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C. S. Lam

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

At least 55 records · Page 3Linked to original sources
arXiv2002

Saturation and Wilson Line Distributions

We introduce a Wilson line distribution function bar{W}_tau(v) to study gluon saturation at small Feynman x_F, or large tau=ln(1/x_F). This new distribution can be obtained from the distribution W_tau(alpha) of the Color Glass Condensate model and the JIMWLK renormalization group equation. bar{W}_tau(v) is physically more relevant, and mathematically simpler to deal with because of unitarity of the Wilson line v. A JIMWLK equation is derived for bar{W}_tau(v); its properties are studied. These properties are used to complete Mueller's derivation of the JIMWLK equation, though for bar{W}_tau(v) and not W_tau(alpha). They are used to derive a generalized Balitsky-Kovchegov equation for higher multipole amplitudes. They are also used to compute the unintegrated gluon distribution at x_F=0, yielding a completely flat spectrum in transverse momentum squared k^2, with a known height. This is similar but not identical to the mean field result at small k^2.

hep-ph↗
arXiv2001

Large Mixing Induced by the Strong Coupling with a Single Bulk Neutrinos

Neutrino is a good probe of extra dimensions. Large mixing and the apparent lack of very complicated oscillation patterns may be an indication of large couplings between the brane and a single bulk neutrino. A simple and realistic five-dimensional model of this kind is discussed. It requires a sterile in addition to three active neutrinos on the brane, all coupled strongly to one common bulk neutrino, but not directly among themselves. Mindful that sterile neutrinos are disfavored in the atmospheric and solar data, we demand induced mixing to occur among the active neutrinos, but not between the active and the sterile. The size $R$ of the extra dimension is arbitrary in this model, otherwise it contains six parameters which can be used to fit the three neutrino masses and the three mixing angles. However, in the model those six parameters must be suitably ordered, so a successful fit is not guaranteed. It turns out that not only the data can be fitted, but as a result of the ordering, a natural connection between the smallness of the reactor angle $θ_{13}$ and the smallness of the mass-gap ratio $ΔM^2_{solar}/ΔM^2_{atmospheric}$ can be derived.

hep-ph↗
arXiv2001

Neutrino Oscillations via the Bulk

We investigate the possibility that the large mixing of neutrinos is induced by their large coupling to a five-dimensional bulk neutrino. In the strong coupling limit the model is exactly soluble. It gives rise to an oscillation amplitude whose squared-mass difference is independent of the channel, thus making it impossible to explain both the solar and the atmospheric neutrino oscillations simultaneously.

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arXiv2001

A 2-3 Symmetry in Neutrino Oscillations

Maximum mixing in atmospheric neutrino oscillation, as well as vanishing of the MNS matrix element $U_{e3}$, are consequences of a 2-3 symmetry, under which the neutrino mass matrix is invariant under the interchange of second and third generation neutrinos. These predictions of the 2-3 symmetry are consistent with the results of Super-Kamiokande, K2K, and CHOOZ experiments. If the symmetry is exact at a high-energy scale set by right-handed neutrinos, a deviation from these predictions generated by renormalization-group corrections will occur at experimental energies. With an MSSM dynamics, the result can be made to agree with a global fit of the neutrino data, if normal hierarchy is assumed on the neutrino mass spectrum and if the mass of the electron-neutrino is at least about 0.025 eV. The presence of this mass lower bound is a novel and interesting feature of the symmetry that can be falsified by future experiments. Of the three viable solar neutrino solutions, only LMA gives a sizable MNS matrix element $U_{e3}$ that can hopefully be detected in future reactor experiments. Inverted neutrino mass hierarchy is not permitted by this symmetry.

hep-ph↗
arXiv2001

Implementing Unitarity in Perturbation Theory

Unitarity cannot be perserved order by order in ordinary perturbation theory because the constraint $UU^\dagger=\1$ is nonlinear. However, the corresponding constraint for $K=\ln U$, being $K=-K^\dagger$, is linear so it can be maintained in every order in a perturbative expansion of $K$. The perturbative expansion of $K$ may be considered as a non-abelian generalization of the linked-cluster expansion in probability theory and in statistical mechanics, and possesses similar advantages resulting from separating the short-range correlations from long-range effects. This point is illustrated in two QCD examples, in which delicate cancellations encountered in summing Feynman diagrams of are avoided when they are calculated via the perturbative expansion of $K$. Applications to other problems are briefly discussed.

hep-ph↗
arXiv2001

Non-Gaussian Correlations in the McLerran-Venugopalan Model

We argue that the statistical weight function W[rho] appearing in the McLerran-Venugopalan model of a large nucleus is intrinsically non-Gaussian, even if we neglect quantum corrections. Based on the picture where the nucleus of radius R consists of a collection of color-neutral nucleons, each of radius a<<R, we show that to leading order in alpha_s and a/R only the Gaussian part of W[rho] enters into the final expression for the gluon number density. Thus, the existing results in the literature which assume a Gaussian weight remain valid.

