On the infrared freezing of perturbative QCD in the Minkowskian region

The infrared freezing of observables is known to hold at fixed orders of perturbative QCD if the Minkowskian quantities are defined through the analytic continuation from the Euclidean region. In a recent paper [1] it is claimed that infrared freezing can be proved also for Borel resummed all-orders quantities in perturbative QCD. In the present paper we obtain the Minkowskian quantities by the analytic continuation of the all-orders Euclidean amplitudes expressed in terms of the inverse Mellin transform of the corresponding Borel functions [2]. Our result shows that if the principle of analytic continuation is preserved in Borel-type resummations, the Minkowskian quantities exhibit a divergent increase in the infrared regime, which contradicts the claim made in [1]. We discuss the arguments given in [1] and show that the special redefinition of Borel summation at low energies adopted there does not reproduce the lowest order result obtained by analytic continuation.Comment: 19 pages, 1 figur

A novel series solution to the renormalization group equation in QCD

Recently, the QCD renormalization group (RG) equation at higher orders in MS-like renormalization schemes has been solved for the running coupling as a series expansion in powers of the exact 2-loop order coupling. In this work, we prove that the power series converges to all orders in perturbation theory. Solving the RG equation at higher orders, we determine the running coupling as an implicit function of the 2-loop order running coupling. Then we analyze the singularity structure of the higher order coupling in the complex 2-loop coupling plane. This enables us to calculate the radii of convergence of the series solutions at the 3- and 4-loop orders as a function of the number of quark flavours $n_{\rm f}$. In parallel, we discuss in some detail the singularity structure of the ${\bar{\rm MS}}$ coupling at the 3- and 4-loops in the complex momentum squared plane for $0\leq n_{\rm f} \leq 16$. The correspondence between the singularity structure of the running coupling in the complex momentum squared plane and the convergence radius of the series solution is established. For sufficiently large $n_{\rm f}$ values, we find that the series converges for all values of the momentum squared variable $Q^2=-q^2>0$. For lower values of $n_{\rm f}$, in the ${\bar{\rm MS}}$ scheme, we determine the minimal value of the momentum squared $Q_{\rm min}^2$ above which the series converges. We study properties of the non-power series corresponding to the presented power series solution in the QCD Analytic Perturbation Theory approach of Shirkov and Solovtsov. The Euclidean and Minkowskian versions of the non-power series are found to be uniformly convergent over whole ranges of the corresponding momentum squared variables.Comment: 29 pages,LateX file, uses IOP LateX class file, 2 figures, 13 Tables. Formulas (4)-(7) and Table 1 were relegated to Appendix 1, some notations changed, 2 footnotes added. Clarifying discussion added at the end of Sect. 3, more references and acknowledgments added. Accepted for publication in Few-Body System

Analogs of noninteger powers in general analytic QCD

In contrast to the coupling parameter in the usual perturbative QCD (pQCD), the coupling parameter in the analytic QCD models has cuts only on the negative semiaxis of the Q^2-plane (where q^2 = -Q^2 is the momentum squared), thus reflecting correctly the analytic structure of the spacelike observables. The Minimal Analytic model (MA, named also APT) of Shirkov and Solovtsov removes the nonphysical cut (at positive Q^2) of the usual pQCD coupling and keeps the pQCD cut discontinuity of the coupling at negative Q^2 unchanged. In order to evaluate in MA the physical QCD quantities whose perturbation expansion involves noninteger powers of the pQCD coupling, a specific method of construction of MA analogs of noninteger pQCD powers was developed by Bakulev, Mikhailov and Stefanis (BMS). We present a construction, applicable now in any analytic QCD model, of analytic analogs of noninteger pQCD powers; this method generalizes the BMS approach obtained in the framework of MA. We need to know only the discontinuity function of the analytic coupling (the analog of the pQCD coupling) along its cut in order to obtain the analytic analogs of the noninteger powers of the pQCD coupling, as well as their timelike (Minkowskian) counterparts. As an illustration, we apply the method to the evaluation of the width for the Higgs decay into b+(bar b) pair.Comment: 29 pages, 5 figures; sections II and III extended, appendix B is ne

