Radiative return at NLO and the measurement of the hadronic cross-section in electron–positron annihilation

Electron–positron annihilation into hadrons plus an energetic photon from initial state radiation allows the hadronic cross-section to be measured over a wide range of energies. The full next-to-leading order QED corrections for the cross-section for annihilation into a real tagged photon and a virtual photon converting into hadrons are calculated where the tagged photon is radiated off the initial electron or positron. This includes virtual and soft photon corrections to the process and the emission of two real hard photons: . A Monte Carlo generator has been constructed, which incorporates these corrections and simulates the production of two charged pions or muons plus one or two photons. Predictions are presented for centre-of-mass energies between 1 and 10 GeV, corresponding to the energies of DANE, CLEO-C and B-meson factories. Received: 14 December 2001 / Published online: 5 April 2002     

Predictions for ${\bar \nu} \nu \gamma$ production at LEP

We study predictions for the reaction . The complete one-loop corrections are taken into account and higher order contributions, in particular those for the observed real photons, are added whenever necessary. The event generator MC, a general-purpose Monte Carlo generator for the process based on the method of exclusive exponentiation, is used as the environment. We extend its applicability to the process ,, where the observation of at least a single is required. The exponentiation is implemented in much the same way as for the s-channel process alone. In particular, all photonic effects present in the case of W exchange, which cannot be included in the s-channel exponentiation scheme, are calculated to a finite order only. The real hard photon matrix element is calculated up to . Leading logarithmic contributions of the two-loop corrections and one-loop photonic corrections accompanying real single-photon emission are included. The electroweak corrections are calculated with the DIZET library of the ZFITTER package. Numerical tests and predictions for typical observables are presented. Received: 30 October 2001 / Revised version: 5 March 2002 / Published online: 22 May 2002     

Pion pair production with higher order radiative corrections in low energy $e^+e^-$ collisions

The complete QED initial state (IS), final state (FS) and initial–final state (IFS) interference corrections to the process are presented. Analytic formulae are given for the virtual and for the real photon corrections. The total cross section (), the pion angular distribution () and the invariant mass distribution () are investigated in the regime of experimentally realistic kinematical cuts. It is shown that in addition to the full corrections also the and leading-log photonic corrections as well as the contributions from IS -pair production have to be taken into account if at least per cent accuracy is required. For the data analysis we focus on an inclusive treatment of all photons. The theoretical error concerning our treatment of radiative corrections is then estimated to be 2 per mill for both the measurement of the total cross section and the invariant mass distribution. In addition we discuss the model uncertainty due to the pion substructure. Altogether the precision of the theoretical prediction matches the requirements of low energy experiments like the ones going on at DANE or VEPP-2M. Received: 6 September 2001 / Revised version: 24 January 2002 / Published online: 5 April 2002     

The radiative return at $\phi$- and B-factories: small-angle photon emission at next-to-leading order

The radiative return offers the unique possibility for a measurement of the cross section of electron-positron annihilation into hadrons over a wide range of energies. The large luminosity of present - and B-factories easily compensates for the additional factor of due to the emission of a hard photon. Final states with photons at large angles can be easily identified. The rate for events with collinear photons, however, is enhanced by a large logarithm and allows, in particular at lower energies, for a complementary measurement. The Monte Carlo generator PHOKHARA, which includes next-to-leading order corrections from virtual and real photon emission, has been extended from large photon angles into the collinear region, using recent results for the virtual corrections. In addition, the present version includes final state radiation for muon and pion pair production and final states with four pions. Implications for the experimental analysis at three typical energies, 1.02, 4 and 10.6 GeV, are presented: the magnitude of these new corrections is studied, possibilities for the separation of initial and final state radiation are proposed, and the differences with respect to the previous treatment based on structure functions are investigated. Received: 16 December 2002 / Published online: 26 February 2003 RID="a" ID="a" e-mail: czyz@us.edu.pl RID="b" ID="b" e-mail: grzel@joy.phys.us.edu.pl, Supported in part by "Marie Curie Training Site" at Karlsruhe University RID="c" ID="c" e-mail: jk@particle.uni-karlsruhe.de RID="d" ID="d" e-mail: german.rodrigo@cern.ch, Supported in part by E.U. TMR grant HPMF-CT-2000-00989     

Virtual photon structure

The structure functions of a real photon are calculable in QCD. The leading contribution is proportional to 1n Q², with a coefficient reflecting the gluon flux in a real photon. We investigate this leading term for non-zero target photon mass. In an appropriate limit the gluon content in a virtual photon is found to vanish. The gluon radiative corrections of QCD can thus be turned off by tuning the target photon mass.     

