31 research outputs found

### Nonleptonic Weak Decays of Bottom Baryons

Cabibbo-allowed two-body hadronic weak decays of bottom baryons are analyzed.
Contrary to the charmed baryon sector, many channels of bottom baryon decays
proceed only through the external or internal W-emission diagrams. Moreover,
W-exchange is likely to be suppressed in the bottom baryon sector.
Consequently, the factorization approach suffices to describe most of the
Cabibbo-allowed bottom baryon decays. We use the nonrelativistic quark model to
evaluate heavy-to-heavy and heavy-to-light baryon form factors at zero recoil.
When applied to the heavy quark limit, the quark model results do satisfy all
the constraints imposed by heavy quark symmetry. The decay rates and up-down
asymmetries for bottom baryons decaying into $(1/2)^++P(V)$ and $(3/2)^++P(V)$
are calculated. It is found that the up-down asymmetry is negative except for
$\Omega_b \to (1/2)^++P(V)$ decay and for decay modes with $\psi'$ in the final
state. The prediction $B(\Lambda_b \to J/\psi\Lambda)=1.6 \times 10^{-4}$ for
$|V_{cb}|=0.038$ is consistent with the recent CDF measurement. We also present
estimates for $\Omega_c \to (3/2)^++P(V)$ decays and compare with various model
calculations.Comment: 24 pages, to appear in Phys. Rev. Uncertainties with form factor q^2
dependence are discusse

### Multi-Stage Facility Location Problems with Transient Agents

We study various models for the one-dimensional multi-stage facility location problems with transient agents, where a transient agent arrives in some stage and stays for a number of consecutive stages. In the problems, we need to serve each agent in one of their stages by determining the location of the facility at each stage. In the first model, we assume there is no cost for moving the facility across the stages. We focus on optimal algorithms to minimize both the social cost objective, defined as the total distance of all agents to the facility over all stages, and the maximum cost objective, defined as the max distance of any agent to the facility over all stages. For each objective, we give a slice-wise polynomial (XP) algorithm (i.e., solvable in m^f(k) for some fixed parameter k and computable function f, where m is the input size) and show that there is a polynomial-time algorithm when a natural first-come-first-serve (FCFS) order of agent serving is enforced. We then consider the mechanism design problem, where the agents' locations and arrival stages are private, and design a group strategy-proof mechanism that achieves good approximation ratios for both objectives and settings with and without FCFS ordering. In the second model, we consider the facility's moving cost between adjacent stages under the social cost objective, which accounts for the total moving distance of the facility. Correspondingly, we design XP (and polynomial time) algorithms and a group strategy-proof mechanism for settings with or without the FCFS ordering