Meson Fields Research Articles

Absence of binding in the Nelson and piezoelectric polaron models

In the context of the massless Nelson model, we prove that two non-relativistic nucleons interacting with a massless meson field do not bind when a sufficiently strong Coulomb repulsion between the nucleons is added to the Hamiltonian. The result holds for both the renormalized and unrenormalized theories, and can also be applied to the so-called piezoelectric polaron model, which describes an electron interacting with the acoustical vibrational modes of a crystal through the piezoelectric interaction. The result can then be interpreted as well as a no-binding statement about piezoelectric bipolarons. The methods used allow also for a significant reduction of about 30% over previously known no-binding conditions for the optical bipolaron model of H. Fröhlich.

Holographic description of heavy-flavored baryonic matter decay involving glueball

We holographically investigate the decay of heavy-flavoured baryonic hadron involving glueball by using the Witten-Sakai-Sugimoto model. Since baryon in this model is recognized as the D4-brane wrapped on $S^{4}$ and the glueball field is identified as the bulk gravitational fluctuations, the interaction of the bulk graviton and the baryon brane could be naturally interpreted as glueball-baryon interaction through the holography which is nothing but the close-open string interaction in string theory. In order to take account into the heavy flavour, an extra pair of heavy-flavoured branes separated from the other flavour branes with a heavy-light open string is embedded into the bulk. Due to the finite separation of the flavour branes, the heavy-light string creates massive multiplets which could be identified as the heavy-light meson fields in this model. As the baryon brane on the other hand could be equivalently described by the instanton configuration on the flavour brane, we solve the equations of motion for the heavy-light fields with the Belavin-Polyakov-Schwarz-Tyupkin (BPST) instanton solution for the $N_{f}=2$ flavoured gauge fields. Then with the solutions, we evaluate the soliton mass by deriving the flavoured onshell action in strongly coupling limit and heavy quark limit. After the collectivization and quantization, the quantum mechanical system for glueball and heavy-flavoured baryon is obtained in which the effective Hamiltonian is time-dependent. Finally we use the standard technique for the time-dependent quantum mechanical system to analyze the decay of heavy-flavoured baryon involving glueball and we find one of the decay process might correspond to the decay of baryonic B-meson involving the glueball candidate $f_{0}\left(1710\right)$. This work is a holographic approach to study the decay of heavy-flavoured hadron in nuclear physics.

Comment on scalar glueball mass

We study the interaction of scalar glueball with quark–antiquark and four-quark spinless meson fields within the framework of a generalized linear sigma model in which the trace anomaly of QCD is exactly realized. To determine the pure scalar glueball mass (mh), we consider the decoupling limit in which the scalar glueball decouples from the meson fields. We find the exact relationship mh=2h0 where h0 is the vacuum expectation value of the scalar glueball field independent of the properties of the framework used.

Analysis of Dalitz decays with intrinsic parity-violating interactions in resonance chiral perturbation theory

Observables of light hadron decays are analyzed in a model of chiral Lagrangian which includes resonance fields of vector mesons. In particular, transition form factors are investigated for Dalitz decays of $V\to Pl^+l^-$ and $P\to \gamma l^+l^-$ $(V=1^-, P=0^-)$. Moreover, the differential decay width of $P\to \pi^+\pi^-\gamma$ and the partial widths of $P\to2\gamma, V\to P\gamma, \eta^\prime\to V\gamma, \phi(1020)\to\omega(782)\pi^0$ and $V\to 3P$ are also calculated. In this study, we consider a model which contains octet and singlet fields as representation of $SU(3)$. As an extension of chiral perturbation theory, we include 1-loop ordered interaction terms. For both pseudoscalar and vector meson, we evaluate mixing matrices in which isospin/$SU(3)$ breaking is taken into account. Furthermore, intrinsic parity violating interactions are considered with singlet fields. For parameter estimation, we carry out $\chi^2$ fittings in which a spectral function of $\tau$ decays, vector meson masses, decay widths of $V\to P\gamma$ and transition form factor of $V\to Pl^+l^-$ are utilized as input data. Using the estimated parameter region in the model, we give predictions for decay widths and transition form factors of intrinsic parity violating decays. As further model predictions, we calculate the transition form factors of $\phi(1020)\to \pi^0l^+l^-$ and $\eta^\prime\to\gamma l^+l^-$ in the vicinity of resonance regions, taking account of the contribution for intermediate $\rho(770)$ and $\omega(782)$.

