On the enumeration of finite LL-algebras

We use Constraint Satisfaction Methods to construct and enumerate finite $L$-algebras up to isomorphism. These objects were recently introduced by Rump and appear in Garside theory, algebraic logic, and the study of the combinatorial Yang-Baxter equation. There are 377322225 isomorphism classes of $L$-algebras of size eight. The database constructed suggest the existence of bijections between certain classes of $L$-algebras and well-known combinatorial objects. On the one hand, we prove that Bell numbers enumerate isomorphism classes of finite linear $L$-algebras. On the other hand, we also prove that finite regular $L$-algebras are in bijective correspondence with infinite-dimensional Young diagrams.Comment: 17 pages, 3 tables, 2 figures. Postprint versio

Electric dipole and magnetic quadrupole moments of the WW boson via a CP-violating HWWHWW vertex in effective Lagrangians

The possibility of nonnegligible $W$ electric dipole ($\widetilde{\mu}_W$) and magnetic quadrupole ($\widetilde{Q}_W$) moments induced by the most general $HWW$ vertex is examined via the effective Lagrangian technique. It is assumed that new heavy fermions induce an anomalous CP-odd component of the $HWW$ vertex, which can be parametrized by an $SU_L(2)\times U_Y(1)$-invariant dimension-six operator. This anomalous contribution, when combined with the standard model CP-even contribution, lead to CP-odd electromagnetic properties of the $W$ boson, which are characterized by the form factors $\Delta \widetilde{\kappa}$ and $\Delta \widetilde{Q}$. It is found that $\Delta \widetilde{\kappa}$ is divergent, whereas $\Delta \widetilde{Q}$ is finite, which reflects the fact that the latter cannot be generated at the one-loop level in any renormalizable theory. Assuming reasonable values for the unknown parameters, we found that $\widetilde{\mu}_W\sim 3-6\times 10^{-21}$ e-cm, which is eight orders of magnitude larger than the SM prediction and close to the upper bound derived from the neutron electric dipole moment. The estimated size of the somewhat less-studied $\widetilde{Q}_W$ moment is of the order of $-10^{-36}$ e-cm^2, which is fifteen orders of magnitude above the SM contribution.Comment: 7 pages, 6 figures, REVTEX styl

CP-odd static electromagnetic properties of the W gauge boson and the t quark via the anomalous tbW coupling

In the framework of the electroweak chiral Lagrangian, the one-loop induced effects of the anomalous $tbW$ coupling, which includes both left- and right-handed complex components, on the static electromagnetic properties of the $W$ boson and the $t$ quark are studied. The attention is focused mainly on the CP-violating electromagnetic properties. It is found that the $tbW$ anomalous coupling can induce both CP-violating moments of the $W$ boson, namely, its electric dipole ($\tilde{\mu}_W$) and magnetic quadrupole ($\tilde{Q}_W$) moments. As far as the $t$ quark is concerned, a potentially large electric dipole moment $(d_t)$ can arise due to the anomalous $tbW$ coupling. The most recent bounds on the left- and right-handed parameters from $B$ meson physics lead to the following estimates $\tilde{\mu}_W ~ 10^{-23}-10^{-22}$ e-cm and $\tilde{Q}_W~ 10^{-38}-10^{-37}$ e-cm$^2$, which are 7 and 14 orders of magnitude larger than the standard model (SM) predictions, whereas $d_t$ may be as large as $10^{-22}$ e-cm, which is about 8 orders of magnitude larger than its SM counterpart.Comment: This paper has been merged with hep-ph/0612171 for publication in Physical Review

Effective Lagrangian approach to fermion electric dipole moments induced by a CP--violating WWγWW\gamma vertex

The one--loop contribution of the two CP--violating components of the $WW\gamma$ vertex, $\tilde{\kappa}_\gamma W^+_\mu W^-_\nu \tilde{F}^{\mu \nu}$ and $(\tilde{\lambda}_\gamma / m^2_W)W^+_{\mu \nu}W^{-\nu}_{\ \rho}\tilde{F}^{\rho \mu}$, on the electric dipole moment (EDM) of fermions is calculated using dimensional regularization and its impact at low energies reexamined in the light of the decoupling theorem. The Ward identities satisfied by these couplings are derived by adopting a$SU_L(2)\times U_Y(1)$--invariant approach and their implications in radiative corrections discussed. Previous results on$\tilde{\kappa}_\gamma$, whose bound is updated to$|\tilde{\kappa}_\gamma| <5.2\times 10^{-5}$, are reproduced, but disagreement with those existing for$\tilde{\lambda}_\gamma$is found. In particular, the upper bound$|\tilde{\lambda}_\gamma|<1.9\times10^{-2}$is found from the limit on the neutron EDM, which is more than 2 orders of magnitude less stringent than that of previous results. It is argued that this difference between the$\tilde{\kappa}_\gamma$and$\tilde{\lambda}_\gamma$bounds is the one that might be expected in accordance with the decoupling theorem. This argument is reinforced by analyzing careful the low--energy behavior of the loop functions. The upper bounds on the$W$EDM,$|d_W|<6.2\times 10^{-21} e\cdot cm$, and the magnetic quadrupole moment,$|\tilde{Q}_W|<3\times 10^{-36} e\cdot cm^2$, are derived. The EDM of the second and third families of quarks and charged leptons are estimated. In particular, EDM as large as$ 10^{-20} e\cdot cm$and$10^{-21} e\cdot cm$are found for the$t$and$b$ quarks, respectively.Comment: 14 pages and 2 figure

