Showing papers on "Vertex function published in 2009"

Remodeling the B-Model

Abstract: We propose a complete, new formalism to compute unambiguously B-model open and closed amplitudes in local Calabi–Yau geometries, including the mirrors of toric manifolds. The formalism is based on the recursive solution of matrix models recently proposed by Eynard and Orantin. The resulting amplitudes are non-perturbative in both the closed and the open moduli. The formalism can then be used to study stringy phase transitions in the open/closed moduli space. At large radius, this formalism may be seen as a mirror formalism to the topological vertex, but it is also valid in other phases in the moduli space. We develop the formalism in general and provide an extensive number of checks, including a test at the orbifold point of Ap fibrations, where the amplitudes compute the ’t Hooft expansion of vevs of Wilson loops in Chern-Simons theory on lens spaces. We also use our formalism to predict the disk amplitude for the orbifold \({{mathbb {C}}^3 /{mathbb{Z}}_3}\) .

Efficient Parametrization of the Vertex Function, $Ω$-Scheme, and the (t,t')-Hubbard Model at Van Hove Filling

Abstract: We propose a parametrization of the four-point vertex function in the one-loop one-particle irreducible renormalization group (RG) scheme for fermions. It is based on a decomposition of the effective two-fermion interaction into fermion bilinears that interact via exchange bosons. The numerical computation of the RG flow of the boson propagators reproduces the leading weak-coupling instabilities of the two-dimensional Hubbard model at van Hove filling as they were obtained in a temperature RG scheme [C. Honerkamp and M. Salmhofer, Phys. Rev. B 64, 184516 (2001)]. Instead of regularizing with temperature, we here use a soft frequency $\ensuremath{\Omega}$ regularization that likewise does not artificially suppress ferromagnetism. Besides being more efficient than previous $N$-patch schemes, this parametrization also reduces the ambiguities in introducing boson fields.

Nonequilibrium functional RG with frequency dependent vertex function: A study of the single impurity Anderson model

Abstract: We investigate nonequilibrium properties of the single impurity Anderson model by means of the functional renormalization group (fRG) within Keldysh formalism. We present how the level broadening Γ/2 can be used as flow parameter for the fRG. This choice preserves importan t aspects of the Fermi liquid behaviour that the model exhibits in case of particle-hole symmetry. An approximation scheme for the Keldysh fRG is developed which accounts for the frequency dependence of the two-particle vertex in a way similar but not equivalent to a recently published approximation to the equilibrium Matsubara fRG. Our method turns out to be a flexible tool for the study of weak to intermediate on-site interactions U . 3Γ. In equilibrium we find excellent agreement with NRG results for the linear conductance at finite gate vol tage, magnetic field, and temperature. In nonequilibrium, our results for the current agree well with TD-DMRG. For the nonlinear conductance as function of the bias voltage, we propose reliable results at finite magne tic field and finite temperature. Furthermore, we demonstrate the exponentially small scale of the Kondo temperature to appear in the second order derivative of the self-energy. We show that the approximation is, however, not able to reproduce the scaling of the effective mass at large interactions.

The self-energy beyond GW: local and nonlocal vertex corrections.

Abstract: It is commonly accepted that the GW approximation for the electron self-energy is successful for the description of the band structure of weakly to moderately correlated systems, whereas it will fail for strongly correlated materials. In the present work, we discuss two important aspects of this approximation: first, the "self-screening error," which is due to an incorrect treatment of induced exchange, and second, the atomic limit, in which, instead, correlation is directly responsible for the observed problem. Using the example of the removal of a particle from a box, we show that the self-screening error stems from the use of test charge-test charge screening and that it can be corrected by a two-point vertex contribution to the self-energy derived from time-dependent density functional theory (TDDFT). We explain why the addition of a particle, instead, requires the use of a different approximate vertex. This illustrates why the general vertex function, valid both for valence and conduction states, must be a three-point function. Moreover, we show that also the bad performance of GW in the atomic limit is due to the neglect of the vertex in the self-energy; in that case, the TDDFT-derived vertex correction is not sufficient in order to remove the error even qualitatively. We discuss the effects of the self-screening error as well as the atomic limit using GW for the exactly solvable two-site Hubbard model.