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arXiv2000

Longitudinal Resolution in a Large Relativistic Nucleus: Adding a Dimension to the McLerran-Venugopalan Model

We extend the McLerran-Venugopalan model for the gluon distribution functions of very large nuclei to larger values of the longitudinal momentum fraction xF. Because gluons with larger values of xF begin to resolve the longitudinal structure of the nucleus, we find that it is necessary to set up a fully three-dimensional formalism for performing the calculation. We obtain a relatively compact expression for the gluon number density provided that the nucleus is sufficiently large and consists of color-neutral nucleons. Our expressions for the gluon number density saturate at small transverse momenta. The nuclear dependence we obtain is such that the number of gluons increases more slowly than the number of nucleons is increased.

hep-ph↗
arXiv2000

Consequences of a Z_2 Symmetry for Neutrino Oscillation

A $Z_{2L}\times Z_{2R}$ generation symmetry in the neutrino sector predicts the atmospheric neutrino mixing to be maximal, and the MNS matrix element $U_{e3}$ to be zero, consistent with observations. Solar neutrino mixing may be maximal but is not required by the symmetry. Neutrino masses of the first two generations are predicted to vanish, providing a first approximation to the oscillation data. The consequence of a smaller $Z_2$ symmetry is also discussed. In that case, deviation from the $Z_{2L}\times Z_{2R}$ result is of the order of the neutrino mass ratio between the first two generations and the third generation.

hep-ph↗
arXiv1999

Color Neutrality and the Gluon Distribution in a Very Large Nucleus

We improve the McLerran-Venugopalan model for the gluon distribution functions in very large nuclei by imposing the condition that the nucleons should be color neutral. We find that enforcing color neutrality cures the infrared divergences in the transverse coordinates which are present in the McLerran-Venugopalan model. Since we obtain well-defined expressions for the distribution functions, we are able to draw unambiguous conclusions about various features of the model. In particular, we show that the gluon distribution functions in the absence of quantum corrections behave as 1/x to all orders in the coupling constant. Furthermore, our distribution functions exhibit saturation at small transverse momenta. The normalization of the distribution function we obtain is not arbitrary but specified in terms of the nucleon structure. We derive a sum rule for the integral of the gluon distribution function over transverse momenta, and show that the non-Abelian contributions serve only to modify the shape of the transverse momentum distribution. We obtain a relatively simple expression for the mean value of the transverse momentum-squared. The connection between the McLerran-Venugopalan model and the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation is discussed quantitatively. Finally, we illustrate our results in terms of a simple nuclear model due to Kovchegov.

hep-ph↗
arXiv1999

Time Ordering, Energy Ordering, and Factorization

Relations between integrals of time-ordered product of operators, and their representation in terms of energy-ordered products are studied. Both can be decomposed into irreducible factors and these relations are discussed as well. The energy-ordered representation was invented to separate various infrared contributions in gauge theories. It is shown that the irreducible time-ordered expressions can be used to accomplish the same purpose. Besides, it has the added advantage of being factorizable.

hep-ph↗
arXiv1999

High Order Perturbative QCD Approach to Multiplicity Distributions of Quark and Gluon Jets

The second and third factorial moments of the multiplicity distributions of gluon and quark jets are calculated up to the next-to-next-to-next-to leading order in perturbative QCD, using the equations for generating functions. The results are confronted with experimental data. A general discussion on high order corrections revealed by such an approach is given. Other possible corrections and approaches are discussed as well.

