Leading Log Approximation Research Articles

CP violation in the minimal supersymmetric seesaw model

We study CP violation in the lepton sector of the supersymmetric extension of the Standard Model with three generations of massive singlet neutrinos with Yukawa couplings Y ν to lepton doublets, in a minimal seesaw model for light neutrino masses and mixing. This model contains six physical CP-violating parameters, namely the phase δ observable in oscillations between light neutrino species, two Majorana phases φ 1,2 that affect ββ 0 ν decays, and three independent phases appearing in Y νY ν † , that control the rate of leptogenesis. Renormalization of the soft supersymmetry-breaking parameters induces observable CP violation at low energies, including T-odd asymmetries in polarized μ→ eee and τ→ℓℓℓ decays, as well as lepton electric dipole moments. In the leading-logarithmic approximation in which the massive singlet neutrinos are treated as degenerate, these low-energy observables are sensitive via Y ν †Y ν to just one combination of the leptogenesis and light-neutrino phases. We present numerical results for the T-odd asymmetry in polarized μ→ eee decay, which may be accessible to experiment, but the lepton electric dipole moments are very small in this approximation. To the extent that the massive singlet neutrinos are not degenerate, low-energy observables become sensitive also to two other combinations of leptogenesis and light-neutrino phases, in this minimal supersymmetric seesaw model.

Charged-particle multiplicity pp collisions at square root of (s) = 1.8 TeV.

We report on a measurement of the mean charged-particle multiplicity of jets in dijet events with dijet masses in the range 80-630 GeV/c(2), produced at the Tevatron in pp collisions with square root (s) = 1.8 TeV and recorded by the Collider Detector at Fermilab. The data are fit to perturbative-QCD calculations carried out in the framework of the modified leading log approximation and the hypothesis of local parton-hadron duality. The fit yields values for two parameters in that framework: the ratio of parton multiplicities in gluon and quark jets, r identical withN(g-jet)(partons)/N(q-jet)(partons) = 1.7+/-0.3, and the ratio of the number of charged hadrons to the number of partons in a jet, K(charged)(LPHD) identical with N(charged)(hadrons)/N(partons) = 0.57+/-0.11.

The Monte Carlo event generator YFSWW3 version 1.16 for W-pair production and decay at LEP2/LC energies

We present the Monte Carlo event generator YFSWW3 version 1.16 for the process of W-pair production and decay in electron–positron collisions. It includes O(α) electroweak radiative corrections in the WW production stage together with the O(α 3) initial-state-radiation (ISR) corrections in the leading-logarithmic (LL) approximation, implemented within the Yennie–Frautschi–Suura (YFS) exclusive exponentiation framework. The photon radiation in the W decays is generated by the dedicated program PHOTOS up to O(α 2) LL, normalized to the W branching ratios. The program is interfaced with the τ decay library TAUOLA and the quark fragmentation/hadronization package JETSET. The semi-analytical code KorWan for the calculations of the differential and total cross-sections at the Born level and in the ISR approximation is included.

Higher order pair corrections to electron-positron annihilation

Radiative corrections due to pair production in process of electron-positron annihilation are considered. The main attention is paid to the corrections of the third order. Simultaneous emission of photons and pairs is taken into account. The leading log approximation and convolution procedure are used. Exponentiation is discussed. Theoretical uncertainty in description of higher order secondary pairs is estimated.

Multiplicities in parton and dipole QCD cascades

Evolution equations for multiplicities in QCD cascades can, both in the parton and dipole picture, be used to estimate corrections beyond the formal accuracy of the modified leading log approximation (MLLA). The differences between the two pictures, and other uncertainties beyond first order MLLA corrections, are here investigated in some detail. For example, I discuss how some colour suppressed corrections, which cannot be determined without better knowledge of non-perturbative QCD, are related to the question of colour reconnection. A generalized evolution equation for the dipole cascade is also presented.

The renormalization group equation for the color glass condensate

We present an explicit and simple form of the renormalization group equation which governs the quantum evolution of the effective theory for the Color Glass Condensate (CGC). This is a functional Fokker–Planck equation for the probability density of the color field which describes the CGC in the covariant gauge. It is equivalent to the Euclidean time evolution equation for a second quantized current–current Hamiltonian in two spatial dimensions. The quantum corrections are included in the leading log approximation, but the equation is fully non-linear with respect to the generally strong background field. In the weak field limit, it reduces to the BFKL equation, while in the general non-linear case it generates the evolution equations for Wilson-line operators previously derived by Balitsky and Kovchegov within perturbative QCD.

