arXiv subjects
Publications and source records attributed to W. A. Bardeen.
The indication from deep inelastic electron scattering experiments at SLAC that Bjorken scaling may really hold has motivated an extension of the hypotheses of current algebra to what may be called light-cone current algebra.
In the virtual presence of a heavy quark t, the interactions of a CP-odd scalar boson A, with mass M_A << 2M_t, with gluons and light quarks can be described by an effective Lagrangian. We analytically derive the coefficient functions of the respective physical operators to three loops in quantum chromodynamics (QCD), adopting the modified minimal-subtraction (MS-bar) scheme of dimensional regularization. Special attention is paid to the proper treatment of the gamma_5 matrix and the Levi-Civita epsilon tensor in D dimensions. In the case of the effective ggA coupling, we find agreement with an all-order prediction based on a low-energy theorem in connection with the Adler-Bardeen non-renormalization theorem. This effective Lagrangian allows us to analytically evaluate the next-to-leading QCD correction to the A -> gg partial decay width by considering massless diagrams. For M_A = 100GeV, the resulting correction factor reads 1+(221/12)alpha_s^(5)(M_A)/pi +165.9(alpha_s^(5)(M_A)/pi)^2 approx 1+0.68+0.23. We compare this result with predictions based on various scale-optimization methods.
We calculate long-distance contributions to the amplitudes A(K^0 --> pi pi, I) induced by the gluon and the electroweak penguin operators Q_6 and Q_8, respectively. We use the 1/N_c expansion within the effective chiral lagrangian for pseudoscalar mesons. In addition, we adopt a modified prescription for the identification of meson momenta in the chiral loop corrections in order to achieve a consistent matching to the short-distance part. Our approach leads to an explicit classification of the loop diagrams into non-factorizable and factorizable, the scale dependence of the latter being absorbed in the low-energy coefficients of the effective theory. Along these lines we calculate the one-loop corrections to the O(p^0) term in the chiral expansion of both operators. In the numerical results, we obtain moderate corrections to B_6^(1/2) and a substantial reduction of B_8^(3/2).
We analyze the implications of the infrared quasi fixed point solution for the top quark mass in the Minimal Supersymmetric Standard Model. This solution could explain in a natural way the relatively large value of the top quark mass and, if confirmed experimentally, may be suggestive of the onset of nonperturbative physics at very high energy scales. In the framework of grand unification, the expected bottom quark - tau lepton Yukawa coupling unification is very sensitive to the fixed point structure of the top quark mass. For the presently allowed values of the electroweak parameters and the bottom quark mass, the Yukawa coupling unification implies that the top quark mass must be within ten percent of its fixed point values.
A wide class of models involve the fine--tuning of significant hierarchies between a strong--coupling ``compositeness'' scale, and a low energy dynamical symmetry breaking scale. We examine the issue of whether such hierarchies are generally endangered by Coleman--Weinberg instabilities. A careful study using perturbative two--loop renormalization group methods finds that consistent large hierarchies are not generally disallowed.