Field Theory Of Strong Interactions Research Articles

Nuclei Using Topological Solitons: Skyrmions and rho Mesons

The Skyrme model is a low-energy effective field theory of strong interactions where nuclei and baryons appear as topological solitons, more concretely as collective excitations of pionic degrees of freedom. In the last years, there has been a revival of Skyrme’s ideas and new related models have been proposed to overcome two of the main drawbacks of the theory, namely, the too large binding energies and the lack of cluster structures. In this paper, we shortly review how to address both issues by extending the standard Skyrme model with the inclusion of the rho meson and how important the pion mass contribution is.

Neutron stars within the Skyrme model

The Skyrme model is a low energy effective field theory of strong interactions where nuclei and baryons appear as collective excitations of pionic degrees of freedom. In the last years, there has been a revival of Skyrme’s ideas and new related models, and some of them with BPS bounds (topological lower energy bounds) have been proposed. It is the aim of this paper to review how they can be applied to the study of neutron stars allowing for a description by means of topological solitons. We will focus on different aspects as the equation of state or the mass-radius relation, where we find that high maximal masses are supported.

Time-dependent AdS/CFT correspondence and the Quark-Gluon plasma

Experiments on high-energy heavy-ion collisions reveal the formation and some intriguing properties of the Quark-Gluon Plasma (QGP), a new phase of matter predicted by Quantum Chromodynamics (QCD), the quantum field theory of strong interactions. The phenomenological success of relativistic hydrodynamic simulations with remarkably weak shear viscosity, modeling QGP as an almost perfect fluid, are in favor of the occurrence of a strongly-coupled QGP expanding and cooling during the reaction. A derivation of these features in QCD at strong coupling is still lacking and represents a very intricate theoretical challenge. As a quite unique modern tool to relate these dynamical features to a microscopic gauge field theory at strong coupling, time-dependent realizations of the AdS/CFT correspondence provide a fruitful way to study these properties in a realistic kinematic configuration. Relating a 4-dimensional Yang-Mills gauge theory with four supersymmetries (which is a conformal field theory, CFT) with gravity in Anti-de Sitter space in five dimensions (AdS), the AdS/CFT correspondence provides a useful "laboratory" to study yet unknown strong coupling properties of QCD. Besides the interest of revealing new aspects of the AdS/CFT correspondence in a dynamical set-up, the application to plasma formation leads to non trivial theoretical properties, as we will discuss in the lectures. The highlights of the present lectures are: 1. Emergence of an (almost) perfect hydrodynamic fluid at late proper-times after the collision. 2. Duality between an expanding 4-dimensional plasma and a black hole moving radially in the bulk. 3. Intimate link between conformal hydrodynamics and Einstein's equations in the asymptotically AdS space. 4. Possibility of studying the far-from-equilibrium stage of a gauge field theory at early collisional proper-times.

Chiral Perturbation Theory from Charged Kaon Decays at NA48/2

Chiral Perturbation Theory, as a low-energy effective field theory of strong interactions, is a very useful tool to study the interactions of kaons. The NA48/2 experiment, whose primary goal was the measurement of direct CP violation in the decays of charged kaons, has however collected enough statistics to check the ChPT predictions for several decay modes of charged kaons.

Review of Chiral Perturbation Theory experimental results in kaon decays

Chiral Perturbation Theory, as a low-energy effective field theory of strong interactions, is a very useful tool to study the interactions of kaons. Both in the semileptonic sector and in the non-leptonic one, several results have been achieved by NA48, KTeV, KLOE and ISTRA+. Recent results from both neutral and charged kaons are reviewed.

S-matrix renormalization in effective theories

This is the fifth paper in the series devoted to explicit formulation of the rules needed to manage an effective field theory of strong interactions in $S$-matrix sector. We discuss the principles of constructing the meaningful perturbation series and formulate two basic ones: uniformity and summability. Relying on these principles, one obtains the bootstrap conditions which restrict the allowed values of the physical (observable) parameters appearing in the extended perturbation scheme built for a given localizable effective theory. The renormalization prescriptions needed to fix the finite parts of counterterms in such a scheme can be divided into two subsets: minimal, needed to fix the $S$-matrix, and nonminimal, for eventual calculation of Green functions; in this paper we consider only the minimal one. In particular, it is shown that, in theories with the asymptotic behavior governed by known Regge intercepts, the system of independent renormalization conditions only contains those fixing the counterterm vertices with $n\ensuremath{\le}3$ lines, while other prescriptions are determined by self-consistency requirements. Moreover, the prescriptions for $n\ensuremath{\le}3$ cannot be taken arbitrarily: an infinite number of bootstrap conditions should be respected. The concept of localizability, introduced and explained in this article, is closely connected with the notion of resonance in the framework of perturbative quantum field theory. We discuss this point and, finally, compare the cornerstones of our approach with the philosophy known as ``analytic $S$-matrix.''

