A new Monte Carlo model is proposed for radiative corrections to Bhabha scattering by extending QEDPS developed for multi-photon emission in muon pair production in $e^+e^-$ annihilation. This is the QED version of the model known as parton shower in QCD. The main difference between muon pair production and Bhabha scattering is that the latter cross section shows the singularity of $1/t^2$. A shower algorithm is constructed on the radiator formalism modified in a suitable form for this singularity. Some results of the model are presented and compared with $O(α)$ corrections.
The Standard Model radiative corrections to the Bhabha scattering process are considered within the one-loop approximation. Both virtual corrections and corrections for the real photon emission are taken into consideration. The calculation was performed at the energy assumed at the Belle II (Japan) facility.
Theoretical predictions for Bhabha scattering observables are presented including complete one-loop electroweak radiative corrections. A longitudinal polarization of the initial beams is taken into account. Numerical results for the asymmetry $A_{LR}$ and the relative correction $δ$ are given for the set of the energy $E_{cm}=250, 500, 1000$~GeV with various polarization degrees.
The lowest order QED radiative corrections to the radiative large angle Bhabha scattering process in the region where all kinematic invariants are large compared to the electron mass are considered. We show that the leading logarithmic corrections do not factorize before the Born cross section, contrary to the picture assumed in the renormalization group approach. The leading and non leading contributions for typical kinematics of the hard process at the energy of the $Φ$ factory are estimated.
SABSPV is a code designed to perform a theoretical evaluation of small-angle Bhabha scattering cross sections by suitably matching fixed-order perturbative calculations and structure-function techniques. The implementation of realistic experimental triggering conditions is achieved by using Monte Carlo integration.
A Monte Carlo event generator is presented. An original algorithm is developed to simulate electron-positron scattering at energies and momentum transferred much more than the electron mass. The first-order electroweak radiative corrections are included completely. Higher order corrections are taken into account by means of electron structure functions.
We present an approximation to the matrix element for the process e+e- --> e+e-gamma, appropriate to the situation where one or both of the fermions are scattered over very small angles. The leading terms in the situation where all scattering angles are small contains not only terms quadratic in the electron mass, but also quartic and even sextic terms must be included. Special attention is devoted to the numerical stability of the resultant expression. Its relation to several existing formulae is discussed.
We review the status of Monte Carlo generators presently used for simulations of the large-angle Bhabha process at electron-positron colliders of moderately high energy (flavour factories), operating at centre-of-mass energies between about 1 GeV and 10 GeV. It is shown how the theoretical accuracy reached by present Bhabha programs for physics at flavour factories is at the level of 0.1% and, therefore, comparable with that reached about a decade ago for luminosity monitoring through small-angle Bhabha scattering at LEP.
LABSMC Monte Carlo event generator is used to simulate Bhabha scattering at high energies. Different sources of radiative corrections are considered. The resulting precision is discussed.
A fast and simple Monte Carlo program is presented that simulates single Bremsstrahlung in Bhabha scattering, e+e- --> e+e-gamma, without constraints on scattering angles. This allows the study of this process at arbitrarily small, or even vanishing, scattering angles. Experimental cuts can be imposed on an event-by-event basis, allowing for detailed studies of the process as a limitation to beam lifetimes, or a luminosity-measuring device, in e+e- storage rings. As an application, we show that the easy introduction of a cutoff parameter, corresponding to the characteristic distance between pa…
The luminosity measurement at the projected International Linear $e^+e^-$ Collider ILC is planned to be performed with forward Bhabha scattering with an accuracy of the order of $10^{-4}$. A theoretical prediction of the differential cross-section has to include one-loop weak corrections, with leading higher order terms, and the complete two-loop QED corrections. Here, we present the weak part and the virtual one-loop photonic corrections. For the photonic corrections, the expansions in $ε= (4-d)/2$ are derived with inclusion of the terms of order $ε$ in order to match the two-loop accuracy. F…
The process of large-angle high energy electron-positron scattering with emission of one hard photon almost collinear to one of the charged particles momenta is considered. The differential cross section with radiative corrections due to emission of virtual and soft real photons calculated to a power accuracy is presented. Emission of two hard photons and total expressions for radiative correction are given in leading logarithmical approximation. The latter are illustrated by numeric estimates. A relation of the results with structure function formalism is discussed.
We describe the details of the evaluation of the two-loop radiative photonic corrections to Bhabha scattering. The role of the corrections in the high-precision luminosity determination at present and future electron-positron colliders is discussed.
A new Monte Carlo event generator for wide angle Bhabha scattering and muon pair production in $e^+e^-$ collisions is described. The program includes complete one-loop electroweak corrections, and QED radiative corrections. The O($α$) QED correction uses the exact matrix element. Higher order QED corrections are included in an improved soft photon approximation with exponentiation of initial state radiation. Events are generated in the full phase space of the final state including explicit mass effects in the region of collinear mass singularities. The program is intended for centre of mass en…
The two-loop radiative photonic corrections to the Bhabha scattering are computed in the leading order of the small electron mass expansion up to nonlogarithmic term. After including the soft photon bremsstrahlung we obtain the infrared finite result for the differential cross section, which can be directly applied to precise luminosity determination of the present and future $e^+e^-$ colliders.
Soft and virtual loop photonic contributions to the second order next-to-leading QED radiative corrections to Bhabha scattering are calculated with help of the renormalization group approach. The results are in agreement with earlier calculations, where other methods were used. Scale dependence and the present theoretical accuracy of Bhabha cross section description are discussed.