A NLO calculation of the large-p_T photon + photon \to photon + jet cross section

We study the production of an isolated large- photon as well as the production of an isolated prompt photon plus a jet in collisions. Our results are obtained by a NLO Monte Carlo program of partonic event generator type. We discuss the possibilities to constrain the parton densities in the real photon and compare to preliminary OPAL data. Received: 18 December 2001 / Revised version: 21 January 2002 / Published online: 22 February 2002     

Perturbative and non-perturbative QCD corrections to wide-angle Compton scattering

We investigate corrections to the handbag approach for wide-angle Compton scattering off protons at moderately large momentum transfer: the photon–parton subprocess is calculated to next-to-leading order in and contributions from the generalized parton distribution E are taken into account. Photon and proton helicity flip amplitudes are non-zero due to these corrections, which leads to a wealth of polarization phenomena in Compton scattering. Thus, for instance, the incoming photon asymmetry or the transverse polarization of the proton is non-zero, although small. Received: 31 October 2001 / Revised version: 11 December 2001 / Published online: 8 February 2002     

Scanning of the ee\rightarrow \pi\pi cross-section below 1 GeV by radiative events with untagged photon

We discuss an inclusive approach to the measurement of the cross-section by the radiative return method without photon tagging. The essential part of this approach is the choice of rules for event selection which provide rejection of events with 3 (or more) pions and decrease the final-state radiation background. The radiative corrections to the initial-state radiation process are computed for DANE conditions, using the quasi-real electron approximation for both, the cross-section and the underlying kinematics. The two cases of restricted and unrestricted pion phase space are considered. Some numerical calculations illustrate our analytical results. Received: 4 February 2002 / Published online: 5 July 2002     

(Quasi)elastic electron-muon large-angle scattering within the two-loop approximation: Vertex contributions

We consider quasielastic large-angle electron-muon scattering at high energies with radiative corrections up to the two-loop level. The lowest order radiative corrections arising from the one-loop virtual photon emission and a real soft emission are presented within a power accuracy. Two-loop corrections are supposed to be of three gauge-invariant classes. One of them, the so-called vertex contribution, is given in the logarithmic approximation. The relation to the renormalization group approach is discussed.     

The QCD pomeron in ultraperipheral heavy ion collisions: I. The double $J/\Psi$ production

The contribution of the QCD pomeron to the process is discussed. We focus on the photon-photon collision, with the quasi-real photon coming from the Weizs?cker-Williams spectrum of the nuclei. We calculate the cross section for this process considering the solution of the LLA BFKL equation at zero momentum transfer using a small t approximation for the differential cross section of the subprocess. Furthermore, the impa ct of non-leading corrections to the BFKL equation is also analyzed. In both cases the cross section is found to increase with the energy, predicting considerable values for the LHC energies. Moreover, we compare our results with the Born two-gluon approximation, which is energy independent at the photon level. Our results indicate that the experimental analyses of this process can be useful to discriminate the QCD dynamics at high energies. Received: 12 December 2002 / Published online: 7 March 2003 RID="a" ID="a" e-mail: barros@ufpel.tche.br RID="b" ID="b" e-mail: magnus@if.ufrgs.br     

(Quasi)elastic large-angle electron-muon scattering in the two-loop approximation: Contributions of the eikonal type

A part of the eikonal-type contributions to the eμ large-angle high-energy scattering cross section is considered in a quasielastic experimental setup. In addition to virtual corrections, we examine inelastic processes with emission of one and two soft real photons and soft lepton and pion pairs. Virtual photon contributions are given within a logarithmic accuracy. Box-type Feynman amplitudes with leptonic and a hadronic vacuum polarization insertion and double-box ones are considered explicitly. Wherever appropriate, the analytic expressions obtained are compared with those predicted by the structure function approach.     

Production of hard photons and jets in deep inelastic lepton proton scattering at order O(\alpha_s)

We calculate the corrections to the production of a hard and isolated photon accompanied by one or two jets in deep inelastic lepton nucleon scattering at HERA. Numerical results are presented and the potential of this process for studies of parton distribution functions is discussed. Received: 18 December 1997 / Published online: 10 March 1998     

CompleteO(α) corrections to polarized Compton scattering

General expressions for Compton scattering and itsO(α) real and virtual corrections are given for electron and photon beams with arbitrary polarization. The expressions obtained are suitable for use in Monte Carlo simulations of Compton polarimeters planned for polarizede ⁺ e ^? colliders. The basis for the calculation is the spinor techniques recently applied to photon and gluon bremsstrahlung. The practical application of these techniques for massive fermions is discussed.     

