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Michael D. Scadron

Publications and source records attributed to Michael D. Scadron.

17 recordsLinked to original sources
arXiv2013

The Quark-Level Linear σ Model

This review of the quark-level linear σmodel is based upon the dynamical realization of the pseudoscalar and scalar mesons as a linear representation of SU(2) x SU(2) chiral symmetry, with the symmetry weakly broken by current quark masses. In its simplest SU(2) incarnation, with two non-strange quark flavors and three colors, this nonperturbative theory, which can be selfconsistently bootstrapped in loop order, is shown to accurately reproduce a host of low-energy observables with only one parameter, namely the pion decay constant f_π. Extending the scheme to SU(3) by including the strange quark, equally good results are obtained for many strong, electromagnetic, and weak processes just with two extra constants, viz. f_K and $\langleπ|H_{\mbox{\scriptsize weak}}|K\rangle$. Links are made with the vector-meson-dominance model, the BCS theory of superconductivity, and chiral-symmetry restoration at high temperature. Finally, these ideas are cautiously generalized to the electroweak sector, including the W, Z, and Higgs bosons, and also to CP violation.

hep-ph↗
arXiv2013

Dispersion theory of nucleon Compton scattering and polarizabilities

A status report on the topic Compton scattering and polarizabilities is presented with emphasis on the scalar t-channel as entering into dispersion theory. Precise values for the polarizabilities are obtained leading to $α_p = 12.0\pm 0.6$ $(12.0)$, $β_p=1.9\mp 0.6$ $(1.9)$, $α_n= 12.5\pm 1.7$ $(13.4)$, $β_n= 2.7 \mp 1.8$ $(1.8)$ in units of $10^{-4}$ fm$^3$ and $γ^{(p)}_π= -36.4 \pm 1.5$ $(-36.6)$, $γ^{(n)}_π= 58.6 \pm 4.0$ $(58.3)$, $(γ^{(p)}_0= -0.58\pm 0.20)$, $(γ^{(n)}_0 = +0.38\pm 0.22)$ in units of $10^{-4}$ fm$^4$, for the proton (p) and neutron (n), respectively. The data given with an error are {\it recommended} experimental values with updates compared to [1] where necessary, the data in parentheses are predicted values. These predicted values are not contained in [1], but are the result of a newly developed analysis which is the main topic of the present paper. The most important recent discovery is that the largest part of the electric polarizability and the total diamagnetic polarizability of the nucleon are properties of the $σ$ meson as part of the constituent-quark structure, as expected from the mechanism of chiral symmetry breaking. This view is supported by an experiment on Compton scattering by the proton carried out in the second resonance region, where a large contribution from the $σ$ meson enters into the scattering amplitudes. This experiment led to a determination of the mass of the $σ$ meson of $m_σ= 600 \pm 70$ MeV. From the experimental $α_p$ and predicted differences $(α_n - α_p)$ neutron polarizabilities in the range $α_n= 12.0 - 13.4$ are predicted, where the uncertainties are related to the $f_0(980)$ and $a_0(980)$ scalar mesons.

hep-ph↗
arXiv2008

Comment on "Two-photon decay of the sigma meson"

We comment on a recent paper by Giacosa, Gutsche, and Lyobovitskij, in which it is argued that a quarkonium interpretation of the $σ$ meson should give rise to a much smaller two-photon decay width than commonly assumed. The reason for this claimed discrepancy is a term in the transition amplitude, necessary for gauge invariance, which allegedly is often omitted in the literature, including the work of the present authors. Here we show their claims to be incorrect by demonstrating, in the context of the Quark-Level Linear $σ$ Model, that the recently extracted experimental value $Γ_{σ\to2γ}=(4.1\pm0.3)$ keV is compatible with a $q\bar{q}$ assignment for the $σ$, provided that meson loops are taken into account as well.

hep-ph↗
arXiv2006

Pion and Kaon Masses and Pion Form Factors from Dynamical Chiral-Symmetry Breaking with Light Constituent Quarks

Light constituent quark masses and the corresponding dynamical quark masses are determined by data, the quark-level linear sigma model, and infrared QCD. This allows to define effective nonstrange and strange current quark masses, which reproduce the experimental pion and kaon masses very accurately, by simple additivity. In contrast, the usual nonstrange and strange current quarks employed by the Particle Data Group and Chiral Perturbation Theory do not allow a straightforward quantitative explanation of the pion and kaon masses.

