A note on the Mumford-Tate Conjecture for CM abelian varieties

The Mumford-Tate conjecture is first proved for CM abelian varieties by H. Pohlmann [Ann. Math., 1968]. In this note we give another proof of this result and extend it to CM motives.Comment: 10 pages, to appear in Taiwanese J. Mat

Endomorphism algebras of QM abelian surfaces

We determine endomorphism algebras of abelian surfaces with quaternion multiplication.Comment: 14 pages. Lemma 2.10 correcte

bsuˉdˉbs\bar u\bar d : A Promising Detectable Tetraquark

We propose to investigate a particle with four different flavors, $bs\bar u\bar d$, which is a promising detectable tetraquark state. Its $BK$ threshold, 5773 MeV, is 270 MeV higher than the $B_s\pi$ threshold of $bd\bar u\bar s$ and $bu\bar d\bar s$, leading to a large mass region to be stable. If the lowest-lying \bsud state exists below threshold, it can be definitely observed via the weak decay mode $J/\Psi K^-K^-\pi^+$, with the expectation of hundreds of events in the current LHCb data sample but rejecting backgrounds due to its long lifetime. This can be a benchmark of the existence of $X(5568)$ which is a partner of $bs\bar u\bar d$ under the flavor $SU(3)$ symmetry. If no signal is observed in this mode, it constrain the mass of the ground tetraquark state to be larger than the threshold. In the case above threshold, it can be detected via the strong decay mode $\overline B^0K^-$. The $cs\bar u\bar d$ state has similar features.Comment: 5 pages, 2 figures and 2 table