Low-energy Hadron Phenomenology Research Articles

Constraints on the two-pion contribution to hadronic vacuum polarization

At low energies hadronic vacuum polarization (HVP) is strongly dominated by two-pion intermediate states, which are responsible for about $70\%$ of the HVP contribution to the anomalous magnetic moment of the muon, $a_\mu^\text{HVP}$. Lattice-QCD evaluations of the latter indicate that it might be larger than calculated dispersively on the basis of $e^+e^-\to\text{hadrons}$ data, at a level which would contest the long-standing discrepancy with the $a_\mu$ measurement. In this Letter we study to which extent this $2\pi$ contribution can be modified without, at the same time, producing a conflict elsewhere in low-energy hadron phenomenology. To this end we consider a dispersive representation of the $e^+e^- \to 2\pi$ process and study the correlations which thereby emerge between $a_\mu^\text{HVP}$, the hadronic running of the fine-structure constant, the $P$-wave $\pi\pi$ phase shift, and the charge radius of the pion. Inelastic effects play an important role, despite being constrained by the Eidelman-Lukaszuk bound. We identify scenarios in which $a_\mu^\text{HVP}$ can be altered substantially, driven by changes in the phase shift and/or the inelastic contribution, and illustrate the ensuing changes in the $e^+e^-\to 2\pi$ cross section. In the combined scenario, which minimizes the effect in the cross section, a uniform shift around $4\%$ is required. At the same time both the analytic continuation into the space-like region and the pion charge radius are affected at a level that could be probed in future lattice-QCD calculations.

Low energy hadron phenomenology

This talk discusses some of latest theoretical, phenomenological and experimental results is hadron spectroscopy.

HEAVY HADRON SPECTROSCOPY: A QUARK MODEL PERSPECTIVE

We present recent results of hadron spectroscopy and hadron–hadron interaction from the perspective of constituent quark models. We pay special attention to the role played by higher-order Fock space components in the hadron spectra and the connection of this extension with the hadron–hadron interaction. The main goal of our description is to obtain a coherent understanding of the low-energy hadron phenomenology without enforcing any particular model, to constrain its characteristics and learn about the low-energy realization of the theory.

Heavy hadron spectroscopy: A quark model perspective

Abstract We present recent results of hadron spectroscopy and hadron–hadron interaction from the perspective of constituent quark models. We pay special attention to the role played by higher order Fock space components in the hadron spectra and the connection of this extension with the hadron–hadron interaction. The main goal of our description is to obtain a coherent understanding of the low-energy hadron phenomenology without enforcing any particular model, to constrain its characteristics and learn about low-energy realization of the theory.

Quark-model study of the hadron structure and the hadron-hadron interaction

Recent results of hadron spectroscopy and hadron-hadron interaction within a quark model framework are reviewed. Higher order Fock space components are considered based on new experimental data on low-energy hadron phenomenology. The purpose of this study is to obtain a coherent description of the low-energy hadron phenomenology to constrain QCD phenomenological models and try to learn about low-energy realizations of the theory.

Dynamical study ofQQ–u¯d¯mesons

It has been recently conjectured by Selem and Wilczek 1 the existence of a ss-[ud] meson due to strong correlations between the two light antiquarks. We make a detailed study of this system within a dynamical quark model which has proven to be successful in reproducing the most important features of low-energy hadron phenomenology. Our results, obtained within a parameter-free calculation, show that the antidiquark component of the ssud system indeed entails the stronger attraction, and drives its energy much lower than the N{xi} threshold, but still above the K{sup 0}K*{sup -} or K*{sup 0}K{sup -} thresholds. We have also studied the ccud and bbud systems. Exotic mesons are only expected to exist in the limit of large mass for the two-quark subsystem, bbud, since the calculated mass is below the B{sup 0}B*{sup -} or B*{sup 0}B{sup -} thresholds.

Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with UA(1) Breaking

Low energy hadron phenomenology involving the (u,d,s) quarks is often ap- proached through effective multi-quark Lagrangians with the symmetries of QCD. A very successful approach consists in taking the four-quark Nambu-Jona-Lasinio Lagrangian with the chiral UL(3)◊UR(3) symmetry in the massless limit, combined with the UA(1) breaking six-quark flavour determinant interaction of 't Hooft. We review the present status and some very recent developments related to the functional integration over the cubic term in auxi- liary mesonic variables that one introduces to bosonize the system. Various approaches for handling this functional, which cannot be integrated exactly, are discussed: the stationary phase approximation, the perturbative expansion, the loop expansion, their interrelation and importance for the evaluation of the effective action. The intricate group structure rules out the method of Airy's integral. The problem of the instability of the vacuum is stated and a solution given by including eight-quark interactions.

