Search Results (17 total)

We investigate decoupling of heavy Kaluza-Klein (KK) modes in an Abelian Higgs model with space-time topologies R^3,1×S¹ and R^3,1×S¹/Z₂. After integrating out only the heavy KK modes we find the one-loop, light-particle (irreducible) effective action (LPEA) for the zero-mode fields. We find that in the R^3,1×S¹ topology the heavy modes do not decouple in this low-energy effective action, due to the zero mode of the 5th component of the 5D gauge field A₅. Because A₅ is a scalar under 4D Lorentz transformations, there is no gauge symmetry protecting it from getting mass and A₅⁴ interaction terms after loop corrections. In addition, after symmetry breaking, we find that the effective action has new divergences in the A₅ mass that did not appear in the symmetric phase. The new divergences are traced back to the gauge-goldstone mixing that occurs after symmetry breaking. We find that when considering low-energy physical processes, however, the divergences of the zero-mode loop diagrams will cancel the divergences in the effective action, rendering the radiatively corrected couplings finite. Although, this clears up the extra divergences in the A₅ sector, the gauge coupling still has a different compactification scale dependence in the A₅ then it does in the A_μ sector, leading to an explicit violation of decoupling. If instead of the LPEA one considers the Wilsonian effective action by integrating out zero modes of momenta |p|>M (M is the mass of the lowest KK excitation) in addition to the heavy modes, then decoupling is manifest. However, as is well known the price is the difficulty in maintaining 4D Lorentz and gauge invariance. In order to get a more sensible effective theory in the LPEA formalism, we investigate the S¹/Z₂ compactification. With this kind of compact topology, the A₅ zero mode disappears. With no A₅, there are no new divergences and the heavy modes decouple. We also discuss the dependence of the couplings and masses on the compactification scale, and derive a set of renormalization group-like equations for the running of the effective couplings with respect to the compactification scale. It is found that magnitudes of both couplings decrease as the scale M increases.

We study the resummation of large QCD radiative corrections up to the next-to-leading logarithmic accuracy to the process γγ→bb̅ ; i.e., we resum logarithms of the type α_s^pln^2pm²/s and α_s^pln^2p-1m²/s (m is the quark mass). The only source of all the logarithms to this accuracy is the off-shell Sudakov form factor included into the triangle topologies of the one-loop box diagram. We prove that any other configurations of diagrams to this accuracy either cancel in subgroups or develop a universal on-shell Sudakov exponent due to the final quark antiquark lines. We study the mechanism of cancellations between the different diagrams, which leads to the simple resummed results. We show the cancellation explicitly at three loops for the leading and at two loops for the next-to-leading logarithms. We also point out the general mechanism responsible for it, and discuss how it can be extended to higher orders.

We study the strong corrections to the Higgs coupling to two photons. This coupling is the dominant mechanism for Higgs boson production in photon-photon collisions. In addition, the two photon decay mode of the Higgs boson is an important and relatively background free channel of relevance at the CERN LHC and the Fermilab Tevatron. We develop a method for the resummation of large QCD corrections in the form of Sudakov-like logarithms of the type α_s^p ln^2p(m²/m_H²) and α_s^p ln^2p-1(m²/m_H²) (where m is the light quark mass) which can contribute to this process in certain models (for example, the MSSM for large tan β) up to next-to-leading-logarithmic (NLL) accuracy. The NLL correction is moderate, the substantial part of which comes from terms not related to running coupling effects.

We consider the infrared sensitivity of the inclusive heavy quark decay width in perturbation theory. It is shown by explicit calculations to the second loop order (when the non-Abelian nature of the QCD interactions first become apparent) that all infrared sensitive terms to logarithmic and linear accuracy cancel when the decay width is expressed in terms of the short distance mass. This in turn implies the absense of any nonperturbative 1/m_Q power corrections to the decay width. The cancellation is shown algebraically at the level of the Feynman integrands without any use of an explicit infrared cutoff. This result is in accordance with the implications of the KLN theorem.

A leading twist expansion in terms of bilocal operators is proposed for the structure functions of deeply inelastic scattering near the elastic limit x→1, which is also applicable to a range of other processes. Operators of increasing dimensions contribute to logarithmically enhanced terms which are suppressed by corresponding powers of 1-x. For the longitudinal structure function, in moment (N) space, all the logarithmic contributions of order ln^kN/N are shown to be resummable in terms of the anomalous dimension of the leading operator in the expansion.

The wave function of a light pseudoscalar meson is considered and nonperturbative corrections as signaled by perturbation theory are calculated. Two schemes are used: the massive gluon and the running coupling scheme. Both indicate the presence of leading power corrections of O(b²), whose exponentiation leads to a Gaussian dependence of the wave function on the impact parameter b. The dependence of this correction on the light cone energy fractions of the quark and the antiquark is discussed and compared with other models for the meson.

