Search

It is established that the new boundary element-free Galerkin method, namely the virtual boundary element-free Galerkin method (VBEFGM), using dual compactly supported radial basis function interpolation (CSRBFI) for 2D inhomogeneous heat conduction problems with variable heat sources, whose solutions are divided into homogeneous and particular solutions. The virtual loads of the homogeneous solutions and undetermined coefficients of particular solutions are interpolated by CSRBFI. Its formula is established by the Galerkin method. The homogeneous solutions are obtained by the virtual boundary element-free method (VBEFM). The recommended method for 2D inhomogeneous heat conduction problems is real meshfree without background integration elements and exhibits the merits of the meshfree method, Galerkin method, and boundary element method. Its calculation scheme is deduced in detail and easily programmed. The coefficient matrix has symmetrical characteristics. The implementation steps and implementation flow-chart are also shown in detail. Seven numerical examples, such as exponential functionally graded material, are calculated and contrasted with other numerical methods. The precision and stableness of the proposed method for 2D inhomogeneous heat conduction problems are verified.

In this article, a 2×2 broadband circularly polarized antenna array using the sequential rotation (SR) technique in the feed network is presented. This antenna covers the 5G-band of 3.5–3.6 GHz and...

In this paper, we consider the imbedding of the popular and well-motivated trimaximal mixing and $\mu$-$\tau$ reflection symmetry (which can help us shape the forms of the neutrino mass matrix) in the minimal seesaw model (which contains much fewer parameters than the general seesaw model) with two TeV-scale right-handed neutrinos (for realizing a low-scale seesaw) of nearly degenerate masses (for realizing a resonant leptogenesis). However, either for the trimaximal mixing scenario (which is realized through the Form Dominance approach here) or for the $\mu$-$\tau$ reflection symmetry scenario, leptogenesis cannot proceed. To address this issue, we consider the possibility that the special forms of the neutrino mass matrix for the trimaximal mixing and $\mu$-$\tau$ reflection symmetry are slightly broken by the renormalization group evolution effect, thus allowing leptogenesis to proceed. It is found that in the normal case of the neutrino mass ordering, the baryon asymmetry thus generated can reproduce the observed value. For completeness, we have also extended our analysis to the scenario that two right-handed neutrinos are not nearly degenerate any more. Unfortunately, in this scenario the final baryon asymmetry is smaller than the observed value by several orders of magnitude., Comment: 25 pages, 4 figures, version to appear in JHEP

For some theoretical and experimental considerations, the relatively light Majorana neutrinos at the GeV scale have been attracting some interest. In this article we consider a scenario with only one Majorana neutrino $N$, negligible mixing with the active neutrinos $\nu_{L}$, where the Majorana neutrino interactions could be described in a model independent approach based on an effective theory. Under such a framework, we particularly study the feasibility of observing the $N$ with mass in the range 0$-$30 GeV via the process $e^+ e^- \to \nu N \to\gamma + \slashed E$ in the future Belle-II and ILC experiments. The results show that it is unpromising for Belle-II to observe the signal, while ILC may easily make a discovery for the Majorana neutrino., Comment: 14 pages, 7 figures, 2 tables

In this paper, we attempt to implement the neutrino $\mu$-$\tau$ reflection symmetry (which predicts $\theta^{}_{23} = \pi/4$ and $\delta = \pm \pi/2$ as well as trivial Majorana phases) in the minimal seesaw (which enables us to fix the neutrino masses). For some direct (the preliminary experimental hints towards $\theta^{}_{23} \neq \pi/4$ and $\delta \neq - \pi/2$) and indirect (inclusion of the renormalization group equation effect and implementation of the leptogenesis mechanism) reasons, we particularly study the breakings of this symmetry and their phenomenological consequences., Comment: 20 pages, 7 figures, accepted for publication in JHEP

The neutrino μ-τ reflection symmetry has been attracting a lot of attention as it predicts the interesting results θ 23 = π/4 and δ = ±π/2. But it is reasonable to consider breakings of such a symmetry either from the theoretical considerations or on the basis of experimental results. We thus perform a systematic study for the possible symmetry-breaking patterns and their implications for the mixing parameters. The general treatment is applied to some specific symmetry breaking arising from the renormalization group effects for illustration.

