Leading Log Approximation Research Articles

N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution

We further investigate, in the planar limit of N=4 supersymmetric Yang–Mills theories, the high energy Regge behavior of six-point MHV scattering amplitudes. In particular, for the new Regge cut contribution found in our previous paper, we compute in the leading logarithmic approximation (LLA) the energy spectrum of the BFKL equation in the color octet channel, and we calculate explicitly the two-loop corrections to the discontinuities of the amplitudes for the transitions 2→4 and 3→3. We find an explicit solution of the BFKL equation for the octet channel for arbitrary momentum transfers and investigate the intercepts of the Regge singularities in this channel. As an important result we find that the universal collinear and infrared singularities of the BDS formula are not affected by this Regge-cut contribution. Any improvement of the BDS formula should reproduce this cut to all orders in the coupling.

Neutrality Point of Graphene with Coplanar Charged Impurities

The ground state and the transport properties of graphene subject to the potential of in-plane charged impurities are studied. The screening of the impurity potential is shown to be nonlinear, producing a fractal structure of electron and hole puddles. Statistical properties of this density distribution as well as the charge compressibility of the system are calculated in the leading-log approximation. The conductivity depends logarithmically on alpha, the dimensionless strength of the Coulomb interaction. The theory is asymptotically exact when alpha is small, which is the case for graphene on a substrate with a high dielectric constant.

Collimation of average multiplicity in QCD jets

The collimation of average multiplicity inside quark and gluon jets is investigated in perturbative QCD in the modified leading logarithmic approximation (MLLA). The role of higher order corrections accounting for energy conservation and the running of the coupling constant leads to smaller multiplicity collimation as compared to leading logarithmic approximation (LLA) results. The collimation of jets produced in heavy-ion collisions has also been explored by using medium-modified splitting functions enhanced in the infrared sector. As compared to elementary collisions, the angular distribution of the jet multiplicity is found to broaden in QCD media at all energy scales.

Scaled momentum distributions of charged particles in dijet photoproduction at HERA

The scaled momentum distributions of charged particles in jets have been measured for dijet photoproduction with the ZEUS detector at HERA using an integrated luminosity of 359 pb-1. The distributions are compared to predictions based on perturbative QCD carried out in the framework of the modified leading-logarithmic approximation (MLLA) and assuming local parton-hadron duality (LPHD). The universal MLLA scale, Lambda_eff, and the LPHD parameter, kappa^ch, are extracted.

Measurement of thekTDistribution of Particles in Jets Produced inpp¯Collisions ats=1.96 TeV

We present a measurement of the transverse momentum with respect to the jet axis (k(t)) of particles in jets produced in pp collisions at sqrt(s)=1.96 TeV. Results are obtained for charged particles in a cone of 0.5 radians around the jet axis in events with dijet invariant masses between 66 and 737 GeV/c(2). The experimental data are compared to theoretical predictions obtained for fragmentation partons within the framework of resummed perturbative QCD using the modified leading log and next-to-modified leading log approximations. The comparison shows that trends in data are successfully described by the theoretical predictions, indicating that the perturbative QCD stage of jet fragmentation is dominant in shaping basic jet characteristics.

Running inflation in the Standard Model

An interacting scalar field with largish coupling to curvature can support a distinctive inflationary universe scenario. Previously this has been discussed for the Standard Model Higgs field, treated classically or in a leading log approximation. Here we investigate the quantum theory using renormalization group methods. In this model the running of both the effective Planck mass and the couplings is important. The cosmological predictions are consistent with existing WMAP5 data, with 0.967≲ns≲0.98 (for Ne=60) and negligible gravity waves. We find a relationship between the spectral index and the Higgs mass that is sharply varying for mh∼120–135 GeV (depending on the top mass); in the future, that relationship could be tested against data from PLANCK and LHC. We also comment briefly on how similar dynamics might arise in more general settings, and discuss our assumptions from the effective field theory point of view.

Inclusive hadronic distributions in jets and sub-jets with jet axis from color current

The hadronic $\kt$-spectrum and the gluon to quark average multiplicity ratio $r=N_g/N_q$ inside a high energy sub-jet are determined from a precise definition of the jet axis, including corrections of relative magnitude ${\cal O}(\sqrt{\alpha_s})$ with respect to the Modified Leading Logarithmic Approximation (MLLA), in the limiting spectrum approximation (assuming an infrared cut-off $Q_0 =\lqcd$). The results for the $\kt$-spectrum in the limiting spectrum approximation are found to be, after normalization, in impressive agreement with measurements by the CDF collaboration and the ratio has not been measured yet.