Evaluating decay rates and asymmetries of {lambda}{sub b} into light baryons in the light-front quark model

Abstract: In this work we calculate the branching ratios of semileptonic and nonleptonic decays of {lambda}{sub b} into light baryons (p and {lambda}), as well as the measurable asymmetries which appear in the processes, in the light-front quark model. In the calculation, we adopt the diquark picture and discuss the justifiability of applying the picture in our case. Our result on the branching ratio of {lambda}{sub b}{yields}{lambda}+J/{psi} is in good agreement with the data. More predictions are made in the same model and the results will be tested in the future experiments which will be conducted at the Large Hadron Collider beauty and even the International Linear Collider.

T-odd correlations from CP violating anomalous top-quark couplings revisited

Abstract: We revisit the effect of $CP$ violating anomalous top-quark couplings in $t\overline{t}$ production and decay. We consider $t\overline{t}$ production through gluon fusion (and light $q\overline{q}$ annihilation) followed by top-quark decay into $bW$ or $b\ensuremath{\ell}\ensuremath{ u}$. We find explicit analytic expressions for all the triple products generated by the anomalous couplings that fully incorporate all spin correlations. Our results serve as a starting point for numerical simulations for the CERN LHC.

Strange mesons and kaon-to-pion transition form factors from holography

Abstract: We present a calculation of the K{sub l3} transition form factors using the AdS/QCD correspondence. We also solidify and extend our ability to calculate quantities in the flavor-broken versions of AdS/QCD. The normalization of the form factors is a crucial ingredient for extracting |V{sub us}| from data, and the results obtained here agree well with results from chiral perturbation theory and lattice gauge theory. The slopes and curvature of the form factors agree well with the data, and with what results are available from other methods of calculation.

Quark number susceptibility around the critical end point

Abstract: The quark number susceptibility is expressed as an integral in terms of dressed quark propagator and dressed vector vertex. It is then investigated with the latter two- and three-point functions confronted with a Dyson-Schwinger equation model which accommodates both finite temperature and baryon chemical potential. The critical end point in the phase diagram is identified and the behavior of the quark number susceptibility around the critical end point is highlighted. The qualitative features found agree with recent lattice QCD simulation results.

The high energy behavior of QCD: The effective action and the triple-Pomeron-vertex

Abstract: We study integrations over light-cone momenta in the high energy effective action of QCD. After a review of the effective action, we arrive on a regularization mechanism from matching with QCD diagrams, which we apply to a re-derivation of the reggeized gluon and of the BFKL-equation. We study consequences of the proposed regularization on the analytic structure of 2->3 and 2->4 production amplitudes in the Multi-Regge-Kinematics. We derive a certain part of the 1-loop corrections to the production vertex and demonstrate that they yield the on-set of corrections demanded by the Steinmann-relations. The Reggeon-Particle-2-Reggeon vertex is determined and applied to the construction of various signature configurations of the production amplitudes. We extend the regularization method to states of three and four reggeized gluons and propose a supplement to the effective Lagrangian. We derive vertices for the 1-3 and 2-4 reggeized gluon transition for the elastic amplitude and verify that signature conservation is obeyed. Integral equations for the state of three and four reggeized gluons are formulated and shown to agree with a result by Bartels and Wusthoff. In a second part we investigate the high-energy behavior of QCD for different surface topologies of color graphs. After a brief review of the planar limit (bootstrap and gluon reggeization) and of the cylinder topology (BFKL) we investigate the 3-3 scattering in the triple Regge limit which belongs to the pair-of-pants topology. We re-derive the triple Pomeron vertex function and show that it belongs to a specific set of graphs in color space which we identify as the analog of the Mandelstam diagram. We then extend the study to the high-energy behavior of N=4 SYM where we find a new class of color graphs not present in QCD.

Photoproduction through Chern-Simons Term Induced Interactions in Holographic QCD

Abstract: We employ both top-down and bottom-up holographic dual models of QCD to calculate vertex functions and couplings that are induced by the five-dimensional Chern-Simons term. We use these couplings to study the photoproduction of ${f}_{1}$ mesons. The Chern-Simons-term-induced interaction leads to a simple relation between the polarization of the incoming photon and the final state ${f}_{1}$ meson which should allow a clear separation of this interaction from competing processes.

