arXiv subjects
Publications and source records attributed to R. R. Mendel.
We study the coupling arising via perturbative QCD of zero 4-momentum Higgs bosons to light quarks inside the nucleon. Qualitative comparison with the results obtained from one-loop-order low energy theorems for the Higgs-nucleon interaction suggests the existence of a dynamical light-quark mass which falls off with momentum. Quantitative comparison leads to an estimate of $α_s$ at very low $q^2$ quite near unity.
We examine the heavy-quark-induced Yukawa interaction between light quarks and a light Higgs field, which is facilitated in the chiral limit by the dynamical mass of light quarks anticipated from the chiral-noninvariance of the QCD vacuum. A low-energy estimate of the strong coupling near unity can be obtained from a comparison of the explicit perturbative calculation of the induced Yukawa interaction at zero momentum to a Higgs-low-energy theorem prediction for the same interaction.
We extend our recent work, in which the Dirac equation with a ``(asymptotically free) Coulomb + (Lorentz scalar $γ_0σr$) linear '' potential is used to obtain the light quark wavefunction for $q\bar Q$ mesons in the limit $m_Q\to \infty$, to estimate the decay constant $f_P$ and the mixing parameter $B$ of the pseudoscalar mesons. We compare our results for the evolution of $f_P$ and $B$ with the meson mass $M_P$ to the non-relativistic formulas for these quantities and show that there is a significant correction in the subasymptotic region. For $σ=0.14{\rm ~GeV}^{-2}$ and $\lms =0.240{\rm ~GeV}$ we obtain: $f_D =0.371\; ,\; f_{D_s}=0.442\; ,\; f_B=0.301\; ,\; f_{B_s}=0.368 {\rm ~GeV}$ and $B_D=0.88\; ,\; B_{D_s}=0.89\; ,\; B_B=0.95\; ,\; B_{B_s}=0.96\; ,\;$ and $B_K=0.60$.
We find a large CP violation effect within the Two-Higgs-Doublet-Model for the reaction $e^+e^-\to t\bar{t}H^0$ at future linear colliders. The CP-asymmetry arises already at the tree level as a result of interference between diagrams with $H^0$ emission from $t$ (and $\bar{t}$) and its emission from a $Z^0$ and can be about 10--20\%. In the best case one needs a few hundred $t\bar{t}H^0$ events to observe CP violation at the 3$σ$ level.
We calculate to the leading twist 2 accuracy the rate for the decay $ B_{u} \rightarrow l νγ$ using the light cone QCD sume rules. We find $ Br( B_{u} \rightarrow l νγ) \simeq 2 \cdot 10^{-6} $. The results are used to test the applicability of the constituent quark model approximation to the same process.The latter estimate is proportional to $ 1/m_{u}^{2} $, where $ m_{u} \simeq \barΛ_{u} $ is the "constituent quark mass", indicating that the process is of long distance type. We find that the two approaches yield similar results for the rate with the choice $ m_{u} \simeq 430-480 \;MeV $. This indicates that the constituent quark model may be used for estimates of the radiative "annihilation" contribution to this and other radiative decays. We point out that this decay may be useful for the measurement of $ |V_{ub}|$.
We estimate the long distance (LD) contribution to the magnetic part of the $s \to dγ$ transition using the Vector Meson Dominance approximation $(V=ρ,ω,ψ_i)$. We find that this contribution may be significantly larger than the short distance (SD) contribution to $s \to dγ$ and could possibly saturate the present experimental upper bound on the $Ω^-\to Ξ^-γ$ decay rate, $Γ^{\rm MAX}_{Ω^-\to Ξ^-γ} \simeq 3.7\times10^{-9}$eV. For the decay $B_s \to B^*_dγ$, which is driven by $s \to dγ$ as well, we obtain an upper bound on the branching ratio $BR(B_s \to B_d^*γ)<3\times10^{-8}$ from $Γ^{\rm MAX}_{Ω^-\to Ξ^-γ}$. Barring the possibility that the Quantum Chromodynamics coefficient $a_2(m_s)$ be much smaller than 1, $Γ^{\rm MAX}_{Ω^-\to Ξ^-γ}$ also implies the approximate relation $\frac{2}{3} \sum_i \frac{g^2_{ψ_i}(0)}{m^2_{ψ_i}} \simeq \frac{1}{2} \frac{g^2_ρ(0)}{m^2_ρ} + \frac{1}{6}\frac{g^2_ω(0)}{m^2_ω}$. This relation agrees quantitatively with a recent independent estimate of the l.h.s. by Deshpande et al., confirming that the LD contributions to $b \to sγ$ are small. We find that these amount to an increase of $(4\pm2)\%$ in the magnitude of the $b \to s γ$ transition amplitude, relative to the SD contribution alone.
We demonstrate that the long distance contribution to $B^{\pm} \to ρ^{\pm} γ$ may have a large effect on the decay rate and through it on the CP violating partial rate asymmetry. The change in the asymmetry can be between a factor of 0.4 and 1.4 with respect to the effect of the short distance contribution alone, depending on the values of the CKM parameters $ρ$ and $η$ .
We use a simple perturbation theory argument and measurements of charmonium leptonic widths $Γ(ψ_{NS} \rightarrow e^+e^-)$ to estimate the ratio \mbox{$R_\circ \equiv {\vert Ψ_{η_{c1S}}(0) \vert}^2 /{\vertΨ_{ψ_{1 S}}(0)\vert}^2$} in the general context of non- relativistic potential models. We obtain $R_\circ = 1.4 \pm 0.1$. We then apply well known potential model formulas, which include lowest order QCD corrections, to find $Γ(η_c \rightarrow γγ)/Γ(ψ_{1S} \rightarrow e^+e^-) \approx 2.2\pm 0.2$. The central value for $Γ(ψ_{1S} \rightarrow e^+ e^-)$in the 1992 Particle Data Tables then leads to a (non relativistic) prediction $Γ(η_c \rightarrow γγ)\approx 11.8\pm 0.8 $ keV. This prediction is in good agreement with a recent measurement by the ARGUS collaboration, is consistent with a recent measurement by the L3 collaboration but is significantly higher than several earlier measurements and than previous theoretical estimates, which usually assume $R_\circ =1$. The correction to $R_\circ =1$ is estimated to be smaller but nonnegligible for the $b\bar b$ system. Using the current central measurement for $Γ(Υ_{1S}\rightarrow e^+e^-)$ we find $Γ(η_b\rightarrow γγ)\approx 0.58\pm 0.03$ keV. A rough estimate of relativistic corrections reduces the expected two photon rates to about 8.8 keV and 0.52 keV for the $η_c$ and $η_b$ mesons respectively. Such corrections