A parton picture of de Sitter space during slow-roll inflation

It is well-known that expectation values in de Sitter space are afflicted by infra-red divergences. Long ago, Starobinsky proposed that infra-red effects in de Sitter space could be accommodated by evolving the long-wavelength part of the field according to the classical equations of motion plus a stochastic source term. I argue that — when quantum-mechanical loop corrections are taken into account — the separate universe picture of superhorizon evolution in de Sitter space is equivalent, in a certain leading-logarithm approximation, to Starobinsky's stochastic approach. In particular the time evolution of a box of de Sitter space can be understood in exact analogy with the DGLAP evolution of partons within a hadron, which describes a slow logarithmic evolution in the distribution of the hadron's constituent partons with the energy scale at which they are probed.

A simplified quantum gravitational model of inflation

Inflationary quantum gravity simplifies drastically in the leading logarithm approximation. We show that the only counterterm which contributes in this limit is the 1-loop renormalization of the cosmological constant. We go further to make a simplifying assumption about the operator dynamics at leading logarithm order. This assumption is explicitly implemented at 1- and 2-loop orders, and we describe how it can be implemented nonperturbatively. We also compute the expectation value of an invariant observable designed to quantify the quantum gravitational back-reaction on inflation. Although our dynamical assumption may not prove to be completely correct, it does have the right time dependence, it can naturally produce primordial perturbations of the right strength, and it illustrates how a rigorous application of the leading logarithm approximation might work in quantum gravity. It also serves as a partial test of the ‘null hypothesis’ that there are no significant effects from infrared gravitons.

Systematic study of the jet fragmentation function for inclusive jet-production in p+p collisions at $\sqrt{s}=200$ GeV in STAR

Jet fragmentation functions measured in e + e − and $p+\bar{p}$ experiments are well-described on an inclusive hadron level by QCD-based calculations. Fragmentation is expected to be modified by the presence of a strongly interacting medium, but full theoretical description of this modification must still be developed. It has recently been suggested that particle-identified fragmentation functions may provide additional insight into the processes underlying jet quenching. To assess the applicability of QCD-based fragmentation calculations to RHIC data, and to provide a baseline with which to compare fragmentation function measurements in heavy ion collisions, we present the first measurements of charged hadron and particle-identified fragmentation functions of jets reconstructed via a midpoint-cone algorithm from p+p collisions at 200 GeV in STAR. We study the dependence on jet cone-size and jet-energy, and compare the results to PYTHIA simulations based on the Modified Leading Log Approximation (MLLA).

Simple formula for high-energy gluon bremsstrahlung in a finite, expanding medium

Previous authors have considered the problem of the medium effects on single gluon bremsstrahlung associated with producing a high-energy particle in a finite, time-dependent QCD plasma. Working to leading logarithmic order, I show that the result for the bremsstrahlung gluon spectrum can be cast into a remarkably simple form in the general case. I similarly analyze the process of pair production. Also, I comment on the radius of convergence of the opacity expansion in cases where the leading-log approximation holds, showing that the opacity expansion does not converge when the thickness of the plasma is greater than roughly the bremsstrahlung formation time.

Jet quenching and broadening: The transport coefficientq̂in an anisotropic plasma

The jet quenching parameter (q) over cap is analyzed for a quark jet propagating in an anisotropic plasma. The momentum anisotropy is calculated at high temperature of the underlying quark-gluon plasma. (q) over cap is explicitly estimated in leading-logarithmic approximation by the broadening of the massless quark interacting via gluon exchange. A plasma instability is present. Strong indications are found that (q) over cap is increasing with increasing anisotropy. Possible implications for the saturation scale Q(s) in A-A collisions are pointed out.

Study of hadronic event shape in flavour tagged events in e+e- annihilation at "Equation missing" = 197 GeV

Results are presented from a study of the structure of hadronic events in high-energy e+e- interactions detected by the L3 detector at LEP. Various event shape distributions and their moments are measured at several energy points at and above the Z-boson mass. The event flavour is tagged by using the decay characteristics of b-hadrons. Measurements of distributions of event shape variables for all hadronic events, for light (u, d, s, c) and heavy (b) quark flavours are compared to several QCD models with improved leading log approximation: JETSET, HERWIG and ARIADNE. A good description of the data is provided by the models.

Particles production in expanding color flux tube

This article generalizes Schwinger’s mechanism for particle production in the time dependent field volume in the quasi-static approximation. Solution of DGLAP equations in the double leading log approximation for a small x gluon distribution function was used to derive the new formula for initial chromofield energy density. This initial chromofield energy is distributed among color neutral clusters or strings. These strings are stretched by the receding nucleus. From the proposed mechanism of string fragmentation or color field decay, the new formula for the rapidity spectrum of produced partons was derived.