Study of the theta dependence of the vacuum energy density in chiral effective Lagrangian models at zero temperature

We perform a systematic study of the modifications to the QCD vacuum energy density ${\ensuremath{\epsilon}}_{\mathrm{vac}}$ in the zero-temperature case ($T=0$) caused by a small, but nonzero, value of the parameter $\ensuremath{\theta}$, using different effective Lagrangian models which include the flavor-singlet meson field and implement the $U(1)$ axial anomaly of the fundamental theory. In particular, we derive the expressions for the topological susceptibility $\ensuremath{\chi}$ and for the second cumulant ${c}_{4}$ starting from the $\ensuremath{\theta}$ dependence of ${\ensuremath{\epsilon}}_{\mathrm{vac}}(\ensuremath{\theta})$ in the various models that we have considered. Moreover, we evaluate numerically our results, so as to compare them with each other, with the predictions of the chiral effective Lagrangian and, finally, also with the available lattice data.

Lagrange-Mesh Method for Deformed Nuclei With Relativistic Energy Density Functionals

The application of relativistic energy density functionals to the description of nuclei leads to the problem of solving self-consistently a coupled set of equations of motion to determine the nucleon wave functions and meson fields. In this work the Lagrange-mesh method in spherical coordinates is proposed for the numerical calculation. The essential field equations are derived from the relativistic energy density functional and the basic principles of the Lagrange-mesh method are delineated for this particular application. The numerical accuracy is studied for the case of a deformed relativistic harmonic oscillator potential with axial symmetry. Then the method is applied to determine the point matter distributions and deformation parameters of self-conjugate even-even nuclei from 4He to 40Ca.

Morbidity of Pediatric Obstructive Sleep Apnea in Children: Myth, Reality, or Hidden Iceberg?

We study the interaction of scalar glueball with quark–antiquark and four-quark spinless meson fields within the framework of a generalized linear sigma model in which the trace anomaly of QCD is exactly realized. To determine the pure scalar glueball mass (mh), we consider the decoupling limit in which the scalar glueball decouples from the meson fields. We find the exact relationship mh=2h0 where h0 is the vacuum expectation value of the scalar glueball field independent of the properties of the framework used.

A Dark Energy Model in the Presence of Scalar Meson Fields in General Relativity

A Dark Energy Model in the Presence of Scalar Meson Fields in General Relativity

Meson properties in magnetized quark matter

We study neutral and charged meson properties in magnetic field. Taking bosolization method in a two-flavor Nambu--Jona-Lasinio model, we derive effective meson Lagrangian density with minimal coupling to the magnetic field, by employing derivative expansion for both the meson fields and Schwinger phases. We extract from the effective Lagrangian density the meson curvature, pole and screening masses. As the only Goldstone mode, the neutral pion controls the thermodynamics of the system and propagates the lang range quark interaction. The magnetic field breaks down the space symmetry, and the quark interaction region changes from a sphere in vacuum to a ellipsoid in magnetic field.

Massive neutron star with strangeness in a relativistic mean-field model with a high-density cutoff

The properties of strangeness neutron star are studied within relativistic mean-field (RMF) model via including a logarithmic interaction as a function of scalar meson field. This logarithmic interaction, named as the $\sigma$-cut potential, can largely reduce the attractive contributions of scalar meson field at high density without any influence on nuclear structure around normal saturation density. In this work, the TM1 parameter set is chosen as the RMF interaction, while the strengths of logarithmic interaction are constrained by the properties of finite nuclei so that we can obtain a reasonable effective nucleon-nucleon interaction. The hyperons, $\Lambda,~\Sigma$, and $\Xi$ are also considered in neutron stars within this framework, whose coupling constants with mesons are determined by the latest hyperon-nucleon and $\Lambda$-$\Lambda$ potentials extracted from the experimental data of hypernuclei. The maximum mass of neutron star can be larger than two solar mass with these hyperons. Furthermore, the nucleon mass at high density will be saturated due to this additional $\sigma$-cut potential, which is consistent with the conclusions from the microscopic calculations such as, Brueckner-Hartree-Fock theory and quark mean-field model.

