0000000000631530
AUTHOR
J. Bordes
Bottom-quark mass from finite energy QCD sum rules
Finite energy QCD sum rules involving both inverse and positive moment integration kernels are employed to determine the bottom quark mass. The result obtained in the $\bar{\text {MS}}$ scheme at a reference scale of $10\, {GeV}$ is $\bar{m}_b(10\,\text{GeV})= 3623(9)\,\text{MeV}$. This value translates into a scale invariant mass $\bar{m}_b(\bar{m}_b) = 4171 (9)\, {MeV}$. This result has the lowest total uncertainty of any method, and is less sensitive to a number of systematic uncertainties that affect other QCD sum rule determinations.
Corrections to the ${\bf SU(3)\times SU(3)}$ Gell-Mann-Oakes-Renner relation and chiral couplings $L^r_8$ and $H^r_2$
Next to leading order corrections to the $SU(3) \times SU(3)$ Gell-Mann-Oakes-Renner relation (GMOR) are obtained using weighted QCD Finite Energy Sum Rules (FESR) involving the pseudoscalar current correlator. Two types of integration kernels in the FESR are used to suppress the contribution of the kaon radial excitations to the hadronic spectral function, one with local and the other with global constraints. The result for the pseudoscalar current correlator at zero momentum is $\psi_5(0) = (2.8 \pm 0.3) \times 10^{-3} GeV^{4}$, leading to the chiral corrections to GMOR: $\delta_K = (55 \pm 5)%$. The resulting uncertainties are mostly due to variations in the upper limit of integration in…
Corrections to the SU(3) × SU(3) Gell-Mann-Oakes-Renner relation and chiral couplings $ L_8^r $ and $ H_2^r $
Next to leading order corrections to the SU(3) × SU(3) Gell-Mann-Oakes-Renner relation (GMOR) are obtained using weighted QCD Finite Energy Sum Rules (FESR) involving the pseudoscalar current correlator. Two types of integration kernels in the FESR are used to suppress the contribution of the kaon radial excitations to the hadronic spectral function, one with local and the other with global constraints. The result for the pseudoscalar current correlator at zero momentum is ψ 5(0) = (2.8 ± 0.3) ×10-3 GeV4, leading to the chiral corrections to GMOR: δ K = (55 ± 5)%. The resulting uncertainties are mostly due to variations in the upper limit of integration in the FESR, within the stability reg…
Finite Energy Sum Rules with Legendre Polynomial Kernels
Abstract In this note we report about a method to deal with finite energy sum rules. With a reasonable knowledge of the main resonances of the spectrum, the method guarantees that we can find a nice duality matching between the low energy hadronic data and asymptotic QCD at high energies.
Bottom quark mass and QCD duality
The mass of the bottom quark is analyzed in the context of QCD finite energy sum rules. In contrast to the conventional approach, we use a large momentum expansion of the QCD correlator including terms to order \alpha _{s}^{2}(m_{b}^{2}/q^{2})^{6} with the upsilon resonances from e^{+}e^{-} annihilation data as main input. A stable result m_{b}(m_{b})=4.19\pm 0.05 GeV} for the bottom quark mass is obtained. This result agrees with the independent calculations based on the inverse moment analysis.
On the Corner Elements of the CKM and PMNS Matrices
Recent experiments show that the top-right corner element ($U_{e3}$) of the PMNS, like that ($V_{ub}$) of the CKM, matrix is small but nonzero, and suggest further via unitarity that it is smaller than the bottom-left corner element ($U_{\tau 1}$), again as in the CKM case ($V_{ub} < V_{td}$). An attempt in explaining these facts would seem an excellent test for any model of the mixing phenomenon. Here, it is shown that if to the assumption of a universal rank-one mass matrix, long favoured by phenomenologists, one adds that this matrix rotates with scale, then it follows that (A) by inputting the mass ratios $m_c/m_t, m_s/m_b, m_\mu/m_\tau$, and $m_2/m_3$, (i) the corner elements are small…
Parity violation correlations in light muonic atoms
The 2 S -1 S transition in light muonic atoms is very sensitive to parity violation correlations induced via neutral currents. Observables depending on these transitions such as the photon polarization and the angular correlation between the emitted radiation and the atom polarization are a clear signal of weak neutral currents in atoms. We find the relation between the lepton and quark couplings and these observables emphasizing the effect of the nuclear spin. The results expected in muonic, atoms μ- 4 He and μ- 3 He are given.