Sliding vacua in dense skyrmion matter

In continuation of our systematic effort to understand hadronic matter at high density, we study dense skyrmion matter and its chiral phase structure in an effective field theory implemented with the trace anomaly of QCD applicable in the large N c limit. By incorporating a dilaton field χ associated with broken conformal symmetry of QCD into the simplest form of skyrmion Lagrangian, we simulate the effect of “sliding vacua” influenced by the presence of matter and obtain what could correspond to the “intrinsic dependence” on the background of the system, i.e., matter density or temperature, that results when a generic chiral effective field theory of strong interactions is matched to QCD at a matching scale near the chiral scale Λ χ ∼4 πf π ∼1 GeV. The properties of the Goldstone pions and the dilaton scalar near the chiral phase transition are studied by looking at the pertinent excitations of given quantum numbers on top of a skyrmion matter and their behavior in the vicinity of the phase transition from Goldstone mode to Wigner mode characterized by the changeover from the FCC crystal to the half-skyrmion CC crystal. We recover from the model certain features that are connected to Brown–Rho scaling and that suggest how to give a precise meaning to the latter in the framework of an effective field theory that is matched to QCD.

Open string field theory of strong interactions in two dimensions

This is a review of some old work by the author from a new perspective: as a string field theory of strong interactions in two dimensional space-time that is equivalent to two dimensional QCD. The open string field, in light cone co-ordinates, is just a function of the endpoints. The key idea is that this field must satisfy a quadratic constraint, analogous to the constraint satisfied by the field of the non-linear sigma model. All the interactions arise as a result of this constraint: the manifold of solutions of the constraints is an infinite dimensional Grassmannian. The classical string field theory is equivalent to the large N limit of 2DQCD; by quantizing it we recover 2DQCD for finite N. The linear approximation to our theory is the original large N limit of 2DQCD constructed by 't Hooft. Baryons arise as topological solitons.

DIQUARKS IN ELEMENTARY PARTICLE PHYSICS

Many phenomena in elementary particle physics show indications of clustering of two quarks inside baryons. Although the existence of such diquark systems cannot be presently rigorously proven in quantum field theory of strong interactions, phenomenological models require some quark-quark binding to explain effects ranging from the baryon mass spectrum to large pT proton production in high energy pp collisions. This review confronts diquark models predictions with experimental results in low and high transverse momentum hadron-hadron collisions, lepton-nucleon scattering and e+e− annihilations. The recent data from the Split Field Magnet detector on high pT proton production in pp, dd and αα collisions at ISR energies are particularly emphasized.

Dual field theory of strong interactions

A dual field theory of strong interactions is derived from a Lagrangian of the Yang-Mills and Higgs fields. The existence of a magnetic monopole of mass 2397 MeV and Dirac chargeg=(137/2)e is incorporated into the theory. Unification of the strong, weak, and electromagnetic forces is shown to converge at the mass of the intermediate vector bosonW±. The coupling constants of the strong and weak interactions are derived in terms of the fine-structure constantα=1/137.

Tests of QCD and non-asymptotically-free theories of the strong interaction by an analysis of the nucleon structure functionsx F 3,F 2, and $$\bar q$$

The scaling violations of the structure functionsF 2,xF 3, and $$\bar q$$ , as measured in deep-inelastic neutrino-nucleon scattering at high hadron massW, have been compared with the predictions of QCD and other candidate field theories of strong interactions. Non-asymptotically free theories with scalar and vector gluons are incompatible with the data. This leaves QCD as the only field theory that gives a consistent description of all the observed scaling violations. The data do not, however, permit a sensitive test of the existence of the gluon self-coupling.

Can recently measured moments of F3vN discriminate between field theories of strong interactions?

It is demonstrated that moments of the flavor non-singlet structure function F 3 vN cannot discriminate, contrary to recent claims, between QCD and other nontrivial fixed point theories of strong interactions, even by taking into account the CDHS precision measurements. Only quantities, such as F 2( x, Q 2), which receive also flavor singlet contributions (dominant at small x) can provide us with discriminative tests of strong interaction theories using present experiments; it is not sufficient to study just moments ( n > 2) of F 2, since these are sensitive mainly to the non-singlet (large- x) contribution.