Braided racks, Hurwitz actions and Nichols algebras with many cubic relations

We classify Nichols algebras of irreducible Yetter-Drinfeld modules over groups such that the underlying rack is braided and the homogeneous component of degree three of the Nichols algebra satisfies a given inequality. This assumption turns out to be equivalent to a factorization assumption on the Hilbert series. Besides the known Nichols algebras we obtain a new example. Our method is based on a combinatorial invariant of the Hurwitz orbits with respect to the action of the braid group on three strands.Comment: v2: 35 pages, 6 tables, 14 figure

Super-conservative interpretation of muon g-2 results applied to supersymmetry

The recent developments in theory and experiment related to the anomalous magnetic moment of the muon are applied to supersymmetry. We follow a very cautious course, demanding that the supersymmetric contributions fit within five standard deviations of the difference between experiment and the standard model prediction. Arbitrarily small supersymmetric contributions are then allowed, so no upper bounds on superpartner masses result. Nevertheless, non-trivial exclusions are found. We characterize the substantial region of parameter space ruled out by this analysis that has not been probed by any previous experiment. We also discuss some implications of the results for forthcoming collider experiments.Comment: 10 pages, latex, 3 fig

Characterization of variable EST SSR markers for Norway spruce (Picea abies L.)

<p>Abstract</p> <p>Background</p> <p>Norway spruce is widely distributed across Europe and the predominant tree of the Alpine region. Fast growth and the fact that timber can be harvested cost-effectively in relatively young populations define its status as one of the economically most important tree species of Northern Europe. In this study, EST derived simple sequence repeat (SSR) markers were developed for the assessment of putative functional diversity in Austrian Norway spruce stands.</p> <p>Results</p> <p>SSR sequences were identified by analyzing 14,022 publicly available EST sequences. Tri-nucleotide repeat motifs were most abundant in the data set followed by penta- and hexa-nucleotide repeats. Specific primer pairs were designed for sixty loci. Among these, 27 displayed polymorphism in a testing population of 16 <it>P. abies </it>individuals sampled across Austria and in an additional screening population of 96 <it>P. abies </it>individuals from two geographically distinct Austrian populations. Allele numbers per locus ranged from two to 17 with observed heterozygosity ranging from 0.075 to 0.99.</p> <p>Conclusions</p> <p>We have characterized variable EST SSR markers for Norway spruce detected in expressed genes. Due to their moderate to high degree of variability in the two tested screening populations, these newly developed SSR markers are well suited for the analysis of stress related functional variation present in Norway spruce populations.</p

Very light CP-odd scalar in the Two-Higgs-Doublet Model

We show that a general two-Higgs-doublet model (THDM) with a very light CP-odd scalar (A) can be compatible with the rho parameter, Br(b --> s\gamma), R_b, A_b, (g-2) of muon, Br(Upsilon --> A gamma), and the direct search via the Yukawa process at LEP. For its mass around 0.2 GeV, the muon (g-2) and Br(Upsilon --> A \gamma) data require tan(beta) to be about 1. Consequently, A can behave like a fermiophobic CP-odd scalar and predominantly decay into a photon pair ("gamma gamma"), which registers in detectors of high energy collider experiments as a single photon signature when the momentum of A is large. We compute the partial decay width of Z --> A A A and the production rate of f \bar{f} --> Z A A --> Z +"gamma gamma", f^' {\bar f} --> W^{\pm} A A --> W^\pm + "gamma gamma" and f \bar f --> H^+ H^- --> W^+ W^- A A --> W^+ W^- + "gamma gamma" at high energy colliders such as LEP, Tevatron, LHC, and future Linear Colliders. Other production mechanisms of a light A, such as gg --> h --> AA --> "gamma gamma", are also discussed.Comment: Some improvementes, references updated, 3 new figures, one new appendix, abstract and conclusions unchaged. Version to appear in Physical Review

Muon anomalous magnetic dipole moment in supersymmetric theories

We study the muon anomalous magnetic dipole moment in supersymmetric theories. The impact of the recent Brookhaven E821 experimental measurement on both model-independent and model-dependent supersymmetric parameter spaces is discussed in detail. We find that values of tan\beta as low as 3 can be obtained while remaining within the E821 one-sigma bound. This requires a light smuon; however, we show that, somewhat surprisingly, no model-independent bound can be placed on the mass of the lightest chargino for any tan\beta greater than or equal to 3. We also show that the maximum contributions to the anomalous magnetic moment are insensitive to CP-violating phases. We provide analyses of the supersymmetric contribution to the muon anomalous magnetic moment in dilaton-dominated supergravity models and gauge-mediated supersymmetry-breaking models. Finally, we discuss how other phenomena, such as $B(b\to s\gamma)$, relic abundance of the lightest superpartner, and the Higgs mass may be correlated with the anomalous magnetic moment, but do not significantly impact the viability of a supersymmetric explanation, or the mass limits obtainable on smuons and charginos.Comment: 28 page