In this paper, we derive in a novel approach the possible textures of neutrino mass matrix that can lead to maximal atmospherical mixing angle ($\theta^{}_{23} = \pi/4$) and Dirac CP phase ($\delta = - \pi/2$) in two phenomenologically appealing scenarios: (1) one neutrino mass matrix element being vanishing (2) one neutrino mass being vanishing. For the obtained textures, some neutrino mass sum rules which relate the neutrino masses and mixing parameters will emerge. With the help of these sum rules, the unknown absolute neutrino mass scale and Majorana CP phases can be determined. Some discussions about the possible textures of neutrino mass matrix that can lead to $\theta^{}_{23} = \pi/4$, $\delta = - \pi/2$ and maximal Majorana CP phases ($\rho, \sigma = \pi/4$ or $3\pi/4$) as well as the model realization and breakings of the obtained textures are also given., Comment: 25 pages, no figures, major revisions, references added, version accepted for publication in PRD

Following the Occam's razor principle, we explore the particular textures (featuring texture zeros and equalities) of the Dirac neutrino mass matrix in the minimal seesaw model (where only two right-handed neutrinos $N^{}_1$ and $N^{}_2$ are responsible for the generation of the light neutrino masses), in light of current neutrino experimental results and leptogenesis. The study will be performed for two particular patterns of the Majorana mass matrix $M^{}_{\rm R}$ for $N^{}_1$ and $N^{}_2$: (A) $M^{}_{\rm R}$ being diagonal $ \left( \begin{array}{cc} M^{}_1 & 0 \cr 0 & M^{}_2 \cr \end{array} \right)$; (B) $M^{}_{\rm R}$ being of the form $\left( \begin{array}{cc} 0 & M \cr M & 0 \cr \end{array} \right)$., typos corrected and some references added

Given its briefness and predictability, the minimal seesaw -- a simplified version of the canonical seesaw mechanism with only two right-handed neutrino fields -- has been studied in depth and from many perspectives, and now it is being pushed close to a position of directly facing experimental tests. This article is intended to provide an up-to-date review of various phenomenological aspects of the minimal seesaw and its associated leptogenesis mechanism in neutrino physics and cosmology. Our focus is on possible flavor structures of such benchmark seesaw and leptogenesis scenarios and confronting their predictions with current neutrino oscillation data and cosmological observations. In this connection particular attention will be paid to the topics of lepton number violation, lepton flavor violation, discrete flavor symmetries, CP violation and antimatter of the Universe., Comment: 111 pages, 23 figures, 9 tables, final version published in Reports on Progress in Physics as a Review Article

Virtual boundary meshfree Galerkin method (VBMGM) is developed to solve the multi-domain variable coefficient heat conduction problem with heat source. Both the virtual source function on the virtual boundary and heat source within each subdomain are approximate by the radial basis function interpolation. The equation of the proposed technique is derived by one of the weighted residual methods, namely the Galerkin method, for multi-domain variable coefficient heat conduction problem with heat source. Therefore, VBMGM simultaneously possesses the merits of Galerkin method, boundary element method and meshfree method. And the numerical meanings of the weighted values are definite, such as the partial derivative heat source expressions, the temperature, the heat flux and the continuity conditions, in VBMGM for multi-domain variable coefficient heat conduction problem with heat source. The specific and detailed equation of VBMGM is obtained for multi-domain variable coefficient heat conduction problem with heat source. The accuracy and the stability of the proposed technique are validated by two numerical examples for multi-domain variable coefficient heat conduction problem with heat source.

In this work, we consider the multi-wall braneworld arisen from multi-scalar fields, and investigate the localization and resonances of spin-1/2 fermion on the multi-walls. We build two analytic multi-wall solutions with a polynomial superpotential and a modified sine-Gordon superpotential respectively. The massless fermion is the only bound state and localized between the two outermost sub-branes. The factors affecting the number of massive resonant fermions are analyzed. What interesting is that all the fermion resonant states are non-degenerate for the cases of single- and two-walls, however, doubly-degenerate fermion resonant states emerge for the cases of three- and four-walls. This novel phenomenon could be potentially interesting in phenomenology., 21 pages, 45 figures, added the lifetime estimation of resonances, version accepted to CQG

In this paper, we emphasize why it is important for future neutrinoless double-beta ($0\nu\beta\beta$) decay experiments to reach the sensitivity to the effective neutrino mass $|m^{}_{\beta\beta}| \approx 1~{\rm meV}$. Assuming such a sensitivity and the precisions on neutrino oscillation parameters after the JUNO experiment, we fully explore the constrained regions of the lightest neutrino mass $m^{}_1$ and two Majorana-type CP-violating phases $\{\rho, \sigma\}$. The implications for the neutrino mass spectrum, the effective neutrino mass $m^{}_\beta$ in beta decays and the sum of three neutrino masses $\Sigma \equiv m^{}_1 + m^{}_2 + m^{}_3$ relevant for cosmological observations are also discussed., Comment: 16 pages, 6 figures

In this paper, we study the phenomenological implications of enforcing one texture zero on the inverse matrix of the neutrino mass matrix [Formula: see text] that can lead to the trimaximal mixing. It is found that the condition of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text] can hold in the case of normal neutrino mass ordering, while the condition of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text] can hold in the case of inverted neutrino mass ordering, where [Formula: see text] (for [Formula: see text], [Formula: see text]) denotes the [Formula: see text] entry of the inverse matrix of [Formula: see text]. The ranges of the absolute neutrino mass scale and three CP phases for these cases to hold are studied in some detail. The implications of these cases for the effective neutrino mass [Formula: see text] which controls the rates of the neutrino-less double beta decay processes are also given.