Particle phenomenology on noncommutative spacetime

Abstract: We introduce particle phenomenology on the noncommutative spacetime called the Groenewold-Moyal plane. The length scale of spacetime noncommutativity is constrained from the $CPT$ violation measurements in the ${K}^{0}\ensuremath{-}{\overline{K}}^{0}$ system and $g\ensuremath{-}2$ difference of ${\ensuremath{\mu}}^{+}\ensuremath{-}{\ensuremath{\mu}}^{\ensuremath{-}}$. The ${K}^{0}\ensuremath{-}{\overline{K}}^{0}$ system provides an upper bound on the length scale of spacetime noncommutativity of the order of ${10}^{\ensuremath{-}32}\text{ }\text{ }\mathrm{m}$, corresponding to a lower energy bound $E$ of the order of $E\ensuremath{\gtrsim}{10}^{16}\text{ }\text{ }\mathrm{GeV}$. The $g\ensuremath{-}2$ difference of ${\ensuremath{\mu}}^{+}\ensuremath{-}{\ensuremath{\mu}}^{\ensuremath{-}}$ constrains the noncommutativity length scale to be of the order of ${10}^{\ensuremath{-}20}\text{ }\text{ }\mathrm{m}$, corresponding to a lower energy bound $E$ of the order of $E\ensuremath{\gtrsim}{10}^{3}\text{ }\text{ }\mathrm{GeV}$. We also present the phenomenology of the electromagnetic interaction of electrons and nucleons at the tree level on the noncommutative spacetime. We show that the distributions of charge and magnetization of nucleons are affected by spacetime noncommutativity. The analytic properties of electromagnetic form factors are also changed and it may give rise to interesting experimental signals.

Proposal for Studying N* Resonances with anti-p p ---> anti-p n pi+ Reaction

Abstract: A theoretical study of the $\overline{p}p\ensuremath{\rightarrow}\overline{p}n{\ensuremath{\pi}}^{+}$ reaction for antiproton beam energy from $1$ to $4$ GeV is made by including contributions from various known ${N}^{*}$ and ${\ensuremath{\Delta}}^{*}$ resonances. It is found that for the beam energy around $1.5$ GeV, the contribution of the Roper resonance ${N}_{(1440)}^{*}$ produced by the $t$-channel $\ensuremath{\sigma}$ exchange dominates over all other contributions. Since such a reaction can be studied in the forthcoming PANDA experiment at the GSI Facility of Antiproton and Ion Research (FAIR), the reaction will be realistically the cleanest place for studying the properties of the Roper resonance and the best place for looking for other ``missing'' ${N}^{*}$ resonances with large coupling to $N\ensuremath{\sigma}$.

Leptonic radiative decay in supersymmetry without R parity

Abstract: We present a detailed analysis together with exact numerical calculations on one-loop contributions to the branching ratio of the radiative decay of µ and � , namely µ ! e, � ! e, and � ! µ from supersymmetry without R parity, focusing on contributions involving bilinear couplings. A numerical study is performed to obtain explicit bounds on the parameters under the present experimental limit. We present, and use in the calculation, formulas for exact mass eigenstate effective couplings. In this sense, we present an exact analysis free from approximation for the first time. After comparing our results against the closest early analysis, we discovered a major difference in resulted constraints on some µ ∗ Bj combinations. Constraints from neutrino masses on the parameters were considered. Our result indicates that the branching ratio measurement on µ ! e down to 10 −13 10 −14 and beyond, as targeted by the MEG experiment, has a chance of observing decay from the R-parity violating scenario.

The triple Pomeron vertex in large-N QCD and the pair-of-pants topology

Abstract: We investigate the high energy behavior of QCD for different surface topologies of color graphs. After a brief review of the planar limit (bootstrap and gluon reggeization) and of the cylinder topology (BFKL) we investigate the 3 ? 3 scattering in the triple Regge limit which belongs to the pair-of-pants topology. We re-derive the triple Pomeron vertex function and show that it belongs to a specific set of graphs in color space which we identify as the analogue of the Mandelstam diagram.

