Flavor and CP Violation with Fourth Generations Revisited

The Standard Model predicts a very small CP violation phase $\sin2\Phi^{\rm SM}_{B_s} \simeq -0.04$%= \arg M_{12} \simeq \arg\,(V^*_{ts}V_{tb})^2$in$B_s$--$\bar B_s$mixing.$\lambda^2\eta$. Any finite value of$\Phi_{B_s}$measured at the Tevatron would imply New Physics. With recent hints for finite$\sin2\Phi_{B_s}$, experiments at the Tevatron, we reconsider the possibility of a 4th generation. As recent direct search bounds have become considerably heavier than 300 GeV, we take the$t'$mass to be near the unitarity bound of 500 GeV. Combining the measured values of$\Delta m_{B_s}$with${\cal B}(B \to X_s\ell^+\ell^-)$, together with typical$f_{B_s}$values, we find a sizable$\sin2\Phi^{\rm SM4}_{B_s} \sim -0.33$. Using$m_{b'} = 480$GeV, we extract the range$0.06 < |V_{t'b}| < 0.13$from the constraints of$\Gamma(Z\to b\bar b)$,$\Delta m_{D}$and${\cal B}(K^+\to\pi^+\nu\bar\nu)$. A future measurement of${\cal B}(K_L\to\pi^0\nu\bar\nu)$will determine$V_{t'd}$.Comment: 8 pages, 11 figure

Bi-collinear antiferromagnetic order in the tetragonal α\alpha-FeTe

By the first-principles electronic structure calculations, we find that the ground state of PbO-type tetragonal $\alpha$-FeTe is in a bi-collinear antiferromagnetic state, in which the Fe local moments ($\sim2.5\mu_B$) are ordered ferromagnetically along a diagonal direction and antiferromagnetically along the other diagonal direction on the Fe square lattice. This bi-collinear order results from the interplay among the nearest, next nearest, and next next nearest neighbor superexchange interactions $J_1$, $J_2$, and $J_3$, mediated by Te $5p$-band. In contrast, the ground state of $\alpha$-FeSe is in the collinear antiferromagnetic order, similar as in LaFeAsO and BaFe$_2$As$_2$.Comment: 5 pages and 5 figure

Inhomogeneous Diophantine approximation over the field of formal Laurent series

AbstractDe Mathan [B. de Mathan, Approximations diophantiennes dans un corps local, Bull. Soc. Math. France, Suppl. Mém. 21 (1970)] proved that Khintchine's theorem on homogeneous Diophantine approximation has an analogue in the field of formal Laurent series. Kristensen [S. Kristensen, On the well-approximable matrices over a field of formal series, Math. Proc. Cambridge Philos. Soc. 135 (2003) 255–268] extended this metric theorem to systems of linear forms and gave the exact Hausdorff dimension of the corresponding exceptional sets. In this paper, we study the inhomogeneous Diophantine approximation over a field of formal Laurent series, the analogue Khintchine's theorem and Jarnik–Besicovitch theorem are proved

Fourth Generation Leptons and Muon g−2g-2

We consider the contributions to $g_\mu-2$ from fourth generation heavy neutral and charged leptons, $N$ and $E$, at the one-loop level. Diagrammatically, there are two types of contributions: boson-boson-$N$, and $E$-$E$-boson in the loop diagram. In general, the effect from $N$ is suppressed by off-diagonal lepton mixing matrix elements. For $E$, we consider flavor changing neutral couplings arising from various New Physics models, which are stringently constrained by $\mu\to e\gamma$. We assess how the existence of a fourth generation would affect these New Physics models.Comment: Minor changes, with references update