ensuremath{'}}$) and of gluonia (${\ensuremath{\alpha}}_{g}^{\ensuremath{'}}$). This relation agrees with experimental data remarkably well provided that gluonia are identified with states lying on the Pomeranchuk trajectory.

Supersymmetric dual string theory: (III). Loops and renormalization

Single-loop amplitudes with three or four external particles are constructed in the supersymmetric dual theory. The three-particle loops vanish, signifying the absence of coupling constant renormalization. The four-particle planar-loop amplitude has a divergence that can be absorbed into a renormalization of α′, the Regge slope, since it is proportional to the derivative of the tree amplitude with respect to α′. Furthermore, we demonstrate that this divergence can be expressed as the divergence in the non-planar loop that couples one external SU(n) singlet [the states of the model are SU(n) singlet and adjoint representations] to three other particles. This divergence can be interpreted as a wave-function renormalization for external singlets. The non-planar loop with s-channel SU(n) singlet quantum numbers is shown to contain poles corresponding to the states of the closed-string sector of the theory (which includes the massless states of simple d = 10 supergravity).

N = 4 Yang-Mills and N = 8 supergravity as limits of string theories

The formulation of supersymmetric string theories in ten dimensions is generalized to incorporate compactified dimensions. Expressions for the one-loop four-particle S-matrix elements of N = 4 Yang-Mills and N = 8 supergravity in four dimensions are obtained by studying the string-theory loop amplitudes in the limit that the radii of the compactified dimensions and the Regge slope parameter simultaneously approach zero. If certain patterns that emerge should persist in the higher orders of perturbation theory, then N = 4 Yang-Mills in four dimensions would be ultraviolet finite to all orders, whereas N = 8 supergravity in four dimensions would have ultraviolet divergences starting at three loops.

Unified approach to the study of light and heavy mesons in the framework of the vacuum-polarization-corrected potential model

Phenomenological evidence from meson spectroscopy is presented to support the view that a unified description of bound light- and heavy-quark systems is possible within the scope of a nonrelativistic-potential-model approach. The vacuum-polarization-corrected potential with its confinement part in the form of an approximately equal admixture of vector and scalar components is found to be a suitable one for the purpose. The overall systematics of the predictions based on this potential model for the meson masses, fine-hyperfine splittings, leptonic decay widths, and the Regge slopes are observed to be consistent with the premise that the forces between quarks and antiquarks are independent of the quark flavors.

Particle trajectories and quarkonium potentials

We examine the compatibility of potential models for quarkonium with conventional Regge trajectories, exploring in particular questions of linearity and the existence of daughter trajectories. Using, for practical calculations, an effective power behaved potential, it is found that linearity of Regge trajectories is not a universal characteristic. It occurs only in a specific range of the effective quark mass, namely in the ordinary mesons. The Regge slope is in fact a decreasing function of the effective quark mass. Linearity of the ϱ trajectory requires the ϱ′ to have a mass 1.62 GeV.

The Makeenko-Migdal equation in a domained QCD vacuum

We present a solution for simple curves of the Makeenko-Migdal equation which leads to string dynamics. By the non-renormalized nature of the equation, any formal solution requires some extra physics input before it can be meaningfully interpreted. We then propose a “minimal” renormalization both of the Wilson loop for a large number of colors and of the corresponding Makeenko-Migdal equation. This scheme is based on Witten's idea of a master field. The regularized solution contains a scale (related to the Regge slope) which we connect to a gauge-invariant domain size in the QCD vacuum, and the solution can only make sense for loops that are large relative to this scale. Using a vortex condensate model for the QCD vacuum, the length parameter is related to the QCD length scale.

Regge slopes in dual topological expansion

The structure of the dual topological expansion is studied up to the cylinder level by concentrating on the determination of Reggeon and Pomeron slopes. A precise formulation for the generation of Regge behavior in terms of an effective random walk is presented, and a well-defined meaning is provided for the trajectory slope in terms of average step lengths in the rapidity and the impact-parameter directions. The smallness of the Pomeron slope, $\frac{{\ensuremath{\alpha}}_{P}^{\ensuremath{'}}}{{\ensuremath{\alpha}}_{0}^{\ensuremath{'}}}\ensuremath{\sim}0.3$, is shown to represent a nontrivial constraint for theories satisfying the requirement of short-range ordering; a topological phase consideration is shown to be the primary mechanism responsible for this phenomenon. The relation between our finding to the naive expectation $\frac{{\ensuremath{\alpha}}_{P}^{\ensuremath{'}}}{{\ensuremath{\alpha}}_{0}^{\ensuremath{'}}}\ensuremath{\simeq}\frac{1}{2}$, based on a string picture and to the general phenomenon of the $\frac{f}{P}$ identity is clarified.

Regge Slope and theΛParameter in Quantum Chromodynamics: An Empirical Approach via Quarkonia

The string constant (or, equivalently, the asymptotic Regge slope α′) is related to the Λ parameter in quantum chromodynamics (QCD). The empirical information from the Ψ, ϒ spectroscopies is used to determine this relation. In so doing a quarkonium potential in excellent agreement with experimental data is also obtained. It is found that Λms―=0.5 GeV and α′=1 GeV−2.

Universal regge slope α′ from the QCD gluon propagator

An effective gluon propagator is estimated in the present of a fluctuating color magnetic field in the vacuum. Using the dual honeycomb diagram the universal slope is estimated to yield Λp=0.34 GeV when correcte by instantons, for α′=0.88 GeV −2.

An upper bound for thet-quark mass from duality and unitarity

We attempt to predict the mass of thet-quark from the approach based on duality and unitarity, employing the values of known Regge slopes and vector meson masses. Thet-quark mass is shown to be bounded approximately by 65 GeV, using the maximum possible value for the γ slope. This upper bound is sensitive, however, to the γ slope, and hence it will be considerably reduced if the reliable value is obtained. The importance to find the χ b state ((bb)3P2) is emphasized. The χ b mass is also predicted to be less than 9.89 GeV.