QCD inequalities

Nussinov, S.; Lampert, Melissa A.

doi:10.1016/s0370-1573(01)00091-6

Cited by 82 publications

(70 citation statements)

References 179 publications

(340 reference statements)

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“…This can be seen directly from the Bohr formula. The results is in fact more general, as noticed by Bertlmann and Martin [140] and by Nussinov [141]: if a given two-body potential provides two constituent of masses m and m ′ with a ground-state energy E 2 (m, m ′ ), then…”

Section: A Lowest Thresholdsupporting

confidence: 56%

Stability of few-charge systems in quantum mechanics

2005

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We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the studies that have been made of specific mass configurations and also the properties of the domain of stability in the space of masses or inverse masses. These rigorous results are supplemented by numerical investigations using accurate variational methods. A section is devoted to systems of three arbitrary charges and another to molecules in a world with two space-dimensions.

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Section: A Lowest Thresholdsupporting

confidence: 56%

Stability of few-charge systems in quantum mechanics

2005

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“…In Table III we compare our model predictions for the mass spectrum of the B c meson with other quark model results [33][34][35][36]. We see that the differences between the predictions in most cases do not exceed 30 MeV.…”

Section: Heavy Quarkonium and B C Meson Mass Spectramentioning

confidence: 84%

Properties of heavy quarkonia andBcmesons in the relativistic quark model

2003

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The mass spectra and electromagnetic decay rates of charmonium, bottomonium and B c mesons are comprehensively investigated in the relativistic quark model. The presence of only heavy quarks allows the expansion in powers of their velocities. All relativistic corrections of order v 2 /c 2 , including retardation effects and one-loop radiative corrections, are systematically taken into account in the computations of the mass spectra. The obtained wave functions are used for the calculation of radiative magnetic dipole (M1) and electric dipole (E1) transitions. It is found that relativistic effects play a substantial role. Their account and the proper choice of the Lorentz structure of the quark-antiquark interaction in a meson is crucial for bringing theoretical predictions in accord with experimental data. A detailed comparison of the calculated decay rates and branching fractions with available experimental data for radiative decays of charmonium and bottomonium is presented. The possibilities to observe the currently missing spin-singlet S and P states as well as D states in bottomonium are discussed. The results for B c masses and decays are compared with other quark model predictions.

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“…and the difference m 2 η − m 2 π is positive (like the analogous one in QCD [37][38][39][40] for a review see [41]) provided that…”

Section: Chirally Broken Phasementioning

confidence: 88%

Chemical potentials and parity breaking: the Nambu–Jona-Lasinio model

2014

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We consider the 'two flavour' Nambu-JonaLasinio model in the presence of a vector and an axial external chemical potential and study the phase structure of the model at zero temperature. The Nambu-Jona-Lasinio model is often used as a toy replica of QCD and it is therefore interesting to explore the consequences of adding external vector and axial chemical potentials in this model, mostly motivated by claims that such external drivers could trigger a phase where parity could be broken in QCD. We are also motivated by some lattice analysis that attempt to understand the nature of the so-called Aoki phase using this simplified model. Analogies and differences with the expected behaviour in QCD are discussed and the limitations of the model are pointed out. MotivationIn the last years, the possibility that parity breaks in QCD at high temperatures and/or densities has received a lot of attention [1][2][3][4][5][6][7][8]. Although parity is well known to be a symmetry of strong interactions, there are reasons to believe that it may be broken under extreme conditions. On the one hand, theoretical work using effective meson Lagrangians satisfying the QCD symmetries at low energies suggest that for some values of the vector chemical potential μ a new phase with an isotriplet pseudoscalar condensate may arise [7,8]. On the other hand, thermal fluctuations in a finite volume may lead to large topological fluctuations that induce a non-trivial axial quark charge that could be described in a quasi-equilibrium situation by an axial chemical potential μ 5 [1][2][3][4][5][6][9][10][11][12][13].Checking these claims in QCD is unfortunately very difficult. For one thing, finite density numerical simulations in the lattice present serious difficulties [14][15][16][17][18][19]. A vector chemical potential in gauge theories like QCD cannot easily be a e-mail: xumeu@icc.ub.edu treated and therefore simpler models hopefully reproducing the main features of the theory may be useful. Needless to say, non-equilibrium effects are also notoriously difficult to study non-perturbatively. However, an axial chemical potential is tractable on the lattice [20,21] and with other methods [22,23].In the present paper we shall consider the Nambu-JonaLasinio model (NJL) [24][25][26][27][28][29][30], which shares interesting features with QCD such as the appearance of chiral symmetry breaking. In the NJL modelisation, QCD gluon interactions among fermions are assumed to be replaced by some effective four-fermion couplings. Confinement is absent in the NJL model, but global symmetries can be arranged to be identical in both theories.However, NJL is definitely not QCD and the present work does not attempt to draw definite conclusions on the latter theory; just to point out possible phases requiring further analysis.Previously some authors have studied the effect of a vector chemical potential μ with three flavours [31] in the NJL model, but the consequences of including both a vector and an axial chemical potentials have not been considered so...

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QCD inequalities

Abstract: We review the subject of QCD inequalities, using both a Hamiltonian variational approach, and a rigorous Euclidean path integral approach.PACS number(s): 12.35.Eq,12.70.+q Contents

Cited by 82 publications

References 179 publications

Stability of few-charge systems in quantum mechanics

Stability of few-charge systems in quantum mechanics

Properties of heavy quarkonia andBcmesons in the relativistic quark model

Chemical potentials and parity breaking: the Nambu–Jona-Lasinio model

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