120260487
Covariant anomaly and cohomology in connection space
Abstract Vertical cohomology in connection space is formulated using the natural connection forms on a principal bundle and the connection space. It can be used to generate a new set of “descent equations”, the first of which is related to a covariant (current) anomaly. This situation is justified starting with a consistent condition.
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.
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.
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.
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.
119230697
Elliptic functions and maximal unitarity
Modern perturbative scattering amplitudes in gauge theories such as QCD are calculated from general principles of analyticity and unitarity without inspecting Feynman diagrams. By virtue of analyticity, amplitudes are reconstructed from their singularity structure, while unitarity ensures that residues factorize onto simpler objects. Starting from complex internal momenta and three-point amplitudes whose form is entirely xed by eld theory arguments, all trees are generated recursively
119120163
Current experimental bounds on stop mass in natural SUSY
A bstractMotivated by the recent progress of direct search for the productions of stop pair and sbottom pair at the LHC, we examine the constraints of the search results on the stop ($ \widetilde{t} $1) mass in natural SUSY. We first scan the parameter space of natural SUSY in the framework of MSSM, considering the constraints from the Higgs mass, B-physics and electroweak precision measurements. Then in the allowed parameter space we perform a Monte Carlo simulation for stop pair production followed by $ \widetilde{t} $1 → t$ \widetilde{\chi}_1^0 $ or $ \widetilde{t} $1 → b$ \widetilde{\chi}_1^{+} $ and sbottom pair production followed by $ \widetilde{b} $1 → b$ \widetilde{\chi}_1^0 $ or $ \widetilde{b} $1 → t$ \widetilde{\chi}\overline{1} $. Using the combined results of ATLAS with 20.1 fb−1 from the search of ℓ + jets + T , hadronic $ t\overline{t} $ + T and 2b + T , we find that a stop lighter than 600 GeV can be excluded at 95% CL in this scenario.
119280113
Upsilon decay to two-charm quark jets as a Probe of the Color Octet Mechanism
We calculate the decay rate of bottomonium to two charm-quark jets {upsilon}{yields}cc at the tree level and one-loop level including color-singlet and color-octet bb annihilations. We find that the short-distance coefficient of the color-octet piece is much larger than the color-singlet piece, and that the QCD correction will change the end point behavior of the charm quark jet. The color-singlet piece is strongly affected by the one-loop QCD correction. In contrast, the QCD correction to the color-octet piece is weak. Once the experiment can measure the branching ratio and energy distribution of the two charm-quark jets in the {upsilon} decay, the result can be used to test the color-octet mechanism or give a strong constraint on the color-octet matrix elements.
118465032
Integration-by-parts identities from the viewpoint of differential geometry
We present a new method to construct integration-by-part (IBP) identities from the viewpoint of differential geometry. Vectors for generating IBP identities are reformulated as differential forms, via Poincar\'{e} duality. Using the tools of differential geometry and commutative algebra, we can efficiently find differential forms which generate on-shell IBP relation without doubled propagator. Various $D=4$ two-loop examples are presented.
119165682
Electroweak cogenesis
A bstractWe propose a simple renormalizable model of baryogenesis and asymmetric dark matter generation at the electroweak phase transition. Our setup utilizes the two Higgs doublet model plus two complex gauge singlets, the lighter of which is stable dark matter. The dark matter is charged under a global symmetry that is broken in the early universe but restored during the electroweak phase transition. Because the ratio of baryon and dark matter asymmetries is controlled by model parameters, the dark matter need not be light. Thus, new force carriers are unnecessary and the symmetric dark matter abundance can be eliminated via Higgs portal interactions alone. Our model places a rough upper bound on the dark matter mass, and has implications for direct detection experiments and particle colliders.