hep-ph↗
arXiv1999

Small-Recoil Approximation

In this review we discuss a technique to compute and to sum a class of Feynman diagrams, and some of its applications. These are diagrams containing one or more energetic particles that suffer very little recoil in their interactions. When recoil is completely neglected, a decomposition formula can be proven. This formula is a generalization of the well-known eikonal formula, to non-abelian interactions. It expresses the amplitude as a sum of products of irreducible amplitudes, with each irreducible amplitude being the amplitude to emit one, or several mutually interacting, quasi-particles. For abelian interaction a quasi-particle is nothing but the original boson, so this decomposition formula reduces to the eikonal formula. In non-abelian situations each quasi-particle can be made up of many bosons, though always with a total quantum number identical to that of a single boson. This decomposition enables certain amplitudes of all orders to be summed up into an exponential form, and it allows subleading contributions of a certain kind, which is difficult to reach in the usual way, to be computed. For bosonic emissions from a heavy source with many constituents, a quasi-particle amplitude turns out to be an amplitude in which all bosons are emitted from the same constituent. For high-energy parton-parton scattering in the near-forward direction, the quasi-particle turns out to be the Reggeon, and this formalism shows clearly why gluons reggeize but photons do not. The ablility to compute subleading terms in this formalism allows the BFKL-Pomeron amplitude to be extrapolated to asymptotic energies, in a unitary way preserving the Froissart bound. We also consider recoil corrections for abelian interactions in order to accommodate the Landau-Pomeranchuk-Migdal effect.

hep-ph↗
arXiv1999

Coherent States in High-Energy Physics

The amplitude for emitting $n$ bosons factorizes into the product of $n$ single-boson emission amplitudes, if the source is energetic and abelian. If it is energetic but {\it non-abelian}, the amplitude is given by a sum of factorized {\it quasi-particle} amplitudes. A quasi-particle is made up of an arbitrary number of bosons, but couples to the source like a single one. Factorization is related to coherence, and it allows computation of subleading contributions not obtainable by usual means. Its importance is illustrated in two applications: to solve the baryon problem in large-$N_c$ QCD, and to obtain a total cross section satisfying the Froissart bound.

hep-ph↗
arXiv1999

Unitarization of Total Cross Section and Coherent Effect in pQCD

A formula to unitarize the leading-log BFKL-Pomeron amplitude is derived using a coherent property of two-body collision in the peripheral region. This procedure also allows an algebraic characterization of the Reggeon in QCD based on color, instead of the total angular momentum of the gluons being exchanged.

hep-ph↗
arXiv1999

Unitarized Diffractive Scattering in QCD and Application to Virtual Photon Total Cross Sections

The problem of restoring Froissart bound to the BFKL-Pomeron is studied in an extended leading-log approximation of QCD. We consider parton-parton scattering amplitude and show that the sum of all Feynman-diagram contributions can be written in an eikonal form. In this form dynamics is determined by the phase shift, and subleading-logs of all orders needed to restore the Froissart bound are automatically provided. The main technical difficulty is to find a way to extract these subleading contributions without having to compute each Feynman diagram beyond the leading order. We solve that problem by using nonabelian cut diagrams introduced elsewhere. They can be considered as colour filters used to isolate the multi-Reggeon contributions that supply these subleading-log terms. Illustration of the formalism is given for amplitudes and phase shifts up to three loops. For diffractive scattering, only phase shifts governed by one and two Reggeon exchanges are needed. They can be computed from the leading-log-Reggeon and the BFKL-Pomeron amplitudes. In applications, we argue that the dependence of the energy-growth exponent on virtuality $Q^2$ for $γ^*P$ total cross section observed at HERA can be interpreted as the first sign of a slowdown of energy growth towards satisfying the Froissart bound. An attempt to understand these exponents with the present formalism is discussed.

hep-ph↗
arXiv1998

Abelian Landau-Pomeranchuk-Migdal effects

It is shown that the high-energy expansion of the scattering amplitude calculated from Feynman diagrams factorizes in such a way that it can be reduced to the eikonalized form up to the terms of inverse power in energy in accordance with results obtained by solving the Klein-Gordon equation. Therefore the two approaches when applied to the suppression of the emission of soft photons by fast charged particles in dense matter should give rise to the same results. A particular limit of thin targets is briefly discussed.

hep-ph↗
arXiv1998

QCD Phase Shifts and Rising Total Cross-Sections

Energy dependence of $γ^*p$ total cross section is considered. It is known from the HERA data that the cross section grows with energy, and the rate of growth is an increasing function of the virtuality $Q^2$ of the photon $γ^*$. This dependence can be explained in a simple and generic way by the Froissart bound. To implement this mechanism quantitatively a theory satisfying $s$-channel unitarity is required. This is achieved by computing the total cross section from the optical theorem, and the forward elastic amplitude from the phase shifts in the impact-parameter representation. A recipe to do so in perturbative QCD is discussed, together with an expose of the advantage to calculate the elastic amplitude via phase shift, rather than direct sum of all Feynman diagrams. A two-loop computation of phase shift and total cross section is presented, and compared with the HERA data with good agreements.

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