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Using previously described functional techniques for some non--perturbative, gauge invariant, renormalized QCD processes, a simplified version of the amplitudes --- in which forms akin to Pomerons naturally appear --- provides fits to ISR and LHC--TOTEM $pp$ elastic scattering data. Those amplitudes rely on a specific function $\varphi (\vec b)$ which describes the fluctuations of the transverse position of quarks inside hadrons., Comment: 23 pages, 12 figures. arXiv admin note: text overlap with arXiv:1611.02691

A particular choice of renormalization, within the simplifications provided by the non-perturbative property of Effective Locality, leads to a completely finite, non-perturbative approach to renormalized QCD, in which all correlation functions can, in principle, be defined and calculated. In this Model of renormalization, only the Bundle chain-Graphs of the cluster expansion are non-zero. All Bundle graphs connecting to closed quark loops of whatever complexity, and attached to a single quark line, provided no ‘self-energy’ to that quark line, and hence no effective renormalization. However, the exchange of momentum between one quark line and another, involves only the cluster-expansion’s chain graphs, and yields a set of contributions which can be summed and provide a finite color-charge renormalization that can be incorporated into all other QCD processes. An application to High Energy elastic pp scattering is now underway.

This letter is meant to be a brief survey of several recent publications providing a simple, sequential explanation of Dark Energy, Inflation and Dark Matter, which leads to a simple picture of the why and the how of the Big Bang, and thence to a possible understanding of the birth and death of a Universe., Comment: 4 pages, 1 figure

Removal of the quenched approximation in the mechanism which produced an analytic estimate of quark-binding potentials, along with a reasonable conjecture of the color structure of the nucleon formed by such a binding potential, is shown to generate an effective nucleon scattering and binding potential. The mass-scale factor on the order of the pion mass, previously introduced to define the transverse imprecision of quark coordinates, is again used, while the strength of the potential is proportional to the square of a renormalized quantum chromodynamics (QCD) coupling constant. The potential so derived does not include corrections due to spin, angular momentum, nucleon structure, and electroweak interactions; rather, it is qualitative in nature, showing how Nuclear Physics can arise from fundamental QCD.

A new non-perturbative, gauge-invariant model QCD renormalization is applied to high energy elastic pp-scattering. The differential cross-section deduced from this model displays a diffraction dip that resembles those of experiments. Comparison with ISR and LHC data is currently underway., Conference proceedings for 4th International Conference on New Frontiers in Physics, ICNFP2015. Greece, 2015. subsequent work of Ann. Phys. 359, (2015); or arXiv:1412.2072, and arXiv:1502.04378

A new, analytic, non-perturbative, gauge-invariant formulation of realistic QCD is presented, with a discussion of two of its results as of this date.

A QED-based model of a new version of Vacuum Energy has recently been suggested, which leads to a simple, finite, one parameter representation of Dark Energy. An elementary, obvious, but perhaps radical generalization is then able to describe both Dark Energy and Inflation in the same framework of Vacuum Energy. One further, obvious generalization then leads to a relation between Inflation and the Big Bang, to the automatic inclusion of Dark Matter, and to a possible understanding of the birth (and death) of a Universe., Comment: 10 pages and 1 figure There has been a minor modification in the previous version (arXiv:1403.2651v1, 03/12/2014) : a reference has been added in [3] and an Appendix has been added

A new, non perturbative, eikonal method called the “quasi abelian limit” (QAL) is suggested for high energy quark (nucleon) scattering involving the exchange of all possible, non interacting, non abelian gluons (mesons). With this method, those functional integrals defining, e.g., the exchange of color cooordinates in quark–quark scattering, are replaced by a finite number of quadratures over a subset of their coordinates. Mathematically, this procedure is not rigourous, because an unjustified interchange of limits has been performed; physically, it corresponds to the observation that the non perturbative sum over all color–moment fluctuations can vanish at arbitrarily high energies. The QAL generates a result in agreement with a corrected, “contiguity” calculation, when the latter is summed over all perturbative orders.

A QED--based "bootstrap" mechanism is suggested as an explanation for the vacuum energy that furnished the initial impulse for Inflation, and continues on to provide present day Dark Energy. Virtual vacuum fluctuations are assumed to generate effective electromagnetic fields whose average value corresponds to an effective c--number $A_{\mu}^{\rm vac}(x)$, which is itself equal to the vacuum expectation value of the operator $A_{\mu}(x)$ in the presence of that $A_{\mu}^{\rm vac}(x)$. Lorentz invariance is manifest, as every observer would measure the same electric field in his or her own reference frame. The model has one arbitrary parameter $\xi$, and fits the energy density of present day Dark Energy for $\xi\sim O(1)$.