Resummation of angular dependent corrections in spontaneously broken gauge theories

Recent investigations of electroweak radiative corrections have revealed the importance of higher order contributions in high energy processes, where the size of typical corrections can exceed those associated with QCD considerably. Beyond one loop, only universal (angular independent) corrections are known to all orders except for massless processes, where also angle dependent corrections exist in the literature. In this paper we present general arguments for the consistent resummation of angle dependent subleading (SL) logarithmic corrections to all orders in the regime where all invariants are still large compared to the gauge boson masses. We discuss soft isospin correlations, fermion mass and gauge boson mass gap effects, the longitudinal and Higgs boson sector as well as mixing contributions including CKM effects for massive quarks. Two loop results for the right handed Standard Model are generalized in the context of the high energy effective theory based on the standard model Lagrangian in the symmetric basis with the appropriate matching conditions to include the soft QED regime. The result is expressed in exponentiated operator form in a CKM extended isospin space in the symmetric basis. Thus, a full electroweak SL treatment based on the infrared evolution equation method is formulated for arbitrary high energy processes at future colliders. Comparisons with known results are presented. Received: 12 February 2002 / Revised version: 7 March 2002 / Published online: 8 May 2002     

Radiative return at $\Phi$ - and B-factories: FSR for muon pair production at next-to-leading order

Muon pair production through the radiative return is of importance for a measurement of the hadronic production cross section in two ways: it provides an independent calibration and it may give rise to an important background for the measurement of the pion form factor. With this motivation the Monte Carlo event generator PHOKHARA is extended to include next-to-leading order radiative corrections to the reaction . Furthermore, virtual ISR corrections to FSR from pions are introduced, which extends the applicability of the generator into a new kinematical regime. Finally, the effect of photon vacuum polarization is introduced into this new version of the generator.Received: 8 April 2004, Revised: 3 December 2004, Published online: 25 January 2005Work supported in part by BMBF under grant number 05HT9VKB0, EC 5th Framework Programme under contract HPRN-CT-2002-00311 (EURIDICE network), TARI project HPRI-CT-1999-00088, Polish State Committee for Scientific Research (KBN) under contract 2 P03B 017 24, BFM2002-00568, Generalitat Valenciana under grant GRUPOS03/013, and MCyT under grant FPA-2001-3031.     

Dispersion corrections to the forward Rayleigh scattering amplitudes around the L‐shell of tantalum and lead

Dispersion corrections to the forward Rayleigh scattering amplitudes of tantalum and lead in the photon energy range 6.4–24.14 keV were determined by a numerical evaluation of the dispersion integral that relates them through the optical theorem to the photoelectric cross‐sections. The photoelectric cross‐sections were extracted by subtracting the coherent and incoherent scattering contribution from the measured total attenuation cross‐section, using a high‐resolution, high‐purity germanium detector in a narrow‐beam good geometry setup. The real part of the dispersion correction to which the relativistic corrections calculated by Kissel and Pratt (S‐matrix approach) or Creagh and McAuley (multipole corrections) have been included are in better agreement with the available theoretical values than those values to which the relativistic corrections calculated by Cromer and Liberman (dipole corrections) are added. Copyright © 2006 John Wiley & Sons, Ltd.     

New approach to quantum corrections in synchrotron radiation

Owing to a recent controversy over the importance of the second-order quantum corrections to the power spectrum of synchrotron radiation, we here reexamine this question by using a proper time method to calculate the forward Compton scattering of a real photon on a spin-0 charged particle in external magnetic fields. This approach, aside from being the simplest method found so far, has the feature that it resembles the classical procedure so that the quantum corrections can be identified at every stage of the computation. The option of being able to perform first the angular integration before doing the proper time integral enables us to simplify the calculation and to obtain the quantum corrections unambiguously. We find that the criterion for the quantum corrections to be important is the same as that found more than two decades ago.     

QCD anatomy of B\to X_s\gamma decays

We present an updated next-to-leading order analysis of the branching ratio and photon spectrum, including consistently the effects of Fermi motion in the heavy-quark expansion. For the Standard Model, we obtain for the integral over the high-energy part of the photon spectrum with GeV, where the first error reflects the uncertainty in the input parameters, and the second one the uncertainty in the calculation of Fermi motion. This prediction agrees with the CLEO measurement of the same quantity within one standard deviation. From a reanalysis of the CLEO data, we obtain for the total branching ratio using the measured rate above 2.2 GeV, and using a fit to the photon energy spectrum. Both values are consistent with the Standard Model prediction of . Our analysis contains an improved discussion of renormalization-scale dependence and QED corrections. We also study the sensitivity of the branching ratio and photon spectrum to hadronic parameters such as the b-quark mass, and to possible contributions from New Physics beyond the Standard Model. Received: 13 May 1998 / Published online: 3 September 1998