Many-body Forces in Magnetic Neutron Stars

Abstract In this work, we study in detail the effects of many-body forces on the equation of state and the structure of magnetic neutron stars. The stellar matter is described within a relativistic mean field formalism that takes into account many-body forces by means of a nonlinear meson field dependence on the nuclear interaction coupling constants. We assume that matter is at zero temperature, charge neutral, in beta equilibrium, and populated by the baryon octet, electrons, and muons. In order to study the effects of different degrees of stiffness in the equation of state, we explore the parameter space of the model, which reproduces nuclear matter properties at saturation, as well as massive neutron stars. Magnetic field effects are introduced both in the equation of state and in the macroscopic structure of stars by the self-consistent solution of the Einstein–Maxwell equations. In addition, the effects of poloidal magnetic fields on the global properties of stars, as well as density and magnetic field profiles, are investigated. We find that not only different macroscopic magnetic field distributions but also different parameterizations of the model for a fixed magnetic field distribution impact the gravitational mass, deformation, and internal density profiles of stars. Finally, we show that strong magnetic fields significantly affect the particle populations of stars.

Kerson Huang

Kerson Huang, a professor emeritus at MIT who was best known for his contributions to statistical physics, died of cancer on 1 September 2016 in Danvers, Massachusetts. Kerson Huang NANYANG TECHNOLOGICAL UNIVERSITYPPT|High resolutionHuang was born on 15 March 1928 in Nanning, Guangxi Province, China. After the Japanese invaded in 1937, he and his family moved to Manila, the Philippines. Following the end of World War II, he went to the US, where he obtained his BS in 1950 and his PhD in 1953, both in physics and both from MIT. His earliest research was on the zitterbewegung (“trembling motion”) of the Dirac electron. Victor Weisskopf was his thesis adviser, but Huang worked more closely with Sidney Drell on meson field theory. He learned the pseudopotential method from Weisskopf and applied it to the study of the quantum mechanical problem of hard spheres.In the fall of 1955, Huang went to the Institute for Advanced Study in Princeton, New Jersey, for his postdoc and introduced to Chen Ning Yang the pseudopotential method. Together with Tsung-Dao Lee, they collaborated on the problem of dilute hard-sphere bosons and demonstrated the superfluidity of dilute Bose gases due to Bose–Einstein condensation. Huang presented that work at the institute to an audience that included Eugene Wigner, Freeman Dyson, J. Robert Oppenheimer, and Wolfgang Pauli. Pauli slept during the seminar and only woke up to comment that he did not like the pseudopotential because it is not Hermitian. However, he said later that Huang’s work was nicht dumm (“not dumb”). Fifty years later the work was confirmed by experiments on Bose– Einstein condensation in alkali gases.Huang returned to MIT in 1957 as an assistant professor and continued his studies in both many-body problems and particle physics. Ranging from high-energy to low-temperature physics, his research covered numerous topics, including pion decay, muon capture, high-energy scattering, bootstrap solutions, and imperfect Fermi and Bose gases. MIT mathematician John Nash frequently engaged Huang in discussions about the fundamentals and philosophy of quantum mechanics.In the 1960s and 1970s, Huang worked on the dual resonance model. During a weekend vacation at his log cabin in New Hampshire in 1970 with colleague Steven Weinberg, Huang mentioned the concept of ultimate temperature, above which adding energy to a system only produces particles instead of raising the system’s temperature. Weinberg immediately realized its importance in the early universe. They spent the weekend doing calculations, and soon after they published an influential article on the subject.Huang made many substantial contributions during the development of the standard model in particle physics. By considering the possibility of asymptotic freedom in scalar field theories, he challenged the common perception that only non-abelian gauge theories are asymptotically free. He and his student Kenneth Halpern showed that some scalar theories could become asymptotically free provided that what’s now known as the Halpern–Huang potential is used to describe the interaction.Huang also devoted great effort to physics education. He wrote eight physics books, including Statistical Mechanics (Wiley, 1963; 2nd edition, 1987), Introduction to Statistical Physics (Taylor & Francis, 2001), and Quantum Field Theory: From Operators to Path Integrals (Wiley, 1998; 2nd edition, 2010), which continue to be widely used as textbooks and references.Huang became a professor emeritus in 1999 and remained with the Center for Theoretical Physics at MIT until 2005. He then became a visiting professor at Tsinghua University in China and at Nanyang Technological University in Singapore. His interests shifted to biophysics and quantum cosmology. Huang proposed a conditioned self-avoiding walk model and wrote a MATLAB program to study the problem of protein folding. In quantum cosmology, he proposed a superfluid-universe scenario for inflation, matter creation, dark matter, and dark energy. He also suggested using a vortex boundary layer, now known as the Kerson layer, to solve the matching problem in the gravitational collapse of rotating black holes. Of his more than 100 research articles, about one-fifth were written in his last decade.Besides his physics accomplishments, Huang was famous for his translations, in particular The Rubaiyat of Omar Khayyam: A Rendition in Classical Chinese Quatrains and I Ching, the Oracle. He also wrote many English and Chinese poems and published several books of original poetry; people in the poetry community referred to Huang as “a poet [who] also did physics research.”© 2017 American Institute of Physics.

