Timelike-helicity B→ππB\to \pi\pi form factor from light-cone sum rules with dipion distribution amplitudes

We complete the set of QCD light-cone sum rules for $B\to \pi\pi$ transition form factors, deriving a new sum rule for the timelike-helicity form factor $F_t$ in terms of dipion distribution amplitudes. This sum rule, in the leading twist-2 approximation, is directly related to the pion vector form factor. Employing a relation between $F_t$ and other $B\to \pi\pi$ form factors we obtain also the longitudinal-helicity form factor $F_0$. In this way, all four (axial-)vector $B\to \pi\pi$ form factors are predicted from light-cone sum rules with dipion distribution amplitudes. These results are valid for small dipion masses with large momentum.Comment: 7 pages, 3 figure

Multiplicity Preserving Triangular Set Decomposition of Two Polynomials

In this paper, a multiplicity preserving triangular set decomposition algorithm is proposed for a system of two polynomials. The algorithm decomposes the variety defined by the polynomial system into unmixed components represented by triangular sets, which may have negative multiplicities. In the bivariate case, we give a complete algorithm to decompose the system into multiplicity preserving triangular sets with positive multiplicities. We also analyze the complexity of the algorithm in the bivariate case. We implement our algorithm and show the effectiveness of the method with extensive experiments.Comment: 18 page

B→ππB\to\pi\pi Form Factors from Light-Cone Sum Rules with BB-meson Distribution Amplitudes

We study $B\to\pi\pi$ form factors using QCD light-cone sum rules with $B$-meson distribution amplitudes. These form factors describe the semileptonic decay $B\to \pi\pi \ell\bar{\nu}_{\ell}$, and constitute an essential input in $B\to \pi\pi \ell^+\ell^-$ and $B\to \pi\pi\pi$ decays. We employ the correlation functions where a dipion isospin-one state is interpolated by the vector light-quark current. We obtain sum rules where convolutions of the $P$-wave $\bar{B}^0\to \pi^+\pi^0$ form factors with the time-like pion vector form factor are related to universal $B$-meson distribution amplitudes. These sum rules are valid in the kinematic regime where the dipion state has a large energy and a low invariant mass, and reproduce analytically the known light-cone sum rules for $B\to \rho$ form factors in the limit of $\rho$-dominance with zero width, thus providing a systematics for so-far-unaccounted corrections to $B\to\rho$ transitions. Using data for the pion vector form factor, we estimate finite width-effects and the contribution of excited $\rho$-resonances to the $B\to\pi\pi$ form factors. We find that these contributions amount up to $\sim 20\%$ in the small dipion mass region where they can be effectively regarded as a nonresonant ($P$-wave) background to the $B\to\rho$ transition.Comment: 28 pages, 3 figures. A few comments added. Version published in JHE

Personalized Acoustic Modeling by Weakly Supervised Multi-Task Deep Learning using Acoustic Tokens Discovered from Unlabeled Data

It is well known that recognizers personalized to each user are much more effective than user-independent recognizers. With the popularity of smartphones today, although it is not difficult to collect a large set of audio data for each user, it is difficult to transcribe it. However, it is now possible to automatically discover acoustic tokens from unlabeled personal data in an unsupervised way. We therefore propose a multi-task deep learning framework called a phoneme-token deep neural network (PTDNN), jointly trained from unsupervised acoustic tokens discovered from unlabeled data and very limited transcribed data for personalized acoustic modeling. We term this scenario "weakly supervised". The underlying intuition is that the high degree of similarity between the HMM states of acoustic token models and phoneme models may help them learn from each other in this multi-task learning framework. Initial experiments performed over a personalized audio data set recorded from Facebook posts demonstrated that very good improvements can be achieved in both frame accuracy and word accuracy over popularly-considered baselines such as fDLR, speaker code and lightly supervised adaptation. This approach complements existing speaker adaptation approaches and can be used jointly with such techniques to yield improved results.Comment: 5 pages, 5 figures, published in IEEE ICASSP 201