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H. J. Pirner

Publications and source records attributed to H. J. Pirner.

At least 55 records · Page 3Linked to original sources
arXiv2005

Volume Dependence of the Pion Mass from Renormalization Group Flows

We investigate finite volume effects on the pion mass and the pion decay constant with renormalization group (RG) methods in the framework of a phenomenological model for QCD. An understanding of such effects is important in order to interpret results from lattice QCD and extrapolate reliably from finite lattice volumes to infinite volume. We consider the quark-meson-model in a finite Euclidean 3+1 dimensional volume. In order to break chiral symmetry in the finite volume, we introduce a small current quark mass. In the corresponding effective potential for the meson fields, the chiral O(4)-symmetry is broken explicitly, and the sigma and pion fields are treated individually. Using the proper-time renormalization group, we derive renormalization group flow equations in the finite volume and solve these equations in the approximation of a constant expectation value. We calculate the volume dependence of pion mass and pion decay constant and compare our results with recent results from chiral perturbation theory in finite volume.

hep-ph↗
arXiv2004

Vacuum Expectation Value of a Wegner-Wilson Loop near the Light Cone

Vacuum expectation values for one Wegner-Wilson loop representing a moving quark-antiquark pair are calculated in four-dimensional Euclidean and Minkowski space-time. The calculation uses gluon field strength correlators with perturbative gluon exchange and non-perturbative correlations from the stochastic vacuum model. The expectation value of a Wegner-Wilson loop forming a hyperbolic angle in Minkowski space-time is connected by an analytical continuation to the expectation value of the Wegner-Wilson loop in Euclidean four-space. The obtained result shows how confinement enters into the light-cone Hamiltonian for valence quarks independently of the chosen model.

hep-ph↗
arXiv2003

Particle Production and Propagation in Nuclei

We discuss the effects of gluon radiation by the struck quark and the subsequent absorption of the produced hadron in deep inelastic lepton-nucleus scattering. The theoretical picture is compared with HERMES results on multiplicity ratios.

hep-ph↗
arXiv2003

Confining QCD Strings, Casimir Scaling, and a Euclidean Approach to High-Energy Scattering

We compute the chromo-field distributions of static color-dipoles in the fundamental and adjoint representation of SU(Nc) in the loop-loop correlation model and find Casimir scaling in agreement with recent lattice results. Our model combines perturbative gluon exchange with the non-perturbative stochastic vacuum model which leads to confinement of the color-charges in the dipole via a string of color-fields. We compute the energy stored in the confining string and use low-energy theorems to show consistency with the static quark-antiquark potential. We generalize Meggiolaro's analytic continuation from parton-parton to gauge-invariant dipole-dipole scattering and obtain a Euclidean approach to high-energy scattering that allows us in principle to calculate S-matrix elements directly in lattice simulations of QCD. We apply this approach and compute the S-matrix element for high-energy dipole-dipole scattering with the presented Euclidean loop-loop correlation model. The result confirms the analytic continuation of the gluon field strength correlator used in all earlier applications of the stochastic vacuum model to high-energy scattering.

hep-ph↗
arXiv2002

Evolving QCD

We give an overview of the current theoretical status of proper time renormalization group flow equations applied to QCD. These equations give the evolution of coupling constants in an effective QCD Lagrangian as a function of an infra-red cut-off parameter. This parameter characterizes the resolution with which the system is looked at. Decreasing resolution transforms partonic quarks into constituent quarks and generates pion bound states. The evolution equations can also be applied to finite temperature and finite density QCD.

hep-ph↗
arXiv2002

Decomposition of the QCD String into Dipoles and Unintegrated Gluon Distributions

We present the perturbative and non-perturbative QCD structure of the dipole-dipole scattering amplitude in momentum space. The perturbative contribution is described by two-gluon exchange and the non-perturbative contribution by the stochastic vacuum model which leads to confinement of the quark and antiquark in the dipole via a string of color fields. This QCD string gives important non-perturbative contributions to high-energy reactions. A new structure different from the perturbative dipole factors is found in the string-string scattering amplitude. The string can be represented as an integral over stringless dipoles with a given dipole number density. This decomposition of the QCD string into dipoles allows us to calculate the unintegrated gluon distribution of hadrons and photons from the dipole-hadron and dipole-photon cross section via kT-factorization.

hep-ph↗
arXiv2002

S-Matrix Unitarity, Impact Parameter Profiles, Gluon Saturation and High-Energy Scattering

A model combining perturbative and non-perturbative QCD is developed to compute high-energy reactions of hadrons and photons and to investigate saturation effects that manifest the S-matrix unitarity. Following a functional integral approach, the S-matrix factorizes into light-cone wave functions and the universal amplitude for the scattering of two color-dipoles which are represented by Wegner-Wilson loops. In the framework of the non-perturbative stochastic vacuum model of QCD supplemented by perturbative gluon exchange, the loop-loop correlation is calculated and related to lattice QCD investigations. With a universal energy dependence motivated by the two-pomeron (soft + hard) picture that respects the unitarity condition in impact parameter space, a unified description of pp, pip, Kp, gamma* p, and gamma gamma reactions is achieved in good agreement with experimental data for cross sections, slope parameters, and structure functions. Impact parameter profiles for pp and longitudinal gamma* p reactions and the gluon distribution of the proton xG(x,Q^2,b) are calculated and found to saturate in accordance with S-matrix unitarity. The c.m. energies and Bjorken x at which saturation sets in are determined.

hep-ph↗
arXiv2002

Gluon Saturation and S-Matrix Unitarity

The impact parameter dependent gluon distribution of the proton xG(x,Q^2,b) is investigated in a loop-loop correlation model that respects the S-matrix unitarity condition in impact parameter space. We find low-x saturation of G(x,Q^2,b) as a manifestation of S-matrix unitarity. The integrated gluon distribution xG(x,Q^2) does not saturate because of the growth of the effective proton radius with decreasing x.

