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We consider the relativistic scattering of unequal-mass scalar particles through graviton exchange in the small-angle high-energy regime. We show the self-consistency of expansion around the eikonal limit and compute the scattering amplitude up to the next-to-leading power correction of the light particle energy, including gravitational effects of the same order. The first power correction is suppressed by a single power of the ratio of momentum transfer to the energy of the light particle in the rest frame of the heavy particle, independent of the heavy particle mass. We find that only gravitational corrections contribute to the exponentiated phase in impact parameter space in four dimensions. For large enough heavy-particle mass, the saddle point for the impact parameter is modified compared to the leading order by a multiple of the Schwarzschild radius determined by the mass of the heavy particle, independent of the energy of the light particle., Comment: Basic results are unchanged, but many arguments have been revised, and several calculations given in dimensional regularization. One new figure. 17 pages, six figures

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. {copyright} {ital 1997} {ital The American Physical Society}

In this paper we discuss the theoretical difficulties in extracting Vub using the data from inclusive B decays. Specifically, we address the issue of the end point singularities. We perform the resummation of both the leading and next to leading end point logs 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 sub-leading logs dominate the resummed double logs. The consequences of this result for a model independent extraction of the mixing angle Vub are explored.

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 \ensuremath{\pi} and \ensuremath{\rho} 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 decoupling of heavy Kaluza-Klein modes in an Abelian Higgs model with space-time topologies $\mathbb{R}^{3,1} \times S^{1}$ and $\mathbb{R}^{3,1} \times S^{1}/\mathbb{Z}_{2}$. After integrating out heavy KK modes we find the effective action for the zero mode fields. We find that in the $\mathbb{R}^{3,1} \times S^{1}$ topology the heavy modes do not decouple in the effective action, due to the zero mode of the 5-th component of the 5-d gauge field $A_{5}$. Because $A_{5}$ is a scalar under 4-d Lorentz transformations, there is no gauge symmetry protecting it from getting mass and $A_{5}^{4}$ interaction terms after loop corrections. In addition, after symmetry breaking, we find new divergences in the $A_{5}$ 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. The relevance of these new divergences to Symanzik's theorem is discussed. In order to get a more sensible theory we investigate the $S^{1}/\mathbb{Z}_{2}$ compactification. With this kind of compact topology, the $A_{5}$ zero mode disappears. With no $A_{5}$, there are no new divergences and the heavy modes decouple. We also discuss the dependence of the couplings and masses on the compactification scale. We derive a set of RG-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. The effective masses are also shown to decrease with increasing compactification scale. All of this opens up the possibility of placing constraints on the size of extra dimensions., 35 pages, 6 figures

We study the resummation of large QCD radiative corrections up to the next-to-leading logarithmic accuracy to the process $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}}b\overline{b};$ i.e., we resum logarithms of the type ${\ensuremath{\alpha}}_{s}^{p}{\mathrm{ln}}^{2p}{m}^{2}/s$ and ${\ensuremath{\alpha}}_{s}^{p}{\mathrm{ln}}^{2p\ensuremath{-}1}{m}^{2}/s$ $(m$ 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 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.

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 ${\cal O}(b^2)$, 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., Comment: 15 pp, Latex, 2 figures, uses axodraw. Discussion of comparison with other models modified. One reference added

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 ${\ensuremath{\varphi}}^{4}$ theories.

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.

We study the limit when the $\ensuremath{\sigma}$ mass is very large compared to other scales in the renormalized light-particle-irreducible Green's functions of the linear $\ensuremath{\sigma}$ model with $\mathrm{SO}(N+1)$ 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 $\ensuremath{\sigma}$ model.