119698561
Exact solutions to relativistic singular fractional power potentials
We present (exact) solutions of the Dirac equation with equally mixed interactions for a single fermion bounded by the family of fractional power singular potentials. Closed-form expressions as well as numerical values for the energies were obtained. The wave functions and the allowed values of the potential parameters for the first two members of the family are obtained in terms of a set of algebraic equations. The non-relativistic limit is also discussed and using the Hellmann–Feynmann theorem, some useful expectation values are obtained.
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.
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.
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.
119470349
Kaon Fragmentation Function and $K/\pi$ Ratios in Nuclear Collisions
An improved leading order fragmentation functions set of kaon is proposed based on the experimental data. We compare it with currently available sets, and use it to calculate high-$p_T$ $K/\pi$ ratios in relativistic proton-proton collisions. A prediction of $K/\pi$ ratios in relativistic nucleus-nucleus collisions ($d + Au$ and $Au + Au$) at RHIC $\sqrt{s} = 200$ GeV is given.
119107710
Hartle–Hawking no-boundary proposal in dRGT massive gravity: making inflation exponentially more probable
It is known that the no-boundary proposal in the traditional Einstein gravity does not prefer inflation, that is, the probability of realizing a large number of e-folds is exponentially suppressed. This situation may be changed drastically in a class of nonlinear massive gravity theories recently proposed by de Rham, Gabadadze and Tolley, called dRGT massive gravity. We show that the contribution from the massive gravity sector can enhance the probability of a large number of e-folds substantially for a sufficiently large mass parameter mg comparable to the Hubble parameter during inflation, say mg ? 1012 GeV. We illustrate possible models to trigger such a large mass parameter in the early universe while it is negligibly small in the present universe. This opens a new window to explore the inflationary scenario in the context of quantum cosmology.
118384195
Dark matter as the trigger of strong electroweak phase transition
In this paper, we propose a new possible connection between dark matter relic density and baryon asymmetry of the universe. The portal between standard model sector and dark matter not only controls the relic density and detections of dark matter, but also allows the dark matter to trigger the first order electroweak phase transition. We discuss systematically possible scalar dark matter candidates, starting from a real singlet to arbitrary high representations. We show that the simplest realization is provided by a doublet, and that strong first-order electroweak phase transition implies a lower bound on the dark matter direct detection rate. The mass of dark matter lies between 45 and 80 GeV, allowing for an appreciable invisible decay width of the Standard Model Higgs boson, which is constrained to be lighter than 130 GeV for the sake of the strong phase transition.
30742433
Yukawa bound states of a large number of fermions
A bstractWe consider the bound state problem for a field theory that contains a Dirac fermion χ that Yukawa couples to a (light) scalar field ϕ. We are interested in bound states with a large number N of χ particles. A Fermi gas model is used to numerically determine the dependence of the radius R of these bound states on N and also the dependence of the binding energy on N. Since scalar interactions with relativistic χ’s are suppressed two regimes emerge. For modest values of N the state is composed of non-relativistic χ particles. In this regime as N increases R decreases. Eventually the core region becomes relativistic and the size of the state starts to increase as N increases. As a result, for fixed Yukawa coupling and χ mass, there is a minimum sized state that occurs roughly at the value of N where the core region first becomes relativistic. We also compute an elastic scattering form factor that can be relevant for direct detection if the dark matter is composed of such χ particles.
118288760
First Limits on Left-Right Symmetry Scale from LHC Data
We use the early Large Hadron Collider data to set the lower limit on the scale of Left-Right symmetry, by searching for the right-handed charged gauge boson $W_R$ via the final state with two leptons and two jets, for 33/pb integrated luminosity and 7 TeV center-of-mass energy. In the absence of a signal beyond the Standard Model background, we set the bound M_WR > 1.4 TeV at 95% C.L.. This result is obtained for a range of right-handed neutrino masses of the order of few 100 GeV, assuming no accidental cancelation in right-handed lepton mixings.