ttˉt\bar{t} + ZZ / WW / ttˉt\bar{t} at ATLAS

The newest results from the ATLAS Collaboration for the production of a top-quark pair in association with a $Z$ or $W$ boson, and for the production of four top quarks, are summarised in these proceedings. The measurements were performed with 36.1 fb$^{-1}$ of proton-proton collision data from the Large Hadron Collider at a centre-of-mass energy of 13 TeV.Comment: 7 pages, 3 figures, TOP2018 Conference Proceeding

The Rare Top Decays t→bW+Zt \to b W^+ Z and t→cW+W−t \to c W^+ W^-

The large value of the top quark mass implies that the rare top decays $t \rightarrow b W^+ Z, s W^+ Z$ and $d W^+ Z$, and $t \rightarrow c W^+ W^-$ and $u W^+ W^-$, are kinematically allowed decays so long as $m_t \ge m_W + m_Z + m_{d_i} \approx 171.5 GeV + m_{d_i}$ or $m_t \ge 2m_W + m_{u,c} \approx 160.6 GeV + m_{u,c}$, respectively. The partial decay widths for these decay modes are calculated in the standard model. The partial widths depend sensitively on the precise value of the top quark mass. The branching ratio for $t\rightarrow b W^+ Z$ is as much as $2 \times 10^{-5}$ for $m_t = 200 GeV$, and could be observable at LHC. The rare decay modes $t \rightarrow c W^+ W^-$ and $u W^+ W^-$ are highly GIM-suppressed, and thus provide a means for testing the GIM mechanism for three generations of quarks in the u, c, t sector.Comment: 19 pages, latex, t->bWZ corrected, previous literature on t->bWZ cited, t->cWW unchange

Some New Bounds For Cover-Free Families Through Biclique Cover

An $(r,w;d)$ cover-free family $(CFF)$ is a family of subsets of a finite set such that the intersection of any $r$ members of the family contains at least $d$ elements that are not in the union of any other $w$ members. The minimum number of elements for which there exists an $(r,w;d)-CFF$ with $t$ blocks is denoted by $N((r,w;d),t)$. In this paper, we show that the value of $N((r,w;d),t)$ is equal to the $d$-biclique covering number of the bipartite graph $I_t(r,w)$ whose vertices are all $w$- and $r$-subsets of a $t$-element set, where a $w$-subset is adjacent to an $r$-subset if their intersection is empty. Next, we introduce some new bounds for $N((r,w;d),t)$. For instance, we show that for $r\geq w$ and $r\geq 2$ $$N((r,w;1),t) \geq c{{r+w\choose w+1}+{r+w-1 \choose w+1}+ 3 {r+w-4 \choose w-2} \over \log r} \log (t-w+1),$$ where $c$ is a constant satisfies the well-known bound $N((r,1;1),t)\geq c\frac{r^2}{\log r}\log t$. Also, we determine the exact value of $N((r,w;d),t)$ for some values of $d$. Finally, we show that $N((1,1;d),4d-1)=4d-1$ whenever there exists a Hadamard matrix of order 4d

New signals in pair production of heavy Q=2/3 singlets at LHC

New quark singlets T can be produced in pairs at LHC through standard QCD interactions, with a large cross section for masses of several hundreds of GeV. Their charged current decays T Tbar T -> W+ b W- bbar, with semileptonic decay of the W pair, give a final state l nu bb jj$, as in top pair production. The mixed decay modes T Tbar -> W+ b H tbar, H t W- bbar -> W+ b W- bbar H, T Tbar -> W+ b Z tbar, Z t W- bbar -> W+ b W- bbar Z, with H,Z -> jj, yield two more jets, l nu bb jjjj, or the same state in the latter case for Z -> nu nubar. We extend previous work examining in detail the extra H and Z contributions and stressing one of the salient features of the T Tbar -> W+ b W- bbar signal: the presence of a very energetic charged lepton. We finally compare with the discovery potential in l nu bbbb jj final states, with four b tags.Comment: LaTeX, 10 pages, 11 PS figures, uses PoS.cls. Contribution to the International Workshop on Top Quark Physics, January 12-15, 2006, Coimbra, Portugal. To appear in the proceeding

Nonparametric identification of dynamic models with unobserved state variables

We consider the identification of a Markov process {W t, X t*} for t=1,2,...,T when only {W t} for t=1, 2,..,T is observed. In structural dynamic models, W t denotes the sequence of choice variables and observed state variables of an optimizing agent, while X t* denotes the sequence of serially correlated state variables. The Markov setting allows the distribution of the unobserved state variable X t* to depend on W t-1 and X t-1 *. We show that the joint distribution of (W t, X t*, W t-1 , X t-1 *) is identified from the observed distribution of (W t+1 , W t, W t-1 , W t-2 , W t-3 ) under reasonable assumptions. Identification of the joint distribution of (W t, X t*, W t-1 , X t-1 *) is a crucial input in methodologies for estimating dynamic models based on the "conditional-choice-probability (CCP)" approach pioneered by Hotz and Miller.