Broken Scale Invariance Research Articles

An effective lagrangian for the pure N = 1 supersymmetric Yang-Mills theory

An effective lagrangian for the pure, N=1, supersymmetric Yang-Mills theory is proposed by suitably modifying that of QCD. The quantum breaking of scale and chiral invariance by the corresponding anomalies generates a massive Wess-Zumino supermultiplet while preserving supersymmetry. The large- N c limit is discussed for an SU( N c ) gauge group.

Cosmology and broken scale invariance

The cosmological consequences of a simple scalar field model for the generation of Newton's constant through the spontaneous breaking of scale invariance in a curved space are presented and discussed.Received 13 October 1981DOI:https://doi.org/10.1103/PhysRevD.24.3338©1981 American Physical Society

Gravitation and broken scale invariance

We examine the consequences, in a simple scalar-field model, of the relation between the breaking of scale invariance and gravitation.

How to extract the gluon fragmentation function from large P⊥ photoproduction

A clear determination of the gluon fragmentation function D g h( z, Q 2) is accessible in near to come large P ⊥ photoproduction experiments. This is done by analyzing differences of double inclusive cross sections. The scale invariance breaking effect is shown to be measurable.

Proton-neutron mass difference, electroproduction, and photoabsorption in an analytic model of the virtual Compton amplitude

An analytic model of the forward (virtual) Compton amplitude is proposed which satisfies $v$ plane analyticity, $s\ensuremath{-}u$ crossing symmetry, Regge behavior, and Bjorken scale invariance in appropriate limits. The model is constructed using the method of conformal mapping. Very good fits are obtained to the electroproduction data on $v{W}_{2}^{p}$, $2m{W}_{1}^{p}$, $v{W}_{2}^{p}\ensuremath{-}v{W}_{2}^{n}$, $\frac{v{W}_{2}^{n}}{v{W}_{2}^{p}}$, $v{R}_{p}$, and $1+v\frac{{W}_{2}^{n}}{v{W}_{2}^{p}}$, and to the photoabsorption data on ${\ensuremath{\sigma}}_{T}(\ensuremath{\gamma}p)$, ${\ensuremath{\sigma}}_{T}(\ensuremath{\gamma}n)$, and ${\ensuremath{\sigma}}_{T}(\ensuremath{\gamma}p)\ensuremath{-}{\ensuremath{\sigma}}_{T}(\ensuremath{\gamma}n)$. The scale-invariance breaking at finite ${Q}^{2}$ as exhibited by the data on $v{W}_{2}^{p}$ plotted as a function of ${Q}^{2}$ with $\ensuremath{\omega}$ fixed is also successfully reproduced. The $p\ensuremath{-}n$ mass difference calculated using the Cottingham formula is finite. In particular, it is shown that a set of parameters exists for which the general condition for no logarithmic divergence even in the presence of Bjorken scaling given by $limit of\text{}{Q}^{4}\ensuremath{\Delta}{t}_{1}^{I}(\ensuremath{-}{Q}^{2},0)\text{as}{Q}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}=(\frac{\ensuremath{\alpha}m}{\ensuremath{\pi}})\ensuremath{\int}{0}^{1}dx[\ensuremath{\Delta}{F}_{2}(x)+2x\ensuremath{\Delta}{F}_{1}(x)]$ can be realized consistent with theoretical consideration and experimental data. The final result of our calculation of the mass difference is (-1.96 \ifmmode\pm\else\textpm\fi{} 0.52) MeV, which is to be compared with the experimental value of -1.293 MeV.

Spontaneously broken scale invariance and gravitation

It is proposed to combine the scalar-tensor theory of gravitation with the hypothesis of ‘spontaneously broken scale invariance’, which has been developed in quantum field theory and seems to give a better understanding of the origin of the masses of elementary particles. The general theoretical background of this approach is reviewed. In our model theory we predict that the Newtonian gravitational potential acquires an anomalous part with a force-range typically of the order of 105 cm.The experimental consequences are also discussed.

