Constraints and Soliton Solutions for the KdV Hierarchy and AKNS Hierarchy

It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator.We generalize the result to a special form of Lax pair, from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed. A direct result is that the $n$-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations (ODEs), which may be gotten by a simple but unfamiliar Lax pair. Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies. The key is a special form of Lax pair for the AKNS hierarchy. It is proved that under the constraints all equations of the AKNS hierarchy are linearizable.Comment: 12 pages, 0 figur

Strong Phases and Factorization for Color Suppressed Decays

We prove a factorization theorem in QCD for the color suppressed decays B0-> D0 M0 and B0-> D*0 M0 where M is a light meson. Both the color-suppressed and W-exchange/annihilation amplitudes contribute at lowest order in LambdaQCD/Q where Q={mb, mc, Epi}, so no power suppression of annihilation contributions is found. A new mechanism is given for generating non-perturbative strong phases in the factorization framework. Model independent predictions that follow from our results include the equality of the B0 -> D0 M0 and B0 -> D*0 M0 rates, and equality of non-perturbative strong phases between isospin amplitudes, delta(DM) = delta(D*M). Relations between amplitudes and phases for M=pi,rho are also derived. These results do not follow from large Nc factorization with heavy quark symmetry.Comment: 38 pages, 6 figs, typos correcte

Remarks on Form Factor Bounds

Improved model independent upper bounds on the weak transition form factors are derived using inclusive sum rules. Comparison of the new bounds with the old ones is made for the form factors h_{A_1} and h_V in B -> D* decays.Comment: 8 pages, 2 figures, title changed and typos corrected for journal publicatio

Short-term effects of a gain-focused reappraisal intervention for dementia caregivers: A double-blind cluster-randomized controlled trial

Objectives To examine the effects of a benefit-finding intervention, the key feature being the use of gain-focused reappraisal strategies to find positive meanings and benefits in caring for someone with dementia. Design: Cluster-randomized double-blind controlled trial. Setting: Social centers and clinics. Participants: 129 caregivers. Inclusion criteria were (a) primary caregiver aged 18+ and without cognitive impairment, (b) providing ≥14 care hours per week to a relative with mild-to-moderate Alzheimer's disease, and (c) scoring ≥3 on the Hamilton Depression Rating Scale. Exclusion criterion was care-recipient having parkinsonism or other forms of dementia. Interventions: The benefit-finding intervention was evaluated against two treatment-as-usuals, namely, simplified psychoeducation (lectures only) and standard psychoeducation. Each intervention lasted eight weeks, with a 2-hour session per week. Randomization into these conditions was based on center/clinic membership. Measurements: Primary outcome was depressive symptom. Secondary outcomes were Zarit Burden Interview, role overload, and psychological well-being. Self-efficacy beliefs and positive gains were treated as mediators. Measures were collected at baseline and posttreatment. Results: Regression analyses showed BF treatment effects on all outcomes when compared with SIM-PE, and effects on depressive symptoms and Zarit burden when compared with STD-PE. Effect sizes were medium-to-large for depressive symptoms (d=-0.77– -0.96), and medium for the secondary outcomes (d=|0.42–0.65|). Furthermore, using the bootstrapping method, we found significant mediating effects by self-efficacy in controlling upsetting thoughts and positive gains, with the former being the primary mediator. Conclusions: Finding positive gains reduces depressive symptoms and burden and promotes psychological well-being primarily through enhancing self-efficacy in controlling upsetting thoughts

Flavor symmetry breaking and scaling for improved staggered actions in quenched QCD

We present a study of the flavor symmetry breaking in the pion spectrum for various improved staggered fermion actions. To study the effects of link fattening and tadpole improvement, we use three different variants of the p4 action - p4fat3, p4fat7, and p4fat7tad. These are compared to Asqtad and also to naive staggered. To study the pattern of symmetry breaking, we measure all 15 meson masses in the 4-flavor staggered theory. The measurements are done on a quenched gauge background, generated using a one-loop improved Symanzik action with $\beta=10/g^2 = 7.40, 7.75,$ and 8.00, corresponding to lattice spacings of approximately a = .31 fm., .21 fm., and .14 fm. We also study how the lattice scale set by the $\rho$ mass on each of these ensembles compares to one set by the static quark potential.Comment: 18 pages, 6 figure

Hadronic Charmed Meson Decays Involving Tensor Mesons

Charmed meson decays into a pseudoscalar meson P and a tensor meson T are studied. The charm to tensor meson transition form factors are evaluated in the Isgur-Scora-Grinstein-Wise (ISGW) quark model. It is shown that the Cabibbo-allowed decay $D_s^+\to f_2(1270)\pi^+$ is dominated by the W-annihilation contribution and has the largest branching ratio in $D\to TP$ decays. We argue that the Cabibbo-suppressed mode $D^+\to f_2(1270)\pi^+$ should be suppressed by one order of magnitude relative to $D_s^+\to f_2(1270)\pi^+$. When the finite width effect of the tensor resonances is taken into account, the decay rate of $D\to TP$ is generally enhanced by a factor of $2\sim 3$. Except for $D_s^+\to f_2(1270)\pi^+$, the predicted branching ratios of $D\to TP$ decays are in general too small by one to two orders of magnitude compared to experiment. However, it is very unlikely that the $D\to T$ transition form factors can be enhanced by a factor of $3\sim 5$ within the ISGW quark model to account for the discrepancy between theory and experiment. As many of the current data are still preliminary and lack sufficient statistic significance, more accurate measurements are needed to pin down the issue.Comment: 11 page