We present a covariant formulation of the Kinoshita-Lee-Nauenberg (KLN) theorem for processes involving the radiation of soft particles. The role of the disconnected diagrams is explored and a rearrangement of the perturbation theory is performed such that the purely disconnected diagrams are factored out. The remaining effect of the disconnected diagrams results in a simple modification of the usual Feynman rules for the S-matrix elements. As an application, we show that, when combined with the Low theorem, this leads to a proof of the absence of the 1/Q corrections to inclusive processes (such as the Drell-Yan process). In this paper the Abelian case is discussed to all orders in the coupling.

In this paper we discuss the theoretical difficulties in extracting V_ub using the data from inclusive B decays. Specifically, we address the issue of end point singularities. We perform the resummation of both the leading and next to leading end point logarithms and include the leading corrections to the hard scattering amplitude. We find that the resummation is a 20%-50% effect in the end point region where the resummation is valid. Furthermore, the resummed subleading logarithms dominate the resummed double logarithms. The consequences of this result for a model-independent extraction of the mixing angle V_ub are explored.

We consider powerlike corrections in QCD which can be viewed as power suppressed infrared singularities. We argue that the presence of these singularities depends crucially on the energy resolution. In the case of poor energy resolution, i.e., inclusive cross sections, there are constraints on infrared singularities expressed by the Kinoshita-Lee-Nauenberg (KLN) theorem. We rewrite the theorem in covariant notations and argue that the KLN theorem implies the extension of the Bloch-Nordsieck cancellation of logarithmic singularities to the case of linear corrections.

We present a QCD-based calculation of the exclusive semileptonic decay Λ_b→plν¯_l. Using the ideas of heavy quark effective theory we discuss the factorization of the amplitude. Further, resummed Sudakov effects are put in to ensure a consistent perturbative expansion. © 1996 The American Physical Society.

Using heavy quark effective field theory, exponentiation of Sudakov double logarithms, and perturbative factorization theorems for exclusive processes, we calculate the amplitude for the semileptonic decay of mesons with a single, very heavy quark into π and ρ for a large hadronic recoil momentum. A formula for these large-recoil widths is obtained in terms of two-particle wave functions of the heavy and light mesons and applied to semileptonic decays of the B.

The effect of possible non-standard-model physics in the form of a scalar singlet on the absolute upper bound and cutoff dependence of the Higgs-boson mass is evaluated. It is found that the previous absolute upper bounds on the Higgs-boson mass within the context of the standard model are unchanged at about 800 GeV.

We investigate the theory of a closed bosonic string propagating in a background consisting of a condensate of its massless modes. At the classical level, the Virasoro operators and the Hamiltonian are identified and their Poisson-brackets algebra verified. The massless-mode vertex operators for a string in background fields are constructed from the requirement that they have the appropriate Poisson brackets with the Virasoro operators. In the quantum theory, a weak-field expansion of the Virasoro operators is used. The commutators of the Virasoro operators are explicitly evaluated to first order in the weak-field expansion using the Bjorken-Johnson-Low procedure. The equations of motion to first order in weak fields are seen to follow from the requirement of the closure of the Virasoro algebra on the two-dimensional world sheet.

We study the limit when the σ mass is very large compared to other scales in the renormalized light-particle-irreducible Green's functions of the linear σ model with SO(N+1) symmetry. This is a strong-coupling limit. The resulting theory is summarized by an effective Lagrangian, from which Green's functions, not just the S-matrix elements, can be reproduced to O (1). At the one-loop level, the effective Lagrangian is explicitly constructed and the relationship between the infinities of the nonlinear model and the heavy-mass effects is clarified. We then discuss the construction of the effective Lagrangian to all orders via the method of oversubtraction. This investigation can either be looked upon as a systematic way of organizing the heavy-Higgs-boson effects or it may be interpreted as a method of defining a renormalization program for the nonlinear σ model.

Fermionic solitons are defined in terms of localized self-consistent solutions of the classical equations of motion for bosons and Dirac fields. The one-loop quantum-mechanical correction to the mass of such a state is given by the diagonal S-matrix element in a self-consistent interaction picture. The various contributions to the energy shift are discussed, and the gauge invariance of our result is verified explicitly. Our operator formulation for fermionic solitons is shown to be equivalent to a Feynman path-integral prescription proposed by Dashen, Hasslacher, and Neveu.

The Bogomolny equation for linear perturbations of the Prasad-Sommerfield monopole is solved exactly. Explicit expressions for all the normalizable and unnormalizable nongauge modes are obtained, and previous results of Mottola on the normalizable modes are confirmed. A new choice of gauge facilitates the solution. Open questions and possible applications are mentioned.

The mass divergences of wide-angle scattering amplitudes are examined in a class of field theories including those with elementary vector fields. Power-counting arguments are used to show that, apart from renormalization effects, the wide-angle gauge-singlet scattering amplitude has a well-defined zero-mass limit and hence satisfies the renormalization-group equations. The same techniques also reproduce the earlier results for Yukawa and φ⁴ theories.