Search

Machine learning has been successfully applied to identify phases and phase transitions in condensed matter systems. However, quantitative characterization of the critical fluctuations near phase transitions is lacking. In this study we propose a finite-size scaling approach based on a convolutional neural network and analyze the critical behavior of a quantum Hall plateau transition. The localization length critical exponent learned by the neural network is consistent with the value obtained by conventional approaches. We show that the general-purposed method can be used to extract critical exponents in models with drastically different physics and input data, such as the two-dimensional Ising model and 4-state Potts model., Comment: 11 pages, 12 figures

Unsupervised machine learning via a restricted Boltzmann machine is an useful tool in distinguishing an ordered phase from a disordered phase. Here we study its application on the two-dimensional Ashkin-Teller model, which features a partially ordered product phase. We train the neural network with spin configuration data generated by Monte Carlo simulations and show that distinct features of the product phase can be learned from non-ergodic samples resulting from symmetry breaking. Careful analysis of the weight matrices inspires us to define a nontrivial machine-learning motivated quantity of the product form, which resembles the conventional product order parameter., Comment: 9 pages, 11 figures

The functional renormalization group equation is expanded to a two-loop form. This two-loop form equation involves one-loop effective action. An intermediate effective action perspective is adopted toward the one-loop effective action. That is to say, the intermediate effective action could not be of the same form of the bare action and one can make an ansatz to it. Thus by focusing on different high dimensional operators, effects of the chosen operators can be investigated. QCD through intermediate fermion-4 interactions is investigated. Of the 6 kinds of fermion-4 interactions generated by one-loop QCD, 4 kinds generate fermion mass while the other 2 kinds degenerate it. The net effect is fermion mass degeneration when dimensionless mass is large. Flow patterns on the $\tilde{m}^2_{\text{phys.}}-\tilde{g}^2$ plane are drawn., Comment: 6 pages, 5 figures, revtex4

The dependence of function renormalization group equation on regulators is investigated. A parameter is introduced to control the suppression of regulators. Functional renormalization group equations will become regulator-independent if this newly introduced parameter is sent to infinity in the end of calculation. One-loop renormalization flow equations of QCD are derived. The novelty is that both the coupling running equation and the mass running equation are mass-dependent. Different flow patterns are explored. A mechanism for non-occurrence of dynamical chiral symmetry breaking is arrived at. The existence of a conformal window is also discussed in the language of renormalization flow., Comment: 12 pages, 8 figures, revtex4; typos fixed

This article provides an introduction to on-shell recursion relations for calculations of tree-level amplitudes. Starting with the basics, such as spinor notations and color decompositions, we expose analytic properties of gauge-boson amplitudes, BCFW-deformations, the large $z$-behavior of amplitudes, and on-shell recursion relations of gluons. We discuss further developments of on-shell recursion relations, including generalization to other quantum field theories, supersymmetric theories in particular, recursion relations for off-shell currents, recursion relation with nonzero boundary contributions, bonus relations, relations for rational parts of one-loop amplitudes, recursion relations in 3D and a proof of CSW rules. Finally, we present samples of applications, including solutions of split helicity amplitudes and of N= 4 SYM theories, consequences of consistent conditions under recursion relation, Kleiss-Kuijf (KK) and Bern-Carrasco-Johansson (BCJ) relations for color-ordered gluon tree amplitudes, Kawai-Lewellen-Tye (KLT) relations., Comment: 80 pages, 8 figures; references added; minor changes of text

In this paper, we emphasize that a UV SUSY-breaking theory can be realized either linearly or nonlinearly. Both realizations form the dual descriptions of the UV SUSY-breaking theory. Guided by this observation, we find subtle identities involving the Goldstino field and matter fields in the standard nonlinear realization from trivial ones in the linear realization. Rather complicated integrands in the standard nonlinear realization are identified as total-divergences. Especially, identities only involving the Goldstino field reveal the self-consistency of the Grassmann algebra. As an application of these identities, we prove that the nonlinear Kahler potential without or with gauge interactions is unique, if the corresponding linear one is fixed. Our identities pick out the total-divergence terms and guarantee this uniqueness., Comment: 15 pages, more discussions added, accepted by Nucl Phys B