hep-ph↗
arXiv2006

Small Strange Quark Content of Protons

The contribution of strange sea quarks to the proton mass and spin, as well as the related pion-nucleon sigma term, are briefly revisited, in the light of new experimental and lattice results. Also the predictions of chiral perturbation theory for these quantities are discussed.

hep-ph↗
arXiv2006

Pion Chiral Symmetry Breaking in the Quark-Level Linear Sigma Model and Chiral Perturbation Theory

Chiral symmetry breaking (ChSB) is reviewed to some extent within the quark-level-linear-sigma-model (QLL$σ$M) theory and standard chiral perturbation theory (ChPT). It is shown, on the basis of several examples related to the pion, as a well-known Goldstone boson of chiral symmetry breaking, that even the non-unitarized QLL$σ$M approach accounts, to a good approximation, for a rather simple, self-consistent, linear, and very predictive description of Nature. On the other hand, ChPT -- even when unitarized -- provides a highly distorted, nonlinear, hardly predictive picture of Nature, which fits experiment only at the price of a lot of parameters, and requires a great deal of unnecessary theoretical effort. As the origin of this distortion, we identify the fact that ChPT, reflecting only direct ChSB by nonvanishing, current-quark-mass values, does not -- contrary to Quantum Chromodynamics (QCD) and the QLL$σ$M -- contain any mechanism for the spontaneous generation of the dynamical component of the constituent quark mass. This leads to a very peculiar picture of Nature, since the strange current quark mass has to compensate for the absence of nonstrange dynamical quark masses. We thus conclude that standard ChPT -- contrary to common wisdom -- is unlikely to be the low-energy limit of QCD. On the contrary, a chiral perturbation theory derived from the QLL$σ$M, presumably being the true low-energy limit of QCD, is expected instead to provide a distortion-free description of Nature, which is based on the heavy standard-model Higgs boson as well as light scalar mesons, as the source of spontaneous generation of current and dynamical quark masses, respectively.

hep-ph↗
arXiv2005

Constituent quark-based linear $σ$ model (L$σ$M) quark and scalar mesons, vector meson dominance

After describing the SU(2) linear sigma model (L$σ$M), we dynamically generate it using the B.W. Lee null tadpole sum (characterizing the true vacuum) together with the dimensional regularization lemma. Next we generate the chiral-limiting (CL) nonstrange and strange constituent quark masses ${\hat m}=325.7$ MeV; $m_s=486$ MeV away from the CL. Finally, we study vector meson dominance (VMD) and the pion, kaon charge radii and the loop-order $ρ\toπγ$, $π^0\toγγ$ amplitudes in the quark model. Lastly, we verify this procedure using tree-order VMD graphs.

hep-ph↗
arXiv2004

CP Violation and $ΔI=1/2$ Enhancement for $K \to ππ$, $K \to ππγ$ Weak Decays

Data indicate that $ΔI=1/2$ transitions account for 4.5-4.7% of both CP conserving and CP violating $K \to 2π$ decays, as well as CP conserving radiative $K \to ππγ$ processes. Observed $K \to ππγ/ππ$ branching ratios are shown to scale near $α/π$ or $α/2π$. The $K_L$-$K_S$ mixing angle $ϕ$ and the semileptonic weak-rate asymmetry $δ$ are reviewed, and theory is shown to be consistent with data. Also, $K \to 2π$ $ΔI=1/2$ dominance is studied in the context of the chiral constituent quark model, displaying again excellent agreement with data. Finally, indirect and direct kaon CP violation are successfully described in the framework of photon-mediated loop graphs. This suggests that kaon CPV can be understood via second-order weak transitions, radiatively corrected.

hep-ph↗
arXiv2003

Ground-State Scalar $\bar{q}q$ Nonet: SU(3) Mass Splittings and Strong, Electromagnetic, and Weak Decay Rates