Baryon number fluctuations in chiral effective models and their phenomenological implications

We study the critical properties of net-baryon-number fluctuations at the chiral restoration transition in a medium at finite temperature and net baryon density. The chiral dynamics of quantum chromodynamics (QCD) is modeled by the Polykov-loop extended Quark-Meson Lagrangian, that includes the coupling of quarks to vector meson and temporal gauge fields. The Functional Renormalization Group is employed to properly account for the $O(4)$ criticality at the phase boundary. We focus on the properties and systematics of ratios of the net-baryon-number cumulants $\chi_B^n$, for ${1\leq n\leq 6}$, near the phase boundary. The results are presented in the context of the recent experimental data of the STAR Collaboration on fluctuations of the net proton number in heavy ion collisions at RHIC. We show that the model results for the energy dependence of the cumulant ratios are in good overall agreement with the data, with one exception. At center-of-mass energies below ${19.6\;\mathrm{GeV}}$, we find that the measured fourth-order cumulant deviates considerably from the model results, which incorporate the expected $O(4)$ and $Z(2)$ criticality. We assess the influence of model assumptions and in particular of repulsive vector-interactions, which are used to modify the location of the critical endpoint in the model, on the cumulants ratios. Finally, we discuss a possibility to test to what extent the fluctuations are affected by nonequilibrium dynamics by comparing certain ratios of cumulants.

Derivation of the effective chiral Lagrangian for pseudoscalar, scalar, vector, and axial-vector mesons from QCD

A previous formal derivation of the effective chiral Lagrangian for low-lying pseudoscalar mesons from first-principles QCD without approximations [Wang et al., Phys. Rev. D61, (2000) 54011] is generalized to further include scalar, vector, and axial-vector mesons. In the large Nc limit and with an Abelian approximation, we show that the properties of the newly added mesons in our formalism are determined by the corresponding underlying fundamental homogeneous Bethe--Salpeter equation in the ladder approximation, which yields the equations of motion for the scalar, vector, and axial-vector meson fields at the level of an effective chiral Lagrangian. The masses appearing in the equations of motion of the meson fields are those determined by the corresponding Bethe--Salpeter equation.

Neutron Electric Dipole Moment from Gauge-String Duality.

We compute the electric dipole moment of nucleons in the large N_{c} QCD model by Witten, Sakai, and Sugimoto with N_{f}=2 degenerate massive flavors. Baryons in the model are instantonic solitons of an effective five-dimensional action describing the whole tower of mesonic fields. We find that the dipole electromagnetic form factor of the nucleons, induced by a finite topological θ angle, exhibits complete vector meson dominance. We are able to evaluate the contribution of each vector meson to the final result-a small number of modes are relevant to obtain an accurate estimate. Extrapolating the model parameters to real QCD data, the neutron electric dipole moment is evaluated to be d_{n}=1.8×10^{-16}θ e cm. The electric dipole moment of the proton is exactly the opposite.