In a recent paper [arXiv:1106.0166], boundary contributions in BCFW recursion relations have been related to roots of amplitudes. In this paper, we make several analyses regarding to this problem. Firstly, we use different ways to re-derive boundary BCFW recursion relations given in [arXiv:1106.0166]. Secondly, we generalize factorization limits to z-dependent ones, where information of roots is more transparent. Then, we demon- strate our analysis with several examples. In general, relations from factorization limits cannot guarantee to find explicit expressions for roots., Comment: 29p, no figure

By using recent data, we directly determine the dark matter (DM) induced $e^\pm$ spectrum at the source from experimental measurements at the earth, without reference to specific particle physics models. The DM induced gamma rays emitted via inverse Compton scattering are then obtained in a model independent way. However the results depend on the choice of the astrophysical $e^\pm$ background, which is not reliably known. Nevertheless, we calculate, as an illustration, the fluxes of gamma rays from the Fornax cluster in the decaying DM scenario with various astrophysical $e^\pm$ backgrounds. Without any assumptions on details of the DM model, the predictions turn out to be either in disagreement with or only marginally below the upper limits measured recently by the Fermi-LAT Collaboration. In addition, these DM induced ICS gamma rays in the GeV range are shown to be almost independent of choices of cosmic ray propagation model and of DM density profile, when a given astrophysical $e^\pm$ background is assumed. This provides a strong constraint on decaying DM scenario as the gamma rays may be produced in other processes besides inverse Compton scattering, such as the bremsstrahlung and neutral pion decays., Comment: 14 pages, 5 figures, Latex, to match the published version

We study the Bondi-Sachs rockets with nonzero cosmological constant. We observe that the acceleration of the systems arises naturally in the asymptotic symmetries of (anti-) de Sitter spacetimes. Assuming the validity of the concepts of energy and mass previously introduced in asymptotically flat spacetimes, we find that the emission of pure radiation energy balances the loss of the Bondi mass in certain special families of the Bondi-Sachs rockets, so in these there is no gravitational radiation., Comment: 12 pages, to appear in General Relativity and Gravitation

We consider extended cosmological gravities with Ricci tensor and scalar squared terms in diverse dimensions. These theories admit solutions of Einstein metrics, including the Schwarzschild-Tangherlini AdS black holes, whose mass and entropy vanish at the critical point. We perform linearized analysis around the black holes and show that in general the spectrum consists of the usual spin-2 massless and ghost massive modes. We demonstrate that there is no exponentially-growing tachyon mode in the black holes. At the critical point, the massless spin-2 modes have zero energy whilst the massive spin-2 modes are replaced by the log modes. There always exist certain linear combination of massless and log modes that has negative energy. Thus the stability of the black holes requires that the log modes to be truncated out by the boundary condition., Comment: 16 pages, minor corrections, further comments and references added

Recently, the Fermi-LAT collaboration reported upper limits on the GeV gamma-ray flux from nearby clusters of galaxies. Motivated by these limits, we study corresponding constraints on gamma-ray emissions from two specific decaying dark matter models, one via grand unification scale suppressed operators and the other via R-parity violating operators. Both can account for the PAMELA and Fermi-LAT excesses of e^\pm. For GUT decaying dark matter, the gamma-rays from the M49 and Fornax clusters, with energy in the range of 1 to 10 GeV, lead to the most stringent constraints to date. As a result, this dark matter is disfavored with conventional model of e^\pm background. In addition, it is likely that some tension exists between the Fermi-LAT e^\pm excess and the gamma ray constraints for any decaying dark matter model, provided conventional model of e^\pm background is adopted. Nevertheless, the GUT decaying dark matter can still solely account for the PAMELA positron fraction excess without violating the gamma-ray constraints. For the gravitino dark matter model with R-parity violation, cluster observations do not give tight constraints. This is because a different e^\pm background has been adopted which leads to relatively light dark matter mass around 200 GeV., Comment: 17 pages, 4 figures, version to appear in Phys. Lett. B