Ten years of the Analytic Perturbation Theory in QCD

The renormalization group method enables one to improve the properties of the QCD perturbative power series in the ultraviolet region. However, it ultimately leads to the unphysical singularities of observables in the infrared domain. The Analytic Perturbation Theory constitutes the next step of the improvement of perturbative expansions. Specifically, it involves additional analyticity requirement which is based on the causality principle and implemented in the K\"allen--Lehmann and Jost--Lehmann representations. Eventually, this approach eliminates spurious singularities of the perturbative power series and enhances the stability of the latter with respect to both higher loop corrections and the choice of the renormalization scheme. The paper contains an overview of the basic stages of the development of the Analytic Perturbation Theory in QCD, including its recent applications to the description of hadronic processes.Comment: 26 pages, 9 figures, to be published in Theor. Math. Phys. (2007

The Adler Function for Light Quarks in Analytic Perturbation Theory

The method of analytic perturbation theory, which avoids the problem of ghost-pole type singularities and gives a self-consistent description of both spacelike and timelike regions, is applied to describe the "light" Adler function corresponding to the non-strange vector channel of the inclusive decay of the $\tau$ lepton. The role of threshold effects is investigated. The behavior of the quark-antiquark system near threshold is described by using a new relativistic resummation factor. It is shown that the method proposed leads to good agreement with the ``experimental'' Adler function down to the lowest energy scale.Comment: 13 pages, one ps figure, REVTe

Search for squarks and gluinos with the ATLAS detector in final states with jets and missing transverse momentum using √s=8 TeV proton-proton collision data

A search for squarks and gluinos in final states containing high-p T jets, missing transverse momentum and no electrons or muons is presented. The data were recorded in 2012 by the ATLAS experiment in s√=8 TeV proton-proton collisions at the Large Hadron Collider, with a total integrated luminosity of 20.3 fb−1. Results are interpreted in a variety of simplified and specific supersymmetry-breaking models assuming that R-parity is conserved and that the lightest neutralino is the lightest supersymmetric particle. An exclusion limit at the 95% confidence level on the mass of the gluino is set at 1330 GeV for a simplified model incorporating only a gluino and the lightest neutralino. For a simplified model involving the strong production of first- and second-generation squarks, squark masses below 850 GeV (440 GeV) are excluded for a massless lightest neutralino, assuming mass degenerate (single light-flavour) squarks. In mSUGRA/CMSSM models with tan β = 30, A 0 = −2m 0 and μ > 0, squarks and gluinos of equal mass are excluded for masses below 1700 GeV. Additional limits are set for non-universal Higgs mass models with gaugino mediation and for simplified models involving the pair production of gluinos, each decaying to a top squark and a top quark, with the top squark decaying to a charm quark and a neutralino. These limits extend the region of supersymmetric parameter space excluded by previous searches with the ATLAS detector

Inclusive search for same-sign dilepton signatures in pp collisions at root s=7 TeV with the ATLAS detector

An inclusive search is presented for new physics in events with two isolated leptons (e or mu) having the same electric charge. The data are selected from events collected from p p collisions at root s = 7 TeV by the ATLAS detector and correspond to an integrated luminosity of 34 pb(-1). The spectra in dilepton invariant mass, missing transverse momentum and jet multiplicity are presented and compared to Standard Model predictions. In this event sample, no evidence is found for contributions beyond those of the Standard Model. Limits are set on the cross-section in a fiducial region for new sources of same-sign high-mass dilepton events in the ee, e mu and mu mu channels. Four models predicting same-sign dilepton signals are constrained: two descriptions of Majorana neutrinos, a cascade topology similar to supersymmetry or universal extra dimensions, and fourth generation d-type quarks. Assuming a new physics scale of 1 TeV, Majorana neutrinos produced by an effective operator V with masses below 460 GeV are excluded at 95% confidence level. A lower limit of 290 GeV is set at 95% confidence level on the mass of fourth generation d-type quarks