Decay constants of pseudoscalar mesons in bethe–salpeter framework with generalized structure of hadron-quark vertex

Abstract: We employ the framework of Bethe–Salpeter equation under Covariant Instantaneous Ansatz to study the leptonic decays of pseudoscalar mesons. The Dirac structure of hadron-quark vertex function Γ is generalized to include various Dirac covariants besides γ5 from their complete set. The covariants are incorporated in accordance with a power counting rule, order-by-order in powers of the inverse of the meson mass. The decay constants are calculated with the incorporation of leading order covariants. Most of the results are dramatically improved.

The triple Pomeron vertex in large-N QCD and the pair-of-pants topology

Abstract: We investigate the high energy behavior of QCD for different surface topologies of color graphs. After a brief review of the planar limit (bootstrap and gluon reggeization) and of the cylinder topology (BFKL) we investigate the 3 -> 3 scattering in the triple Regge limit which belongs to the pair-of-pants topology. We re-derive the triple Pomeron vertex function and show that it belongs to a specific set of graphs in color space which we identify as the analogue of the Mandelstam diagram.

Electromagnetic Properties for Arbitrary Spin Particles. Part 1. Electromagnetic Current and Multipole Decomposition

Abstract: In a set of two papers, we propose to study an old-standing problem, namely the electromagnetic interaction for particles of arbitrary spin. Based on the assumption that light-cone helicity at tree level and $Q^2=0$ should be conserved non-trivially by the electromagnetic interaction, we are able to derive \emph{all} the natural electromagnetic moments for a pointlike particle of \emph{any} spin. In this first paper, we propose a transparent decomposition of the electromagnetic current in terms of covariant vertex functions. We also define in a general way the electromagnetic multipole form factors, and show their relation with the electromagnetic moments. Finally, by considering the Breit frame, we relate the covariant vertex functions to multipole form factors.

Decays Z→ggg and Z ' →ggg in the minimal 331 model

Abstract: We perform a complete calculation at the one-loop level for the $Zggg$ and ${Z}^{\ensuremath{'}}ggg$ couplings in the context of the minimal 331 model, which predicts the existence of a new ${Z}^{\ensuremath{'}}$ gauge boson and new exotic quarks. Bose symmetry is exploited to write a compact and manifest $S{U}_{C}(3)$-invariant vertex function for the $Vggg$ ($V=Z$, ${Z}^{\ensuremath{'}}$) coupling. Previous results on the $Z\ensuremath{\rightarrow}ggg$ decay in the standard model are reproduced. It is found that this decay is insensitive to the effects of the new exotic quarks. This in contrast with the ${Z}^{\ensuremath{'}}\ensuremath{\rightarrow}ggg$ decay, which is sensitive to both the standard model and exotic quarks, whose branching ratio is larger than that of the $Z\ensuremath{\rightarrow}ggg$ transition by about a factor of 4.

On the decoupling solution for pinch technique gluon propagator

Abstract: Within a simple Ansatz for renormalized gluon propagator and using gauge invariant pinch-technique for Schwinger-Dyson equation, the limits on the effective gluon mass is derived We calculated scheme invariant running coupling, which in order to be well defined, gives the lower limit on the gluon mass We conclude mass should be larger as $m>04\Lambda$ in order to avoid Landau ghost The upper limit is estimated from assumed quark mass generation which requires gauge coupling must be large enough to trigger chiral symmetry breaking It allows only small range of $m$, which lead to a reasonably large infrared coupling Already for $m\simeq \Lambda$ we get no chiral symmetry breaking at all Further, we observe that sometimes assumed or postulated Khallen-Lehmann representation for running coupling is not achieved for any value of $m$