It has been found that the zero mode of a five-dimensional Elko spinor could be localized on branes by introducing a Yukawa-type coupling between the Elko spinor and the background scalar field or the Ricci scalar. However, the Yukawa-type coupling is not appropriate for all brane models. In this paper, we explore other localization mechanism for the Elko spinor by introducing the non-minimal coupling $f(\phi)\mathfrak{L}_{Elko}$ between the five-dimensional Elko spinor and the background scalar field. We give the general expressions of the Elko zero mode and the function $f(\phi)$. Through two thick brane models and three concrete examples, we show that the Elko zero mode can be localized on the branes by this new mechanism. This provides us more possibilities of localizing the Elko zero mode., Comment: 11 pages, 4 figures

In order to localize $U(1)$ gauge vector field on Randall-Sundrum-like braneworld model with infinite extra dimension, we propose a new kind of non-minimal coupling between the $U(1)$ gauge field and the gravity. We propose three kinds of coupling methods and they all support the localization of zero mode. In addition, one of them can support the localization of massive modes. Moreover, the massive tachyonic modes can be excluded. And our method can be used not only in the thin braneword models but also in the thick ones., Comment: Added acknowledgments to the refree. Appeared on JHEP

In this paper, we derive in a novel approach the possible textures of neutrino mass matrix that can lead us to maximal atmospheric mixing angle and Dirac CP phase which are consistent with the current neutrino oscillation data. A total of eleven textures are thus found. Interestingly, the specific texture given by the $\mu$-$\tau$ reflection symmetry can be reproduced from one of the obtained textures. For these textures, some neutrino mass sum rules which relate the neutrino masses and Majorana CP phases will emerge., Comment: 21 pages, 10 figures, version to appear in JHEP, a new paragraph discussing the physical meaning of the textures obtained is added at the end of section 3

Different from the Dirac spinor, the localization of a five-dimensional Elko spinor on a brane with codimension one is very difficult because of the special structure of the Elko spinor. By introducing the coupling between the Elko spinor and the scalar field generating the brane, we have two mechanisms for localization of the zero mode of a five-dimensional Elko spinor on a brane. One is the Yukawa-type coupling and the other is the non-minimal coupling. In this paper, we investigate the localization of the Elko zero mode on de Sitter and Anti-de Sitter thick branes with the two localization mechanisms, respectively. It shows that both the mechanisms can realize the localization. The forms of the coupling functions of the scalar field in the two mechanisms have similar properties respectively and they play similar role for the localization., Comment: 15 pages, 5 figures

The neutrino $\mu$-$\tau$ reflection symmetry has been attracting a lot of attention as it predicts the interesting results $\theta^{}_{23} = \pi/4$ and $\delta = \pm \pi/2$. But it is reasonable to consider breakings of such a symmetry either from the theoretical considerations or on the basis of experimental results. We thus perform a systematic study for the possible symmetry-breaking patterns and their implications for the mixing parameters. The general treatment is applied to some specific symmetry breaking arising from the renormalization group effects for illustration., Comment: 18 pages, 6 figures, 5 tables, minor revision, accepted for publication in JHEP

If massive neutrinos are the Majorana particles and have a normal mass ordering, the effective mass term $\langle m\rangle^{}_{ee}$ of a neutrinoless double-beta ($0\nu 2\beta$) decay may suffer significant cancellations among its three components and thus sink into a decline, resulting in a "well" in the three-dimensional graph of $|\langle m\rangle^{}_{ee}|$ against the smallest neutrino mass $m^{}_1$ and the relevant Majorana phase $\rho$. We present a new and complete analytical understanding of the fine issues inside such a well, and discover a novel threshold of $|\langle m\rangle^{}_{ee}|$ in terms of the neutrino masses and flavor mixing angles: $|\langle m\rangle^{}_{ee}|^{}_* = m^{}_3 \sin^2\theta^{}_{13}$ in connection with $\tan\theta^{}_{12} = \sqrt{m^{}_1/m^{}_2}$ and $\rho =\pi$. This threshold point, which links the {\it local} minimum and maximum of $|\langle m\rangle^{}_{ee}|$, can be used to signify observability or sensitivity of the future $0\nu 2\beta$-decay experiments. Given current neutrino oscillation data, the possibility of $|\langle m\rangle^{}_{ee}| < |\langle m\rangle^{}_{ee}|^{}_*$ is found to be very small., Comment: 9 pages, 3 figures, version to appear in Eur. Phys. J. C

