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.