A model of baryons based on duality and unitarity

A model of “planar” baryons with (10 + 8) ? (1 + 8) exchange degeneracy is proposed, based on duality and unitarity. Dynamical mechanisms for deviation from the “planar” baryons are considered and the consequent pattern of broken exchange degenerate trajectories is compared with observed baryon spectra. Our model suggests a string picture of linear molecule type for baryons.     

Magnetic flux lines as relativistic strings

It is suggested that the relativistic string of the dual resonance model of hadrons is a line of quantised magnetic flux. Accordingly, quarks have magnetic charge. Assuming quarks of magnetic charge ${}^{\mathrm{+}}\text{g,?g}$, baryons are composed of three quarks. States of one, two, four or five quarks will not normally occur.     

A possible description of baryon dynamics in dual and gauge theories

We present an attempt to generalize to baryons a framework recently proposed in order to unify gauge, dual and Regge-Gribov theories of mesons. We find it necessary to depart from the $\text{1}\text{N}{}_{\mathrm{<mtext>colour</mtext>}}$ expansion of quantum chromodynamics (QCD) and to replace it by a more general definition of a “dual” approximation of QCD, based on the zero-width limit. Theoretical and phenomenological consequences of the scheme are derived. For N_colour = 3, the baryon resembles a Y shaped string; three families of new “baryonium” bound states are predicted and rough estimates of intercepts and slopes of the associated Regge trajectories are given. A new type of Zweig-like selection rule is found to hold in leading order and its violations through higher-order topologies are discussed. Duality diagrams for baryons are ambiguous unless implemented with extra lines indicating the flow of certain colour indices. Duality between scattering and annihilation channels is found in B$\text{B}$ scattering and its consequences are discussed. Some justification is given for the quark counting rule for total cross sections. Finally, implications of our scheme for the Regge-Gribov calculus in processes involving baryons are discussed.     

String model with baryons: Topology; classical motion

We consider the model in which a meson is an open string with a quark at one end an anti-quark at the other end; a baryon is made of three strings joining at a point, and carrying quarks at their free ends. The triality condition is ensured by orienting the strings according to simple rules. These rules suggest the existence of an underlying magnetic monopole theory. Independently of this “explanation”, we investigate first the topological properties of the model, by looking at the duality diagrams: existence of exotic hadrons, of five basic interactions between strings. Some renormalization diagrams are assigned a negative power of the Veneziano coupling constant. Then, taking the same action (the world-sheet area) as in the conventional string model, we set down the equations of motion of a junction. We argue that the slope of the leading baryonic Regge trajectory is the same as that for the mesons. As an example of an application, we study the “sticking together” of two colliding strings; we find that it is classically forbidden at relative velocities greater than $\text{(}\text{6}\text{7}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$.     

Baryons in dual unitarization and dynamical thresholds

Baryon exchange and baryon resonance production is introduced in the dual unitarisation scheme. The dynamical threshold for the production of meson and baryon resonances is incorporated. It is shown that the intercepts of the ω and the f, which are generated by baryons, are suppressed by the above dynamical threshold effects to $\text{α}{}_{\mathrm{\omega }}\text{(0) ? 0}$ and α_f(0) < 0. The pomeron is shifted slightly upwards by baryon production. An upper limit is determined for the ratio of the crossed and uncrossed produced baryon lines. The breaking of the Freund-Rosner-Walz rule is discussed.     

Regge trajectories in the quark model

We prove that the large angular momentum behaviour of the leading Regge trajectory of a meson (q \(\bar q\) ) or a baryon (qqq) can be obtained by minimizing the classical energy of the system for given angular momentum. A two-body quark-antiquark linear potential plus relativistic kinematics produces asymptotically linear Regge trajectories for mesons. For baryons we take either a sum of two-body potentials with half strength or a string of minimum length connecting the quarks, and find in both cases that the favoured configuration is a quark-diquark system and that the baryon and meson trajectories have the same slope. Short-distance singularities of the potential are shown to be unimportant.     

Precise hadron mass calculations from lattice QCD

By using scalar as opposed to spin-$\text{1}\text{2}$ quarks and treating spin effects perturbatively, the masses of the lowest lying 0^- and 1^- mesons above 1 GeV (the J/Ψ, η_c, D, D¹, F, F¹, and φ) are calculated to 1%. The masses of the K¹, ?, and K are respectively obtained to 3%, 8% and 30%. Certain (spin-averaged) linear combinations of baryon masses are also computed. The nucleon-delta result differs from experiment by 8%. For heavier baryons the error is smaller. Scalar lattice QCD seems to be a promising approach to the strong interactions.     

The properties of charmed baryon (Λc+) and the proton revisited

A statistical model for baryons was suggested leading to an analytical expression for the square modulus ∥ψ(r)∥² of baryon wavefunctions, which is not only free of constituent quark masses but also devoid of the interaction parameters of the effective linear potential in which a quark moves. Using ∥ψ(r)∥² as an input the lifetimes of the newly established charmed baryon ($\text{Λ}{}_{\mathrm{c}}{}^{\mathrm{+}}$) and the proton were studied and compared with other existing theoretical estimates.     

Renormalized Hartree-Fock equations in a nuclear relativistic quantum field theory

Renormalized Hartree-Fock equations are derived for an infinite system of mesons and baryons in the framework of a relativistic quantum field theory. Direct and exchange diagrams in the baryon propagator are summed self-consistently to all orders, and the effects of occupied negative-energy states in the Dirac sea are included. The required counterterm subtractions are defined by conventional renormalization conditions, but they need not be evaluated explicitly. The result is a set of finite nonlinear integral equations for the baryon self-energy that includes vacuum fluctuation effects from virtual N$\text{N}$ pairs in the many-body wavefunction at finite density.     