Broken scale invariance in $$p\bar p \to \ell ^ + \ell ^ - + $$ anything in functional approach to quantum field theoryanything in functional approach to quantum field theory

Broken scale invariance in $$p\bar p \to \ell ^ + \ell ^ - + $$ anything in functional approach to quantum field theoryanything in functional approach to quantum field theory

Chiral symmetry breaking and meson-nucleon sigma commutators: A review

Chiral symmetries are discussed in considerable detail, and their importance and consequences for the study of elementary particle physics are reviewed. For the study of broken symmetries we concentrate mainly on meson-nucleon sigma terms, $\ensuremath{\pi}\ensuremath{\pi}$ scattering, and ${K}_{l3}$ decays. In addition to giving a critical and detailed review of most of the "experimental" estimates for pion-nucleon and kaon-nucleon sigma terms done so far, we also outline the most common chiral symmetry-breaking schemes at present, such as $(3,\overline{3})+(\overline{3},3)$, $(6,\overline{6})+(\overline{6},6)$, (8,8) and (1, 8) + (8, 1) representations of SU(3) \ifmmode\times\else\texttimes\fi{} SU(3) and possible mixtures of them, and discuss and compare their predictions with experiment. Nonlinear effective Lagrangians are briefly discussed, and the connection between broken scale invariance and chiral symmetry breaking is outlined, with emphasis on our present knowledge of meson-nucleon sigma terms.

Coupling-Constant Sum Rules for Broken SU(3)

Both theoretical and phenomenological aspescts of broken-SU(3) coupling- constant sum rules are considered. Assumptions underlying the conventional derivation of these sum rules are discussed. A coupling-constant sum rule is derived in a model involving broken scale invariance. A phenomenological analysis of tensor-meson decays is carried out. Four coupling-constant sum rules are analyzed, and the ambiguity problem in defining empirical coupling constants is studied. (auth)

Comment on Broken Scale Invariance

S>Broken scale invariance is briefly reviewed. A constraint on the equal-time commutator between the trace of the energy-momentum tensor and symmetry-breaking terms is discussed. A sum rule relating matrix elements of chiral-symmetry-breaking terms with their dimensions is derived. (auth)

Further Remarks About theε(700)Meson and Broken Scale Invariance

We modify an earlier paper to remove an inconsistency in our previous approach, and we report a somewhat improved agreement between empirical sets of ($\ensuremath{\pi}\ensuremath{\pi}$) phase shifts and constraints from broken scale invariance.

Comments on a Model of Spontaneously Broken Scale Invariance

Comments on a Model of Spontaneously Broken Scale Invariance

Nature of the scale-invariance breaking term in inelastic e-p scattering from DGS representation

Using the DGS representation and the scaling phenomena we suggest that the nature of the scale breaking term of νW 2 in inelastic e-p scattering, should be of the form G 2(ω)M 2 Q 2 . Using Regge theory it is then predicted that G 2( ω) would be a constant for large ω, and is estimated to be approximately −0.06. These predictions, in particular the constancy of the slopes for νW 2 versus 1 Q 2 plots for large ω ( ω>8), compare very well with the recent experimental data. Similar results for W 1( ν, Q 2) are also discussed.

Is theε(700)Meson the Goldstone Boson of Broken Scale Invariance?

We examine low-energy theorems of broken scale invariance, using for our tests phenomenological ($\ensuremath{\pi}\ensuremath{\pi}$) phase shifts and thus improving on the usual pole approximation for the $\ensuremath{\epsilon}(700)$ meson, commonly assumed to act as a Goldstone boson. Approximate consistency is found for a model based on broken S${\mathrm{U}}_{3}$ \ifmmode\times\else\texttimes\fi{} S${\mathrm{U}}_{3}$ symmetry, provided that a certain subtraction constant, already present on the level of pole models, is used as a free parameter to be fitted by the data. Yet there are definite indications that contrary to the role of the pion in broken chiral symmetry, broken scale invariance cannot be understood in terms of the $\ensuremath{\epsilon}(700)$ meson alone and contributions from higher states are needed in an essential manner.

Broken scale invariance in inelastic lepton—Nucleon scattering

Broken scale invariance in inelastic lepton—nucleon scattering is discussed studying current commutators near to light-cone and their equal time limits. Models, based onWilson’s ideas, are proposed here to provide a more general frame than canonical models.