Subleading uncertainties in QCD cascades

Evolution equations for multiplicities in QCD cascades can, both in the parton and dipole picture, be used to estimate corrections beyond the formal accuracy of the modified leading log approximation (MLLA). The differences between the two pictures, and other uncertainties beyond first order MLLA corrections, are here investigated in some detail. For example, I discuss how some colour suppressed energy conservation corrections, which cannot be determined without better knowledge of non-perturbative QCD, are related to the question of colour reconnection.

On the energy loss of high energy quarks in a finite-size quark-gluon plasma

We study within the light-cone path integral approach the induced gluon emission from a fast quark passing through a finite-size QCD plasma. We show that the leading log approximation used in previous studies fails when the gluon formation length becomes of the order of the length of the medium traversed by the quark. Calculation of the energy loss beyond the leading log approximation gives the energy loss which grows logarithmically with quark energy contrary to the energy independent prediction of the leading log approximation.

Intercepts of the non-singlet structure functions

Infrared evolution equations for small-$x$ behaviour of the non-singlet structure functions $f_1^{NS}$ and $g_1^{NS}$ are obtained and solved in the next-to-leading approximation, to all orders in $\alpha_s$, and including running $\alpha_s$ effects. The intercepts of these structure functions, i.e. the exponents of the power-like small-$x$ behaviour, are calculated. A detailed comparison with the leading logarithmic approximation (LLA) and DGLAP is made. We explain why the LLA predictions for the small-$x$ dependence of the structure functions may be more reliable than the prediction for the $Q^2$ dependence in the range of $Q^2$ explored at HERA.

QCD dipole model and factorization

Abstract It is shown that the colour dipole approach to hard scattering at high energy is fully compatible with k T factorization at the leading logarithm approximation (in − log x Bj ). The relations between the dipole amplitudes and unintegrated diagonal and non-diagonal gluon distributions are given. It is also shown that including the exact gluon kinematics in the k T factorization formula destroys the conservation of transverse position vectors and thus is incompatible with the dipole model for both elastic and diffractive amplitudes.

Nonperturbative dynamics of hot non-Abelian gauge fields: Beyond the leading log approximation

Many aspects of high-temperature gauge theories, such as the electroweak baryon number violation rate, color conductivity, and the hard gluon damping rate, have previously been understood only at leading logarithmic order (that is, neglecting effects suppressed only by an inverse logarithm of the gauge coupling). We discuss how to systematically go beyond leading logarithmic order in the analysis of physical quantities. Specifically, we extend to next-to-leading-log order (NLLO) the simple leading-log effective theory due to B\"odeker that describes non-perturbative color physics in hot non-Abelian plasmas. A suitable scaling analysis is used to show that no new operators enter the effective theory at next-to-leading-log order. However, a NLLO calculation of the color conductivity is required, and we report the resulting value. Our NLLO result for the color conductivity can be trivially combined with previous numerical work by Moore to yield a NLLO result for the hot electroweak baryon number violation rate.

QCD improved parton distribution functions of [formula omitted

QCD corrections to the QED formula for parton distribution functions of the longitudinal virtual photon are derived in the leading-logarithmic approximation. It is shown that the resulting PDF satisfy the same homogeneous evolution equations as those of hadrons, but contrary to the latter are perturbatively calculable. Properties of these distribution functions are discussed and their phenomenological consequences outlined.

The extended chiral quark model confronts QCD

We discuss the truncation of low energy effective action of QCD below the chiral symmetry breaking (CSB) scale, including all operators of dimensionality less or equal to 6 which can be built with quark and chiral fields. We perform its bosonization in the scalar, pseudoscalar, vector and axial-vector channels in the large- N c and leading-log approximation. Constraints on the coefficients of the effective lagrangian are derived from the requirement of Chiral Symmetry Restoration (CSR) at energies above the CSB scale in the scalar-pseudoscalar and vector-axial-vector channels, from matching to QCD at intermediate scales, and by fitting some hadronic observables. In this truncation two types of pseudoscalar states (massless pions and massive II-mesons), as well as a scalar, vector and axial-vector one arise as a consequence of dynamical chiral symmetry breaking. Their masses and coupling constants as well as a number of chiral structural constants are derived. A reasonable fit of all parameters supports a relatively heavy scalar meson (quarkonium) with the mass ∼ 1 GeV and a small value of axial pion-quark coupling constant g A ≅ 0.55.

