Narrow Results

Investigations of the mass and decays of the J^PC=1^-+ hybrid are reviewed, including calculation of the π₁(1^-+)→ηπ, η′π decay widths within the QCD sum rules technique. In this calculation, the recently-proposed η, η′ quark mixing scheme is employed. The results indicate that the decay width Γ_π1→ηπ≈250 MeV is large compared with the decay width Γ_{π1→η′π}≈20 MeV. Inspired by these results, some phenomenological approaches are suggested to gain an understanding of the underlying mechanism of ηπ and η′π hybrid decays.

We investigate the possible corrections to the linear Regge trajectories for the light-quark meson sector by matching two-point correlators of quark currents to the Operator Product Expansion. We find that the allowed modifications to the linear behavior must decrease rapidly with the principal quantum number. After fitting the lightest states in each channel and certain low-energy constants the whole spectrum for meson masses and residues is obtained in a satisfactory agreement with phenomenology. The perturbative corrections to our results are discussed.

The modern status of the problem of axial anomaly in QED and QCD is reviewed. Two methods of the derivation of the axial anomaly are presented: (1) by splitting of coordinates in the expression for the axial current and (2) by calculation of triangle diagrams, where the anomaly arises from the surface terms in momentum space. It is demonstrated, that the equivalent formulation of the anomaly can be given, as a sum rule for the structure function in dispersion representation of three point function of AVV interaction. It is argued, that such integral representation of the anomaly has some advantages in the case of description of the anomaly by contribution of hadronic states in QCD. The validity of the 't Hooft consistency condition is discussed. A few examples of the physical application of the axial anomaly are given.

We update the extraction of V_us from hadronic τ decay data in light of recent BaBar and Belle results on the branching fractions of a number of important strange decay modes. A range of sum rule analyses is employed, particular attention being paid to those based on “non-spectral weights”, developed previously to bring the slow convergence of the relevant integrated D = 2 OPE series under improved control. Results from the various sum rules are in good agreement with one another, but ~ 3σ below expectations based on 3-family unitarity.

The AdS/QCD models are known to be closely related to the QCD sum rules in the large-N_c (called also planar) limit. Rewriting the theory of infinite tower of free stable mesons expected in the large-N_c QCD as a five-dimensional theory, we scrutinize to what extend the bottom-up holographic models may be viewed as an alternative language expressing the phenomenology of planar QCD sum rules. It is found that many features of AdS/QCD models can be thereby obtained without invoking prescriptions from the original AdS/CFT correspondence. Under some assumptions, all possibilities leading to simple Regge trajectories are classified, and it is argued that the most phenomenologically consistent model is the one called "soft wall model" in the holographic approach, with a preference to the positive-sign dilaton background.

Using the fact that the neutrino mixing matrix , where U_e and U_ν result from the diagonalization of the charged lepton and neutrino mass matrices, we analyze the predictions based on the sum rules which the Dirac phase δ present in U satisfies when U_ν has a form dictated by, or associated with, discrete flavor symmetries and U_e has a "minimal" form (in terms of angles and phases it contains) that can provide the requisite corrections to U_ν, so that the reactor, atmospheric and solar neutrino mixing angles θ₁₃, θ₂₃ and θ₁₂ have values compatible with the current data.

The masses and decay constants of the light tensor mesons were calculated with quantum numbers $J^P=2^{+}$ in the framework of the QCD sum rules in the standard model. The non perturbative contributions up to dimension-5 are considered as important terms of the operator product expansion.

We present generalized evolution equations and factorization in terms of the truncated Mellin moments (TMM) of the parton distributions and structure functions. We illustrate the x and Q² dependence of TMM in the polarized case. Using the TMM approach we compare the integrals of g₁ with HERMES and COMPASS data from the limited x-ranges.