In the framework in which supersymmetry is used for understanding fermion masses rather than stabilizing the electroweak scale, we elaborate the phenomenological analysis for the neutrino physics. A relatively large $\sin{\theta_{13}}$ is the natural result. The model further predicts vanishingly small CP violation in neutrino oscillations. And $\theta_{23}$ is not necessarily maximal. While the high scale supersymmetry generically results in a Higgs mass of about 141 GeV, our model reduces this mass via introducing SU(2)$_L$ triplet fields which also contribute to neutrino masses., Comment: 13 pages, no figure, revtex4, revised version

In light of the observation of a relatively large $\theta^{}_{13}$, one has to consider breaking the $\mu$-$\tau$ symmetry properly which would otherwise result in a vanishing $\theta^{}_{13}$ (as well as $\theta^{}_{23} = \pi/4$). Therefore, we investigate various symmetry-breaking patterns and accordingly identify those that are phenomenologically viable. Furthermore, the symmetry-breaking effects arising from some specific physics (e.g., the renormalization group equation running effect) are discussed as well., Comment: 14 pages, a contribution to the Conference on New Physics at the Large Hadron Collider (29 February to 4 March 2016), Singapore

Behind the observed pattern of lepton flavor mixing is a partial or approximate mu-tau flavor symmetry --- a milestone on our road to the true origin of neutrino masses and flavor structures. In this review article we first describe the features of mu-tau permutation and reflection symmetries, and then explore their various consequences on model building and neutrino phenomenology. We pay particular attention to soft mu-tau symmetry breaking, which is crucial for our deeper understanding of the fine effects of flavor mixing and CP violation., 105 pages, 10 figures. The text reorganized, more references added, minor typos fixed. Invited review article being published in Reports on Progress in Physics

Recently, the MINOS collaboration reported an anomaly that the mass-squared difference and mixing angle of $\bar{\nu}_\mu$ $\leftrightarrow$ $\bar{\nu}_\tau$ are both different from that of $\nu_\mu$ $\leftrightarrow$ $\nu_\tau$. In this paper, based on the framework of neutrino oscillations, terms that break the Lorentz symmetry are used as perturbation to explain this anomaly and satisfactory results are got. Remarkably, some surprising conclusions, one of which is that in the high energy limit (hundreds of GeV) neutrino oscillation pattern will be independent of energy, are also arrived., Comment: 9 pages, 4 figures, references added, accepted for publication in PLB

In this paper, we realize the tri-bimaximal mixing in the lepton sector in the context of minimal seesaw in which only two right-handed neutrinos are introduced, with the discrete group $S4$ as the family symmetry. In order to constrain the form of superpotential, a $Z3$ symmetry is also introduced. In the model, the mass matrices for charged leptons and right-handed neutrinos are diagonal. The unitary matrix that diagonalizes the light Majorana neutrino mass matrix is exact tri-bimaximal at LO, and is corrected by small quantities of $\mathcal{O}(0.01)$ at NLO. The mechanism to get the particular scalar VEV alignments used is also presented. Phenomenologically, the mass spectrum is of normal hierarchy with $m_1=0$, and $\sum m_i$ and $|m_{ee}|$ are about $0.058 eV$ and $0.003 eV$ respectively., 11 pages, accepted for publication in PLB

The neutrino masses can be ascribed to some operators of higher dimension than the Weinberg operator, so that the energy scale of underlying theory can be lowered to an accessible level for the ongoing or upcoming colliders. We hereby consider an interesting model in this connection where quintuplet fermions with hypercharge [Formula: see text]2 are introduced and therefore the neutrino masses are produced by dimension-11 operators. These exotic fermions can be pairly produced at the LHC via electroweak interactions and subsequently decay to multiple leptons. We simulate the relevant signal and backgrounds of the triply charged fermion in this model, and give the needed integrated luminosity to observe such a particle at the 13 TeV LHC.

