The Friedberg-Lee model is studied at finite temperature and density. By using the finite temperature field theory, the effective potential of the Friedberg-Lee model and the bag constant $B(T)$ and $B(T,μ)$ have been calculated at different temperatures and densities. It is shown that there is a critical temperature $T_{C}\simeq 106.6 \mathrm{MeV}$ when $μ=0 \mathrm{MeV}$ and a critical chemical potential $μ\simeq 223.1 \mathrm{MeV}$ for fixing the temperature at $T=50 \mathrm{MeV}$. We also calculate the soliton solutions of the Friedberg-Lee model at finite temperature and density. It turns out that when $T\leq T_{C}$ (or $μ\leq μ_C$), there is a bag constant $B(T)$ (or $B(T,μ)$) and the soliton solutions are stable. However, when $T>T_{C}$ (or $μ>μ_C$) the bag constant $B(T)=0 \mathrm{MeV}$ (or $B(T,μ)=0 \mathrm{MeV}$) and there is no soliton solution anymore, therefore, the confinement of quarks disappears quickly.
We present two novel dynamical features of flux tubes in the Friedberg-Lee model. First the fusion of two (anti-)parallel flux tubes, where we extract a string-string interaction potential which has a qualitative similarity to the nucleon-nucleon potential in the Friedberg-Lee model obtained by Koepf et al. Furthermore we show the dynamical breakup of flux tubes via $q\bar{q}-$particle production and the disintegration into mesons. We find, as a shortcoming of the present realization of the model, that the full dynamical transport approach presented in a previous publication fails to provide t…
We point out a generic correlation between the Friedberg-Lee symmetry of quark mass operators and the vanishing of quark masses. We make phenomenological explorations on two textures of quark mass matrices with the broken Friedberg-Lee symmetry. We present a new pattern of quark mass matrices in agreement with current experimental data. Both analytical and numerical results of our calculations are discussed in detail.
We study the possible origin of Friedberg-Lee symmetry. First, we propose the generalized Friedberg-Lee symmetry in the potential by including the scalar fields in the field transformations, which can be broken down to the FL symmetry spontaneously. We show that the generalized Friedberg-Lee symmetry allows a typical form of Yukawa couplings, and the realistic neutrino masses and mixings can be generated via see-saw mechanism. If the right-handed neutrinos transform non-trivially under the generalized Friedberg-Lee symmetry, we can have the testable TeV scale see-saw mechanism. Second, we pres…
A dynamical model of confinement based on a microscopic transport description of the Friedberg-Lee model is extended to explicit color degrees of freedom. The string tension is reproduced by an adiabatic string formation from the nucleon ground state. As a particular application, we address the question of how a charmonium state might be dissociated by the strong color electric fields when moving through a color electric flux tube and speculate on the importance of such an effect with respect to the issue of $J/ψ$--suppression observed in ultrarelativistic heavy ion collisions. Furthermore, we…
We study the matter-antimatter asymmetry through the leptogenesis mechanism in a specific model with the Friedberg-Lee (FL) symmetry.We relate the leptogenesis with the CP violating Dirac and Majorana phases in the Maki-Nakagawa-Sakata leptonic mixing matrix and illustrate the net baryon asymmetry of the universe in terms of these phases.
We consider the Friedberg-Lee symmetry for the quark sector and show that the symmetry closely relates to both quark masses and mixing angles. We also extend our scheme to the fourth generation quark model and find the relation $|V_{tb^{'}}| \simeq |V_{t^{'}b}| \simeq m_b/m_{b^{'}}< λ^2$ with $λ\simeq0.22$ for $m_b=4.2\ \gev$ and $m_{b^{'}}>199\ \gev$.
We have discussed the vacuum tunnelling in Friedberg-Lee model. The tunnelling coefficient is derived in the field configuration space by calculating the transition amplitude using the path integral under the stationary phase approximation and the dilute instanton gas approximation. By studying the tunnelling effect between the two degenerating vacuums at the critical temperature and chemical potential, we find that the system could be deconfined by tunnelling, which could possibly change the first order deconfinement phase transition to crossover.
We write out the generic Dirac neutrino mass operator which possesses the Friedberg-Lee (FL) symmetry and find that its corresponding neutrino mass matrix is asymmetric. Following a simple way to break the FL symmetry, we calculate the neutrino mass eigenvalues and show that the resultant neutrino mixing pattern is nearly tri-bimaximal. Imposing the Hermitian condition on the neutrino mass matrix, we also show that the simplified ansatz is consistent with current experimental data and favors the normal neutrino mass hierarchy.