hep-ph↗
arXiv2000

Target Fragmentation in $pp$, $ep$ and $γp$ Collisions at High Energies

We calculate target fragmentation in $p p \to n X$ and $γp \to n X $ reactions in the meson cloud picture of the nucleon. The $p p \to n X$ reaction is used to fix the $pnπ^+$ form factor for three different models. We take into account the possible destruction of the residual neutron by the projectile. Using the form factor from the hadronic reaction we calculate photoproduction and small $x_{Bj}$ electroproduction of forward neutrons at HERA. Here the $q \bar q$ dipoles in the photon can rescatter on the residual neutron. In photoproduction we observe slightly less absorption than in the hadronic reaction. For deep inelastic events ($Q^2>10$ GeV$^2$) screening is weaker but still present at large $Q^2$. The signature for this absorptive rescattering is a shift of the $dσ/dE_n$ distribution to higher neutron energies for photofragmentation.

hep-ph↗
arXiv1999

The Semiclassical Gluon Distribution at Next-to-Leading Order

The interaction of the partonic fluctuation of the virtual photon in deep inelastic scattering with soft color fields describing the hadron is treated in an eikonal approximation. It is known that, in this approach, the small-x limit of the leading-order gluon distribution xg(x,Q^2) is a constant characterizing the averaged local field strength in the target. Matching the next-to-leading order calculation in this semiclassical framework with the one-loop parton model result, we obtain the next-to-leading order contribution to xg(x,Q^2). It shows a ln(1/x) enhancement at small x and is sensitive to the large distance structure of the target. The final expression is a simple integral over non-Abelian eikonal factors measuring the target color field. We derive a quantitative relation between the short-distance cutoff of this integral and the scale of the gluon distribution function in the MS-bar scheme. Our calculation demonstrates that higher order contributions can be systematically included in the semiclassical approach.

hep-ph↗
arXiv1999

Soft and Hard Pomeron in the Structure Function of the Proton at Low x and Low Q^2

We study inclusive electroproduction on the proton at low $x$ and low $Q^2$ using a soft and a hard Pomeron. The contribution of the soft Pomeron is based on the Stochastic Vacuum Model, in which a nonperturbative dipole-dipole cross section can be calculated by means of a gauge invariant gluon field strength correlator. To model the hard Pomeron exchange we phenomenologically extend the leading order evolution of a power-behaved structure function, $F_2 \propto x^{- λ}$, proposed by López and Ynduráin. This extension allows to consider both the case $Q^2 = 0$ and the region of higher $Q^2$ on the basis of the same parametrization. A good simultaneous fit to the data on $F_2$ and on the cross section $σ_{γp}$ of real photoproduction is obtained for $λ=0.37$. With four parameters we achieve a $χ^2/\textrm{d.o.f.} = 0.98$ for 222 data points. In addition, we use our model of the inclusive $γ^{\ast} p$ interaction to compute the longitudinal structure function $F_L$.

hep-ph↗
arXiv1998

Diffractive photo- and leptoproduction of vector mesons $ρ$, $ρ'$ and $ρ''$

We calculate diffractive photo- and leptoproduction of $ρ$-, $ρ'$- and $ρ''$-mesons. The incoming photon dissociates into a $q\bar{q}$-dipole which scatters on the nucleon and transforms into a vector meson state. The scattering amplitude is calculated in non-perturbative QCD with the model of the stochastic vacuum. Assuming that the physical $ρ'$- and $ρ''$-mesons are mixed states of an active 2S-excitation and some residual hybrid state which cannot be produced diffractively in lowest order QCD, we obtain good agreement with the data, especially the markedly different spectrum in the $π^+π^-$-invariant mass for photoproduction and $e^+e^-$-annihilation.

hep-ph↗
arXiv1998

Hamiltonian Flow Equations for the Lipkin Model

We derive Hamiltonian flow equations giving the evolution of the Lipkin Hamiltonian to a diagonal form using continuous unitary transformations. To close the system of flow equations, we present two different schemes. First we linearize an operator with three pairs of creation and destruction operators by reducing it to the $z$ component of the quasi spin. We obtain the well known RPA-result in the limit of large particle number. In the second scheme we introduce a new operator which improves the resulting spectrum considerably especially for few particles.

nucl-th↗
arXiv1998

Non-Perturbative Hamiltonian Approaches To Strong Interaction Physics

The theory of the strong interactions, Quantum Chromodynamics (QCD), has been addressed by a variety of non-perturbative techniques over the decades since its introduction. We have investigated Hamiltonian formulations with different quantization methods and approximation schemes. In one method, we utilize light-front coordinates to investigate the role of bosonic zero modes in leading to confinement. In another method we are able to obtain spectra for the mesons and baryons using constituent quark masses but no phenomenological confinement. We survey our principal accomplishments to date and indicate our future directions.

hep-th↗
arXiv1997

Nonperturbative Flow Equations with Heat-Kernel Methods at finite Temperature

We derive nonperturbative flow equations within an effective constituent quark model for two quark flavors. Heat-kernel methods are employed for a renormalization group improved effective potential. We study the evolution of the effective potential with respect to an infrared cutoff scale $k$ at vanishing temperature. At the first stage we omit corrections coming from the anomalous dimension. This investigation is extrapolated to finite temperature, where we find a second order phase transition in the chiral limit at $T_c \approx 130$ MeV. Due to a smooth decoupling of massive modes, we can directly link the low-temperature four-dimensional theory to the three-dimensional high-temperature theory and can determine universal critical exponents.

hep-ph↗