The latest LHC data suggest an intriguing excess at $m_{\gamma\gamma} = 750$ GeV which apparently requires an explanation from the beyond standard model physics. In this note we explore the possibility for this signal to arise from a top-pion in the Top Triangle Moose model which can be viewed as a dimensional-deconstruction version of the top-color assisted technicolor model. We demonstrate that the observed excess can be accommodated by and has important implications for this interesting model., Comment: 12 pages, 3 figures, Int. J. Mod. Phys. A (2016)

In this paper, we put forward a special neutrino mass matrix which is invariant under a modified Friedberg-Lee (FL) transformation nu(e) -> nu(e) -2 xi and nu(mu,tau) -> nu(mu,tau) + xi with xi being a space-time independent element of the Grassmann algebra. Compared to the original FL symmetry (with the transformation nu(e,mu,tau) -> nu(e,mu,tau) + xi) 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 realistic neutrino mass spectrum, the modified FL symmetry is allowed to remain intact and give us a vanishing m(1). A combination of the FL symmetry with the mu - tau reflection symmetry is also discussed.

We carry out a new study of quark mass matrices $M^{}_{\rm u}$ (up-type) and $M^{}_{\rm d}$ (down-type) which are Hermitian and have four zero entries, and find a new part of the parameter space which was missed in the previous works. We identify two more specific four-zero patterns of $M^{}_{\rm u}$ and $M^{}_{\rm d}$ with fewer free parameters, and present two toy flavor-symmetry models which can help realize such special and interesting quark flavor structures. We also show that the texture zeros of $M^{}_{\rm u}$ and $M^{}_{\rm d}$ are essentially stable against the evolution of energy scales in an analytical way by using the one-loop renormalization-group equations., Comment: 33 pages, 4 figures, minor comments added, version to appear in Nucl. Phys. B

The Majorana nature of massive neutrinos will be crucially probed in the next-generation experiments of the neutrinoless double-beta ($0\nu 2\beta$) decay. The effective mass term of this process, $\langle m\rangle^{}_{ee}$, may be contaminated by new physics. So how to interpret a discovery or null result of the $0\nu 2\beta$ decay in the foreseeable future is highly nontrivial. In this paper we introduce a novel three-dimensional description of $|\langle m\rangle_{ee}^{}|$, which allows us to see its sensitivity to the lightest neutrino mass and two Majorana phases in a transparent way. We take a look at to what extent the free parameters of $|\langle m\rangle_{ee}^{}|$ can be well constrained provided a signal of the $0\nu 2\beta$ decay is observed someday. To fully explore lepton number violation, all the six effective Majorana mass terms $\langle m\rangle_{\alpha\beta}^{}$ (for $\alpha, \beta = e, \mu, \tau$) are calculated and their lower bounds are illustrated with the two-dimensional contour figures. The effect of possible new physics on the $0\nu 2\beta$ decay is also discussed in a model-independent way. We find that the result of $|\langle m\rangle_{ee}^{}|$ in the normal (or inverted) neutrino mass ordering case modified by the new physics effect may somewhat mimic that in the inverted (or normal) mass ordering case in the standard three-flavor scheme. Hence a proper interpretation of a discovery or null result of the $0\nu 2\beta$ decay may demand extra information from some other measurements.

In view of the observation of a relatively large [Formula: see text], one has to break the [Formula: see text]–[Formula: see text] permutation symmetry properly which would otherwise result in a vanishing [Formula: see text] (as well as [Formula: see text]). Motivated by this, we study in a thorough way the various symmetry-breaking patterns and in particular whether an approximate this symmetry can lead to viable consequences. Furthermore, the symmetry-breaking effects arising from some specific physics (e.g. the renormalization group running effect) are discussed as well.

We give some new insights into the effective Majorana neutrino mass [Formula: see text] responsible for the neutrinoless double-beta [Formula: see text] decays. We put forward a three-dimensional way of plotting [Formula: see text] against the lightest neutrino mass and the Majorana phases, which can provide more information as compared with the two-dimensional one. With the help of such graphs we discover a novel threshold of [Formula: see text] in terms of the neutrino masses and flavor mixing angles: [Formula: see text] in connection with [Formula: see text] and [Formula: see text], which can be used to signify observability of the future [Formula: see text]-decay experiments. Fortunately, the possibility of [Formula: see text] turns out to be very small, promising a hopeful prospect for the [Formula: see text]-decay searches.

Tests of Lorentz and CPT violation in the medium baseline reactor antineutrino experiment are presented in the framework of the Standard Model Extension (SME). Both the spectral distortion and sidereal variation are employed to derive the limits of Lorentz violation (LV) coefficients. We do the numerical analysis of the sensitivity of LV coefficients by taking the Jiangmen Underground Neutrino Observatory (JUNO) as an illustration, which can improve the sensitivity by more than two orders of magnitude compared with the current limits from reactor antineutrino experiments., 16 pages, 12 figures, version accepted for publication in PRD

We follow the Chumbes\char21{}Holf da Silva\char21{}Hott mechanism to study the (quasi)localization of the $U(1)$ gauge field on the Bloch brane. The localization and resonances of the $U(1)$ gauge field are discussed for four kinds of Bloch brane solutions: the original and generalized Bloch brane solutions, as well as the degenerate Bloch brane solutions I and II. With the Chumbes\char21{}Holf da Silva\char21{}Hott mechanism, we find that the mass spectrum of the gauge field Kaluza-Klein modes is continuous and there is no tachyonic mode. The zero mode is localized on all the branes and there are resonant Kaluza-Klein modes on the degenerate Bloch branes.