We consider the $μ-τ$ symmetric Friedberg-Lee (FL) symmetry for the neutrino sector and show that a specific FL translation leads to the tribimaximal mixing pattern of the Maki-Nakagawa-Sakata (MNS) matrix. We also apply the symmetry to the type-I seesaw framework and address the baryon asymmetry of the universe through the leptogenesis mechanism. We try to establish a relation between the net baryon asymmetry and CP phases included in the MNS matrix.
We examine a recently proposed symmetry/condition by Friedberg and Lee in the framework where three right-handed neutrinos are added to the spectrum of the three-family Minimal Standard Model. It is found that the right-handed neutrinos are very special, with respect to this symmetry. In the symmetry limit the neutrinos are massless and that may be a hint about why they are light. Imposed as a condition and not as a full symmetry, we find that one of the three right-handed neutrinos simply decouples (has only gravitational interactions) and that there is a massless interacting neutrino. The po…
We investigate the Friedberg-Lee (FL) symmetry and its promotion to include the $μ- τ$ symmetry, and call that the twisted FL symmetry.Based on the twisted FL symmetry, two possible schemes are presented toward the realistic neutrino mass spectrum and the tri-bimaximal mixing.In the first scheme, we suggest the semi-uniform translation of the FL symmetry.The second one is based on the $S_3$ permutation family symmetry.The breaking terms, which are twisted FL symmetric, are introduced.Some viable models in each scheme are also presented.
The Friedberg-Lee (FL) symmetry is generated by a transformation of a fermionic field $q$ to $q + ξz$. This symmetry puts very restrictive constraints on allowed terms in a Lagrangian. Applying this symmetry to $N$ fermionic fields, we find that the number of independent fields is reduced to $N-1$ if the fields have gauge interaction or the transformation is a local one. Using this property, we find that a seesaw model originally with three generations of left- and right-handed neutrinos, with the left-handed neutrinos unaffected but the right-handed neutrinos transformed under the local FL tr…
Assuming the Majorana nature of massive neutrinos, we generalize the Friedberg-Lee neutrino mass model to include CP violation in the neutrino mass matrix M_ν. The most general case with all the free parameters of M_νbeing complex is discussed. We show that a favorable neutrino mixing pattern (with θ_12 \approx 35.3^\circ, θ_23=45^\circ, θ_13 \neq 0^\circ and δ=90^\circ) can naturally be derived from M_ν, if it has an approximate or softly-broken μ-τsymmetry. We also point out a different way to obtain the nearly tri-bimaximal neutrino mixing pattern with δ=0^\circ and non-vanishing Majorana p…
In this letter, we put forward a special neutrino mass matrix which is invariant under a modified Friedberg-Lee (FL) transformation $ν^{}_e \to ν^{}_e-2θ$ and $ν^{}_{μ, τ} \to ν^{}_{μ, τ}+θ$ with $θ$ being a space-time independent element of the Grassmann algebra. Compared to the original FL symmetry (with the transformation $ν^{}_{e, μ, τ} \to ν^{}_{e, μ, τ}+θ$) which results in the TM2 neutrino mixing, the modified FL symmetry will lead us to the TM1 mixing which has a better agreement with the experimental results. While the original FL symmetry has to be broken in order to produce a realis…
The inverse seesaw mechanism with three pairs of gauge-singlet neutrinos offers a natural interpretation of the tiny masses of three active neutrinos at the TeV scale. We combine this picture with the newly-proposed Friedberg-Lee (FL) symmetry in order to understand the observed pattern of neutrino mixing. We show that the FL symmetry requires only two pairs of the gauge-singlet neutrinos to be massive, implying that one active neutrino must be massless. We propose a phenomenological ansatz with broken FL symmetry and exact μ-τsymmetry in the gauge-singlet neutrino sector and obtain the tri-bi…
Friedberg, Lee and Zhao proposed a method for effectively evaluating the eigenenergies and eigen wavefunctions of quantum systems. In this work, we study several special cases to investigate applicability of the method. Concretely, we calculate the ground-state eigenenergy of the Hellmann potential as well as the Cornell potential, and also evaluate the energies of the systems where linear term is added to the Coulomb and harmonic oscillator potentials as a perturbation. The results obtained in this method have a surprising agreement with the traditional method or the numerical results. Since …