Short-Distance Scale Invariance and the Structure of Weak Transitions

The effects of short-distance interactions between hadronic weak currents on the structure of weak transitions are investigated within Wilson's scheme of operator-product expansions and broken scale invariance. It is pointed out that a consistent understanding of these effects can be attained with the hypothesis that the dimensions of nonexotic fields are near-canonical while those of exotic fields are anomalously high. The lack of structure-dependent effects in the $\ensuremath{\Delta}I=\frac{1}{2}$ part of ordinary nonleptonic decay, the suppression of the $\ensuremath{\Delta}I=\frac{3}{2}$ part in the same, and the smallness of the ${K}_{1}^{0}\ensuremath{-}{K}_{2}^{0}$ mass difference are first explained following Wilson's arguments. The structure of higher-order semileptonic decays disobeying the $\ensuremath{\Delta}S=\ensuremath{\Delta}Q$ role is then discussed. Finally, the important role played by short-distance effects in radiative nonleptonic decays of hadrons is elucidated and a mechanism for the large asymmetry parameter observed in the reaction ${\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}p+\ensuremath{\gamma}$ is obtained.

ϵ-meson coupling constants and scale invariance breaking

A general method for obtaining ratios of coupling constants (defined by pole residues) in a way which is completely free of resonance/background separation troubles is devised and applied to the ϵ-meson. Huge discrepancies between previous determinations are shown to arise (i) from inherent ambiguities in the methods used, (ii) from lack of knowledge about the ϵ-pole position and (ii) from the well-known up-down ambiguity in the isospin-0 s-wave ππ phase shift δ o o. Taking as input πN phase shifts, available information on δ o o and including all possible uncertainties we find for down-up or up-up δ o o : g ϵ NN g ϵππ = (6 ± 3) μ −1 , and for down-down or up-down δ 0 0: g ϵ NN g ϵππ = (1.8 ± 0.5) μ −1 . The precise validity of the scale invariance breaking prediction ( g ϵNN / g ϵππ ). m ϵ 2 2M = 1 is fulfilled in some theoretical ππ models having Γ ϵ ≈ m ϵ ≈ 500 MeV and δ o o of up-down type, but is excluded if δ o o is down-up or up-up.

Gauge invariance and mass scale

The self-consistency problem for a spinor fieldψ of mass dimension 1/2 is considered in a theory with a scale-invariant nonlinear spinor equation. It proves possible by the requirement of gauge invariance to maintain dimψ=1/2 also in a theory of interacting fields. The introduction of scale invariance breaking by massive poles into the fermion propagator makes it possible to obtain nontrivial boson solutions, especially zero-mass spin-1 bosons connected with gauge invariance of the theory. These gauge bosons couple directly only to that part of the fermion propagator which does not contain massless fermions.

Quantum Corrections to Stress Tensors and Conformal Invariance

Quantum corrections to the energy-momentum tensors of particles are calculated for these theories: (1) scalar electrodynamics, (2) spinor electrodynamics, and (3) scalar particles with $\ensuremath{\lambda}{\ensuremath{\phi}}^{4}$ self-interaction. It is shown that source theory provides a much more satisfactory approach than conventional means. The primary result of the investigation is the clear establishment of the favored role of the so-called "conformal" stress tensor - that is, the stress tensor that in the zero-mass limit transforms covariantly under the action of the conformal group. In terms of this tensor, unsubtracted spectral forms for the modifications are written down. A heuristic "proof" that this should be generally possible is provided. It is argued that broken scale invariance does not affect this subtraction-free property, and this is confirmed by explicit calculation of the order-${\ensuremath{\lambda}}^{2}$ modifications in the $\ensuremath{\lambda}{\ensuremath{\phi}}^{4}$ theory.

Why dilatation generators do not generate dilatations

We show that the Ward identities associated with broken scale invariance contain anomalies in renormalized perturbation theory. In low orders, these anomalies can be absorbed into a redefinition of the scale dimensions of the fields in the theory, but in higher orders this is not possible. Also, these anomalies cannot be removed by studying the Green's functions for objects other than canonical fields, e.g., currents. These results are established to first nontrivial order in perturbation theory by explicit Feynman calculations (which give us information at all momentum transfers), and in higher orders by the method of Callan and Symanzik (which gives information only at zero momentum transfer). The two approaches are consistent within their common domain of validity. Two appendices contain self-contained treatments of the formal canonical theory of scale and conformal transformations and of the derivation of Ward identities. In another appendix, we derive the Callan-Symanzik equations for Green's functions of currents, and show that no redefinition of scale dimension is necessary for these objects, although the other anomalies remain.