The complexity of the characterization of networks supporting shortest-path interval routing

AbstractInterval Routing is a routing method that was proposed in order to reduce the size of the routing tables by using intervals and was extensively studied and implemented. Some variants of the original method were also defined and studied. The question of characterizing networks which support optimal (i.e., shortest path) Interval Routing has been thoroughly investigated for each of the variants and under different models, with only partial answers, both positive and negative, given so far. In this paper, we study the characterization problem under the most basic model (the one unit cost), and with the most restrictive memory requirements (one interval per edge). We prove that this problem is NP-hard (even for the restricted class of graphs of diameter at most 3). Our result holds for all variants of Interval Routing. It significantly extends some related NP-hardness result, and implies that, unless P=NP, partial characterization results of some classes of networks which support shortest path Interval Routing, cannot be pushed further to lead to efficient characterizations for these classes

Rare Decay of the Top t -> cgg in the Standard Model

We calculate the one-loop flavor changing neutral current top quark decay t -> cgg in the Standard Model. We demonstrate that the rate for t -> cgg exceeds the rate for a single gluon emission t -> cg by about two orders of magnitude, while the rate for t -> cq barq (q=u) is slightly smaller than for t -> cg.Comment: 22 pages, 4 figures and 2 tables. Typo in Eq.2.1 corrected, text slightly modified, references added. Version to appear in Phys.Rev.

Transverse Tau Polarization in Decays of the Top and Bottom Quarks in the Weinberg Model of CP Non-conservation

We show that the transverse polarization asymmetry of the $\tau$-lepton in the decay $t\rightarrow b \tau \nu$ is extremely sensitive to CP violating phases arising from the charged Higgs exchange in the Weinberg model of CP non-conservation. Qualitatively, the polarization asymmetries are enhanced over rate or energy asymmetries by a factor of $\approx {m_t\over m_\tau}\approx O(100)$. Thus for optimal values of the parameters the method requires $\approx 10^4$ top pairs to be observable rather than $10^7$ needed for rate or energy asymmetries. We also examine $\tau$ polarization in b decays via $b \rightarrow c \nu \tau$ and find that it can also be very effective in constraining the CP violation parameters of the extended Higgs sector.Comment: 11,1 figure, SLAC-PUB-608

Bounds on the mass of the b' quark, revisited

Recent results from the DELPHI collaboration led us to review the present bounds on the b' quark mass. We use all available experimental data for m_b' > 96 GeV to constrain the b' quark mass as a function of the Cabibbo-Kobayashi-Maskawa elements in a sequential four generations model. We find that there is still room for a b' with a mass larger than 96 GeV.Comment: 9 pages and 7 figures. REVTEX

Flavor changing t -> c l_1^- l_2^+ decay in the general two Higgs doublet model

We study the flavor changing t-> c l_1^- l_2^+ decay in the framework of the general two Higgs doublet model, the so called model III. We predict the branching ratio for l_1=\tau, l_2=\mu at the order of magnitude of BR \sim 10^{-8}.Comment: 12 Pages, 5 Figure

One-loop flavor changing electromagnetic transitions

We discuss the effect of the external fermion masses in the flavor-changing radiative transitions of a heavy fermion (quark or lepton) to a lighter fermion at the one-loop level, and point out an often overlooked crucial difference in the sign of a charge factor between transitions of the down type $s\to d\gamma$ and the up type $c\to u\gamma$. We give formulas for the $F\to f\gamma$ effective vertex in various approximations and the exact formula for $t\to c\gamma$ and $\tau \to \mu \gamma$.Comment: LaTeX 16 pages + 4 postscript figures. Misprints corrected, some Comments adde

SUSY-QCD Effect on Top-Charm Associated Production at Linear Collider

We evaluate the contribution of SUSY-QCD to top-charm associated production at next generation linear colliders. Our results show that the production cross section of the process $e^+e^-\to t\bar c{or}\bar t c$ could be as large as 0.1 fb, which is larger than the prediction of the SM by a factor of $10^8$.Comment: version to appear in PR

The Complexity of Graph-Based Reductions for Reachability in Markov Decision Processes

We study the never-worse relation (NWR) for Markov decision processes with an infinite-horizon reachability objective. A state q is never worse than a state p if the maximal probability of reaching the target set of states from p is at most the same value from q, regard- less of the probabilities labelling the transitions. Extremal-probability states, end components, and essential states are all special cases of the equivalence relation induced by the NWR. Using the NWR, states in the same equivalence class can be collapsed. Then, actions leading to sub- optimal states can be removed. We show the natural decision problem associated to computing the NWR is coNP-complete. Finally, we ex- tend a previously known incomplete polynomial-time iterative algorithm to under-approximate the NWR

Study of ATLAS sensitivity to FCNC top decays

The ATLAS experiment sensitivity to top quark Flavour Changing Neutral Current (FCNC) decays was studied at LHC using ttbar events. While one of the top quarks is expected to follow the dominant Standard Model decay t->bW, the other decays through a FCNC channel, i.e. t-> Z u(c), t-> gamma u(c) or t-> g u(c). Different types of analyses, applied to each FCNC decay mode, were compared. The FCNC branching ratio sensitivity (assuming a 5sigma signal significance) and 95% confidence level limits on the branching ratios (in the hypothesis of signal absence) were obtained

SUSY-Induced Top Quark FCNC Processes at Linear Colliders

In the Minimal Supersymmetric Model (MSSM) the hitherto unconstrained flavor mixing between top-squark and charm-squark will induce the flavor-changing neutral-current (FCNC) interaction between top quark and charm quark, which then give rise to various processes at the next generation linear collider (NLC), i.e., the top-charm associated productions via $e^+ e^-$, $e^- \gamma$ and $\gamma \gamma$ collisions as well as the top quark rare decays $t \to c V$ ($V=g$, $\gamma$ or $Z$). All these processes involve the same part of the parameter space of the MSSM. Through a comparative analysis for all these processes at the NLC, we found the best channel to probe such SUSY-induced top quark FCNC is the top-charm associated production in $\gamma \gamma$ collision, which occurs at a much higher rate than $e^+ e^-$ or $e^- \gamma$ collision and may reach the detectable level for some part of the parameter space. Since the rates predicted by the Standard Model are far below the detectable level, the observation of such FCNC events would be a robust indirect evidence of SUSY.Comment: 12 pages, 8 figures (more refs added, discussions extended