The Physics of K0−Kˉ0K^0 -\bar K^0 Mixing: B^K\widehat{B}_K and ΔMLS\Delta M_{LS} in the Chiral Quark Model

We compute the $\widehat B_K$ parameter and the mass difference $\Delta M_{LS}$ of the $K^0-\bar K^0$ system by means of the chiral quark model. The chiral coefficients of the relevant $\Delta S=2$ and $\Delta S=1$ chiral lagrangians are computed via quark-loop integration. We include the relevant effects of one-loop corrections in chiral perturbation theory. The final result is very sensitive to non-factorizable corrections of $O(\alpha_S N)$ coming from gluon condensation. The size of the gluon condensate is determined by fitting the experimental value of the amplitude $K^+ \to \pi^+\pi^0$. By varying all the relevant parameters we obtain $\widehat{B}_K= 0.87 \pm 0.33\ .$ We evaluate within the model the long-distance contributions to $\Delta M_{LS}$ induced by the double insertion of the $\Delta S = 1$ chiral lagrangian and study the interplay between short- and long-distance amplitudes. By varying all parameters we obtain $\Delta M_{LS}^{th}/\Delta M_{LS}^{exp} = 0.76 ^{+0.64}_{-0.34} .$ Finally, we investigate the phenomenological constraints on the Kobayashi-Maskawa parameter Im $\lambda _t$ entering the determination of $\epsilon'/\epsilon$.Comment: 31 pages, Latex file including 7 eps figures. Revised version to appear in Nucl. Phys.

Crystallization and Preliminary Analysis of Crystals of the 24-Meric Hemocyanin of the Emperor Scorpion (Pandinus imperator)

Hemocyanins are giant oxygen transport proteins found in the hemolymph of several invertebrate phyla. They constitute giant multimeric molecules whose size range up to that of cell organelles such as ribosomes or even small viruses. Oxygen is reversibly bound by hemocyanins at binuclear copper centers. Subunit interactions within the multisubunit hemocyanin complex lead to diverse allosteric effects such as the highest cooperativity for oxygen binding found in nature. Crystal structures of a native hemocyanin oligomer larger than a hexameric substructure have not been published until now. We report for the first time growth and preliminary analysis of crystals of the 24-meric hemocyanin (MW = 1.8 MDa) of emperor scorpion (Pandinus imperator), which diffract to a resolution of 6.5 Å. The crystals are monoclinc with space group C 1 2 1 and cell dimensions a = 311.61 Å, b = 246.58 Å and c = 251.10 Å (α = 90.00°, β = 90.02°, γ = 90.00°). The asymmetric unit contains one molecule of the 24-meric hemocyanin and the solvent content of the crystals is 56%. A preliminary analysis of the hemocyanin structure reveals that emperor scorpion hemocyanin crystallizes in the same oxygenated conformation, which is also present in solution as previously shown by cryo-EM reconstruction and small angle x-ray scattering experiments

BKB_K and Explicit Chiral Symmetry Breaking

The $B_K$ parameter is discussed in the general context of calculating beyond the factorization approximation for hadronic matrix elements. A variant of the $1/N_c$ method of Bardeen et al. is used. We present calculations within a low energy approach and a calculation within the Nambu--Jona-Lasinio model. Matching with the QCD behaviour and dependence on non-zero current quark masses is studied.Comment: 15 pages, 4 postscript figures included, NORDITA-94/44 N,P. Mistake in the numerics discovered which changed some of the conclusions. One figure also change

Updating the Unitarity Triangle: Top Quark Mass Versus Nonperturbative Uncertainties

We summarize the present knowledge on the non-perturbative hadronic inputs needed in the analysis of $B^0$-$\bar B^0$ mixing and the CP-violating parameter $\varepsilon$ of the $K^0$-$\bar K^0$ system. Using this information, together with the recently determined value of the top-quark mass, we update the phenomenological constraints on the unitarity triangle.Comment: 21 pages, Plain LateX, 7 figures included, preprint FTUV/94-37, IFIC/94-32, NBI-94-3

The BKB_K Parameter in the 1/Nc1/N_c Expansion

We calculate the $B_K$ parameter within the framework of the $1/N_c$ expansion. We essentially use the technique presented by Bardeen, Buras and G\'erard but calculate an off-shell Green function in order to disentangle different contributions. We study this Green function in pure Chiral Perturbation Theory (CHPT) first and afterwards in the $1/N_c$ expansion in the presence of an explicit cut-off to determine $B_K$ and the counterterms appearing in CHPT. The high energy part is done using the renormalization group. For the low-energy contributions we use both CHPT and an Extended Nambu--Jona-Lasinio model. This model has the right properties to match with the high energy QCD behaviour. We then study explicit chiral symmetry breaking effects by calculating with both massless and degenerate quarks together with the real case. A detailed analysis and comparison with the results found within other approaches is done. Consequences for present lattice calculations of this parameter are then obtained. As final result we get $0.60 < \hat B_K < 0.80$. If $m_s=m_d=0$ we get $0.25 < \hat B^\chi_K < 0.55$.Comment: 44 pages, uses epsf.sty, 9 figures included (8 postscript, 1 LaTeX

Standard Model Confronting New Results for epsilon'/epsilon

We analyze the CP violating ratio \epe=epsilon'/epsilon in the Standard Model in view of the new KTeV results. We review the present status of the most important non-perturbative parameters B_6, B_8, B_K and of the strange quark mass m_s. We also briefly discuss the issues of final state interactions and renormalization scheme dependence. Updating the values of the CKM parameters, of m_t and Lambda (MSbar) and using Gaussian errors for the experimental input and flat distributions for the theoretical parameters we find \epe substantially below the NA31 and KTeV data: \epe= (7.7^{+6.0}_{-3.5}) 10^{-4} and \epe= (5.2^{+4.6}_{-2.7}) 10^{-4} in the NDR and HV renormalization schemes respectively. A simple scanning of all input parameters gives on the other hand 1.05 10^{-4} < \epe < 28.8 10^{-4} and 0.26 10^{-4} < \epe < 22.0 10^{-4} respectively. Analyzing the dependence on various parameters we find that only for extreme values of B_6, B_8 and m_s and suitable values of CKM parameters and Lambda(MSbar), the ratio \epe can be made consistent with data. We analyze the impact of these data on the lower bounds for Im(V_{td}V_{ts}^*), Br(K_L to pi^0 nu barnu), Br(K_L to pi^0e^+e^-)_{dir} and on tan(beta) in the Two Higgs Doublet Model II.Comment: main latex-file, 4 figures and related latex files, 47 page