An important phase transition in black hole thermodynamics is associated with the divergence of the specific heat with fixed charge and angular momenta, yet one can demonstrate that neither Ruppeiner's entropy metric nor Weinhold's energy metric reveals this phase transition. In this paper, we introduce a new thermodynamical metric based on the Hessian matrix of several free energy. We demonstrate, by studying various charged and rotating black holes, that the divergence of the specific heat corresponds to the curvature singularity of this new metric. We further investigate metrics on all thermodynamical potentials generated by Legendre transformations and study correspondences between curvature singularities and phase transition signals. We show in general that for a system with n-pairs of intensive/extensive variables, all thermodynamical potential metrics can be embedded into a flat (n,n)-dimensional space. We also generalize the Ruppeiner metrics and they are all conformal to the metrics constructed from the relevant thermodynamical potentials., Comment: Latex, 25 pages, reference added, typos corrected, English polished and the Hawking-Page phase transition clarified; to appear in JHEP

This paper starts with a self-contained discussion of the so-called Akulov-Volkov action S_AV, which is traditionally taken to be the leading-order action of Goldstino field. Explicit expressions for S_AV and its chiral version S_AV^ch are presented. We then turn to the issue on how these actions are related to the leading-order action S_NL proposed in the newly proposed constrained superfield formalism. We show that S_NL may yield S_AV/S_AV^ch or a totally different action S_KS, depending on how the auxiliary field in the former is integrated out. However, S_KS and S_AV/S_AV^ch always yield the same S-matrix elements, as one would have expected from general considerations in quantum field theory., Comment: Minor changes, version to appear in European Physical Journal C

This paper revisits the nonlinear realization of spontaneously broken N=1 supersymmetry. It is shown that the constrained superfield formalism can be reinterpreted in the language of standard realization of nonlinear supersymmetry via a new and simpler route. Explicit formulas of actions are presented for general renormalizable theories with or without gauge interactions. The nonlinear Wess-Zumino gauge is discussed and relations are pointed out for different definitions of gauge fields. In addition, a general procedure is provided to deal with theories of arbitrary Kahler potentials., Comment: 1+18 pages, LaTex

Motivated by recent observations from Pamela, Fermi and H.E.S.S., we consider dark matter decays in the framework of supersymmetric SU(5) grand unification theories. An SU(5) singlet S is assumed to be the main component of dark matters, which decays into visible particles through dimension six operators suppressed by the grand unification scale. Under certain conditions, S decays dominantly into a pair of sleptons with universal coupling for all generations. Subsequently, electrons and positrons are produced from cascade decays of these sleptons. These cascade decay chains smooth the electron/positron spectrum, which permit naturally a good fit to the Fermi LAT data. The observed positron fraction upturn by PAMELA can be reproduced simultaneously. We have also calculated diffuse gamma-ray spectra due to the electron/positron excesses and compared them with the preliminary Fermi LAT data from 0.1 GeV to 10 GeV in the region 0

A Goldstino field in the nonlinear realization of supersymmetry is constructed from an appropriate chiral super-multiplet of the linear theory, in general O'Raifeataigh-like models. The linear theories can thus be reformulated into their nonlinear versions, via the standard procedure. The Goldstino field disappears totally from the original Lagrangian in the process, but reemerges in the Jacobian of the transformation and covariant derivatives. Vertices with Goldstino fields carry at least one space-time derivative, as one would have expected., Comment: 7+1 pages, Latex

