Linear Sigma Model Linkage with Nonperturbative QCD
Linkage is demonstrated between the quark mass, quark condensate and coupling strength in the infrared limit of QCD and in the quark-level linear sigma model.
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arXiv subjects
V. Elias
Publications and source records attributed to V. Elias.
QCD Sum Rules and the Pi(1300) Resonance
Global fits to the shape of the first QCD Laplace sum rule exhibiting sensitivity to pion-resonance [$Π(1300)$] parameters are performed, leading to predictions for the pion-resonance mass and decay constant. Two scenarios are considered which differ only in their treatment of the dimension-six quark condensate $< O_6>$. The first scenario assumes an effective scale for $< O_6>$ from other sum-rule applications which is assumed to be independent of the physical value of the quark mass, while the second scenario requires self-consistency between the value of $< O_6>$ and the current algebra constraint $2m< \bar q q>=-f_π^2m_π^2$. Predictions of the pion-resonance mass $M_π$ and decay constant $F_π$ are obtained in these two scenarios. A byproduct of this analysis is a prediction of the renormalization-group invariant quark mass $(\hat m_u+\hat m_d)/2$.
hep-ph↗
QCD Laplace Sum Rules and the $Π(1300)$ Resonance
A global fit to the shape of the first QCD Laplace sum rule exhibiting sensitivity to pion-resonance [$Π(1300)$] parameters is performed, leading to predictions for the pion-resonance mass and decay constant. This fit leads to predictions of $M_π = 1.15 \pm 0.15 GeV$ for the pion-resonance mass, and $F_π^2=(4.5\pm 2.1).(f_π^2m_π^4/M_π^4)$ for the pion-resonance decay constant.
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Beyond the Narrow Resonance Approximation: Decay Constant and Width of the First Pion-Excitation State
We consider the first pion excitation as a sub-continuum resonance in the pseudoscalar channel, and we obtain parameters characterizing this resonance through a global fit of the Borel-parameter dependence of the field-theoretical pseudoscalar Laplace sum rule to its hadronic (pion + pion-excitation + QCD-continuum) content. Our analysis incorporates finite-width deviations from the narrow resonance approximation, instanton effects, and higher-loop perturbative contributions to the pseudoscalar correlator. We obtain the following values (uncertainties reflect 90% confidence levels): mass $M_Π= 1.15 \pm 0.28 GeV$, width $Γ_Π= < 0.48 GeV$, decay constant $r \equiv [F_ΠM_Π^2 / f_πm_π^2]^2 = 4.7 \pm 2.8$.
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The Gross-Neveu Model and the Supersymmetric and Non-Supersymmetric Nambu-Jona-Lasinio Model in a Magnetic Field
The infrared dynamics in the (3+1)-dimensional supersymmetric and non-supersymmetric Nambu-Jona-Lasinio model in a constant magnetic field is studied. While at strong coupling the dynamics in these two models is essentially different, it is shown that the models become equivalent at weak coupling. In particular, at weak coupling, as the strength of the magnetic field goes to infinity, both the supersymmetric and non-supersymmetric Nambu-Jona-Lasinio models are reduced to a continuum set of independent (1+1)-dimensional Gross-Neveu models, labeled by the coordinates in the plane perpendicular to the magnetic field. The relevance of these results for cosmological models based on supersymmetric dynamics is pointed out.
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Effective Higgs-to-Light-Quark Coupling Induced by Heavy Quark Loops
We study the coupling arising via perturbative QCD of zero 4-momentum Higgs bosons to light quarks inside the nucleon. Qualitative comparison with the results obtained from one-loop-order low energy theorems for the Higgs-nucleon interaction suggests the existence of a dynamical light-quark mass which falls off with momentum. Quantitative comparison leads to an estimate of $α_s$ at very low $q^2$ quite near unity.
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Induced Light-Quark Yukawa Couplings as a probe of Low-Energy Dynamics in QCD
We examine the heavy-quark-induced Yukawa interaction between light quarks and a light Higgs field, which is facilitated in the chiral limit by the dynamical mass of light quarks anticipated from the chiral-noninvariance of the QCD vacuum. A low-energy estimate of the strong coupling near unity can be obtained from a comparison of the explicit perturbative calculation of the induced Yukawa interaction at zero momentum to a Higgs-low-energy theorem prediction for the same interaction.
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Massless Scalar Field Theory in a Quantised Space-Time
A method is developed to construct a non-local massless scalar field theory in a flat quantised space-time generated by an operator algebra. Implicit in the operator algebra is a fundamental length scale of the space-time. The fundamental two-point function of free fields is constructed by assuming that the causal Green functions still have support on the light cone in the operator algebra quantised space-time. In contrast to previous stochastic approaches, the method introduced here requires no explicit averaging over spacetime coordinates. The two- and four-point functions of~$g φ^4$ theory are calculated to the one-loop level, and no ultraviolet divergences are encountered. It is also demonstrated that there are no IR divergences in the processes considered.
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On-Mass-Shell Renormalization of the $\langle \bar{t}t \rangle$ Contribution to the $ΔI = 1/2$ $s \leftrightarrow d$ Self-Energy Transition
In $\langle \bar{t}t \rangle$-scenarios for dynamical electroweak symmetry breaking, the presence of a very large t-quark condensate necessarily generates an $s \leftrightarrow d$ self-energy transition which will contribute exclusively to $ΔI = 1/2$ strangeness-changing matrix elements. This contribution is calculated and compared to the purely perturbative contribution, which is well-known to be far too small to have an appreciable effect on $ΔI = 1/2$ strangeness-changing matrix elements after mass-shell renormalization subtractions are taken into account. The ratio between the t-quark condensate's contribution and the standard-model perturbative contribution to the mass-shell renormalized $s \leftrightarrow d$ self-energy transition is shown to be of order $\mid m_t \langle \bar{t} t \rangle \mid / M_W ^4$, suggesting that the large t-quark condensate proposed for electroweak symmetry breaking may also be responsible for the $Δ
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