Narrow Results

We carry out an analysis of the non-universal supersymmetry breaking scalar masses arising in SO(10) supersymmetric unification. By considering patterns of squark and slepton masses, we derive a set of sum rules for the sfermion masses which are independent of the manner in which SO(10) breaks to the Standard Model gauge group via its SU(5) subgroups. The phenomenology arising from such non-universality is unaffected by the symmetry breaking pattern, so long as the breaking occurs via any of the SU(5) subgroups of the SO(10) group.

New relations between QCD Borel sum rules for masses of Σ⁰ and Λ hyperons are constructed. It is shown that starting from the sum rule for the Σ⁰ hyperon mass it is straightforward to obtain the corresponding sum rule for the Λ hyperon mass and vice versa.

Assuming the existence of one light sterile neutrino, we investigate the neutrino flavor mixing matrix in matter. Sum rules between the mixing parameters in vacuum and their counterparts in matter are derived. By using these new sum rules, we obtain the simple but exact expressions of the effective flavor mixing matrix in matter in terms of neutrino masses and the mixing parameters in vacuum. The rephasing invariants, sides of unitarity quadrangles and oscillation probabilities in matter are also achieved. Our model-independent results will be very helpful for analyzing flavor mixing and CP violation in the future long-baseline neutrino oscillation experiments.

In this paper we calculate the difference between vector and axial-vector correlators with two different vertices: the bare vertex and the Ball–Chiu vertex (BC vertex) ansatz. Through the difference we compare the results drawn from the chiral sum rules. The leading nonzero contribution of the difference of the correlators in the ultraviolet identifies the four-quark condensate, which is the leading nonperturbative phenomenon in QCD. Also the pion decay constant can be drawn. For the quark propagator, we employ two different models. One is calculated in the framework of the rainbow-ladder approximation scheme in the Dyson–Schwinger approach. The other is the analytic fit employed in Ref. 1. Results show that the dressing effects of the vector and axial-vector vertices are very important.

A determination of the strong coupling α_s at rather low energies is possible through the analysis of hadronic decays of the τ lepton. In turn, the low energy necessitates sufficient control over perturbative QCD corrections, the nonperturbative condensate contributions in the framework of the operator product expansion (OPE), as well as corrections going beyond the OPE, the duality violations (DVs). Perturbative QCD uncertainties arise from open questions regarding the renormalization group resummation of the series. The fit quantities are moment integrals of the τ spectral function data in a certain energy window and care should be taken to have good perturbative behavior of those moments as well as control over higher-dimensional operator corrections. Furthermore, all parameters occurring in the theoretical description should be extracted from fits to the data in a self-consistent manner.

Perturbative Quantum Chromodynamics combined with the operator product expansion is expected to provide a framework for the description of phenomena in hadron interactions including contributions of nonperturbative origin. Applied to the correlator of two electromagnetic currents, this framework can be confronted with e⁺ e^- annihilation into hadrons. Data from the total hadronic e⁺e^- cross-section have become much more precise in recent years and the power corrections in the operator product expansion, i.e. the vacuum condensates are expected to be determined with higher precision than previously. We present an analysis of the condensates of dimensions d = 2, 4 and 6 and find reasonably stable results, though still within rather large errors. Our results are in agreement with values obtained from τ-decay. It also appears that the separation into isovector and isoscalar pieces introduces additional uncertainties and errors.

Two methods for determining $\left|V_{us}\right|$ employing inclusive hadronic $\tau$ decay data are discussed. The first is the conventional flavor-breaking sum rule determination whose usual implementation produces results $\sim 3\sigma$ low compared to three-family unitary expectations. The second is a novel approach combining experimental strange hadronic $\tau$ distributions with lattice light-strange current–current two-point function data. Preliminary explorations of the latter show the method promises $\left|V_{us}\right|$ determinations competitive with those from $K_{\ell 3}$ and $\mathrm{\Gamma }[K_{\mu 2}]/\mathrm{\Gamma }[{\pi }_{\mu 2}]$. For the former, systematic issues in the conventional implementation are investigated. Unphysical dependences of $\left|V_{us}\right|$ on the choice of sum rule weight, $w$, and upper limit, $s_0$, of the weighted experimental spectral integrals are observed, the source of these problems identified and a new implementation which overcomes these problems developed. Lattice results are shown to provide a tool for quantitatively assessing truncation uncertainties for the slowly converging $D=2$ OPE series. The results for $\left|V_{us}\right|$ from this new implementation are shown to be free of unphysical $w$- and $s_0$-dependences, and $\sim 0.0020$ higher than those produced by the conventional implementation. With preliminary new $K\pi$ branching fraction results as input, we find $\left|V_{us}\right|$ in excellent agreement with that obtained from $K_{\ell 3}$, and compatible within errors with expectations from three-family unitarity.

An exhaustive number of QCD finite energy sum rules for $\tau$-decay together with the latest updated ALEPH data is used to test the assumption of global duality. Typical checks are the absence of the dimension d = 2 condensate, the equality of the gluon condensate extracted from vector or axial vector spectral functions, the Weinberg sum rules, the chiral condensates of dimensions d = 6 and d = 8, as well as the extraction of some low-energy parameters of chiral perturbation theory. Suitable pinched linear integration kernels are introduced in the sum rules in order to suppress potential quark–hadron duality violations and experimental errors. We find no compelling indications of duality violations in hadronic $\tau$-decay in the kinematic region above s$\simeq$ 2.2 GeV² for these kernels.

Within the framework of the mechanism proposed in our previous works [Duc and Giao, J. Mod. Phys. 5, 477 (2014); Duc et al., Int. J. Theor. Phys. 54, 1071 (2015); Duc and Giao, Int. J. Theor. Phys. 55, 959 (2016)] for mass and charge creation, we consider the charge and mass spectrum of spinor fields in extradimensions. It is shown that a single spinor field in spacetime with extradimensions corresponds to a set of effective spinor fields in ordinary four-dimensional spacetime with charges and masses obeying the sum rules dictated from some specific assumptions related to the compactification of extradimensions. The obtained results allow us to present an example for unifying six existing flavor quarks, as well as for unifying three existing lepton generators. On the base of the derived charge–mass sum rules, we would predict the existence of some hidden tachyon quarks with fractional charges, as well as some hidden tachyon leptons, neutral or negative charged.

In this paper magnetic dipole moment form factor, $G_M^{(2)}(Q^2)$, describing the radial excitation of decuplet baryons to octet baryons electromagnetic transitions as well as the ratios, $R_{SM}=-\frac{1}{4m_2^2}\sqrt{4m_2^2{Q}^2+{(m_2^2-Q^2-m_1^2)}^2}\frac{G_C^{(2)}(Q^2)}{G_M^{(2)}(Q^2)}$ and $R_{EM}=-\frac{G_E^{(2)}(Q^2)}{G_M^{(2)}(Q^2)}$ are calculated in the framework of light-cone sum rules. We also estimate the degree of the violation of U-spin symmetry.

We present a calculation of the masses of the isovector mesons (vector, scalar and pseudoscalar including the established recurrences) using a new method of finite energy QCD sum rules. The method is based on the idea of choosing a suitable integration kernel which minimizes the occurring integral over the cut in the complex energy (squared) plane. We obtain remarkably stable results in a wide range $R$, where $R$ is the radius of the integration contour. The sum rule predictions agree with the experimental values within the expected accuracy showing that QCD describes single resonances.

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 $g_{{\mathrm{\Sigma }}_b^{\ast }NB}=10.54_{-5.23}^{+15.59}\pm 1.82$.