The strong coupling constants not only are important to understand the strong interactions of the heavy baryons, but can also help us reveal the nature and structure of these baryons. Additionally, researchers indeed have made great efforts to calculate some of the strong coupling constants, $g_{{\mathrm{\Omega }}_c^{\ast }{\mathrm{\Omega }}_c^{\ast }\varphi }$, $g_{{\mathrm{\Omega }}_c^{\ast }{\mathrm{\Xi }}_c^{\ast }{K}^{\ast }}$, $g_{{\mathrm{\Xi }}_c^{\ast }{\mathrm{\Sigma }}_c^{\ast }{K}^{\ast }}$, $g_{{\mathrm{\Omega }}_b^{\ast }{\mathrm{\Omega }}_b^{\ast }\varphi }$, $g_{{\mathrm{\Xi }}_b^{\ast }{\mathrm{\Sigma }}_b^{\ast }{K}^{\ast }}$, $g_{{\mathrm{\Xi }}_b^{\ast }{\mathrm{\Xi }}_b\pi }$, $g_{{\mathrm{\Xi }}_c^{\ast }{\mathrm{\Xi }}_c\pi }$, $g_{{\mathrm{\Lambda }}_{b}N{B}^{\ast }}$, $g_{{\mathrm{\Lambda }}_b{N}^{\ast }{B}^{\ast }}$, $g_{{\mathrm{\Lambda }}_{c}N{D}^{\ast }}$, $g_{{\mathrm{\Lambda }}_c{N}^{\ast }{D}^{\ast }}$, $g_{{\mathrm{\Sigma }}_{c}N{D}^{\ast }}$, $g_{{\mathrm{\Sigma }}_b{N}^{\ast }{B}^{\ast }}$, $g_{{\mathrm{\Sigma }}_{b}N{B}^{\ast }}$, $g_{{\mathrm{\Sigma }}_c{N}^{\ast }{D}^{\ast }}$, etc. In this paper, we analyze the strong vertices ${\mathrm{\Sigma }}_c^{\ast }ND$ and ${\mathrm{\Sigma }}_b^{\ast }NB$ using the three-point QCD sum rules under the Dirac structure of $q/p//{\gamma }_{\mu }$. We perform our analysis by considering the contributions of the perturbative part and the condensate terms of $〈\bar{q}q〉$ and $〈\frac{{\alpha }_s}{\pi }GG〉$. After the form factors are calculated, they are then fitted into analytical functions which are used to get the strong coupling constants for these two vertices. The final results are $g_{{\mathrm{\Sigma }}_c^{\ast }ND}=7.19_{-3.11}^{+8.49}\pm 1.76$ and $g_{{\mathrm{\Sigma }}_b^{\ast }NB}=10.54_{-5.23}^{+15.59}\pm 1.82$.

We consider the $A_4$, $S_4$ and $A_5$ discrete lepton flavor symmetries broken down to nontrivial residual symmetries in the charged lepton and neutrino sectors in such a way that at least one of them is a $Z_2$. Such symmetry breaking patterns lead to predictions for some of the three neutrino mixing angles and/or the Dirac CP violation phase $\delta$ of the neutrino mixing matrix. First, we perform a statistical analysis of these predictions, which uses as input the latest global data on the neutrino mixing parameters. We find 14 phenomenologically viable cases. Further, we assess the viability of these cases taking into account the prospective uncertainties in the determination of the mixing angles, planned to be achieved in current and future neutrino oscillation experiments. We find that only six cases would be compatible with the assumed prospective data. We show that this number will be further reduced by a precision measurement of $\delta$.

The possibility of physics beyond the Standard Model is studied. The requirement of finiteness of the zero-point energy density and pressure or the requirement of the Lorentz invariance of the zero-point stress-energy tensor in Minkowski space–time, implies regularization sum rules on the number of degrees of freedom and mass of fundamental particles spectrum. The consequences of these sum rules on the existence of particles beyond the Standard Model are studied. If these sum rules are to be satisfied, it is shown that some simple and minimal extensions of the Standard Model such as the two-Higgs-doublet model, right-handed neutrinos, mirror symmetry cannot be complete extensions in their current forms. The only exception is unbroken supersymmetry and may be broken supersymmetry. A comparison between different regularization schemes is also done. It is shown that while all considered regularization schemes give a Lorentz invariant expression for the zero-point stress-energy tensor in Minkowski space, their physical interpretations are quite different.

In this paper, we obtain the integrated flavor asymmetry of the sea quarks in the proton, ${\int }_0^1(\bar{d}-ū)dx$, with the help of the truncated moments approach elaborated in our previous papers. We use the difference between the light sea-quark distributions $\bar{d}-ū$ extracted from Drell–Yan (DY) NuSea/E866 measurements of the cross-section ratio ${\sigma }^{pd}/{\sigma }^{pp}$ and from the recent global analysis of deep inelastic scattering (DIS) $F_2^{p-n}$ data incorporating the reanalyzed neutron structure function. In our analysis, we also include the most recent DY data from the Fermilab SeaQuest/E906 experiment.

