Note on Strange Quarks in the Nucleon

Scalar matrix elements involving strange quarks are studied in several models. Apart from a critical reexamination of results obtained in the Nambu and Jona-Lasinio model we study a scenario, motivated by instanton physics, where spontaneous chiral symmetry breaking is induced by the flavor-mixing 't Hooft interaction only. We also investigate possible contributions of virtual kaon loops to the strangeness content of the nucleon.Comment: 12 pages, latex style. One figure, available from the author upon request. University of Regensburg TPR-94-0

K_L \ra \mu^\pm e^\mp \nu \overline{\nu} as background to K_L \ra \mu^\pm e^\mp

We consider the process K_L \ra \mu^\pm e^\mp \nu \overline{\nu} at next to leading order in chiral perturbation theory. This process occurs in the standard model at second order in the weak interaction and constitutes a potential background in searches for new physics through the modes K_L \ra \mu^\pm e^\mp. We find that the same cut, $M_{\mu e}>489$~MeV, used to remove the sequential decays K_{l3}\ra \pi_{l2} pushes the B(K_L \ra \mu^\pm e^\mp \nu \overline{\nu}) to the $10^{-23}$ level, effectively removing it as a background.Comment: 8 pages, LaTeX, 1 figure appended as postscript file after \end{document}. Fermilab-Pub-93/024-

Lattice Calculation of the Strangeness Magnetic Moment of the Nucleon

We report on a lattice QCD calculation of the strangeness magnetic moment of the nucleon. Our result is $G_M^s(0) = - 0.36 \pm 0.20$. The sea contributions from the u and d quarks are about 80% larger. However, they cancel to a large extent due to their electric charges, resulting in a smaller net sea contribution of $- 0.097 \pm 0.037 \mu_N$ to the nucleon magnetic moment. As far as the neutron to proton magnetic moment ratio is concerned, this sea contribution tends to cancel out the cloud-quark effect from the Z-graphs and result in a ratio of $-0.68 \pm 0.04$ which is close to the SU(6) relation and the experiment. The strangeness Sachs electric mean-square radius $_E$ is found to be small and negative and the total sea contributes substantially to the neutron electric form factor.Comment: 10 pages, 5 figures, LaTex, UK/97-23, ADP-97-55/T28

Corrections to Sirlin's Theorem in O(p6)O(p^6) Chiral Perturbation Theory

We present the results of the first two-loop calculation of a form factor in full $SU(3) \times SU(3)$ Chiral Perturbation Theory. We choose a specific linear combination of $\pi^+, K^+, K^0$ and $K\pi$ form factors (the one appearing in Sirlin's theorem) which does not get contributions from order $p^6$ operators with unknown constants. For the charge radii, the correction to the previous one-loop result turns out to be significant, but still there is no agreement with the present data due to large experimental uncertainties in the kaon charge radii.Comment: 6 pages, Latex, 2 LaTeX figure

KLe5K_{L e5} decay as a background in search for KL→π0μ±e∓K_{L} \to \pi^{0} \mu^{\pm} e^{\mp}

We consider a process $K_{L e5} ( K_{L} \rightarrow \pi^{0} \pi^{0} \pi^{\pm} e^{\mp} \nu )$ as a standard model background to the experiment $K_{L} \rightarrow \pi^{0} \mu^{\pm} e^{\mp}$, which seeks for possible violation of lepton family number. Using the lowest order chiral lagrangian, we find that the branching ratio for $K_{L} \rightarrow \pi^{0} \pi^{0} \pi^{\pm} e^{\mp} \nu$ to be $6.2 \times 10^{-12}$. A similar decay $K_{L} \rightarrow \pi^{\mp} \pi^{\mp} \pi^{\pm} e^{\pm} \nu$ has a branching ratio, $1.7 \times 10^{-11}$.Comment: RevTeX, 10 pages, 1 figure available upon request, to appear in Phys. Rev.