We propose a novel first-order formalism for a type of $K$-brane systems. An example solution is presented and studied. We illustrate how the noncanonical kinetic term can affect the properties of the model, such as the stability of the solutions, the localization of fermion and graviton. We argue that our solution is stable against linear perturbations. The tensor zero mode of graviton can be localized while the scalar zero mode cannot. The localization condition for fermion is also discussed., Comment: 7 pages, 3 figures

A natural model of realizing effective supersymmetry is presented. Two sets of the Standard Model-like gauge group G(1) x G(2) are introduced, where G(i) = SU(3)(i) x SU(2)(i) x U(1)(i), which break diagonally to the Standard Model gauge group at the energy scale M similar to 107 GeV. Gauge couplings in G(1) are assumed to be much larger than those in G(2). Gauge-mediated supersymmetry breaking is adopted. The first two generations (third generation) are only charged only under G(1) (G(2)). The effective supersymmetry spectrum is obtained. The reproduction of realistic Yukawa couplings is studied. The fine-tuning for a 126 GeV Higgs is reduced by the large A term due to direct Higgs-messenger interaction. Finally, G(2) is found to be a nontrivial realization of the strong unification scenario in which case we can predict alpha(s)(M-Z) without real unification.

Recently, a new scalar-tensor braneworld model was presented in [Phys. Rev. \textbf{D 86} (2012) 127502]. It not only solves the gauge hierarchy problem but also reproduces a correct Friedmann-like equation on the brane. In this new model, there are two different brane solutions, for which the mass spectra of gravity on the brane are the same. In this paper, we investigate localization and mass spectra of various bulk matter fields (i.e., scalar, vector, Kalb-Ramond, and fermion fields) on the brane. It is shown that the zero modes of all the matter fields can be localized on the positive tension brane under some conditions, and the mass spectra of each kind of bulk matter field for the two brane solutions are different, which implies that the two brane solutions are not physically equivalent., Comment: v3: 24 pages, 10 figures, 1 table

In this paper, we give a model for understanding flavor physics in the lepton sector--mass hierarchy among different generations and neutrino mixing pattern. The model is constructed in the framework of supersymmetry, with a family symmetry $S4*U(1)$. There are two right-handed neutrinos introduced for seesaw mechanism, while some standard model(SM) gauge group singlet fields are included which transforms non-trivially under family symmetry. In the model, each order of contributions are suppressed by $\delta \sim 0.1$ compared to the previous one. In order to reproduce the mass hierarchy, $m_\tau$ and $\sqrt{\Delta m_{atm}^2}$, $m_\mu$ and $\sqrt{\Delta m_{sol}^2}$ are obtained at leading-order(LO) and next-to-leading-order(NLO) respectively, while electron can only get its mass through next-to-next-to-next-to-leading-order(NNNLO) contributions. For neutrino mixing angels, $\theta_{12}, \theta_{23}, \theta_{13}$ are $45^\circ, 45^\circ, 0$ i.e. Bi-maximal mixing pattern as first approximation, while higher order contributions can make them consistent with experimental results. As corrections for $\theta_{12}$ and $\theta_{13}$ originate from the same contribution, there is a relation predicted for them $\sin{\theta_{13}}=\displaystyle \frac{1-\tan{\theta_{12}}}{1+\tan{\theta_{12}}}$. Besides, deviation from $\displaystyle \frac{\pi}{4}$ for $\theta_{23}$ should have been as large as deviation from 0 for $\theta_{13}$ if it were not the former is suppressed by a factor 4 compared to the latter., Comment: version to appear in Phys. Rev. D