We consider an effective Majorana neutrino mass operator with the Friedberg-Lee symmetry; i.e., it is invariant under the transformation ν_α-> ν_α+ z (for α= e, μ, τ) with z being a space-time independent constant element of the Grassmann algebra. We show that this new flavor symmetry can be broken in such a nontrivial way that the lightest neutrino remains massless but an experimentally-favored neutrino mixing pattern is achievable. In particular, we get a novel prediction for the unknown neutrino mixing angle θ_13 in terms of two known angles: \sinθ_13 = \tanθ_12 |(1- \tanθ_23)/ (1+\tanθ_23)…
Light sterile neutrinos of mass about an eV with mixing $\tilde U_{ls}$ of a few percent to active neutrinos may solve some anomalies shown in experimental data related to neutrino oscillation. How to have light sterile neutrinos is one of the theoretical problems which have attracted a lot of attentions. In this article we show that such an eV scale light sterile neutrino candidate can be obtained in a seesaw model in which the right-handed neutrinos satisfy a softly-broken Friedberg-Lee (FL) symmetry. In this model a right-handed neutrino is guaranteed by the FL symmetry to be light comparin…
I argue that the observed flavor structures of leptons and quarks might imply the existence of certain flavor symmetries. The latter should be a good starting point to build realistic models towards deeper understanding of the fermion mass spectra and flavor mixing patterns. The μ-τpermutation symmetry serves for such an example to interpret the almost maximal atmospheric neutrino mixing angle (θ_23 \sim 45^\circ) and the strongly suppressed CHOOZ neutrino mixing angle (θ_13 < 10^\circ). In this talk I like to highlight a new kind of flavor symmetry, the Friedberg-Lee symmetry, for the effecti…
Multi-field oscillons/I-balls in the Friedberg-Lee-Sirlin model
RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（RIKEN 跨学科理论与数学科学中心（iTHEMS））；Department of Physics, Tohoku University（东北大学物理系）；Tokyo Denki University（东京电机大学）；Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University（大阪公立大学大阪中央高等数学研究所）；Kavli IPMU (WPI), UTIAS, University of Tokyo（东京大学 Kavli 宇宙物质与宇宙起源国际合作实验室（WPI）、UTIAS）
We propose a phenomenological model of Dirac neutrino mass operator based on the Fridberg-Lee (FL) neutrino mass model to include CP violation. By considering the most general set of complex coefficients, and imposing the condition that the mass eigenvalues are real, we find a neutrino mass matrix which is non-hermitian, symmetric and magic. In particular, we find that the requirement of obtaining real mass eigenvalues by transferring the residual phases to the mass eigenstates self-consistently, dictates the following relationship between the imaginary part of the mass matrix elements $B$ and…
The overall characteristics of the solar and atmospheric neutrino oscillation are approximately consistent with a tribimaximal form of the mixing matrix $U$ of the lepton sector. Exact tribimaximal mixing leads to $θ_{13}=0$. However, recent results from Daya Bay and RENO experiments have established a nonzero value for $θ_{13}$. Keeping the leading behavior of $U$ as tribimaximal, we use a generalized Fridberg-Lee neutrino mass model along with a complementary ansatz to incorporate a nonzero $θ_{13}$ along with CP violation. We generalize this model in two stages: In the first stage we assume…
Quantum-Corrected Q-balls in the Friedberg-Lee-Sirlin Model
School of Physical Sciences, University of Science and Technology of China（中国科学技术大学物理学院）；Interdisciplinary Center for Theoretical Study, University of Science and Technology of China（中国科学技术大学理论中心）；Peng Huanwu Center for Fundamental Theory, Hefei, Anhui 230026, China（合肥基本物理研究中心）
We propose a neutrino mass model with $μτ$-flavored CP symmetry, where the effective light neutrino Lagrangian enjoys an additional invariance under a Friedberg-Lee (FL) transformation on the left-handed flavor neutrino fields, that leads to a highly predictive and testable scenario. While both types of the light neutrino mass ordering, i.e., Normal Ordering (NO) as well as the Inverted Ordering (IO) are allowed, the absolute scale of neutrino masses is fixed by the vanishing determinant of light Majorana neutrino mass matrix $M_ν$. We show that for both types of mass ordering, whilst the atmo…
Motivated in part by the several observed anomalies involving CP asymmetries of B and B_s decays, we consider the Standard Model with a 4th sequential family (SM4) which seems to offer a rather simple resolution. We initially assume T-invariance by taking the up and down-quark 4x4 mass matrix to be real. Following Friedberg and Lee (FL), we then impose a "hidden" symmetry on the unobserved ("hidden") up and down-quark SU(2) states. The hidden symmetry for four generations ensures the existence of two zero-mass eigenstates, which we take to be the (u,c) and (d,s) states in the up and down-quark…