Field theories of strong interactions and scaling deviations in deep-inelastic lepton-hadron processes

Field theories of strong interactions and scaling deviations in deep-inelastic lepton-hadron processes

An SU(3)×SU(3) field theory of strong interactions in 6-ϵ dimensions

It has been proposed that phi 3 field theories in 6- epsilon dimensions may provide calculable models for strong interactions. The authors present the calculation of renormalisation group functions to order epsilon 3 in such a model with SU(3)*SU(3) internal symmetry. Convergence properties of the epsilon expansion are discussed.

Covariant quantization of a quark-binding string

An important tool for the investigation of relativistic quantum field theories of strong interactions is the study of their strong-coupling limits. These lead to semigeometric models in which the quark-binding fields reduce to constraining volumes (bags), surfaces (bubbles), or lines (strings). These models are usually first treated classically and then quantized by canonical quantization. The present model was previously investigated by Giles and Tye and by Tye and originated from the "SLAC bubble." A two-dimensional timelike cylinder is embedded in four-dimensional Minkowski space. Massless Dirac fields (quarks) are constrained to it. These can carry any internal-symmetry label. At a fixed time the model represents a loop (closed string) on which quarks circulate. The covariant quantization is possible in a special guage and for timelike (rather than null plane) dynamics if care is taken to treat the corresponding gauge conditions in an internally consistent way. Simultaneity of relative positions of this extended structure in every instantaneous rest frame leads to additional constraints which ensure the absence of ghost states. All primary constraints are proved to be first class also for the quantized system. There are no secondary constraints. The theory is manifestly covariant; the Poincar\'e algebra is verified explicitly. There are no tachyonic states since the total momentum points into the future light cone. Linearly rising Regge trajectories result as in the free string.

Renormalization Group and Strong Interactions

The renormalization-group method of Gell-Mann and Low is applied to field theories of strong interactions. It is assumed that renormalization-group equations exist for strong interactions which involve one or several momentum-dependent coupling constants. The further assumption that these coupling constants approach fixed values as the momentum goes to infinity is discussed in detail. However, an alternative is suggested, namely, that these coupling constants approach a limit cycle in the limit of large momenta. Some results of this paper are: (1) The ${e}^{+}\ensuremath{-}{e}^{\ensuremath{-}}$ annihilation experiments above 1-GeV energy may distinguish a fixed point from a limit cycle or other asymptotic behavior. (2) If electrodynamics or weak interactions become strong above some large momentum $\ensuremath{\Lambda}$, then the renormalization group can be used (in principle) to determine the renormalized coupling constants of strong interactions, except for $U(3)\ifmmode\times\else\texttimes\fi{}U(3)$ symmetry-breaking parameters. (3) Mass terms in the Lagrangian of strong, weak, and electromagnetic interactions must break a symmetry of the combined interactions with zero mass. (4) The $\ensuremath{\Delta}I=\frac{1}{2}$ rule in nonleptonic weak interactions can be understood assuming only that a renormalization group exists for strong interactions.

Equal-Time Commutation Relations and Divergence Conditions

The connection between divergence conditions for currents or generalized currents and equal-time commutation relations is investigated in terms of the response of physical systems to external fields. We give a simple method of constructing physical amplitudes and of obtaining generalized Ward identities and equal-time commutation relations for currents. In order to set up this scheme, we have to make an assumption about the response of the physical system to a change of the external parameters and also consider the gradient terms. In this way, we try to reproduce the current algebra formalism. It is hoped that, when this has been done, we will have made it plausible that a certain representation of the algebra exist. However, we do not discuss the formal reconstruction of the field theory of strong interactions in terms of electromagnetic, weak, and gravitational scattering data. The discussion in this paper is mostly restricted to finite-dimensional algebras, but a generalization of the method to infinite-dimensional situations is briefly outlined.

Strongly Decaying Particles and Relativistic Invariance

Before the discovery of strongly decaying particles ("resonances"), it was a good approximation to consider that all elementary particles are elementary systems, i.e., that their states transform according to an irreducible representation of the Poincar\'e group. This approximation is not valid for the strongly decaying particles, because they have a mass spectrum which cannot be neglected. To treat these particles on the same footing as the stable (or metastable) ones, one has to give a new definition of an elementary system. We describe the consequences of this definition for the one-particle states. The representation is no longer irreducible, but is multiplicity-free. The mass is a superselection rule; the states are described by density matrices, or better, by characteristic functions, defined on the Poincar\'e group. Specific examples are discussed ($\ensuremath{\rho}$ and $\ensuremath{\omega}$ mesons); the relevance of the new concepts introduced here for the quantum field theory of strong interactions is mentioned.

Possibility of giving a finite mass to the gauge field

The finite mass of particles associated to gauge field theories of strong interactions is shown to appear naturally as the self-energy effect. (R.E.U.)