Quadrupole polarizabilities of the pion in the Nambu–Jona-Lasinio model

The electromagnetic dipole and quadrupole polarizabilities of the neutral and charged pions are calculated in the Nambu–Jona-Lasinio model. Our results agree with the recent experimental analysis of these quantities based on dispersion sum rules. Comparison is made with the results from the chiral perturbation theory.     

Spontaneous Symmetry Breaking in Coupled Bose–Einstein Condensates

Journal of Statistical Physics - We study a system of two hardcore bosonic Hubbard models weakly coupled with each other by tunneling. Assuming that the single uncoupled model exhibits off-diagonal...     

Crust-core properties of neutron stars in the Nambu–Jona-Lasinio model

We adopt the Nambu–Jona-Lasinio(NJL) model to study the crust-core transition properties in neutron stars(NSs). For a given momentum cutoff and symmetry energy of saturation density in the NJL model, decreasing the slope of the symmetry energy gives rise to an increase in the crust-core transition density and transition pressure.Given the slope of the symmetry energy at saturation density, the transition density and corresponding transition pressure increase with increasing symmetry energy. The increasing trend between the fraction of the crustal moment of inertia and the slope of symmetry energy at saturation density indicates that a relatively large momentum cutoff of the NJL model is preferred. For a momentum cutoff of 500 Me V, the fraction of the crustal moment of inertia clearly increases with the slope of symmetry energy at saturation density. Thus, at the required fraction(7%) of the crustal moment of inertia, the NJL model with momentum cutoff of 500 Me V and a large slope of the symmetry energy of saturation density can give the upper limit of the mass of the Vela pulsar to be above 1.40 M_⊙.     

Time-dependent Ginzburg–Landau equation in the Nambu–Jona-Lasinio model

We apply the closed time-path Green function formalism in the Nambu–Jona-Lasinio model. First of all, we use this formalism to obtain the well-known gap equation for the quark condensate in a stationary homogeneous system. We have also used this formalism to obtain the Ginzburg–Landau (GL) equation and the time-dependent Ginzburg–Landau (TDGL) equation for the chiral order parameter in an inhomogeneous system. In our derived GL and TDGL equations, there is no other parameters except for those in the original NJL model.     

Low-energy processes of meson production in the extended Nambu–Jona-Lasinio model

The processes of meson production in electron–positron collisions at low energies are characterized within the extended Nambu–Jona-Lasinio model. It is demonstrated that intermediate vector mesons (both in the ground state and in the first radially excited one) play a critical part in these processes. The obtained results are in reasonable agreement with the available experimental data. A number of theoretical predictions are made, which can be tested experimentally in the near future.     

Spontaneous U（1） Symmetry Breaking in Coupled Bose System

Adding a U(1) symmetry breaking term V^1/2 a(λ₁a₀+λ*₁a^†₀)+V^1/2(λ₂b₀+λ^*₂b^†₀) to Bogoliubov's truncated Hamiltonian H_B for a weakly interacting coupled Bose system, by using the mean-field approximation rather than the c-number approximation, we find that, via a Feshbach resonance at zero temperature, the states of the coupled Bose system are generalized SU(1,1) × SU(1,1) coherent states. The Bose-Einsteincondensation occurs in response to the spontaneous U(1) symmetry breaking.     

Spontaneous Electro-Weak Symmetry Breaking and Cold Dark Matter

In the standard model, the weak gauge bosons and fermions obtain mass after spontaneous electro-weak symmetry breaking, which is realized by one fundamental scalar field, namely the Higgs field. We study the simplest scalar cold dark matter model in which the scalar cold dark matter also obtains mass by interaction with the weakdoublet Higgs field, in the same way as those of weak gauge bosons and fermions. Our study shows that the correct cold dark matter relic abundance within 3a uncertainty （0.093 〈 Ωdmh^2 〈 0.129） and experimentally allowed Higgs boson mass （114.4 ≤ mh≤ 208 GeV） constrain the scalar dark matter mass within 48 ≤ ms ≤ 78 GeV. This result is in excellent agreement with the result of de Boer et al. （50 ~ 100 GeV）. Such a kind of dark matter annihilation can account for the observed gamma rays excess （10σ） at EGRET for energies above 1 GeV in comparison with the expectations from conventional Galactic models. We also investigate other phenomenological consequences of this model. For example, the Higgs boson decays dominantly into scalar cold dark matter if its mass lies within 48 ~ 64 GeV.     

On the Shukla–Nambu–Salimullah potential in magnetized plasmas

In magnetized plasmas, there are two electrostatic potentials, i.e., the almost spherical Debye–Hückel and the strongly anisotropic Shukla–Nambu–Salimullah potentials. The physics of the latter potential due to ion polarization drift is clarified. The exact solution for the Shukla–Nambu–Salimullah potential introduces a new shielding length across the external magnetic field which is much larger than that of the Debye–Hückel potential. There is no exponential decay of the potential for v_t=C_s, where v_t is the test particle velocity and C_s is the ion sound velocity.     

