15985024
A unified and complete construction of all finite dimensional irreducible representations of gl(2∣2)
Representations of the non-semisimple superalgebra gl(2∣2) in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of gl(2∣2) are constructed explicitly through the explicit construction of all gl(2)⊕gl(2) particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of gl(2∣2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.
2107479
Local Quasitriangular Hopf Algebras
We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. The category of modules with finite cycles over a local quasitriangular Hopf algebra is a braided tensor category.
121731174
Some algebraic identities in anomalous gauge theories
Some useful algebraic relations between the anomaly of Dmu Jmu and anomalous commutators are derived using only the canonical commutators and the equation of motion. Their applications are discussed.
119694191
Construction of basis vectors for symmetric irreducible representations of O(5) $ \supset$ O(3)
Abstract.A recursive method for the construction of symmetric irreducible representations of $ O(2l+1)$ in the $ O(2l+1)\supset O(3)$ basis for identical boson systems is proposed. The formalism is realized based on the group chain $ U(2l+1)\supset U(2l-1)\otimes U(2)$ , of which the symmetric irreducible representations are simply reducible. The basis vectors for symmetric irreducible representations of the $ O(2l+1)\supset O(2l-1)\otimes U(1)$ can easily be constructed from those of U(2l + 1) $ \supset$U(2l - 1) ⊗ U(2) $ \supset$O(2l - 1) ⊗ U(1) with no l -boson pairs, namely with the total boson number exactly equal to the seniority number in the system, from which one can construct symmetric irreducible representations of $ O(2l+1)$ in the $ O(2l-1)\otimes U(1)$ basis when all symmetric irreducible representations of O(2l - 1) are known. As a starting point, basis vectors of symmetric irreducible representations of O(5) are constructed in the $ O_{1}(3)\otimes U(1)$ basis, where $ O_{1}(3)\equiv O(2l-1)$ , when l = 2 , which is generated not by the angular momentum operators of the d -boson system, but by the operators constructed from d -boson creation (annihilation) operators $ d^{\dagger}_{\mu}$ ( $ d_{\mu}$ with $ \mu=1$ , 0, -1 . Matrix representations of $ O(5)\supset O_{1}(3)\otimes U(1)$ , together with the elementary Wigner coefficients, are presented. After the angular momentum projection, a three-term relation in determining the expansion coefficients of the $ O(5)\supset O(3)$ basis vectors, where the O(3) group is generated by the angular momentum operators of the d -boson system, in terms of those of $ O_{1}(3)\otimes U(1)$ is derived. The eigenvectors of the projection matrix with zero eigenvalues constructed according to the three-term relation completely determine the basis vectors of $ O(5)\supset O(3)$ . Formulae for evaluating the elementary Wigner coefficients of $ O(5)\supset O(3)$ are derived explicitly. Analytical expressions of some elementary Wigner coefficients of $ O(5)\supset O(3)$ for the coupling $ (\tau 0)\otimes(1 0)$ with resultant angular momentum quantum number L = 2$ \tau$ + 2 - k for $ k=0,2,3,\ldots,6$ with a multiplicity 2 case for k = 6 are presented.
17047722
Infinite Families of Gauge-Equivalent R-Matrices and Gradations of Quantized Affine Algebras
Associated with the fundamental representation of a quantum algebra such as Uq(A1) or Uq(A2), there exist infinitely many gauge-equivalent R-matrices with different spectralparameter dependences. It is shown how these can be obtained by examining the infinitely many possible gradations of the corresponding quantum affine algebras, such as and , and explicit formulae are obtained for those two cases. Spectral-dependent similarity (gauge) transformations relate the R-matrices in different gradations, Nevertheless, the choice of gradation can be physically significant, as is illustrated in the case of quantum affine Toda field theories.
1264030
Elliptic Gaudin models and elliptic KZ equations
The Gaudin models based on the face-type elliptic quantum groups and the XYZ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding face-type Knizhnik–Zamolodchikov equations and their solutions are given.