B→DsπB \to D_s \pi and the tree amplitude in B→π+π−B \to \pi^+ \pi^-

The recently-observed decay $B^0 \to D_s^+ \pi^-$ is expected to proceed mainly by means of a tree amplitude in the factorization limit: $B^0 \to \pi^- {(W^+)}^*$, ${(W^+)}^* \to D_s^+$. Under this assumption, we predict the corresponding contribution of the tree amplitude to $B^0 \to \pi^+ \pi^-$. We indicate the needed improvements in data that will allow a useful estimate of this amplitude with errors comparable to those accompanying other methods. Since the factorization hypothesis for this process goes beyond that proved in most approaches, we also discuss independent tests of this hypothesis.Comment: 7 pages, LaTeX, 1 figure, to be submitted to Phys. Rev. D (Brief Reports

Hadronic Charmed Meson Decays Involving Axial Vector Mesons

Cabibbo-allowed charmed meson decays into a pseudoscalar meson and an axial-vector meson are studied. The charm to axial-vector meson transition form factors are evaluated in the Isgur-Scora-Grinstein-Wise quark model. The dipole momentum dependence of the $D\to K$ transition form factor and the presence of a sizable long-distance $W$-exchange are the two key ingredients for understanding the data of $D\to \bar Ka_1$. The $K_{1A}-K_{1B}$ mixing angle of the strange axial-vector mesons is found to be $\approx \pm37^\circ$ or $\pm58^\circ$ from $\tau\to K_1\nu_\tau$ decays. The study of $D\to K_1(1270)\pi, K_1(1400)\pi$ decays excludes the positive mixing-angle solutions. It is pointed out that an observation of the decay $D^0\to K_1^-(1400)\pi^+$ at the level of $5\times 10^{-4}$ will rule out $\theta\approx -37^\circ$ and favor the solution $\theta\approx -58^\circ$. Though the decays $D^0\to \bar K_1^0\pi^0$ are color suppressed, they are comparable to and even larger than the color-allowed counterparts: $\bar K_1^0(1270)\pi^0\sim K_1^-(1270)\pi^+$ and $\bar K_1^0(1400)\pi^0> K_1^-(1400)\pi^+$. The finite width effect of the axial-vector resonance is examined. It becomes important for $a_1(1260)$ in particular when its width is near 600 MeV.Comment: 19 page

Comments on the Quark Content of the Scalar Meson f0(1370)f_0(1370)

Based on the measurements of $(D_s^+,D^+)\to f_0(1370)\pi^+$ we determine, in a model independent way, the allowed $s\bar s$ content in the scalar meson $f_0(1370)$. We find that, on the one hand, if this isoscalar resonance is a pure $n\bar n$ state [ $n\bar n\equiv(u\bar u+d\bar d)/\sqrt{2} ]$, a very large $W$-annihilation term will be needed to accommodate $D_s^+\to f_0(1370)\pi^+$. On the other hand, the $s\bar s$ component of $f_0(1370)$ should be small enough to avoid excessive $D_s^+\to f_0(1370)\pi^+$ induced from the external $W$-emission. Measurement of $f_0(1370)$ production in the decay $D_s^+\to K^+K^-\pi^+$ will be useful to test the above picture. For the decay $D^0\to f_0(1370)\bar K^0$ which is kinematically barely or even not allowed, depending on the mass of $f_0(1370)$, we find that the finite width effect of $f_0(1370)$ plays a crucial role on the resonant three-body decay $D^0\to f_0(1370)\bar K^0\to\pi^+\pi^-\bar K^0$.Comment: 12 pages, 2 figure

Nonfactorizable contributions to B→D(∗)MB \to D^{(*)} M decays

While the factorization assumption works well for many two-body nonleptonic $B$ meson decay modes, the recent measurement of $\bar B\to D^{(*)0}M^0$ with $M=\pi$, $\rho$ and $\omega$ shows large deviation from this assumption. We analyze the $B\to D^{(*)}M$ decays in the perturbative QCD approach based on $k_T$ factorization theorem, in which both factorizable and nonfactorizable contributions can be calculated in the same framework. Our predictions for the Bauer-Stech-Wirbel parameters, $|a_2/a_1|= 0.43\pm 0.04$ and $Arg(a_2/a_1)\sim -42^\circ$ and $|a_2/a_1|= 0.47\pm 0.05$ and $Arg(a_2/a_1)\sim -41^\circ$, are consistent with the observed $B\to D\pi$ and $B\to D^*\pi$ branching ratios, respectively. It is found that the large magnitude $|a_2|$ and the large relative phase between $a_2$ and $a_1$ come from color-suppressed nonfactorizable amplitudes. Our predictions for the ${\bar B}^0\to D^{(*)0}\rho^0$, $D^{(*)0}\omega$ branching ratios can be confronted with future experimental data.Comment: 25 pages with Latex, axodraw.sty, 6 figures and 5 tables, Version published in PRD, Added new section 5 and reference