In this paper, we investigate thick branes with a nonminimally coupled background scalar field, whose solution is a single-kink or a double-kink. The effects of the nonminimal coupling constant $\xi$ on the structure of the thick branes and the localization of gravity, fermions, scalars and vectors are discussed. It is shown that each brane will split into two sub-branes as increasing the nonminimal coupling constant $\xi$. By investigating the tensor perturbation equations of gravity and the general covariant Dirac equation of fermions, we find that both the gravity zero mode and left-chiral fermion zero mode are localized at the center of the single-kink branes and localized between the two sub-branes generated by the double-kink, which indicates that the constant $\xi$ does not effect the localization of these zero modes. However, the zero mode of scalars is localized on each sub-brane (for both single-kink and double-kink branes) when $\xi$ is larger than its critical value $\xi_0$. The effects of the nonminimal coupling constant $\xi$ on the resonances of gravity and fermions with finite lifetime on the branes are also discussed., Comment: V2: 33 pages, 17 figures, 3 tables, published version

We suggest a thick braneworld model in the squared curvature gravity theory. Despite the appearance of higher order derivatives, the localization of gravity and various bulk matter fields is shown to be possible. The existence of the normalizable gravitational zero mode indicates that our four-dimensional gravity is reproduced. In order to localize the chiral fermions on the brane, two types of coupling between the fermions and the brane forming scalar is introduced. The first coupling leads us to a Schr\"odinger equation with a volcano potential, and the other a P\"oschl-Teller potential. In both cases, the zero mode exists only for the left-hand fermions. Several massive KK states of the fermions can be trapped on the brane, either as resonant states or as bound states., Comment: 18 pages, 5 figures and 1 table, references added, improved version to be published in JHEP

Following Campos's work [Phys. Rev. Lett. 88, 141602 (2002)], we investigate the effects of temperature on flat, de Sitter (dS), and anti-de Following Campos's work [Phys. Rev. Lett. \textbf{88}, 141602 (2002)], we investigate the effects of temperature on flat, de Sitter (dS), and anti-de Sitter (AdS) thick branes in five-dimensional (5D) warped spacetime, and on the fermion (quasi-)localization. First, in the case of flat brane, when the critical temperature reaches, the solution of the background scalar field and the warp factor is not unique. So the thickness of the flat thick brane is uncertain at the critical value of the temperature parameter, which is found to be lower than the one in flat 5D spacetime. The mass spectra of the fermion Kaluza-Klein (KK) modes are continuous, and there is a series of fermion resonances. The number and lifetime of the resonances are finite and increase with the temperature parameter, but the mass of the resonances decreases with the temperature parameter. Second, in the case of dS brane, we do not find such a critical value of the temperature parameter. The mass spectra of the fermion KK modes are also continuous, and there is a series of fermion resonances. The effects of temperature on resonance number, lifetime, and mass are the same with the case of flat brane. Last, in the case of AdS brane, {the critical value of the temperature parameter can less or greater than the one in the flat 5D spacetime.} The spectra of fermion KK modes are discrete, and the mass of fermion KK modes does not decrease monotonically with increasing temperature parameter., Comment: 24 pages, 15 figures, published version

In this paper, we mainly investigate the problems of resonances of massive KK fermions on a single scalar constructed thick brane with a piecewise warp factor matching smoothly. The distance between two boundaries and the other parameters are determined by one free parameter through three junction conditions. For the generalized Yukawa coupling $\eta\bar{\Psi}\phi^{k}\Psi$ with odd $k=1,3,5,...$, the mass eigenvalue $m$, width $\Gamma$, lifetime $\tau$, and maximal probability $P_{max}$ of fermion resonances are obtained. Our numerical calculations show that the brane without internal structure also favors the appearance of resonant states for both left- and right-handed fermions. The scalar-fermion coupling and the thickness of the brane influence the resonant behaviors of the massive KK fermions., Comment: V3: 15 pages, 7 figures, published version

A few years ago, Campos investigated the critical phenomena of thick branes in warped spacetimes [Phys. Rev. Lett. {\bf 88} (2002) 141602]. Inspired by his work, we consider a toy model of thick branes generated by a real scalar field with the potential $V(\phi)=a\phi^2-b\phi^4+c\phi^6$, and investigate the variation of the mass parameter $a$ on the branes as well as the localization and resonances of fermions. An interesting result is found: there is a critical value for the mass parameter $a$, and when the critical value of $a$ is reached the solution of the background scalar field is not unique and has the shape of a double kink. This happens in both cases with and without gravity. It is also shown that the numbers of the bound Kaluza-Klein modes of fermions on the gravity-free brane and the resonant states of fermions on the brane with gravity increase with the value of $a$., Comment: 10 pages, 12 figures, published version