Meson-Baryon-Baryon Vertex Function and the Ward-Takahashi Identity

Ohta proposed a solution for the well-known difficulty of satisfying the Ward-Takahashi identity for a photo-meson-baryon-baryon amplitude ($\gamma$MBB) when a dressed meson-baryon-baryon (MBB) vertex function is present. He obtained a form for the $\gamma$MBB amplitude which contained, in addition to the usual pole terms, longitudinal seagull terms which were determined entirely by the MBB vertex function. He arrived at his result by using a Lagrangian which yields the MBB vertex function at tree level. We show that such a Lagrangian can be neither hermitian nor charge conjugation invariant. We have been able to reproduce Ohta's result for the $\gamma$MBB amplitude using the Ward-Takahashi identity and no other assumption, dynamical or otherwise, and the most general form for the MBB and $\gamma$MBB vertices. However, contrary to Ohta's finding, we find that the seagull terms are not robust. The seagull terms extracted from the $\gamma$MBB vertex occur unchanged in tree graphs, such as in an exchange current amplitude. But the seagull terms which appear in a loop graph, as in the calculation of an electromagnetic form factor, are, in general, different. The whole procedure says nothing about the transverse part of the ($\gamma$MBB) vertex and its contributions to the amplitudes in question.Comment: A 20 pages Latex file and 16 Postscript figures in an uuencoded format. Use epsf.sty to include the figures into the Latex fil

Contributions of order O(mquark2){\cal O}(m_{\rm quark}^2) to Kℓ3K_{\ell 3} form factors and unitarity of the CKM matrix

The form factors for the $K_{\ell 3}$ semileptonic decay are computed to order $O(p^4)$ in generalized chiral perturbation theory. The main difference with the standard $O(p^4)$ expressions consists in contributions quadratic in quark masses, which are described by a single divergence-free low-energy constant, $A_3$. A new simultaneous analysis is presented for the CKM matrix element $V_{us}$, the ratio $F_K/F_{\pi}$, $K_{\ell 3}$ decay rates and the scalar form factor slope $\lambda_0$. This framework easily accommodates the precise value for $V_{ud}$ deduced from superallowed nuclear $\beta$-decays

The treatment of zero eigenvalues of the matrix governing the equations of motion in many-body Green's function theory

The spectral theorem of many-body Green's function theory relates thermodynamic correlations to Green's functions. More often than not, the matrix governing the equations of motion has zero eigenvalues. In this case, the standard text-book approach requires both commutator and anti-commutator Green's functions to obtain equations for that part of the correlation which does not lie in the null space of the matrix. In this paper, we show that this procedure fails if the projector onto the null space is dependent on the momentum vector. We propose an alternative formulation of the theory in terms of the non-null space alone and we show that a solution is possible if one can find a momentum-independent projector onto some subspace of the non-null space. To do this, we enlist the aid of the singular value decomposition (SVD) of the equation of motion matrix in order to project out the null space, thus reducing the size of the matrix and eliminating the need for the anti-commutator Green's function. We extend our previous work, dealing with a ferromagnetic Heisenberg monolayer and a momentum-independent projector onto the null space, where both multilayer films and a momentum-dependent projector are considered. We develop the numerical methods capable of handling these cases and offer a computational algorithmus that should be applicable to any similar problem arising in Green's function theory.Comment: 16 pages, 7 figure

Sigma-term physics in the perturbative chiral quark model

We apply the perturbative chiral quark model (PCQM) at one loop to analyse meson-baryon sigma-terms. Analytic expressions for these quantities are obtained in terms of fundamental parameters of low-energy pion-nucleon physics (weak pion decay constant, axial nucleon coupling, strong pion-nucleon form factor) and of only one model parameter (radius of the nucleonic three-quark core). Our result for the piN sigma term of about 45 MeV is in good agreement with the value deduced by Gasser, Leutwyler and Sainio using dispersion-relation techniques and exploiting the chiral symmetry constraints.Comment: 19 pages, LaTeX-file, 2 Figure