667 research outputs found

    Less Singular Terms and Small x Evolution in a Soluble Model

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    We calculate the effect of the less singular terms at small x on the evolution of the coefficient function in \phi^3 theory in six dimensions, which result from a complete solution of the ladder equation. Scale-invariant next-to-leading order contributions are also studied. We show that the small x approximation does not deliver the dominant contributions.Comment: 7 pages LATEX including 2 eps-file

    Two-loop corrections to Higgs boson production

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    In this paper we present the complete two-loop vertex corrections to scalar and pseudo-scalar Higgs boson production for general colour factors for the gauge group SU(N){\rm SU(N)} in the limit where the top quark mass gets infinite. We derive a general formula for the vertex correction which holds for conserved and non conserved operators. For the conserved operator we take the electromagnetic vertex correction as an example whereas for the non conserved operators we take the two vertex corrections above. Our observations for the structure of the pole terms 1/ϵ41/\epsilon^4, 1/ϵ31/\epsilon^3 and 1/ϵ21/\epsilon^2 in two loop order are the same as made earlier in the literature for electromagnetism. However we also elucidate the origin of the second order single pole term which is equal to the second order singular part of the anomalous dimension plus a universal function which is the same for the quark and the gluon. [3mm]Comment: 27 pages LaTeX.We correct some misprints. Moreover we have discovered that the second order single pole term is equal to the singular part of the second order anomalous dimension plus a universal function which is the same for the quark and the gluon. This holds for vertex corrections as well as for scattering amplitude

    Norm discontinuity and spectral properties of Ornstein-Uhlenbeck semigroups

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    Let EE be a real Banach space. We study the Ornstein-Uhlenbeck semigroup P(t)P(t) associated with the Ornstein-Uhlenbeck operator Lf(x)=12TrQD2f(x)+. Lf(x) = \frac12 {\rm Tr} Q D^2 f(x) + . Here QQ is a positive symmetric operator from EE^* to EE and AA is the generator of a C0C_0-semigroup S(t)S(t) on EE. Under the assumption that PP admits an invariant measure μ\mu we prove that if SS is eventually compact and the spectrum of its generator is nonempty, then \n P(t)-P(s)\n_{L^1(E,\mu)} = 2 for all t,s0t,s\ge 0 with tst\not=s. This result is new even when E=RnE = \R^n. We also study the behaviour of PP in the space BUC(E)BUC(E). We show that if A0A\not=0 there exists t0>0t_0>0 such that \n P(t)-P(s)\n_{BUC(E)} = 2 for all 0t,st00\le t,s\le t_0 with tst\not=s. Moreover, under a nondegeneracy assumption or a strong Feller assumption, the following dichotomy holds: either \n P(t)- P(s)\n_{BUC(E)} = 2 for all t,s0t,s\ge 0, \ tst\not=s, or SS is the direct sum of a nilpotent semigroup and a finite-dimensional periodic semigroup. Finally we investigate the spectrum of LL in the spaces L1(E,μ)L^1(E,\mu) and BUC(E)BUC(E).Comment: 14 pages; to appear in J. Evolution Equation

    Higgs Production at NNLO

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    We describe the calculation of inclusive Higgs boson production at hadronic colliders at next-to-next-to-leading order (NNLO) in perturbative quantum chromodynamics. We have used the technique developed in reference [4]. Our results agree with those published earlier in the literature.Comment: Talk given at PASCOS'03, TIFR, Mumbai, LaTeX, 5 page

    Approximating the coefficients in semilinear stochastic partial differential equations

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    We investigate, in the setting of UMD Banach spaces E, the continuous dependence on the data A, F, G and X_0 of mild solutions of semilinear stochastic evolution equations with multiplicative noise of the form dX(t) = [AX(t) + F(t,X(t))]dt + G(t,X(t))dW_H(t), X(0)=X_0, where W_H is a cylindrical Brownian motion on a Hilbert space H. We prove continuous dependence of the compensated solutions X(t)-e^{tA}X_0 in the norms L^p(\Omega;C^\lambda([0,T];E)) assuming that the approximating operators A_n are uniformly sectorial and converge to A in the strong resolvent sense, and that the approximating nonlinearities F_n and G_n are uniformly Lipschitz continuous in suitable norms and converge to F and G pointwise. Our results are applied to a class of semilinear parabolic SPDEs with finite-dimensional multiplicative noise.Comment: Referee's comments have been incorporate

    Second quantisation for skew convolution products of infinitely divisible measures

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    Suppose λ1\lambda_1 and λ2\lambda_2 are infinitely divisible Radon measures on real Banach spaces E1E_1 and E2E_2, respectively and let T:E1E2T:E_{1} \rightarrow E_{2} be a Borel measurable mapping so that T(λ1)ρ=λ2T(\lambda_1) * \rho = \lambda_2 for some Radon probability measure ρ\rho on E2E_{2}. Extending previous results for the Gaussian and the Poissonian case, we study the problem of representing the `transition operator' PT:Lp(E2,λ2)Lp(E1,λ1)P_{T}:L^{p}(E_{2}, \lambda_{2}) \rightarrow L^{p}(E_{1}, \lambda_{1}) given by PTf(x)=E2f(T(x)+y)dρ(y)unifynotations P_{T}f(x) = \int_{E_{2}}f(T(x) + y)d\rho(y) %% d\rho(y) instead of \rho(dy) in order to unify notations as the second quantisation of a contraction operator acting between suitably chosen `reproducing kernel Hilbert spaces' associated with λ1\lambda_1 and λ2\lambda_2.Comment: Some typos have been corrected. To appear in IDAQ
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