arXiv subjects

C. S. Lam

Publications and source records attributed to C. S. Lam.

At least 73 records · Page 4Linked to original sources

arXiv1998

QCD Phase Shifts and Rising Total Cross-Sections

An attempt is made in QCD to explain the growth of total cross-sections with energy, without violating the Froissart bound. This is achieved by computing the phase shifts of elastic scatterings of partons rather than their amplitudes. To render that possible a general formalism of phase-shifts in QCD is developed. Computed to two-loop order, agreements with hadronic and virtual-photon total cross-sections are quite satisfactory. Predications for the slower rate of growth at higher energies are also presented.

hep-ph↗

arXiv1998

Exponentiation of the Sum of Nonabelian Amplitudes

This paper contains an implicit assumption that the summand in eq. (4.2) for different $n$'s commute. This paper should be replaced by hep-th/9804181 where this assumption is removedand the result generalized.

hep-ph↗

arXiv1998

Bose-Einstein Interference and Factorization at High Energies

We consider the emission or absorption of $n$ identical bosons from an energetic or a massive particle, in which the bosons and the source particle are allowed to be offshell. The Bose-Einstein symmetrized amplitude can be decomposed into sums and products of more elementary objects which we choose to call `atoms'. The origin of this decomposition, its significance and some of its applications will be summarized.

hep-ph↗

arXiv1998

Time-Ordered Products and Exponentials

I discuss a formula decomposing the integral of time-ordered products of operators into sums of products of integrals of time-ordered commutators. The resulting factorization enables summation of an infinite series to be carried out to yield an explicit formula for the time-ordered exponentials. The Campbell-Baker-Hausdorff formula and the nonabelian eikonal formula obtained previously are both special cases of this result.

hep-th↗

arXiv1998

Evaluation of Multiloop Diagrams via Lightcone Integration

We present a systematic method to determine the dominant regions of internal momenta contributing to any two-body high-energy near-forward scattering diagram. Such a knowledge is used to evaluate leading high-energy dependences of loop diagrams. It also gives a good idea where dominant multiparticle cross sections occur.

hep-ph↗

arXiv1998

Decomposition of Time-Ordered Products and Path-Ordered Exponentials

We present a decomposition formula for $U_n$, an integral of time-ordered products of operators, in terms of sums of products of the more primitive quantities $C_m$, which are the integrals of time-ordered commutators of the same operators. The resulting factorization enables a summation over $n$ to be carried out to yield an explicit expression for the time-ordered exponential, an expression which turns out to be an exponential function of $C_m$. The Campbell-Baker-Hausdorff formula and the nonabelian eikonal formula obtained previously are both special cases of this result.

hep-th↗

arXiv1997

Generalized Background-Field Method

The graphical method discussed previously can be used to create new gauges not reachable by the path-integral formalism. By this means a new gauge is designed for more efficient two-loop QCD calculations. It is related to but simpler than the ordinary background-field gauge, in that even the triple-gluon vertices for internal lines contain only four terms, not the usual six. This reduction simplifies the calculation inspite of the necessity to include other vertices for compensation. Like the ordinary background-field gauge, this generalized background-field gauge also preserves gauge invariance of the external particles. As a check of the result and an illustration for the reduction in labour, an explicit calculation of the two-loop QCD $β$-function is carried out in this new gauge. It results in a saving of 45% of computation compared to the ordinary background-field gauge.

hep-ph↗

arXiv1997

Nonabelian Cut Diagrams

Symmetrization of bosonic wave functions produces bunching and low temperature phenomena like Bose-Einstein condensation, superfludity, superconductivity, as well as laser. Since probability is conserved, one might expect such bunchings at one place would lead to a depletion or a destructive interference at another place. This indeed takes place in high-energy scatterings, leading to cancellations between Feynman diagrams with permuted (real or virtual) boson lines. It is such cancellation that allow the Froissart bound to be obeyed, and the meson-baryon amplitudes in large-N_c QCD to be consistent. These lectures review the derivation and some of the applications of ``nonabelian cut diagrams'', which are resummation of Feynman diagrams, but with these interference effects explicitly incorporated. Unlike the traditional method where cancellations occur between Feynman diagrams, making it necessary to compute each diagram to subleading orders, destructive interference has been taken care of from the start in nonabelian cut diagrams. No further cancellation takes place, so each nonabelian cut diagram may be computed only in the leading order.

hep-ph↗

arXiv1997

Consistency of the Baryon-Multimeson Amplitudes for Large-N_c QCD

We study the pion-baryon scattering process $π+B \to (n-1)π+B$ in a QCD theory with a large number (N_c) of colors. It is known that this scattering amplitudes decreases with N_c like N_c^{1-n/2}, and that its individual tree diagrams grow like N_c^{n/2}. The only way these two can be consistent is for n-1 powers of N_c to be cancelled when the Feynman diagrams are summed. We prove this to be true in tree order for any n.