By comparing SU(3)-breaking scales of linear mass formulae, it is shown that the lowest vector and scalar mesons all have a $\bar{q}q$ configuration, while the ground-state octet and decuplet baryons are $qqq$. Also, the quark-level linear $σ$ model is employed to predict similar $\bar{q}q$ and $qqq$ states. Furthermore, the approximate mass degeneracy of the scalar $a_0$(985) and $f_0$(980) mesons is demonstrated to be accidental. Finally, it is shown that various strong, electromagnetic, and weak mesonic decay rates are successfully explained within the framework of the quark-level linear $σ$ model.

hep-ph↗
arXiv2002

Meson Form Factors and the Quark-Level Linear Sigma Model

The quark-level linear sigma model is employed to compute a variety of electromagnetic and weak observables of light mesons, including pion and kaon form factors and charge radii, charged-pion polarizabilities, semileptonic weak $K_{\ell3}$ decay, semileptonic weak radiative pion and kaon form factors, radiative decays of vector mesons, and nonleptonic weak $K_{2π}$ decay. The agreement of all these predicted observables with experiment is striking. In passing, the tight link between the linear sigma model and vector-meson dominance is shown. Some conclusions are drawn on the linear sigma model in connection with lattice and renormalization-group approaches to QCD.

hep-ph↗
arXiv2002

Remarks on the f_0(400-1200) scalar meson as the dynamically generated chiral partner of the pion

The quark-level linear sigma model is revisited, in particular concerning the identification of the f_0(400-1200) (or σ(600)) scalar meson as the chiral partner of the pion. We demonstrate the predictive power of the linear sigma model through the pi-pi and pi-N s-wave scattering lengths, as well as several electromagnetic, weak, and strong decays of pseudoscalar and vector mesons. The ease with which the data for these observables are reproduced in the linear sigma model lends credit to the necessity to include the sigma as a fundamental q\bar{q} degree of freedom, to be contrasted with approaches like chiral perturbation theory or the confining NJL model of Shakin and Wang.

hep-ph↗
arXiv2001

Comment on Intrinsic and dynamically generated scalar meson states

The scalar-meson assignments of Shakin and Wang in a generalized Nambu--Jona-Lasinio model are contradicted by recent experimental information. Also the strict distinction made by these authors between ``intrinsic'' and ``dynamically generated'' states is contested, as well as a number of other statements.

hep-ph↗
arXiv2001

Identifying the quark content of the isoscalar scalar mesons f_0(980), f_0(1370), and f_0(1500) from weak and electromagnetic processes

The assignments of the isoscalar scalar mesons f0(980), f0(1370), and f0(1500) in terms of their qqbar substructure is still a matter of heated dispute. Here we employ the weak and electromagnetic decays D(s)(+) to f0+pi(+) and f0 two-photon decays, respectively, to identify the f0(980) and f0(1500) as mostly ssbar, and the f0(1370) as dominantly nonstrange, in agreement with previous work. The two-photon decays can be satisfactorily described with quark as well as with meson loops, though the latter ones provide a less model-dependent and more quantitative description.

hep-ph↗
arXiv2001

Why the f(0)(980) is mostly ssbar

We exploit the W-emission process to study the measured weak decay of the D(s,+)(1.9686) meson into f(0)(980) and a positively charged pion. We conclude that the scalar f(0)(980) meson contains mostly strange-antistrange flavors, which is supported by different model studies.

hep-ph↗
arXiv2001

Dynamical SU(3) linear sigma model and the mixing of eta'-eta and sigma-f_0 mesons

The SU(3) linear sigma model is dynamically generated in loop-order using the nonstrange-strange basis. Only self-consistent logarithmic divergent graphs are needed, with quadratic divergent graphs replaced by SU(3) mass-shell equal splitting laws. The latter lead to an eta'-eta mixing angle of 41.84 deg which is consistent with phenomenology. Finally this above SU(3) linear sigma model in turn predicts strong decay rates which are all compatible with data.

hep-ph↗
arXiv2000

On the eta-eta' complex in the SD-BS approach

The bound-state Schwinger-Dyson and Bethe-Salpeter (SD-BS) approach is chirally well-behaved and provides a reliable treatment of the eta-eta' complex although a ladder approximation is employed. Allowing for the effects of the SU(3) flavor symmetry breaking in the quark-antiquark annihilation, leads to the improved eta-eta' mass matrix.

hep-ph↗