Constrained MC for QCD evolution with rapidity ordering and minimum kT

With the imminent start of LHC experiments, development of phenomenological tools, and in particular the Monte Carlo programs and algorithms, becomes urgent. A new algorithm for the generation of a parton shower initiated by the single initial hadron beam is presented. The new algorithm is of the class of the so-called “constrained MC” type algorithm (an alternative to the backward evolution MC algorithm), in which the energy and the type of the parton at the end of the parton shower are constrained (predefined). The complete kinematics configurations with explicitly constructed four momenta are generated and tested. Evolution time is identical with rapidity and minimum transverse momentum is used as an infrared cut-off. All terms of the leading-logarithmic approximation in the DGLAP evolution are properly accounted for. In addition, the essential improvements towards the so-called CCFM/BFKL models are also properly implemented. The resulting parton distributions are cross-checked up to the 10 −3 precision level with the help of a multitude of comparisons with other MC and non-MC programs. We regard these tests as an important asset to be exploited at the time when the presented MC will enter as a building block in a larger MC program for W / Z production process at LHC.

Particle multiplicity in jets and subjets with jet axis from color current

We study the particle multiplicity in a jet or subjet as derived from an energy-multiplicity 2-particle correlation. This definition avoids the notion of a globally fixed jet axis and allows for the study of smaller jet cone openings in a more stable way. The results are sensitive to the mean color current (C) A0 in the jet from primary parton A 0 , which takes into account intermediate partonic processes in the subjet production where C F < (C) A0 < N c at high energies. We generalize previous calculations in the leading logarithmic approximation (LLA). The size of the effects related to this jet axis definition is computed for multiplicities in subjets with different opening angles and energies by including contributions from the modified LLA and next-to-modified LLA to the leading order QCD results.

QCD evolution of jets in the quark–gluon plasma

The quark–gluon plasma (QGP) can be explored in relativistic heavy ion collisions by the jet quenching signature, i.e., by the energy loss of a high energy quark or gluon traversing the plasma. We introduce a novel QCD evolution formalism in the leading logarithm approximation, where normal parton radiation is interleaved with scattering on the plasma gluons occuring at a similar time scale. The idea is elaborated in two approaches. One extends the DGLAP evolution equations for fragmentation functions to include scatterings in the medium, which facilitates numerical solutions for comparison with data and provides a basis for a Monte Carlo implementation. The other approach is more general by including also the transverse momentum dependence of the jet evolution, which allows a separation of the scales also for the scattering term and provides a basis for analytical investigations. The two approaches are shown to be related and give the same characteristic softening of the jet depending on the temperature of the plasma. A substantial effect is found at the RHIC energy and is further enhanced at LHC. Systematic studies of data on the energy loss could, therefore, demonstrate the existence of the QGP and probe its properties.

Decayb→(cc¯)sin the leading logarithm approximation

We consider an effective field theory for the nonleptonic decay in which a heavy quark decays into a pair of a heavy quark and antiquark having a small relative velocity and one relativistic (massless) quark. This effective theory is a combination of heavy quark effective theory (HQET), soft-collinear effective theory (SCET), and a covariant modification of nonrelativistic QCD (NRQCD). In the leading logarithm approximation the effective theory decay amplitude factorizes into the product of matrix elements of heavy-to-heavy and heavy-to-light currents. We discuss a possibility of factorization beyond the leading logarithm approximation and find it doubtful. The Wilson coefficients of the effective theory electroweak (EWET) Lagrangian in the next-to-leading logarithm approximation are calculated at the matching scale of the decay. The differential decay rate for the inclusive decay $B\ensuremath{\rightarrow}J/\ensuremath{\psi}+h$ in the effective theory framework is evaluated.

Hadronic Single Inclusivek⊥Distributions inside One Jet Beyond the Modified-Leading-Log Approximation

The hadronic kt-spectrum inside one jet is determined including corrections of relative magnitude sqrt{alpha_s} with respect to the Modified Leading Logarithmic Approximation (MLLA), at and beyond the limiting spectrum (assuming an infrared cut-off Q_0 = Lambda_QCD and Q_0 not = Lambda_QCD). The agreement between our results and preliminary measurements by the CDF collaboration is impressive, much better than at MLLA, pointing out very small overall non-perturbative contributions.

Soft-gluon Resummation in the Evolution of Fragmentation Functions

We review recent progress in the development of an approach valid to any order which unifies the fixed-order DGLAP evolution of fragmentation functions at large x with soft-gluon logarithmic resummation at small x. At leading order, this approach, implemented with the Double Logarithmic Approximation, reproduces exactly the Modified Leading Logarithm Approximation, but it is more complete due to the degrees of freedom given to the quark sector and the inclusion of the fixed-order terms. We find that data from the largest x values to the peak region can be better fitted than with other approaches.