119221055
An integrand reconstruction method for three-loop amplitudes
A bstractWe consider the maximal cut of a three-loop four point function with massless kinematics. By applying Gröbner bases and primary decomposition we develop a method which extracts all ten propagator master integral coefficients for an arbitrary triple-box configuration via generalized unitarity cuts. As an example we present analytic results for the three loop triple-box contribution to gluon-gluon scattering in Yang-Mills with adjoint fermions and scalars in terms of three master integrals.
19788205
CP-violating phenomenology of flavor conserving two Higgs doublet models
We analyze the constraints on CP-violating, flavor conserving two Higgs doublet models implied by measurements of Higgs boson properties at the Large Hadron Collider (LHC) and by the nonobservation of permanent electric dipole moments (EDMs) of molecules, atoms, and neutrons. We find that the LHC and EDM constraints are largely complementary, with the LHC studies constraining the mixing between the neutral CP-even states and the EDMs probing the effect of mixing between the CP-even and CP-odd scalars. Presently, the most stringent constraints are implied by the nonobservation of the ThO molecule EDM signal. Future improvements in the sensitivity of neutron and diamagnetic atom EDM searches could yield competitive or even more severe constraints. We analyze the quantitative impact of hadronic and nuclear theory uncertainties on the interpretation of the latter systems and conclude that these uncertainties cloud the impact of projected improvements in the corresponding experimental sensitivities.
53520209
Pair production of 125 GeV Higgs boson in the SM extension with color-octet scalars at the LHC
A bstractAlthough the Higgs boson mass and single production rate have been determined more or less precisely, its other properties may deviate significantly from its predictions in the standard model (SM) due to the uncertainty of Higgs data. In this work we study the Higgs pair production at the LHC in the Manohar-Wise model, which extends the SM by one family of color-octet and isospin-doublet scalars. We first scanned over the parameter space of the Manohar-Wise model considering experimental constraints and performed fits in the model to the latest Higgs data by using the ATLAS and CMS data separately. Then we calculated the Higgs pair production rate and investigated the potential of its discovery at the LHC14. We conclude that: (i) Under current constrains including Higgs data after Run I of the LHC, the cross section of Higgs pair production in the Manohar-Wise model can be enhanced up to even 103 times prediction in the SM. (ii) Moreover, the sizable enhancement comes from the contributions of the CP-odd color-octet scalar $ S_I^A $. For lighter scalar $ S_I^A $ and larger values of |λI|, the cross section of Higgs pair production can be much larger. (iii) After running again of LHC at 14 TeV, most of the parameter spaces in the Manohar-Wise model can be test. For an integrated luminosity of 100 fb−1 at the LHC14, when the normalized ratio R = 10, the process of Higgs pair production can be detected.
118631762
Multivariate residues and maximal unitarity
A bstractWe extend the maximal unitarity method to amplitude contributions whose cuts define multidimensional algebraic varieties. The technique is valid to all orders and is explicitly demonstrated at three loops in gauge theories with any number of fermions and scalars in the adjoint representation. Deca-cuts realized by replacement of real slice integration contours by higher-dimensional tori encircling the global poles are used to factorize the planar triple box onto a product of trees. We apply computational algebraic geometry and multivariate complex analysis to derive unique projectors for all master integral coefficients and obtain compact analytic formulae in terms of tree-level data.
119109271
Type II Seesaw at LHC: The Roadmap
In this Letter we revisit the type-II seesaw mechanism based on the addition of a weak triplet scalar to the standard model. We perform a comprehensive study of its phenomenology at the LHC energies, complete with the electroweak precision constraints. We pay special attention to the doubly-charged component, object of collider searches for a long time, and show how the experimental bound on its mass depends crucially on the particle spectrum of the theory. Our study can be used as a roadmap for future complete LHC studies.