Evidence for Three-Gluon Coupling ine+e−Annihilation

Abstract

The forward-backward asymmetry of the normal to the event plane for e e" annihilation into three jets in higher-order perturbation-theory (^ o> s 2 ) quantum chromodynamics is calculated. This could serve to establish the non-Abelian gluon self-couplings.PACS numbers: 14.80. Kx, 12.40.Cc, 13.65.+ i Quantum chromodynamics (QCD) predicts a multijet structure in e + e~ annihilation into hadrons, 1 " 8 which has been nicely confirmed by the recent PETRA data. 9 " 11 The mere observation of three-(and higher-) jet final states, however, does not prove QCD. Almost any other field theory with a small fixed-point coupling will lead to a similar structure, and a quantitative test of QCD at this level might be opposed by nonperturbative and the unavoidable higher-twist contributions. 2 ' 12 In order to furnish unambiguous evidence of perturbative QCD, it is essential to construct observables that are sensitive to the distinctive elements of the theory. Since QCD shows its full gauge structure only in order a s 2 , these must either involve four-jet final states or go beyond the tree-graph level. In this note we propose a discriminative test of QCD falling into the latter category, which has the unique feature of giving direct indication of the chromodynamic gluon selfcouplings and which appears to be feasible experi-:mentally.The observables we discuss concern three-jet production in e*e~ annihilation. One requires longitudinally polarized beams, the other the presence of weak and electromagnetic interferences.Let us first assume that the electrons and/or positrons are longitudinally polarized. Electrons and positrons naturally tend to polarize themselves in the direction of the magnetic field, i.e., transversally, and it seems feasible to rotate the transverse polarization into a longitudinal one. 13 The achievement of longitudinal polarization is also important in the exploration of weak-interaction contributions to the e^e" annihilation process. It allows the extraction of physical information similar to that obtainable from helicity measurements of the final state. At DESY PETRA (-19 GeV/beam) and SLAC PEP (-18 GeV/beam) energies and higher we can hope for a large sample of cleanly separated three-jet events. The cross section for e*e~ -^y^^qip^ip^ip^) for longitudinally polarized beams is given by 5 * 14 2ir d 4 G dcos6dxdx 1 dx •=i-(l +Z)(1 + cos 2 e)f Q u + j_ (1 +z)sin 2 e J!£L_ + |-(1+Z)sin 2 0cos2x dx 1 dx 2 d 2 o T dx±dx 2 dx ± dx 2 2V2" 3 (l + z)sin2 ec osx^-+4.isin0 8inx^-, Z = S ( -¥ +) , L = 4 ( -) +l (+) , h 7f J lA/Jv -I LisJv €}(1) where x lt2 = 2E U2 /(q 2 ) 1/2 and ^ and ^ denote the longitudinal polarization of the electron and positron beam, respectively. For pure helicity states £®=±h®, where ft (±) is the helicity of e ± , respectively. The first part of the cross section (1) being proportional to (l+Z) [i.e., the remnant of (1) for L = 0] is familiar. 5 The angle 6 is the polar angle between the electron beam direction and the direction of the fastest of either quark or antiquark jet, while x ...

Comparison of phase space slicing and dipole subtraction methods for $\gamma^* \rightarrow Q\bar{Q}$

“…We now show some results for the fully inclusive cross section, as well as some differential distributions for process (1). We study what effect including the T i contributions has on the s min dependence of the results, and shall see that including all T i removes all s min dependence.…”

“…The matrix elements for the NLO cross section for process (1) are not very complicated, so we can be explicit. At lowest order we have…”

“…There are essentially two types of methods to effect this cancellation. The phase space slicing (PSS) method [1,2,3,4] is based on approximating the matrix elements and the phase space integration measure in boundary regions of phase space so integration may be carried out analytically. The subtraction method [5,6,7] is based on adding and subtracting counter terms designed to approximate the real emission amplitudes in the phase space boundary regions on the one hand, and to be integrable with respect to the momentum of an unresolved parton.…”

Two-loop amplitudes with nested sums: Fermionic contributions toe+e−→qq¯Moch1, Uwer2, Weinzierl3 2002Phys. Rev. D720570View full textAdd to dashboardCite

“…The one-loop box integral is defined by 3 . This integral can be expressed in terms of a combination of Appell functions of the second kind and the series representation is given by: …”

A new calculation of the NLO energy-energy correlation function

“…It was first applied in a NLO calculation of the thrust distribution in e + e − annihilation by Fabricius, Schmidt, Schierholz and Kramer [15]. In this method the integration region in (4) is divided into two parts, 0 < x < y min and y min < x < 1.…”