A constrained superfield formalism has been proposed recently to analyze the low energy physics related to Goldstinos. We prove that this formalism can be reformulated in the language of standard realization of nonlinear supersymmetry. New relations have been uncovered in the standard realization of nonlinear supersymmetry., Comment: 8+1 pages, Latex, expanded discussions on scalar and vector fields

To get the total cross section of one interaction from its amplitude ${\cal M}$, one needs to integrate $|{\cal M}|^2$ over phase spaces of all out-going particles. Starting from this paper, we will propose a new method to perform such integrations, which is inspired by the reduced phase space integration of one-loop unitarity cut developed in the last few years. The new method reduces one constrained three-dimension momentum space integration to an one-dimensional integration, plus one possible Feynman parameter integration. There is no need to specify a reference framework in our calculation, since every step is manifestly Lorentz invariant by the new method. The current paper is the first paper of a series for the new method. Here we have exclusively focused on massless particles in 4D. There is no need to carve out a complicated integration region in the phase space for this particular simple case because the integration region is always simply $[0,1]$., Comment: 28 pages, 1 figure; further comments and references added; Appendix B added

Supersymmetric models with extended group structure beyond the standard model are revisited in the framework of general gauge mediation. Sum rules for sfermion masses are shown to depend genuinely on the group structure, which can serve as important probes for specific models. The left-right model and models with extra U(1) are worked out for illustrations. If the couplings of extra gauge groups are small, supersymmetric hidden valleys of the scale 10-100 GeV can be naturally constructed in companion of a TeV-scale supersymmetric visible sector., Comment: 13 pages, 2 figures

We have studied $R$-symmetrc gauge mediation models with Fayet-Iliopoulos terms. We give a concrete example of hidden sector with an $U(1)_H$ gauge theory and a Fayet-Iliopoulos term, which can induce distinctive soft terms in the visible sector, and help solving fine tuning problems in models of $R$-symmetric gauge mediation., Comment: 11 pages, 1 figure

It was observed recently by Randall and Wise that, any particle in the Standard Model cannot decay to $e^+e^-$ and $\gamma \gamma$ final states with comparably measurable branching ratios. This is also true for most extensions of the Standard Model, with the Randall-Sundrum model as an outstanding exception. In this paper, we show that two-Higgs-Doublet-Models (2HDM) yield another possible exception if certain parameters are properly chosen. In addition, we have checked that this model survives the tests of low energy processes, including the anomalous magnetic moment and electric dipole moment of leptons, lepton-flavor-violating decays $\mu^- \to e^- \gamma$ and $e^- e^+ e^-$., Comment: Minor changes, version to appera in Phys. Lett. B

String instanton effects in Higgs physics are discussed through a type IIA model based on T^{6}/(Z^{2}\times Z^{'2}) orentifold compactifaction. By inclusion of rigid E2-branes, the model exhibits a MSSM-like spectrum, as well as extra mu and quartic Higgs couplings. These extra couplings are induced via E2 instantons non-perturbatively. Setting the string scale at 10^{18} GeV, one gets interesting TeV Higgs physics. In particlular, the tree-level Higgs mass can be uplifted substantially., Comment: 11 pages, 1 figure

We use planar coordinates as well as hyperbolic coordinates to separate the de Sitter spacetime into two parts. These two ways of cutting the de Sitter give rise to two different spatial infinities. For spacetimes which are asymptotic to either half of the de Sitter spacetime, we are able to provide definitions of the total energy, the total linear momentum, the total angular momentum, respectively. And we prove two positive mass theorems, corresponding to these two sorts of spatial infinities, for spacelike hypersurfaces whose mean curvatures are bounded by certain constant from above., Comment: 24 pages, final version, to appear in Nuclear Physics B