hep-ph↗

arXiv1996

Gauge Cancellation for Electroweak Processes and the Gervais-Neveu Gauge

A graphical method is developed to study the total or partial cancellation of gauge-dependent (divergence) terms in electroweak theory. The method is used to work out rules in the Gervais-Neveu gauge, whose triple-gauge vertex contains three terms rather than the usual six. This and other features of the gauge lead to an enormous saving of algebraic labor in the actual computations, as will be illustrated explicitly in the tree process $W^++W^-\to γ+γ$.

hep-ph↗

arXiv1996

Nonabelian Cut Diagrams and their Applications

A new kind of cut diagram is introduced to sum Feynman diagrams with nonabelian vertices. Unlike the Cutkosky diagrams which compute the discontinuity of single Feynman diagrams, the nonabelian cut diagrams represent a resummation of both the real and the imaginary parts of Feynman diagrams related by permutations. Several applications of the technique are reported, including a resolution of the apparent inconsistency of the baryon problem in large-$N_c$ QCD, a simplified calculation of high-energy low-order QCD diagrams, and progress made with this technique on the unitarization of the BFKL equation.

hep-ph↗

arXiv1996

Soft Interaction of Heavy Fermions

We discuss a formula for the sum of tree diagrams of $n$-bosons scattering from a heavy fermion. This formula can be considered as a generalization of the eikonal formula to include non-abelian vertices. It will be used to demonstrate the consistency of multi-meson-fermion scattering in the large-$N_c$ limit.

hep-ph↗

arXiv1996

Multiple Reggeon Exchange from Summing QCD Feynman Diagrams

Multiple reggeon exchange supplies subleading logs that may be used to restore unitarity to the Low-Nussinov Pomeron, provided it can be proven that the sum of Feynman diagrams to all orders gives rise to such multiple regge exchanges. This question cannot be easily tackled in the usual way except for very low-order diagrams, on account of delicate cancellations present in the sum which necessitate individual Feynman diagrams to be computed to subleading orders. Moreover, it is not clear that sums of high-order Feynman diagrams with complicated criss-crossing of lines can lead to factorization implied by the multi-regge scenario. Both of these difficulties can be overcome by using the recently developed nonabelian cut diagrams. We are then able to show that the sum of $s$-channel-ladder diagrams to all orders does lead to such multiple reggeon exchanges.

hep-ph↗

arXiv1996

Cut Diagrams for High Energy Scatterings

A new approach is introduced to study QCD amplitudes at high energy and comparatively small momentum transfer. Novel cut diagrams, representing resummation of Feynman diagrams, are used to simplify calculation and to avoid delicate cancellations encountered in the usual approach. Explicit calculation to the 6th order is carried out to demonstrate the advantage of cut diagrams over Feynman diagrams.

hep-ph↗

arXiv1996

A Multiple Commutator Formula for the Sum of Feynman Diagrams

In the presence of a large parameter, such as mass or energy, leading behavior of individual Feynman diagrams often get cancelled in the sum. This is known to happen in large-$N_c$ QCD in the presence of a baryon, and also in the case of high-energy electron-electron as well as quark-quark scatterings. We present an exact combinatorial formula, involving multiple commutators of the vertices, which can be used to compute such cancellations. It is a non-abelian generalization of the eikonal formula, and will be applied in subsequent publications to study the consistency of large-$N_c$ QCD involving baryons, as well as high-energy quark-quark scattering in ordinary QCD.

hep-ph↗

arXiv1995

Gauge Invariant Geometric Variables For Yang-Mills Theory

In a previous publication [1], local gauge invariant geometric variables were introduced to describe the physical Hilbert space of Yang-Mills theory. In these variables, the electric energy involves the inverse of an operator which can generically have zero modes, and thus its calculation is subtle. In the present work, we resolve these subtleties by considering a small deformation in the definition of these variables, which in the end is removed. The case of spherical configurations of the gauge invariant variables is treated in detail, as well as the inclusion of infinitely heavy point color sources, and the expression for the associated electric field is found explicitly. These spherical geometries are seen to correspond to the spatial components of instanton configurations. The related geometries corresponding to Wu-Yang monopoles and merons are also identified.

hep-th↗

arXiv1995

The Interpretation of Rapidity Gaps at Hera

In leading twist deep inelastic $ep$ scattering, the virtual photon interaction is fast compared to the time scale of soft color rearrangement. We compare the Pomeron exchange model, in which a neutral cluster is preformed, with a gluon exchange model, in which color is exchanged after the hard interaction. We find several features of the DIS data and of data on exclusive hard processes that favor a gluon exchange scenario. If correct, the postulate of soft color interactions between the produced ($q\bar q$) system and the target has important implications for other processes. In particular, this may explain the puzzles of charmonium hadroproduction.

hep-ph↗

arXiv1995

DIAGRAMMATIC ANALYSIS OF QCD GAUGE TRANSFORMATIONS AND GAUGE CANCELLATIONS

Diagrammatic techniques are invented to implement QCD gauge transformations. These techniques can be used to discover how gauge-dependent terms are cancelled among diagrams to yield gauge-invariant results in the sum. In this way a multiloop pinching technique can be developed to change ordinary vertices into background-gauge vertices. The techniques can also be used to design new gauges to simplify calculations by reducing the number of gauge-dependent terms present in the intermediate steps. Two examples are discussed to illustrate this aspect of the applications.

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