Delta isobars in relativistic mean-field models with σ-scaled hadron masses and couplings

We extend the relativistic mean-field models with hadron masses and meson–baryon coupling constants dependent on the scalar σ field, studied previously to incorporate Δ(1232) baryons. Available empirical information is analyzed to put constraints on the couplings of Δs with meson fields. Conditions for the appearance of Δs are studied. We demonstrate that with inclusion of the Δs our equations of state continue to fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, the constraint on the maximum mass of the neutron stars, the direct Urca and the gravitational-baryon mass ratio constraints.

Triton Binding Energy of Kharkov Potential

The Kharkov potential is a recent field theoretical model of nucleon–nucleon (NN) interaction that has been built up in the framework of the instant form of relativistic dynamics starting with the total Hamiltonian of interacting meson and nucleon fields and using the method of unitary clothing transformations. The latter connect the representation of “bare” particles and the representation of “clothed” particles, i.e., the particles with physical properties. Unlike many available NN potentials each of which is the kernel of the corresponding nonrelativistic Lippmann–Schwinger (LS) equation this potential being dependent in momentum space on the Feynman-like propagators and covariant cutoff factors at the meson–nucleon vertices is the kernel of relativistic integral equations for the NN bound and scattering states. Therefore we do not need to invent any transform of a given nonrelativistic potential to its relativistic counterpart. As a feasible study, we have started with the so-called 5ch Faddeev calculation for three-nucleon bound state (triton) and obtained a reasonable value of its binding energy ( $$-7.42$$ MeV).

Final state interactions in Krightarrow pi pi decays: Delta I=1/2 rule vs. varepsilon '/varepsilon

Dispersive effects from strong pi pi rescattering in the final state interaction (FSI) of weak Krightarrow pi pi decays are revisited with the goal to have a global view on their relative importance for the Delta I=1/2 rule and the ratio varepsilon '/varepsilon in the standard model (SM). We point out that this goal cannot be reached within a pure effective (meson) field approach like chiral perturbation theory in which the dominant current–current operators governing the Delta I=1/2 rule and the dominant density–density (four-quark) operators governing varepsilon '/varepsilon cannot be disentangled from each other. But in the context of a dual QCD approach, which includes both long-distance dynamics and the UV completion, that is, QCD at short-distance scales, such a distinction is possible. We find then that beyond the strict large N limit, N being the number of colours, FSIs are likely to be important for the Delta I=1/2 rule but much less relevant for varepsilon '/varepsilon . The latter finding diminishes significantly hopes that improved calculations of varepsilon '/varepsilon would bring its SM prediction to agree with the experimental data, opening thereby an arena for important new physics contributions to this ratio.

The effect of inclusion of Δ resonances in relativistic mean-field model with scaled hadron masses and coupling constants

Knowledge of the equation of state of the baryon matter plays a decisive role in the description of neutron stars. With an increase of the baryon density the filling of Fermi seas of hyperons and Δ isobars becomes possible. Their inclusion into standard relativistic mean-field models results in a strong softening of the equation of state and a lowering of the maximum neutron star mass below the measured values. We extend a relativistic mean-field model with scaled hadron masses and coupling constants developed in our previous works and take into account now not only hyperons but also the Δ isobars. We analyze available empirical information to put constraints on coupling constants of Δs to mesonic mean fields. We show that the resulting equation of state satisfies majority of presently known experimental constraints.

Highly Magnetized Neutron Stars in a Many-body Forces Formalism

In this work, we study the effects of different magnetic field configurations in neutron stars described by a many-body forces formalism (MBF model). The MBF model is a relativistic mean field formalism that takes into account many-body forces by means of a meson field dependence of the nuclear interaction coupling constants. We choose the best parametrization of the model that reproduces nuclear matter properties at saturation and also describes massive neutron stars. We assume matter to be in beta-equilibrium, charge neutral and at zero temperature. Magnetic fields are taken into account both in the equation of state and in the structure of the stars by the self-consistent solution of the Einstein-Maxwell equations. We assume a poloidal magnetic field distribution and calculate its effects on neutron stars, showing its influence on the gravitational mass and deformation of the stars.