Supset SU Research Articles

On the LHC signatures of SU(5)times U(1)' F-theory motivated models

We study low energy implications of F-theory GUT models based on SU(5) extended by a U(1)' symmetry which couples non-universally to the three families of quarks and leptons. This gauge group arises naturally from the maximal exceptional gauge symmetry of an elliptically fibred internal space, at a single point of enhancement, E_8supset SU(5)times SU(5)'supset SU(5)times U(1)^4. Rank-one fermion mass textures and a tree-level top quark coupling are guaranteed by imposing a Z_2 monodromy group which identifies two abelian factors of the above breaking sequence. The U(1)' factor of the gauge symmetry is an anomaly free linear combination of the three remaining abelian symmetries left over by Z_2. Several classes of models are obtained, distinguished with respect to the U(1)' charges of the representations, and possible extra zero modes coming in vector-like representations. The predictions of these models are investigated and are compared with the LHC results and other related experiments. Particular cases interpreting the B-meson anomalies observed in LHCb and BaBar experiments are also discussed.

Hidden SU(2) symmetries, the symmetry hierarchy, and the emergent eightfold way in spin-1 quantum magnets

The largest allowed symmetry in a spin-1 quantum system is an $SU(3)$ symmetry rather than the $SO(3)$ spin rotation. In this work, we reveal some $SU(2)$ symmetries as subgroups of $SU(3)$ that, to the best of our knowledge, have not previously been recognized. Then, we construct $SU(2)$ symmetric Hamiltonians and explore the ground-state phase diagram in accordance with the $SU(3)\supset SU(2)\times U(1)$ symmetry hierarchy. It is natural to treat the eight generators of the $SU(3)$ symmetry on an equal footing; this approach is called the eight-fold way. We find that the spin spectral functions and spin quadrupole spectral functions share the same structure, provided that the elementary excitations are flavor waves at low energies, which serves as a clue to the eight-fold way. An emergent $S=1/2$ quantum spin liquid is proposed to coexist with gapful spin nematic order in one of the ground states. In analogy to quantum chromodynamics, we find the gap relation for hydrodynamic modes in quantum spin-orbital liquid states, which is nothing but the Gell-Mann-Okubo formula.

A hidden classical symmetry of QCD

The classical part of the QCD partition function (the integrand) has, ignoring irrelevant exact zero modes of the Dirac operator, a local SU(2N_F) \supset SU(N_F)_L \times SU(N_F)_R \times U(1)_A symmetry which is absent at the Lagrangian level. This symmetry is broken anomalously and spontaneously. Effects of spontaneous breaking of chiral symmetry are contained in the near-zero modes of the Dirac operator. If physics of anomaly is also encoded in the same near-zero modes, then their truncation on the lattice should recover a hidden classical SU(2N_F) symmetry in correlators and spectra. This naturally explains observation on the lattice of a large degeneracy of hadrons, that is higher than the SU(N_F)_L \times SU(N_F)_R \times U(1)_A chiral symmetry, upon elimination by hands of the lowest-lying modes of the Dirac operator. We also discuss an implication of this symmetry for the high temperature QCD.

SU(4) symmetry of the dynamical QCD string and genesis of hadron spectra

A large degeneracy of mesons of a given spin has recently been discovered upon reduction of the quasi-zero modes of the Dirac operator in a dynamical lattice simulation. Here it is shown that a symmetry group $$SU(4) \supset SU(2)_L \times SU(2)_R \times U(1)_A \times \mathcal{C}_i$$ is consistent with the observed degeneracy. It is argued that this symmetry group is a symmetry of the dynamical QCD string. Implications of this picture for a genesis of light hadron spectra are discussed.

Axial asymmetry in the IVBM

The dynamical symmetry limit of the two-fluid Interacting Vector Boson Model (IVBM), defined through the chain $Sp(12,R) \supset U(3,3) \supset U_{p}(3) \otimes \overline{U_{n}(3)} \supset SU^{\ast}(3) \supset SO(3)$, is considered and applied for the description of nuclear collective spectra exhibiting axially asymmetric features. The effect of the introduction of a Majorana interaction to the $SU^{\ast}(3)$ model Hamiltonian on the $\gamma$-band energies is studied. The theoretical predictions are compared with the experimental data for $^{192}Os$, $^{190}Os$, and $^{112}Ru$ isotopes. It is shown that by taking into account the full symplectic structures in the considered dynamical symmetry of the IVBM, the proper description of the energy spectra and the $\gamma$-band energy staggering of the nuclei under considerations can be achieved. The obtained results show that the potential energy surfaces for the following two nuclei $^{192}Os$ and $^{112}Ru$, possess almost $\gamma$-flat potentials with very shallow triaxial minima, suggesting a more complex and intermediate situation between $\gamma$-rigid and $\gamma$-unstable structures. Additionally, the absolute $B(E2)$ intraband transition probabilities between the states of the ground state band and $\gamma$ band, as well as the $B(M1)$ interband transition probabilities between the states of the ground and $\gamma$ bands for the two nuclei $^{192}Os$ and $^{190}Os$ are calculated and compared with experiment and for the $B(E2)$ values with the predictions of some other collective models incorporating the $\gamma$-rigid or $\gamma$-unstable structures. The obtained results agree well with the experimental data and reveal the relevance of the used dynamical symmetry of IVBM in the description of nuclei exhibiting axially asymmetric features in their spectra.