Remarks on diquarks, strong binding, and a large hidden QCD scale

We present arguments regarding diquarks possible role in low-energy hadron phenomenology that escaped theorists' attention so far. Good diquarks, i.e. the $0^{+}$ states of two quarks, are argued to have a two-component structure with one of the components peaking at distances several times shorter than a typical hadron size (a short-range core). This can play a role in solving two old puzzles of the 't Hooft 1/N expansion: strong quark mass dependence of the vacuum energy density and strong violations of the Okubo-Zweig-Iizuka (OZI) rule in the quark-antiquark $0^\pm$ channels. In both cases empiric data defy 't Hooft's 1/N suppression. If good diquarks play a role at an intermediate energy scale they ruin 't Hoofts planarity because of their mixed-flavor composition. This new scale associated with the good diquarks may be related to a numerically large scale discovered in [V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B 191, 301 (1981)] in a number of phenomena mostly related to vacuum quantum numbers and $0^\pm$ glueball channels. If SU(3)$_{\rm color}$ of bona fide QCD is replaced by SU(2)$_{\rm color}$, diquarks become well-defined gauge invariant objects. Moreover, there is an exact symmetry relating them to pions. In this limit predictions regarding good diquarks are iron-clad. If passage from SU(2)$_{\rm color}$ to SU(3)$_{\rm color}$ does not lead to dramatic disturbances, these predictions remain qualitatively valid in bona fide QCD.

Spectral quark model and low-energy hadron phenomenology

We propose a spectral quark model which can be applied to low energy hadronic physics. The approach is based on a generalization of the Lehmann representation of the quark propagator. We work at the one-quark-loop level. Electromagnetic and chiral invariance are ensured with the help of the gauge technique which provides particular solutions to the Ward-Takahashi identities. General conditions on the quark spectral function follow from natural physical requirements. In particular, the function is normalized, its all positive moments must vanish, while the physical observables depend on negative moments and the so-called log moments. As a consequence, the model is made finite, dispersion relations hold, chiral anomalies are preserved, and the twist expansion is free from logarithmic scaling violations, as requested of a low-energy model. We study a variety of processes and show that the framework is very simple and practical. Finally, incorporating the idea of vector-meson dominance, we present an explicit construction of the quark spectral function which satisfies all the requirements. The corresponding momentum representation of the resulting quark propagator exhibits only cuts on the physical axis, with no poles present anywhere in the complex momentum space. The momentum-dependent quark mass compares very well with recent lattice calculations. A large number of predictions and relations, valid at the low-energy scale of the model, can be deduced from our approach for such quantities as the pion light-cone wave function, non-local quark condensate, pion transition form factor, pion valence parton distribution function, etc. These quantities, obtained at a low-energy scale of the model, have the correct properties, as requested by symmetries and anomalies. They also have pure twist expansion, free of logarithmic corrections, as requested by the QCD factorization property.

Contribution of Sigma Meson Pole to K_L-K_S mass Difference(§5. Low Energy Hadron Phenomenology and Chiral Symmetry,Possible Existence of the σ-Meson and Its Implications to Hadron Physics)

Contribution of Sigma Meson Pole to K_L-K_S mass Difference(§5. Low Energy Hadron Phenomenology and Chiral Symmetry,Possible Existence of the σ-Meson and Its Implications to Hadron Physics)

§5. Low Energy Hadron Phenomenology and Chiral Symmetry(divisional title)

§5. Low Energy Hadron Phenomenology and Chiral Symmetry(divisional title)

ε'/ε and Delta I=1/2 Rule in Nonlinear Sigma Model with Scalar Resonance(§5. Low Energy Hadron Phenomenology and Chiral Symmetry,Possible Existence of the σ-Meson and Its Implications to Hadron Physics)

ε'/ε and Delta I=1/2 Rule in Nonlinear Sigma Model with Scalar Resonance(§5. Low Energy Hadron Phenomenology and Chiral Symmetry,Possible Existence of the σ-Meson and Its Implications to Hadron Physics)

The σ Meson : a Necessity of Nature(§5. Low Energy Hadron Phenomenology and Chiral Symmetry,Possible Existence of the σ-Meson and Its Implications to Hadron Physics)

The σ Meson : a Necessity of Nature(§5. Low Energy Hadron Phenomenology and Chiral Symmetry,Possible Existence of the σ-Meson and Its Implications to Hadron Physics)

Quark Level Linear σ Model (LσM) via Loop Graphs(§5. Low Energy Hadron Phenomenology and Chiral Symmetry,Possible Existence of the σ-Meson and Its Implications to Hadron Physics)

Quark Level Linear σ Model (LσM) via Loop Graphs(§5. Low Energy Hadron Phenomenology and Chiral Symmetry,Possible Existence of the σ-Meson and Its Implications to Hadron Physics)

K → 2π Decay and Nonet Scalar Mesons in the Three-flavor NJL Model(§5. Low Energy Hadron Phenomenology and Chiral Symmetry,Possible Existence of the σ-Meson and Its Implications to Hadron Physics)

K → 2π Decay and Nonet Scalar Mesons in the Three-flavor NJL Model(§5. Low Energy Hadron Phenomenology and Chiral Symmetry,Possible Existence of the σ-Meson and Its Implications to Hadron Physics)

On the Renormalization of the Chiral Fermion Meson Model: An Algebraic Approach

We re-investigate the problem of the renormalizability of the chiral fermion meson model on the light of the regularization-independent algebraic method. The present letter is intended as a useful application of a modern technique in theory of current interest for the description of low energy hadron phenomenology. We show that the model is stable under radiative corrections and anomaly free in a regularization-free way without having to resort to the explicit calculation of Feynman diagrams.