Related papers: Explicit form of the Isgur-Wise function in the BP…

We examine the recent work of de Rafael and Taron where model-independent bounds on the Isgur-Wise function are presented. We first argue that the bounds cannot hold in as much generality as implied. We show that the effects of resonances…

In this note we give a sharp weighted estimate for square function from $L^2(w)$ to $L^2(w)$, $w\in A_2$. This has been known. But we also give a sharpening of this weighted estimate in the spirit of $T1$-type testing conditions. Finally we…

After a brief introduction to the Heavy-Quark Effective Theory (HQET), I review the extraction of the Isgur-Wise function from lattice QCD calculations of the matrix elements for semi-leptonic decays of heavy-light pseudoscalar mesons both…

Solutions to a wide variety of transcendental equations can be expressed in terms of the Lambert $\mathrm{W}$ function. The $\mathrm{W}$ function, occurring frequently in applications, is a non-elementary, but now standard mathematical…

If $\alpha_1,\ldots,\alpha_r$ are algebraic numbers such that $$N=\sum_{i=1}^r\alpha_i \ne \sum_{i=1}^r\alpha_i^{-1}$$ for some integer $N$, then a theorem of Beukers and Zagier gives the best possible lower bound on $$\sum_{i=1}^r\log…

We study the form factors of heavy--to--heavy and heavy--to--light weak decays using the light--front relativistic quark model. For the heavy--to--heavy $B \ra D^{(\ast)}$ semileptonic decays we calculate the corresponding Isgur--Wise…

Assuming Coulomb-like as well as confining scalar potential, we have solved Shr\"odinger equation perturbatively in $1/m_Q$ with a heavy quark mass $m_Q$. The lowest order equation is examined carefully. Mass levels are fitted with…

Within the OPE, we the new sum rules in Heavy Quark Effective Theory in the heavy quark limit and at order 1/m_Q, using the non-forward amplitude. In particular, we obtain new sum rules involving the elastic subleading form factors chi_i(w)…

In this paper, we prove the restriction estimates for 2D surfaces S:= {(xi1, xi2, xi1^3 +/- xi2^3) : (xi1, xi2) in [0,1]^2} by reducing to Wang-Wu's result on the perturbed paraboloid and to the results on the perturbed hyperboloid obtained…

The heavy-to-heavy exclusive semileptonic transitions of singly heavy baryons (SHBs) are investigated within the framework of the Hypercentral Constituent Quark Model (hCQM). The six-dimensional hyperradial Schr\"{o}dinger equation is…

We review the role of the universal Isgur-Wise functions parameterizing the $B$ meson semileptonic matrix elements to charm states in the infinite heavy quark mass limit. We also discuss the determination of one of such form factors by QCD…

The heavy mass limit of quark models based on the Bakamjian-Thomas cons\-truction reveals remarkable features. In addition to previously demonstrated properties of covariance and Isgur-Wise scaling, exact duality, leading to the…

We investigate the form factors for exclusive semileptonic decays of $B$-meson to $D,~D^*$, based on the parton picture and helped by the results of the HQET. We obtain the numerical results for the slope of the Isgur-Wise function, which…

We calculate heavy quark symmetry breaking in the slopes and curvatures of the $B\to D^{(*)}\ell\bar\nu$ spectra at zero recoil, including the order $\alpha_s^2\beta_0$ corrections. We point out that the theoretical uncertainties in the…

Let X,X_1,X_2,... be independent identically distributed random variables and let h(x,y)=h(y,x) be a measurable function of two variables. It is shown that the bounded law of the iterated logarithm, $\limsup_n (n\log\log n)^{-1}|\sum_{1<=…

Let G={G(x), x\in R_+}, G(0)=0, be a mean zero Gaussian process with $E(G(x)-G(y))^2=\sigma ^2(x-y) $. Let $ \rho (x)= \frac12{d^{2}\over dx^2}\sigma^2(x)$, $x\ne 0 $. When $\rho^{k}$ is integrable at zero and satisfies some additional…

We prove that the intermediate long wave (ILW) equation is globally well-posed in the Sobolev spaces $H^s(\mathbb{T})$ for $s > -\frac12$. The previous record for well-posedness was $s\geq 0$, and the system is known to be ill-posed for…

We show that, if $\mathbf{W} \in \mathbb{R}^{N \times N}_{\mathsf{sym}}$ is drawn from the gaussian orthogonal ensemble, then with high probability the degree 4 sum-of-squares relaxation cannot certify an upper bound on the objective…

Taking the Iwaniec explicit formula as a starting point, we give a short proof of a more precise $\frac{2}{3}$ bound for the exponent in the error term of the Gallagher-type prime geodesic theorem for the modular surface.

We construct a double field theory coupled to the fields present in Vasiliev's equations. Employing the "semi-covariant" differential geometry, we spell a functional in which each term is completely covariant with respect to…