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Energy Correlators measure the energy deposited in multiple detectors as a function of the angles between the detectors. In this paper, we analytically compute the three particle correlator in the collinear limit in QCD for quark and gluon jets, and also in $\mathcal{N}=4$ super Yang-Mills theory. We find an intriguing duality between the integrals for the energy correlators and infrared finite Feynman parameter integrals, which maps the angles of the correlators to dual momentum variables. In $\mathcal{N}=4$, we use this duality to express our result as a rational sum of simple Feynman integrals (triangles and boxes). In QCD our result is expressed as a sum of the same transcendental functions, but with more complicated rational functions of cross ratio variables as coefficients. Our results represent the first analytic calculation of a three-prong jet substructure observable of phenomenological relevance for the LHC, revealing unexplored simplicity in the energy flow of QCD jets. They also provide valuable data for improving the understanding of the light-ray operator product expansion., Comment: 52 pages, 12 figures v2. Minor typos corrected, matches journal version

In this paper, we generalize the integration rules for scattering equations to situations where higher-order poles are present. We describe the strategy to deduce the Feynman rules of higher-order poles from known analytic results of simple CHY-integrands, and propose the Feynman rules for single double pole and triple pole as well as duplex-double pole and triplex-double pole structures. We demonstrate the validation and strength of these rules by ample non-trivial examples., 52 pages, 37 figures

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 note, we study the $\mathcal{Q}$-cut representation by combining it with BCFW deformation. As a consequence, the one-loop integrand is expressed in terms of a recursion relation, i.e., $n$-point one-loop integrand is constructed using tree-level amplitudes and $m$-point one-loop integrands with $m\leq n-1$. By giving explicit examples, we show that the integrand from the recursion relation is equivalent to that from Feynman diagrams or the original $\mathcal{Q}$-cut construction, up to scale free terms., Comment: 30 pages, 2 figures

One-loop scattering amplitudes in N=4 super Yang-Mills (SYM) theories are analyzed in the paradigm of maximal helicity violating Feynman diagrams. There are very limited number of loop integrals to be evaluated. For a process with n external particles, there are only [n/2]-1 generically independent integrals. Furthermore, the relations between leading N_c amplitudes A_{n;1} and sub-leading amplitudes A_{n;c} are found to be identical to those obtained from conventional field theory calculations, which can be interpreted as an indirect support for the paradigm., Comment: Minor changes, published version

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

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., 12 pages, 8 figures, revtex4; typos fixed

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., 15 pages, more discussions added, accepted by Nucl Phys B

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., 16 pages, minor corrections, further comments and references added

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

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., 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

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

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

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

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

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., Minor changes. Published version

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

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 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

One-loop maximal helicity violating (MHV) amplitudes in N=4 super Yang-Mills (SYM) theories are analyzed, using the prescription of Cachazo, Svrcek, and Witten (CSW). The relations between leading N_c amplitudes A_{n;1} and sub-leading amplitudes A_{n;c} obtained by the CSW prescription are found to be identical to those obtained from conventional field theory calculations. Combining with existing results, this establishes the validity of the CSW prescription to one-loop in the calculation of MHV amplitudes in N=4 SYM theories of finite N_c., Minor changes and typos fixed. Published version in JHEP

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