Measurement of the top quark-pair production cross section with ATLAS in pp collisions at \sqrt{s}=7\TeV

A measurement of the production cross-section for top quark pairs(\ttbar) in $pp$ collisions at \sqrt{s}=7 \TeV is presented using data recorded with the ATLAS detector at the Large Hadron Collider. Events are selected in two different topologies: single lepton (electron $e$ or muon $\mu$) with large missing transverse energy and at least four jets, and dilepton ($ee$, $\mu\mu$ or $e\mu$) with large missing transverse energy and at least two jets. In a data sample of 2.9 pb-1, 37 candidate events are observed in the single-lepton topology and 9 events in the dilepton topology. The corresponding expected backgrounds from non-\ttbar Standard Model processes are estimated using data-driven methods and determined to be $12.2 \pm 3.9$ events and $2.5 \pm 0.6$ events, respectively. The kinematic properties of the selected events are consistent with SM \ttbar production. The inclusive top quark pair production cross-section is measured to be \sigmattbar=145 \pm 31 ^{+42}_{-27} pb where the first uncertainty is statistical and the second systematic. The measurement agrees with perturbative QCD calculations.Comment: 30 pages plus author list (50 pages total), 9 figures, 11 tables, CERN-PH number and final journal adde

Measurement of the production of a W boson in association with a charm quark in pp collisions at √s = 7 TeV with the ATLAS detector

The production of a W boson in association with a single charm quark is studied using 4.6 fb−1 of pp collision data at s√ = 7 TeV collected with the ATLAS detector at the Large Hadron Collider. In events in which a W boson decays to an electron or muon, the charm quark is tagged either by its semileptonic decay to a muon or by the presence of a charmed meson. The integrated and differential cross sections as a function of the pseudorapidity of the lepton from the W-boson decay are measured. Results are compared to the predictions of next-to-leading-order QCD calculations obtained from various parton distribution function parameterisations. The ratio of the strange-to-down sea-quark distributions is determined to be 0.96+0.26−0.30 at Q 2 = 1.9 GeV2, which supports the hypothesis of an SU(3)-symmetric composition of the light-quark sea. Additionally, the cross-section ratio σ(W + +c¯¯)/σ(W − + c) is compared to the predictions obtained using parton distribution function parameterisations with different assumptions about the s−s¯¯¯ quark asymmetry

Measurement of the top pair production cross section in 8 TeV proton-proton collisions using kinematic information in the lepton plus jets final state with ATLAS

A measurement is presented of the $t\bar{t}$ inclusive production cross-section in $pp$ collisions at a center-of-mass energy of $\sqrt{s}=8$ TeV using data collected by the ATLAS detector at the CERN Large Hadron Collider. The measurement was performed in the lepton+jets final state using a data set corresponding to an integrated luminosity of 20.3 fb$^{-1}$. The cross-section was obtained using a likelihood discriminant fit and $b$-jet identification was used to improve the signal-to-background ratio. The inclusive $t\bar{t}$ production cross-section was measured to be $260\pm 1{\textrm{(stat.)}} ^{+22}_{-23} {\textrm{(syst.)}}\pm 8{\textrm{(lumi.)}}\pm 4{\mathrm{(beam)}}$ pb assuming a top-quark mass of 172.5 GeV, in good agreement with the theoretical prediction of $253^{+13}_{-15}$ pb. The $t\bar{t}\to (e,\mu)+{\mathrm{jets}}$ production cross-section in the fiducial region determined by the detector acceptance is also reported.Comment: Published version, 19 pages plus author list (35 pages total), 3 figures, 2 tables, all figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/TOPQ-2013-06