Six-dimensional Davidson potential as a dynamical symmetry of the symplectic interacting vector boson model

A six-dimensional Davidson potential, introduced within the framework of the Interacting Vector Boson Model (IVBM), is used to describe nuclei that exhibit transitional spectra between the purely rotational and vibrational limits of the theory. The results are shown to relate to a new dynamical symmetry that starts with the $Sp(12,R) \supset SU(1,1) \times SO(6)$ reduction. Exact solutions for the eigenstates of the model Hamiltonian in the basis defined by a convenient subgroup chain of SO(6) are obtained. A comparison of the theoretical results with experimental data for heavy nuclei with transitional spectra illustrates the applicability of the theory.

Coupling coefficients of SO(n) and integrals involving Jacobi and Gegenbauer polynomials

The expressions of the coupling coefficients (3j-symbols) for the most degenerate (symmetric) representations of the orthogonal groups SO(n) in a canonical basis (with SO(n) restricted to SO(n-1)) and different semicanonical or tree bases [with SO(n) restricted to SO(n'})\times SO(n''), n'+n''=n] are considered, respectively, in context of the integrals involving triplets of the Gegenbauer and the Jacobi polynomials. Since the directly derived triple-hypergeometric series do not reveal the apparent triangle conditions of the 3j-symbols, they are rearranged, using their relation with the semistretched isofactors of the second kind for the complementary chain Sp(4)\supset SU(2)\times SU(2) and analogy with the stretched 9j coefficients of SU(2), into formulae with more rich limits for summation intervals and obvious triangle conditions. The isofactors of class-one representations of the orthogonal groups or class-two representations of the unitary groups (and, of course, the related integrals involving triplets of the Gegenbauer and the Jacobi polynomials) turn into the double sums in the cases of the canonical SO(n)\supset SO(n-1) or U(n)\supset U(n-1) and semicanonical SO(n)\supset SO(n-2)\times SO(2) chains, as well as into the_4F_3(1) series under more specific conditions. Some ambiguities of the phase choice of the complementary group approach are adjusted, as well as the problems with alternating sign parameter of SO(2) representations in the SO(3)\supset SO(2) and SO(n)\supset SO(n-2)\times SO(2) chains.

Determination of SU(6) Clebsch-Gordan coefficients and baryon mass and electromagnetic moment relations.

We compute and tabulate the Clesbsch--Gordan coefficients of the $SU(6) \supset SU(3) \times SU(2)$ product ${\overline{\bf 56}} \otimes {\bf 56}$, which are relevant to the nonrelativistic spin-flavor symmetry of the lightest baryons. Under the assumption that the largest representation in this product, the ${\bf 2695}$, gives rise to operators in a chiral expansion that produce numerically small effects, we obtain a set of relations among the masses of the baryons, as well as among their magnetic dipole and higher multipole moments. We compare the mass relations to experiment, and find numerical predictions for the $\Sigma^0$-$\Lambda$ mass mixing parameter and eighteen of the twenty-seven magnetic moments in the ${\bf 56}$.

Q-breaking of dynamical symmetry in the two-dimensional SU(3) interacting boson model for the quantum group symmetry SUq(3) supset SUq(2) supset SOq(2)

Quantum-deformation of the vibrational symmetry SU(3) supset SU(2) supset SO(2) of the two-dimensional SU(3) interacting boson model is studied from the point of view of the breaking of the dynamical symmetry. It is shown that, in agreement with the earlier work of Gupta et al. (1992) for the one-dimensional problem, the real and complex (more so the complex) q-deformations take this dynamical symmetry very close to the other (rotational) dynamical symmetry SU(3) supset SO(3) supset SO(2) of the two-dimensional SU(3) group. Also, the intermediate results of mixing these two symmetries are obtained, since q-deformations vary continuously. The purely imaginary q-deformation in SUq(3) supset SUq(2) supset SOq(2) restores the SU(3) symmetry for a parameter value larger than 1. Applications to real nuclei are also made.