In arXiv:0901.3543, the simplest Yukawa coupling $\eta\bar{\Psi}\phi\chi\Psi$ was considered for a two-scalar-generated Bloch brane model. Fermionic resonances for both chiralities were obtained, and their appearance is related to branes with internal structure. Inspired on this result, we investigate the localization and resonance spectrum of fermions on a one-scalar-generated $dS$ thick brane with a class of scalar-fermion couplings $\eta\bar{\Psi}\phi^k\Psi$ with positive odd integer $k$. A set of massive fermionic resonances for both chiralities are obtained when provided large couple constant $\eta$. We find that the masses and life-times of left and right chiral resonances are almost the same, which demonstrates that it is possible to compose massive Dirac fermions from the left and right chiral resonances. The resonance with lower mass has longer life-time. For a same set of parameters, the number of resonances increases with $k$ and the life-time of the lower level resonance for larger $k$ is much longer than the one for smaller $k$., Comment: 23 pages, 35 figures, discussion and references added, to appear in PRD

Motivated by the recent work on the fermion resonances on scalar-constructed thick branes (arXiv:0901.3543 and arXiv:0904.1785), we extend the idea to multi-scalar generated thick branes and complete previous work. The fermion localization and resonances on the three-field and two-field thick branes are investigated. With the Numerov method, our numerical results show that the resonance states also exist in the brane besides the single-field thick branes and the two-field thick branes in the former cases. This interesting phenomenon is related to the internal structure of the brane and the coupling of fermions and scalars. We find that the Kaluza-Klein chiral decomposition of massive fermion resonances is the parity-chiral decomposition. For the couplings $\eta\bar{\Psi}\phi^{k}\chi\rho\Psi$ and $\eta\bar{\Psi}\phi^{k}\chi\rho\Psi$ for three-field and two-field models with odd positive $k$, respectively, the number of the resonant states decreases with $k$. This result is opposite to the one obtained in the single-field de Sitter thick brane (arXiv:0904.1785)., Comment: 30 pages, 17 figures, to appear in JHEP

An asymmetric thick domain wall solution with de Sitter ($dS$) expansion in five dimensions can be constructed from a symmetric one by using a same scalar (kink) with different potentials. In this paper, by presenting the mass-independent potentials of Kaluza--Klein (KK) modes in the corresponding Schr\"{o}dinger equations, we investigate the localization and mass spectra of various bulk matter fields on the symmetric and asymmetric $dS$ thick branes. It is shown that the spectrum of scalar KK modes on the symmetric $dS$ brane contains only one bound mode (the massless mode). However, for the asymmetric $dS$ brane with a large asymmetric factor $a$, there are two bound scalar KK modes: a zero mode and a massive mode. For spin 1 vectors, the spectra of KK modes on both $dS$ branes consist of a bound massless mode and a set of continuous ones, i.e., the asymmetric factor does not change the number of the bound vector KK modes. For spin 1/2 fermions with the scalar-fermion coupling $\eta\bar\Psi \sin(\phi/\phi_0)\cos^{-\delta}(\phi/\phi_0)\Psi$, there exist some discrete bound KK modes and a series of continuous ones. The asymmetric factor $a$ reduces the number of the bound fermion KK modes., Comment: 28 pages, 28 figures

The first order perturbations of the energy levels of a stationary hydrogen atom in static external gravitational field, with Schwarzschild metric, are investigated. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S, 4P, 4D and 4F levels. The results show that the energy-level shifts of the states with total angular momentum quantum number 1/2 are all zero, and the ratio of absolute energy shifts with total angular momentum quantum number 5/2 is 1:4:5. This feature can be used to help us to distinguish the gravitational effect from other effect., 11 pages

The first order perturbations of the energy levels of a hydrogen atom in central internal gravitational field are investigated. The internal gravitational field is produced by the mass of the atomic nucleus. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S and 4P levels with Schwarzschild metric. The calculated results show that the gravitational corrections are sensitive to the total angular momentum quantum number., 7 pages

In this paper we investigate the localization and mass spectra of bulk matter fields on a Gergory-Rubakov-Sibiryakov-inspired braneworld. In this braneworld model, there are one thick brane located at the origin of the extra dimension and two thin branes at two sides. For spin 1/2 fermions coupled with the background scalar $\phi$ via $\eta\bar{\Psi}\phi^p\Psi$ with $p$ a positive odd integer, the zero mode of left-hand fermions can be localized on the thick brane for finite distance of the two thin branes, and there exist some massive bound modes and resonance modes. The resonances correspond to the quasi-localized massive fermions. For free massless spin 0 scalars, the zero mode can not be localized on the thick brane when the two thin branes are located finitely. While for a massive scalar $\Phi$ coupled with itself and the background scalar field $\phi$, in order to get a localized zero mode on the thick brane, a fine-tuning relation should be introduced. Some massive bound modes and resonances also will appear. For spin 1 vectors, there is no bound KK mode because the effective potential felt by vectors vanishes outside the two thin branes. We also investigate the physics when the distance of the two thin branes tends to infinity.