Quarks and diquarks in a baryon string model

Chew-Frautschi plots are found for baryons containing a quark and a diquark at the extremities of a relativistic string. The quark fields are modelled on free Dirac fields restricted to the ends of the string. Quantum numbers for the diquark field are obtained by adding those for two individual quark fields.The leading trajectory for the quark-diquark configuration is found to be energetically more favourable than the leading trajectories for the linear and Y-shaped baryon configurations considered previously.     

A string model of mesons

A string-type meson model with two massive quarks is presented. It is solved exactly by means of almost periodic functions in 3 + 1 space-time dimensions. The solutions, Poincaré generators, and Hamiltonian bear formal resemblance to the corresponding free string quantities. The leading (rising) Regge trajectory is linear but has negative intercept. The degeneracy of the spectrum is greatly reduced and the breaking of reparametization invariance by the non-zero quark masses requires an asymptotic application of the gauge conditions of Virasoro in order that the physical subspace of the usual Nambu string be obtained in the massless limit. Modifications necessary to construct more realistic models and their extensions to baryons are indicated.     

Bound states in the colored-quark model

The saturation problem in the three-triplet quark model, discussed previously by Nambu and by Lipkin, is investigated. We prove that in a simple version of the model, the only bound states of any color representation and any numbers of quarks and antiquarks are the $\text{q}\text{q}$ (meson), qqq (baryon), and a heavier diquark state.     

Baryon exchange effects in dual unitarisation

The effects of baryon exchanges in the renormalisation of Regge trajectories are studied in the dual unitarisation scheme. The main results are that: (i) the pomeron is boosted above α = 1, giving rising total cross sections beyond baryon-antibaryon thresholds, and (ii) the ω trajectory remains approximately at α = 0.5 but acquires a sizeable admixture of the exotic $\text{q}\text{q}\text{qq}$ state, which enhances its coupling to baryons. There are in addition a number of other interesting predictions.     

QCD predictions for γγ annihilation to baryons

QCD predictions for large-momentum transfer cross sections of the type $\text{γγ →}\text{B}\text{B}\text{′}$ are given, for B and B′ any members of the baryon octet or decuplet, and all possible helicity combinations for photons and baryons.     

Midrapidity production of secondaries in pp collisions at RHIC and LHC energies in the quark–gluon string model

We consider the phenomenological implications of the assumption that baryons are systems of three quarks connected through a gluon string junction. The transfer of baryon number in rapidity space due to the string junction propagation is considered in detail. At high energies this process leads to a significant effect on the net baryon production in hN collisions at midrapidities. The numerical results for midrapidity inclusive densities of different secondaries in the framework of the quark–gluon string model are in reasonable agreement with the experimental data. One universal value, λ≃0.25, for the strangeness suppression parameter correctly describes the yield ratios of Λ/p, Ξ/Λ, and Ω/Ξ. The predictions for pp collisions at LHC energies are also presented. PACS 25.75.Dw     

The nuclear Coulomb sum rule in a relativistic model

The nuclear Coulomb sum rule is investigated in a relativistic quantum field theory of the nucleus based on baryons and mesons. First an effective, local, covariant, conserved electromagnetic current operator is constructed for the many-baryon system. It describes the electromagnetic structure of an isolated nucleon; the lowest-mass two-pion contribution to the spectral weight functions of the form factors is contained in it. The sum rule is then evaluated in a model based on baryons and neutral scalar and vector mesons. In the mean-field approximation (MFT) this model correctly describes the saturation properties of nuclear matter. The “one-body” term in the sum rule can be evaluated exactly through the use of the canonical anticommutation relations for the baryon field and the identification of conserved quantities. The remaining relativistic two-body contribution is evaluated in the MFT. Meson contributions to the sum rule at large momentum transfers $\text{q}\text{2k}{}_{\mathrm{<mtext>F</mtext>}}\text{? 1}$ completely dominate anticipated static, short-range, two-nucleon correlation contributions to the non-relativistic Coulomb sum rule. One possible implication is that the nucleus must (at least) be considered as a dynamic system of mesons and baryons.     

Baryon production by primordial black holes

The evaporation of primordial black holes (PBH's) by the Hawking process can produce an excess of baryons over anti-baryons. Assuming a power-law form of the initial mass spectrum of PBH's and taking into account the observational constraints on that spectrum we calculate the baryon excess produced. We find that if the spectrum is steep ($\text{α?3.5}$) or cut off for masses above ～ 10⁹ g, the observed baryon/photon ratio of ～ 10^?9 can be produced by PBH evaporations.     

Apparent spin-dependent forces in QCD or the quantum chemistry of hadrons

Mesons in QCD are viewed as $\text{q}\text{q}$ pairs at the ends of a string (electric flux line). The (mass)² spectrum is approximately linear in the number of nodes, ν, in the wave function ψ(x), x being the fraction of total momentum carried by one quark. For the equal mass case ψ is even (odd) under reflection x ? (1 ? x) for ν even (odd). Thus this reflection symmetry is to be interpreted as charge conjugation where C = +1 (?1) respectively, and hence by Fermi statistics, singlets (triplets) in spin. Since the spectrum of (mass)² is evenly spaced in ν, one can represent the even and odd states by two Regge trajectories separated by intercept $\text{1}\text{2}$, thereby explaining the famous $\text{1}\text{2}$ intercept difference for the π, ρ system. The argument generalizes to K, K¹ as well, but must be further analyzed before we generalize it to baryons.