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

Relying on the collinear factorization approach, we demonstrate that H1 and ZEUS measurements of exclusive light vector meson and photon electroproduction cross sections can be simultaneously described for photon virtualities of ${\mathcal {Q}}\gtrsim 2\, \mathrm{GeV}$ . Our findings reveal that quark exchanges are important in this small $x_\mathrm{Bj}$ region and that in leading order approximation the gluonic component is suppressed, e.g., the skewness ratio can be much smaller than one.     

Nonlocal Nambu–Jona-Lasinio model and chiral chemical potential

We derive the critical temperature in a nonlocal Nambu–Jona-Lasinio model with the presence of a chiral chemical potential. The model we consider uses a form factor derived from recent studies of the gluon propagator in Yang–Mills theory and has the property to fit in excellent way the form factor arising from the instanton liquid picture for the vacuum of the theory. Nambu–Jona-Lasinio model is derived form quantum chromodynamics providing all the constants of the theory without any need for fits. We show that the critical temperature in this case always exists and increases as the square of the chiral chemical potential. The expression we obtain for the critical temperature depends on the mass gap that naturally arises from Yang–Mills theory at low-energy as also confirmed by lattice computations.     

τ → K–ηντ Decay in the Extended Nambu–Jona-Lasinio Model Including the Final-State Interaction

JETP Letters - The width of the $$\tau \to {{K}^{ - }}\eta {{\nu }_{\tau }}$$ decay has been calculated within the extended Nambu–Jona-Lasinio model including the final-state interaction of...     

τ → K–π0ντ Decay in the Nambu–Jona-Lasinio Model Including the Final-State Interaction of Mesons

JETP Letters - The $$\tau \to {{K}^{ - }}{{\pi }^{0}}{{\nu }_{\tau }}$$ decay has been described within the Nambu–Jona-Lasinio model including the contact term and the contribution from an...     

Replica Symmetry Breaking in Multi-species Sherrington–Kirkpatrick Model

Journal of Statistical Physics - In the Sherrington–Kirkpatrick (SK) and related mixed p-spin models, there is interest in understanding replica symmetry breaking at low temperatures. For...     

Chiral susceptibility and chiral phase transition in Nambu–Jona-Lasinio model

We give a general relation between the chiral susceptibility and the thermodynamical potential and a relation between the chiral susceptibility and the condition for furcations to appear in the Wigner solution(s) in the Nambu–Jona-Lasinio (NJL) model. We find that the chiral susceptibility is a quantity able to represent the appearance of furcation in the solution(s) of the gap equation and the concavo–convexity of the thermodynamical potential in the NJL model. It indicates that the chiral susceptibility can identify the stability of the states and the chiral phase transition in NJL model. We propose that analyzing the chiral susceptibility may play an important role in studying the chiral phase transition in approaches superior to the NJL model.     

Growth and Form in Biology： Generation of the Plant Morphology by Spontaneous Symmetry Breaking Based on a Pressure Field

Considering the role of mechanical forces playing in the morphogenetic pattern formation, we propose a secondorder differential equation for the growth and form of plants based on the turgot pressure field at the organ and cellular level. The solutions can well describe various kinds of morphological features of flowers under certain hypotheses. The plant morphology is considered as the spontaneous symmetry breaking of a circular growing boundary, while the employed hypotheses are subjected to further experimental confirmation.     

Calculation of the Width of the τ → K–K 0 ντ Decay in the Extended Nambu–Jona-Lasinio Model with Estimation of the Contribution from the Final-State Interaction

JETP Letters - The partial width of the $$\tau \to {{K}^{ - }}{{K}^{0}}{{\nu }_{\tau }}$$ decay has been calculated within the extended Nambu–Jona-Lasinio model including the contact and...     

On the Unicity of Discontinuous Transitions in the Two-Dimensional Potts and Ashkin–Teller Models

Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following nontrivial power laws in experimentally relevant distributions. Previous numerical estimates on the critical exponents, when existing, are confirmed and superseded. A physical motivation for both models in the present framework is also discussed.     

On the Interplay of Magnetic and Molecular Forces in Curie–Weiss Ferrofluid Models

We consider a mean-field continuum model of classical particles in R ^d with Ising or Heisenberg spins. The interaction has two ingredients, a ferromagnetic spin coupling and a spin-independent molecular force. We show that a feedback between these forces gives rise to a first-order phase transition with simultaneous jumps of particle density and magnetization per particle, either at the threshold of ferromagnetic order or within the ferromagnetic region. If the direct particle interaction alone already implies a phase transition, then the additional spin coupling leads to an even richer phase diagram containing triple (or higher order) points.