Quintessence field is a widely-studied candidate of dark energy. There is "tracker solution" in quintessence models, in which evolution of the field $\phi$ at present times is not sensitive to its initial conditions. When the energy density of dark energy is neglectable ($\Omega_\phi\ll1$), evolution of the tracker solution can be well analysed from "tracker equation". In this paper, we try to study evolution of the quintessence field from "full tracker equation", which is valid for all spans of $\Omega_\phi$. We get stable fixed points of $w_\phi$ and $\Omega_\phi$ (noted as $\hat w_\phi$ and $\hat\Omega_\phi$) from the "full tracker equation", i.e., $w_\phi$ and $\Omega_\phi$ will always approach $\hat w_\phi$ and $\hat\Omega_\phi$ respectively. Since $\hat w_\phi$ and $\hat\Omega_\phi$ are analytic functions of $\phi$, analytic relation of $\hat w_\phi\sim\hat\Omega_\phi$ can be obtained, which is a good approximation for the $w_\phi\sim\Omega_\phi$ relation and can be obtained for the most type of quintessence potentials. By using this approximation, we find that inequalities $\hat w_\phi

An attempt has been made to address the 3\sigma anomaly of the forward-backward asymmetry of b quark in LEP data via an unparticle sector. For most part of the parameter space except certain particular regions, the anomaly could not be explained away plausibly, when constraints from other LEP observables are taken into account., Comment: Version to appear in Phys. Lett. B. 13 pages, 5 figures

Fermionic unparticles are introduced and their basic properties are discussed. Some phenomenologies related are exploited, such as their effects on charged Higgs boson decays and anomalous magnetic moments of leptons. Also, it has been found that measurements of $B^0-\bar B^0$ mixing could yield interesting constraints on couplings between unparticle operators and standard model fields., Comment: Version to appear in Phys. Letts. B. 9 pages, 3 figures

Analytic form has been obtained for four-dimensional black holes with a minimal Hawking temperature in a theory with cosmological constant, dilaton and gauge fields. In general dimensions, black hole solutions are shown to exist and their asymptotic behaviors are obtained. In theories of ten dimension, N coincident D3-branes as the boundary of an $AdS_5$ space are constructed by embedding black D3-branes, with a five-dimensional compactified space of negligible size if N is large, which provide natural realizations of the Randall-Sundrum scenario. For this $AdS_{5}$ background, the cosmological constant is a higher order perturbation and its effect on the spectra of standard model fields on the branes can be calculated., Comment: 12 pages, no figures

Positivity constraints are derived on pion-nucleon scattering amplitudes and their even-order derivatives inside the Mandelstam Triangle with the help of dispersion relations. Fairly interesting constraints are obtained on some of the low energy constants, by a combination of the chiral perturbation theory for heavy baryons and existing fitting results from available pion-nucleon phase shifts at intermediate energies., Comment: version to appear in Phys. Lett. B. 6 pages

Non-minimally coupled theories of special potentials are analyzed numerically. Such theories yield equations of state $\omega<-1$ and oscillations of the cosmological expansion, which are favored by the recent analysis of observations. Fitting these theories to the Gold SnIa dataset, we obtain results comparable with other models. A potential of the form $V(\phi)=V_0e^{a_1\phi^2}$ yields $\chi^2_{min}=170.127$. Similar results are obtained for potentials of the form $V(\phi)=V_0+a_1\phi^n$., Comment: 8 pages, 7 figures, accepted for publication in Phys. Lett. B

Compact results are obtained for tree-level non-MHV amplitudes of six fermions and of four fermions and two gluons, by using extended BCF/BCFW rules. Combining with previous results, complete set of tree amplitudes of six partons are now available in compact forms., Comment: 11 pages, RevTex. New results for fermions of multi-flavor and in fundamental representations are included

Using newly proposed BCF/BCFW recursion relations, compact formulas are obtained for tree-level n-gluon amplitudes of helicity structure --++...+. We then make an extension of these recursion relations to include fermions of multi-flavors, from which MHV and \bar{MHV} amplitudes are reproduced. We also calculate non-MHV amplitudes of processes with two fermions and four gluons. Results thus obtained are equivalent to those obtained by extended CSW prescriptions, and those by conventional field theory calculations., Comment: Minor changes. Published version