When constructing multivariate framelets, it is often unavoidable to work with matrices of multivariate trigonometric polynomials and complicated matrix decomposition problems. These problems become even harder when good properties such as high-order vanishing moments are required on the framelets. In this paper, we establish a new method for constructing multivariate dual framelets with high-order vanishing moments. The underlying scheme of our algorithm is the famous Mixed Extension Principle that allows us to derive the high-pass filters (or framelet generators) from a given pair of refinable filters with high-order linear-phase moments. Our method only involves two steps: (1) directly constructing the first few pairs of high-pass filters by using the linear-phase moment conditions of the refinement filters; (2) solving a system of linear equations to obtain the rest of the high-pass filters. Both are easy to implement for scientific computation, regardless of what dimension or dilation matrix we work with. Apart from high-order vanishing moments, we will see that if the refinement filters take coefficients from some subfield $𝔽$ of $ℂ$ that is closed under complex conjugation, so do the high-pass filters. Furthermore, our algorithm gives the upper bounds for the number of high-pass filters in arbitrary dimensions. At the end of the paper, we will give several illustrative examples, from which we can also see that the support sizes of the high-pass filters are comparable with those of the refinement filters.

This work is a companion paper of [F. Gamboa, J. Nagel and A. Rouault, Sum rules via large deviations, J. Funct. Anal.270 (2016) 509–559] and [F. Gamboa, J. Nagel and A. Rouault, Sum rules and large deviations for spectral matrix measures, preprint (2016), arXiv:1601.08135] (see also [J. Breuer, B. Simon and O. Zeitouni, Large deviations and sum rules for spectral theory — A pedagogical approach, to appear in J. Spectr. Theory, preprint (2016), arXiv:1608.01467]). We continue to explore the connections between large deviations for random objects issued from random matrix theory and sum rules. Here, we are concerned essentially with measures on the unit circle whose support is an arc that is possibly proper. We particularly focus on two-matrix models. The first one is the Gross–Witten (GW) ensemble. In the gapped regime, we give a probabilistic interpretation of a Simon sum rule. The second matrix model is the Hua–Pickrell (HP) ensemble. Unlike the GW ensemble the potential is here infinite at one point. Surprisingly, but as in [F. Gamboa, J. Nagel and A. Rouault, Sum rules via large deviations, J. Funct. Anal.270 (2016) 509–559], we obtain a completely new sum rule for the deviation to the equilibrium measure of the HP ensemble. The case of spectral matrix measures is also studied. Indeed, in the case of HP ensemble, we extend our earlier works on large deviation for spectral matrix measure [F. Gamboa, J. Nagel and A. Rouault, Sum rules and large deviations for spectral matrix measures, preprint (2016), arXiv:1601.08135] and get here also a completely new sum rule.

We continue to explore the connections between large deviations for objects coming from random matrix theory and sum rules. This connection was established in [Sum rules via large deviations, J. Funct. Anal. 270(2) (2016) 509–559] for spectral measures of classical ensembles (Gauss–Hermite, Laguerre, Jacobi) and it was extended to spectral matrix measures of the Hermite and Laguerre ensemble in [Sum rules and large deviations for spectral matrix measures, Bernoulli 25(1) (2018) 712–741]. In this paper, we consider the remaining case of spectral matrix measures of the Jacobi ensemble. Our main results are a large deviation principle for such measures and a sum rule for matrix measures with reference measure the Kesten–McKay law. As an important intermediate step, we derive the distribution of matricial canonical moments of the Jacobi ensemble.

We prove large deviations principles for spectral measures of perturbed (or spiked) matrix models in the direction of an eigenvector of the perturbation. In each model under study, we provide two approaches, one of which relying on large deviations principle of unperturbed models derived in the previous work “Sum rules via large deviations” (Gamboa et al. [Sum rules via large deviations, J. Funct. Anal. 270(2) (2016) 509–559]).

The standard physical model of contemporary mesoscopic noise and transport consists in a phenomenologically based approach, proposed originally by Landauer and since continued and amplified by Büttiker, Imry and others. Throughout all the years of its gestation and growth, it is surprising that the Landauer–Büttiker approach to mesoscopics has matured with scant attention to the conserving properties lying at its roots: that is, at the level of actual microscopic principles. We systematically apply the sum rules for the electron gas to clarify the issue of conservation within the standard model of mesoscopic conduction. Noise, as observed in quantum point contacts, provides the vital clue.