This Formulation [1], [2], [3] is New, in the sense that it is less than 3 years old. But it could have been done decades ago, since the input information existed, but was overlooked. It is Analytic in the sense that physically-reasonable approximations can be estimated with paper and pencil; and exact amplitudes can be calculated as Meijer G-functions of various orders. It is Non-Perturbative in the sense that sums over all possible gluon exchanges between any pair of quarks and/or antiquarks, including cubic and quartic gluon interactions, are exactly performed. These multiple gluon exchanges combine into "Gluon Bundles" (GBs), as sums over Feynman graphs with finite numbers of exchanged gluons are replaced by "Bundle Graphs". In effect, gluons disappear from the formalism, and GBs remain as the effective carrier of all interactions between quark lines. A simple re-arrangement of the Schwinger/Symanzik functional solution for the Generating Functional of QCD - a rearrangement possible in QCD but not in QED - produces a formal statement of Gauge-Invariance, even though the formulation contains gauge-dependent gluon propagators. After the non-perturbative sums produce GBs, one sees explicit cancelation of all gauge-dependent gluon propagators; gauge-invariance is achieved as gauge-independence. A new insight into Realistic QCD appears in the non-perturbative domain, because quarks do not have individual asymptotic states; they are always asymptotically bound, and their transverse coordinates cannot, in principle, be measured exactly. "Transverse Imprecision" is introduced into the basic Lagrangian, and quark-binding potentials for the construction of mesons and nucleons can then be defined and evaluated. And the greatest surprise of all: A new, non-perturbative property appears, called Effective Locality, with the result that all functional integrals reduce to (a few) sets of ordinary integrals, easy to estimate approximately, or calculate on a desk-top computer. A fantastic simplification! With the aid of the above techniques, this presentation will describe each of the above paragraphs, with explicit descriptions of gauge-invariance, of the summation of all relevant Feynman graphs, of quark-binding into hadrons, and of nucleon-nucleon binding to form a deuteron. To our knowledge, the latter calculation is the first analytic example of Nuclear Physics obtained directly from basic QCD.

A functional method to achieve the summation of all Feynman graphs relevant to a particular Field Theory process is suggested, and applied to QED, demonstrating manifestly gauge invariant calculations of the dressed photon propagator in approximations of increas- ing complexity. These lead in a natural way to the extraction of the leading logarithmic divergences of every perturbative order, and to a demonstration of the possible cancellation of all such divergences in the calculation of the (inverse of the) photon's wavefunction renormalization constant Z3. This analysis provides a qualitative understanding of why the measured value of the renormalized fine structure constant is, approximately, 1/137.

A method of sampling fluctuations in sub-dimensional phase space of (possibly fractal) dimensionD is proposed. Applied to random cascading models of multi-particle production, it gives aD-dependent nonlinear equation for the generating function of particle multiplicities in the sub-domain, whose solutions lead to new properties, e.g. the correction effects of very small scale ressumations on the generic intermittent fluctuations of the model, the unexpected possibility of non vanishing intermittency after dimensional projection and the connection of KNO scaling violations with a structural phase transition. A phenomenological discussion of\(\bar p\)p SPS data allows one to exhibit a simple fragmentation model describing both local and global multiplicity fluctuations observed in these reactions, and compare it with theoretical gluon cascading.

The authors approximately solve the Smoluchowski equation (discrete version), for gelling and non-gelling systems with finite mass and arbitrary initial conditions for various kernels (additive and multiplicative). They show that the approximate scaling form does not depend on the details of the kernel in contrast with already known results. Numerical simulations are presented which show that the predicted form is valid over a large range of the scaling variable n/s. The critical exponent related to the power law dependence of the distribution is shown to scale rapidly, even with low masses. This could clarify the recent difficulties of the standard theory with both experiments and numerical calculations.

The interpretation of virtual gluons as ghosts in the non-linear gluonic structure of QCD permits the formulation and realization of a manifestly gauge-invariant and Lorentz covariant theory of interacting quarks/anti-quarks, for all values of coupling. The simplest example of quark/anti-quark scattering in a high-energy, quenched, eikonal model at large coupling is shown to be expressible as a set of finite, local integrals which may be evaluated numerically; and before evaluation, it is clear that the result will be dependent only on, and is damped by increasing momentum transfer, while displaying physically-reasonable color dependence in a manner underlying the MIT Bag Model and an effective, asymptotic freedom. A similar but more complicated integral will result from all possible gluonic-radiative corrections to this simplest eikonal model. Our results are compatible with an earlier, field-strength analysis of Reinhardt et al., Comment: 35 pages, no figures

We present a two loop calculation of e+−e− annihilation into quarks and gluons at finite temperature in the framework of the real time formalism. We give a self-contained and pedagogical description of the calculation which relies on finite temperature cutting rules. Using a simpler infrared regularization than those of previous works, we confirm the cancellation of mass and infrared singularities, and give in addition a complete analytical and numerical evaluation of finite terms. Some delicate points linked to wave function renormalization are treated in full detail.