Three-particle model of the pion-nucleon system

Abstract: A relativistic, three-particle model of the pion-nucleon system is constructed in the instant form of relativistic quantum mechanics using the Bakamjian-Thomas procedure. The model space includes subspaces for the nucleon $(N)$, the resonances $\ensuremath{\Delta}={P}_{33}(1232)$, ${P}_{11}(1440)$, ${D}_{13}(1520)$, ${S}_{11}(1535)$, and ${S}_{31}(1620)$, as well as $\ensuremath{\pi}N$, $\ensuremath{\pi}\ensuremath{\Delta}$, $\ensuremath{\eta}N$, and $\ensuremath{\pi}\ensuremath{\pi}N$ subspaces. The model specifies a Poincar\'e invariant mass operator that includes vertex interactions that couple the various subspaces, as well as renormalization terms. Projection operator techniques are used to reduce the equations arising from this mass operator to a set of three-dimensional Lippmann-Schwinger integral equations that couple only the $\ensuremath{\pi}N$, $\ensuremath{\pi}\ensuremath{\Delta}$, and $\ensuremath{\eta}N$ channels. After a partial wave analysis these three-dimensional equations simplify to three coupled, one-dimensional integral equations for each partial wave. The mass operator interactions are derived from effective, hadronic Lagrangians that introduce a set of coupling constants. Cutoff functions are introduced to take into account the nonelementary nature of the particles in the model. These cutoff functions introduce a set of cutoff masses. The coupling constants, cutoff masses, and bare baryon masses are determined by fitting to a partial wave analysis of pion-nucleon elastic scattering up to a c.m. energy of $W=1550$ MeV.

Local Interactions of Higher-Spin Potentials That are Gauge Invariant in Linear Approximation

Abstract: We study connected Wightman functions of $N$ conserved currents, each of which is formed from a scalar field and has even spin $l_{i}$. The UV divergence of this vertex function is regularized by the analytic continuation in the space dimension $D\longrightarrow D-\epsilon$. We evaluate the residue of $\epsilon ^{-1}$ only, which is a local interaction Lagrangian density and gauge invariant in linear

Kinks and d-waves from phonons: The intermediate coupling story

Abstract: I present results from an approach that extends the Eliashberg theory by systematic expansion in the vertex function; an essential extension at large phonon frequencies, even for weak coupling. In order to deal with computationally expensive double sums over momenta, a dynamical cluster approximation (DCA) approach is used to incorporate momentum dependence into the Eliashberg equations. First, I consider the effects of introducing partial momentum dependence on the standard Eliashberg theory using a quasi-local approximation; which I use to demonstrate that it is essential to include corrections beyond the standard theory when investigating d-wave states. Using the extended theory with vertex corrections, I compute electron and phonon spectral functions. A kink in the electronic dispersion is found in the normal state along the major symmetry directions, similar to that found in photo-emission from cuprates. The phonon spectral function shows that for weak coupling $W\lambda < \omega_0$, the dispersion for phonons has weak momentum dependence, with consequences for the theory of optical phonon mediated d-wave superconductivity, which is shown to be 2nd order in $\lambda$. In particular, examination of the order parameter vs. filling shows that vertex corrections lead to d-wave superconductivity mediated via simple optical phonons. I map out the order parameters in detail, showing that there is significant induced anisotropy in the superconducting pairing in quasi-2D systems.

Pion-nucleon scattering in Kadyshevsky formalism. I. Meson exchange sector

Abstract: In a series of two articles we present the theoretical results of $\ensuremath{\pi}N$/meson-baryon scattering in the Kadyshevsky formalism. In this article the results are given for meson exchange diagrams. On the formal side we show, by means of an example how general couplings, i.e., couplings containing multiple derivatives and/or higher spin fields, should be treated. We do this by introducing and applying the Takahashi-Umezawa and the Gross-Jackiw method. For practical purposes we introduce the $\overline{P}$ method. We also show how the Takashashi-Umezawa method can be derived using the theory of Bogoliubov and collaborators and the Gross-Jackiw method is also used to study the $n$ dependence of the Kadyshevsky integral equation. Last but not least we present the second quantization procedure of the quasiparticle in Kadyshevsky formalism.

Next-to-leading-order calculation in k(T) factorization

Abstract: We explain the framework for calculating next-to-leading-order (NLO) corrections to exclusive processes in the kT factorization theorem, taking πγ* → γ as an example. Partons off-shell by k2T are considered in both the quark diagrams from full QCD and the effective diagrams for the pion wave function. The gauge dependences in the above two sets of diagrams cancel, when deriving the kT-dependent hard kernel as their difference. The light-cone singularities in the kT-dependent pion wave function are regularized by rotating the Wilson lines away from the light cone. Both the large double logarithms ln2kT and ln2 x, x being a parton momentum fraction, arise from the loop correction to the virtual photon vertex, the former being absorbed into the pion wave function, and the latter into a jet function.