Measurements of αs with the Delphi detector at Lep

The data collected with Delphi during the Lep1 period is used to perform a simultaneous fit to the strong coupling constant α s in 2 nd order perturbation theory and to the renormalisation scale χ μ . The results are compared to α s fits in 2 nd order perturbation theory with fixed scale χ μ and to other theoretically motivated scale setting methods. To determine the energy dependence of α s , event shape distributions and their mean values are measured for √ s = 48 GeV to 189 GeV. The strong coupling α s is extractd in O ( α s 2), Next to Leading Log Approximation (NLLA) and in a combined scheme using hadronisation corrections-evaluated with fragmentation model generators, and an analytical power ansatz.

Reducing model dependence of spectator effects in inclusive decays of heavy baryons

The dependence of the inclusive weak decay rates of heavy hadrons on light spectator quarks is considered. The analysis of a previous work relating the effects in b baryons to those in charmed baryons is extended to explicit evaluation of the matrix elements of certain four-quark operators over heavy baryons. It is shown that the usually postulated color antisymmetry of these matrix elements is significantly broken. The flavor-singlet shift of the inclusive decay rates of b baryons due to spectator effects is shown to be strongly suppressed in the leading-logarithmic approximation. Combined with the results for the flavor-nonsinglet splittings, this observation allows us to argue, in a less model-dependent way than before, that within the present understanding of spectator effects it is highly unlikely that the lifetimes of the ${\ensuremath{\Lambda}}_{b}$ and the ${B}_{d}$ can be split by more than 10%.

High-energy Scattering in Gauge Theories and Integrable Spin Chains

In the leading log approximation and at large NC the interaction of two fermionic and one gluonic reggeons is described by an integrable system corresponding to an open spin chain.

Relationship between the cross section for deep-inelastic scattering and the cross section for inclusive annihilation

Arguments have been presented that suggest that available experimental data on the structure functions for the processes ep → eX and e + e − → p( $$\bar p$$ )X do not confirm the so-called reciprocity relation, which was obtained in the leading-logarithm approximation of perturbation theory. It has also been shown that the asymptotic relationship between the above processes that was obtained on the basis of more general considerations is compatible with existing data.

A QED Shower Including the Next-to-Leading Order Logarithmic Correction in e+e- Annihilation

We develop an event generator, NLL-QEDPS, based on the QED shower including the next-to-leading logarithm correction in the e^+e^- annihilation. The shower model is the Monte Carlo technique to solve the renormalization group equation so that they can calculate contributions of alpha^m log^n(S/m_e^2) for any m and n systematically. Here alpha is the QED coupling, m_e is the mass of electron and S is the square of the total energy in the e^+e^- system. While the previous QEDPS is limited to the leading logarithm approximation which includes only contributions of (alpha log(S/m_e^2))^n, the model developed here contains terms of alpha(alpha log(S/m_e^2))^n, the the next-to-leading logarithm correction. The shower model is formulated for the initial radiation in the e^+e^- annihilation. The generator based on it gives us events with q^2, which is a virtual mass squared of the virtual photon and/or Z-boson, in accuracy of 0.04%, except for small q^2/S.

Vector mesons in the extended chiral quark model

We extend our previous formulation of low-energy QCD in terms of an effective lagrangian containing operators of dimensionality $d\le 6$ constructed with pseudoscalars and quark fields, describing physics below the scale of chiral symmetry breaking. We include in this paper the vector and axial-vector channels. We follow closely the Extended Chiral Quark Model approach and consistently work in the large-$N_c$ and leading log approximation and take into account the constraints from chiral symmetry and chiral symmetry restoration. The optimal fit of all parameters gives further support to a heavy scalar meson with a mass $\sim 1$ GeV and a value of the axial pion-quark coupling constant $g_A \simeq 0.55$ to 0.66, depending on some assumptions concerning the Weinberg sum rules.

Formula omitted] total cross-section in the dipole picture of BFKL dynamics

The total γ ∗γ ∗ cross-section is derived in the Leading Order QCD dipole picture [1] of BFKL dyamics [2], and compared with the one from 2-gluon exchange. The Double Leading Logarithm approximation of the DGLAP cross-section is found to be small in the phase space studied. Cross sections are calculated for realistic data samples at the e + e − collider LEP and a future high energy linear collider. Next to Leading order corrections to the BFKL evolution have been determined phenomelologically, and are found to give very large corrections to the BFKL cross-section, leading to a reduced sensitivity for observing BFKL effects.