A physically reasonable model is introduced in order to estimate, in a functional way, the vast number of distinct graphs which are conventionally neglected in eikonal scattering models that lead to total cross sections increasing with energy in the form of the Froissart bound., 23 pages, 5 figures

We examine recently published results, on the thermal production of massive vector bosons in a quark-gluon plasma. We claim the production rate of a massive boson is a collinear safe observable.

We discuss the intrinsically nonperturbative probability ${P}_{0}$ for electron-positron production in the overlap region of a pair of high-intensity lasers, by adapting the Fradkin representation for the logarithm of the fermion determinant to several models defined as approximations to the exact problem. In each case we find for ${P}_{0}$ an expression resembling Schwinger's 1951 expression for the vacuum persistence probability of pair production in an external electric field, proportional to an exponential factor that contains an essential singularity, and hence does not admit a perturbative expansion about zero coupling. Qualitative estimates of the best of these models suggest that realistic yields for ${e}^{+}{e}^{\ensuremath{-}}$ production must await lasers of intensity ${10}^{29} {\mathrm{W}/\mathrm{m}}^{2},$ roughly seven orders of magnitude more powerful than the highest intensity of currently known lasers. We comment on the possibility of producing a quark-antiquark pair in this way, and note the possibility of achieving temporary, but large separations of the produced $q\ensuremath{-}\overline{q}.$

A functional formulation and partial solution is given of the non-abelian eikonal problem associated with the exchange of non-interacting, charged or colored bosons between a pair of fermions, in the large $s$/small $t$ limit. A simple, functional ``contiguity" prescription is devised for extracting those terms which exponentiate, and appear to generate the leading, high-energy behavior of each perturbative order of this simplest non-abelian eikonal function; the lowest non-trivial order agrees with the corresponding SU(N) perturbative amplitude, while higher-order contributions to this eikonal generate an ``effective Reggeization" of the exchanged bosons, resembling previous results for the perturbative amplitude. One exact and several approximate examples are given, including an application to self-energy radiative corrections. In particular, for this class of graphs and to all orders in the coupling, we calculate the leading-log eikonal for SU(2). Based on this result, we conjecture the form of the eikonal scattering amplitude for SU(N)., 19 pages, latex

New and precise experimental results on Drell-Yan pair production at accelerator energies are now available, both in π− andp-nucleus interactions. These data are analyzed within the QCD framework including soft gluon resummation. It is shown that a quantitative agreement of the theory with experimental data can be reasonably managed. In particular, the soft gluon resummation is shown to build up nicely the so-calledK-factor. The pion formfactor is deduced from experimental data, but is rather sensitive to the nuclear structure functions we use. Definite nuclear structure functions are needed.

We present a detailed study of scaling violations for non-singlet, singlet and glue distribution functions in the framework of several approximation schemes of QCD. Our formalism consists of direct resolution of the Altarelli-Parisi type equations and leads to a simple exponential form for the function q ( x , Q 2 ). This form is very suitable for the analysis of experimental data and for the exploration of different evolution schemes. In particular, we examine the implications on the QCD scaling parameter Λ and the gluon parameter n G .

We argue that lepton pair production from proton beams provides a good tool for the study of the sea of the target; it may supply a rather accurate measurement of the relative strength of the sea between heavy nuclei and free nucleons. As a consequence, it can be used for the discrimination between various theoretical explanations of the so-called EMC effect.

We use a simple and transparent method for the resolution of the modified Altarelli-Parisi equation (including soft gluon emission) in the non-singlet case. We point out some of the phenomenological consequences of this modification. In particular, we show that the QCD Λ mass scale has to be lowered by a factor of two.

The longitudinal and transverse properties of the QCD contribution to semi-inclusive deep inelastic scattering is worked out within the soft gluon resummation procedure. The Λ parameter needed to reproduce the data is in agreement with the value extracted from scaling violations. The intrinsic transverse momentum squared of a quark inside a proton is around 0.45 GeV2. Predictions for the transverse correlations 〈p1⊥·p2⊥〉 of two outgoing pions are guven.

We propose a way of testing scaling violations and subsidiarily soft gluons present in pp and π N induced reactions.

We compute the first order supersymmetric QCD correction to wino\((\tilde W)\) and zino\((\tilde Z)\) production in\(p\bar p\) collisions via subprocesses involving two massless partons inside the nucleon or one massless parton and a massive SUSY parton (squark or gluino). The first order SQCD corrections to the rapidity dependence at CERN collider and Tevatron energies are found large (K∼2). The rates are important (∼10−2 nb at\(\sqrt s = 630\) GeV and ∼10−1 nb at\(\sqrt s = 2\) TeV), as soon as the\((\tilde W)\) and\((\tilde Z)\) production by squarks is allowed. Transverse momentum distributions are also given and their shape is found very sensitive to the presence of SUSY partons inside the nucleon.