Based on Friedberg and Lee's geometric picture by which the tribimaximal Pontecorvo-Maki-Nakawaga-Sakata leptonic mixing matrix is constructed, namely, corresponding mixing angles correspond to the geometric angles among the sides of a cube. We suggest that the three realistic mixing angles, which slightly deviate from the values determined for the cube, are due to a viable deformation from the perfectly cubic shape. Taking the best-fitted results of $θ_{12}$ and $θ_{23}$ as inputs, we determine the central value of $\sin^22θ_{13}$ should be 0.0238, with a relatively large error tolerance; thi…
The Lee-Wick Standard Model at temperatures near electroweak scale is considered, with the aim of studying the electroweak phase transition. While Lee-Wick theories possess states of negative norm, they are not pathological but instead are treated by imposing particular boundary conditions and using particular integration contours in the calculation of S-matrix elements. It is not immediately clear how to extend this prescription to formulate the theory at finite temperature; we explore two different pictures of finite-temperature LW theories, and calculate the thermodynamic variables and the …
An extension of the standard model, the Lee-Wick standard model, based on ideas of Lee and Wick was recently introduced. It does not contain quadratic divergences in the Higgs mass and hence solves the hierarchy puzzle. The Lee-Wick standard model contains new heavy Lee-Wick resonances at the TeV scale that decay to ordinary particles. In this paper we examine the behavior of Lee-Wick resonances at high temperature. We argue that they contribute negatively to the energy density rho and pressure p and at temperatures much greater than their mass M their O(T^4) contributions to rho and p cancel …
Canonical partition functions and Lee-Yang zeros of QCD at finite density and high temperature are studied. Recent lattice simulations have confirmed that the free energy of QCD is a quartic function of quark chemical potential at temperature slightly above pseudo-critical temperature $T_c$, as in the case with a gas of free massless fermions. We present analytic derivation of the canonical partition functions and Lee-Yang zeros for this type of free energy using the saddle point approximation. We also perform lattice QCD simulation in a canonical approach using the fugacity expansion of the f…
The relative interfacial thermal contraction as a possible origin of the low-energy excess in cryogenic calorimeters
Max Planck Institute for Physics（马克斯·普朗克物理研究所）；Marietta Blau Institute for Particle Physics of the Austrian Academy of Sciences（奥地利科学院玛丽埃塔·布劳粒子物理研究所）；Humboldt-Universität zu Berlin（柏林洪堡大学）
In typical statistical mechanical systems the grand canonical partition function at finite volume is proportional to a polynomial of the fugacity $e^{μ/T}$. The zero of this Lee-Yang polynomial closest to the origin determines the radius of convergence of the Taylor expansion of the pressure around $μ=0$. The computationally cheapest formulation of lattice QCD, rooted staggered fermions, with the usual definition of the rooted determinant, does not admit such a Lee-Yang polynomial. We argue that the radius of convergence is then bounded by the spectral gap of the reduced matrix of the unrooted…
We consider the cosmological model of a self-interacting $ϕ^4 - ϕ^2$ quantum scalar field and extend our previous results, [3], on resonant tunneling and consequent particle production, to the case of finite temperature. Using the mathematical equivalence between, the Euclidean path integral of a $ϕ^4 - ϕ^2$ quantum field theory (in the saddle point approximation), on one hand, and the partition function of a 4-dimensional ferromagnet (in the Ising model approximation), on the other, we derive the following results. Tunneling is a first order phase transition. The creation of metastable bound …
Lee-Yang zeros and edge singularity in a mean-field approach
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Institute of Theoretical Physics, University of Wrocław（弗罗茨瓦夫大学理论物理研究所）；Institute for Particle and Nuclear Physics, HUN-REN Wigner Research Centre for Physics（匈牙利研究网络维格纳物理研究中心粒子与核物理研究所）；J-PARC Branch, KEK Theory Center, Institute of Particle and Nuclear Studies, KEK（高能加速器研究机构理论中心J-PARC分部粒子与核研究研究所）；Division of Physics and Astronomy, Graduate School of Science, Kyoto University（京都大学理学研究科物理学天文学专攻）
We comment on the Lee-Yang zero analysis for the study of the phase structure of QCD at high temperature and baryon number density by Monte-Carlo simulations. We find that the sign problem for non-zero density QCD induces a serious problem in the finite volume scaling analysis of the Lee-Yang zeros for the investigation of the order of the phase transition. If the sign problem occurs at large volume, the Lee-Yang zeros will always approach the real axis of the complex parameter plane in the thermodynamic limit. This implies that a scaling behavior which would suggest a crossover transition wil…
