Isospin-breaking effects on alpha extracted in B --> pi pi, rho rho, rho pi

Isospin-breaking in B --> pi pi caused by pi^0-eta-eta' mixing is studied in a model-independent way using flavor SU(3). Measured branching ratios for B^+ --> pi^+ pi^0, B^+ --> pi^+ eta^(') and B^0 --> pi^0 eta^(') imply an uncertainty in alpha smaller than 1.4 degree. We find a negligible effect of pi^0-eta-eta' mixing on alpha in B --> rho pi. Characterizing the effect of rho^0-omega mixing in B --> rho rho and in B --> rho pi by the two-pion invariant mass dependence, we point out a way of constraining this effect experimentally or eliminating it altogether. We show that a model-independent shift in alpha caused by electroweak penguin amplitudes in B --> pi pi and B --> rho rho, \Delta alpha_{EWP}=1.5+- 0.3 degree, may be slightly different in B --> rho pi. Other sources of isospin-breaking in these processes are briefly discussed.Comment: 21 pages, very slight changes, same version as in Physical Review

Regio and Stereospecific 2 + 2 Photoaddition of Cyclopentene to Pentafluoro-alkoxybenzene

2 + 2 photoaddition of cyclopentene to pentafluoro-alkoxybenzene in cyclohexane solution proceeds stereoselectively anti and regiospecifically to the 3,4 position

Electronic Structure of Hydrazinium (2 + ) Ion. A Semiempirical MO Treatment

A simple semiempjrical MO treatment of the electronic structure of hydrazinium (2 + ) ion was carried out on the basis of an extended Htickel method. The electronic population analysis for nitrogen and hydrogen atoms in this ion was calculated to b e (ls) 2 (2s)1 -121 (2px)1 ·3Go (2py)t·3Go (2p z)o .9BG and (ls)0o122, respectively

On measuring alpha in B(t)-> rho^\pm pi^\mp

Defining a most economical parametrization of time-dependent B-> rho^\pm pi^\mp decays, including a measurable phase alpha_{eff} which equals the weak phase alpha in the limit of vanishing penguin amplitudes, we propose two ways for determining alpha in this processes. We explain the limitation of one method, assuming only that two relevant tree amplitudes factorize and that their relative strong phase, delta_t, is negligible. The other method, based on broken flavor SU(3), permits a determination of alpha in B^0-> rho^\pm pi^\mp in an overconstrained system using also rate measurements of B^{0,+}-> K^* pi and B^{0,+}->rho K. Current data are shown to restrict two ratios of penguin and tree amplitudes, r_\pm, to a narrow range around 0.2, and to imply an upper bound |alpha_{eff} - alpha| < 15 degrees. Assuming that delta_t is much smaller than 90 degrees, we find alpha =(93\pm 16) degrees and (102 \pm 20) degrees using BABAR and BELLE results for B(t)-> rho^\pm pi^mp. Avoiding this assumption for completeness, we demonstrate the reduction of discrete ambiguities in alpha with increased statistics, and show that SU(3) breaking effects are effectively second order in r_\pm.Comment: 23 pages, 2 figures, data and references updated, to be published in Phys. Rev.

Investigating the reward cycle of play in pigs (Sus scrofa)

Observations of play in animals have been suggested as a promising indicator of positive emotions and thus of positive animal welfare. However, if play can follow the proposed reward cycle concept where animals estimate and value reward differently in different phases of the cycle (anticipation, consummation and post-consummation) is unclear. To investigate if a reward cycle for play exists in growing pigs, we carried out an exploratory study where pigs were tested when they were naïve to a reward cycle test (first occasion) against when they were accustomed to going through the test after having the access to an open play arena with objects. Forty undocked pigs were housed in a weaner stable with two castrated males and two females per pen. Within each litter, we randomly selected and tested one male and one female test pig, each being tested as naïve or accustomed to the testing environment. The first week the pigs (n = 20) were tested four times and regarded as naïve during the first day. After that they were regarded as accustomed, and were tested twice a week for 3 weeks. We observed the behavior of the tested pairs in three subsequent stages: (1) in a holding pen 3 min, (2) in a play arena 15 min, and (3) in their home pen 10 min. When accustomed, pigs showed more locomotor play, social interactions and standing, and a tendency of more orientation toward the play arena and exploring bars facing the play arena (i.e., reward-seeking behavior) in the holding pen than when they were naïve, suggesting an anticipation to enter the play arena. Performing high numbers of object play in all sessions, and for accustomed pigs more exploration and social interaction, but less locomotor play and walking in the play arena may suggest consumption of play and exploration. Finding more lying and sitting in accustomed pigs, but less standing and walking in the home pen is in line with the previous hypothesis of the post-consummatory behaviors. Our study showed mixed results for the existence of a reward cycle for play in pigs and generated questions for future research

Bridge trisections and classical knotted surface theory

We seek to connect ideas in the theory of bridge trisections with other well-studied facets of classical knotted surface theory. First, we show how the normal Euler number can be computed from a tri-plane diagram, and we use this to give a trisection-theoretic proof of the Whitney-Massey Theorem, which bounds the possible values of this number in terms of the Euler characteristic. Second, we describe in detail how to compute the fundamental group and related invariants from a tri-plane diagram, and we use this, together with an analysis of bridge trisections of ribbon surfaces, to produce an infinite family of knotted spheres that admit non-isotopic bridge trisections of minimal complexity.Comment: v1 has been divided into two papers: the present article and "Bridge trisections and Seifert solids," which will be posted simultaneously; 29 pages, 11 figure