We present the Monte Carlo program BHAGEN95, for calculating the cross-section of the Bhabha scattering process at LEP1/SLC and LEP2 energies, usable with continuity from small to large-angle configurations. We discuss some improvements in the event generator BHAGEN94, which is now part of the new code. In particular the weak and QCD corrections are implemented up to two loops for the relevant contributions, and the emission of one hard photon is treated exactly. We have included all the radiative corrections which are necessary to obtain, for a typical experimental event selection, a precisio…
For the small-angle Bhabha-scattering process, we consider the error budget for the calculation of the LEP/SLC luminosity in the Monte Carlo event generator BHLUMI 4.04, from the standpoint of new calculations of exact results for the respective O(alpha**2) photonic corrections in the context of the Yennie-Frautchi-Suura exponentiation. We find that an over-all precision tag for the currently available program BHLUMI 4.04 can be reduced from 0.11% to 0.061% at LEP1 and from 0.25% to 0.122% at LEP2. For the large-angle Bhabha process, we present the Monte Carlo program BHWIDE and compare its pr…
A critical assessment is given of the theoretical uncertainty in the predicted cross-sections for large-angle Bhabha scattering at LEP 1, with or without t-channel subtraction. To this end a detailed comparison is presented of the results obtained with the programs ALIBABA and TOPAZ0. Differences in the implementation of the radiative corrections and the effect of missing higher-order terms are critically discussed.
Upper limits on doubly charged bilepton couplings and masses are extracted from LEP data for Bhabha scattering at energy range $\sqrt{s}=183-202$ GeV using standard model program ZFITTER which calculates radiative corrections. We find that $g_{L}^{2}/M_{L}^{2}<O(10^{-5})GeV^{-2}$ at 95% C.L. for scalar and vector bileptons.
We present O(alpha) YFS exponentiated results for wide angle Bhabha scattering at LEP/SLC energies using a new Monte Carlo event generator BHWIDE 1.xx. Our calculations include two options for the pure weak corrections, as presented in Beenakker et al. and in Bohm et al. From comparison with the results of Beenakker et al., Montagna et al. and Cacciari et al., we conclude that the total precision of our BHWIDE results is 0.3% (0.5%) in the LEP1/SLC regime within +-100 MeV (+2.75/-2.5 GeV) of the Z peak. For LEP2, the corresponding precision is currently estimated at 1.5%; the latter could be i…
BHAGEN-1PH is a FORTRAN program providing fast Monte Carlo event generation of the process $e^+ e^- \to e^+ e^- γ$, within electroweak theory, for both unpolarized beams and also for the longitudinally polarized electron beam. The program is designed for final leptons outside a small cone around the initial leptons direction and has a new algorithm allowing also for a fast generation of non collinear initial and final emission, as well as for asymmetric and different angular cuts for final leptons.
This manual describes version 2.2 of the Monte Carlo event generator UNIBAB for large angle Bhabha scattering at LEP and SLC. UNIBAB implements higher order electromagnetic radiative corrections and the effects of soft photon exponentiation in a photon shower approach. Weak corrections are included through the use of an electroweak library.
Radiative corrections due to the production of virtual as well as real soft and hard pairs in small-angle Bhabha scattering are calculated analytically. Both the collinear and the semi-collinear kinematical regions of hard pair production are considered. The calculation, within the leading and next-to-leading logarithmic approximation, provides an accuracy of O(0.1%). Numerical results show that the effects of pair production have to be taken into account for a luminosity determination accurate to O(0.1%) at LEP.
The method for obtaining functional equations, recently proposed by one of the authors, is applied to one-loop box integrals needed in calculations of radiative corrections to heavy-quark production and Bhabha scattering. We present relationships between these integrals with different arguments and box integrals with all propagators being massless. It turns out that functional equations are rather useful for finding imaginary parts and performing analytic continuations of Feynman integrals. For the box master integral needed in Bhabha scattering, a new representation in terms of hypergeometric…
We will describe radiative corrections to bremsstrahlung, focusing on applications to luminosity, fermion pair production, and radiative return at high-energy e+ e- colliders. A precise calculation of the Bhabha luminosity process was essential at SLC and LEP, and will be equally important in ILC physics. We will review the exact results for two-photon radiative corrections to Bhabha scattering which led to the precision estimates for the BHLUMI MC. We will also compare the implementation of the virtual photon correction to bremsstrahlung for fermion pair production in the KK MC to similar exa…
Analytical method is applied for description of the small angle Bhabha scattering at LEP1. Inclusive event selection for asymmetrical wide-narrow circular detectors is considered. The QED correction to the Born cross-section is calculated with leading and next-to-leading accuracy in the second order of perturbation theory and with leading one --- in the third order. All contributions in the second order due to photonic radiative corrections and pair production are calculated starting from essential Feynman diagrams. The third order correction is computed by means of electron structure function…
We present the results of our calculations to a one, two, and three loop approximation of the e$^+$e$^-$$\rightarrow$e$^+$e$^-$ Bhabha scattering cross-section at small angles. All terms contributing to the radiatively corrected cross-section, within an accuracy of $δσ/ σ= 0.1 \% $, are explicitely evaluated and presented in an analytic form. $O(α)$ and $O(α^2)$ contributions are kept up to next-to-leading logarithmic accuracy, and $O(α^3)$ terms are taken into account to the leading logarithmic approximation. We define an experimentally measurable cross-section by integrating the calculated d…
Analitical calculations have been used to describe the calorimeter event selection in small-angle electron-positron scattering at LEP1. The first-order QED correction to the Born cross-section has been derived with leading log and the next-to-leading log approximations. The second- and the third-order corrections were computed with leading accuracy. The present analytical results are illustated by Tabeles and compared with the corresponding results obtained with the Monte Carlo generator BHLUMI.
A critical subject in fully differential QED calculations originates from numerical instabilities due to small fermion masses that act as regulators of collinear singularities. At next-to-next-to-leading order (NNLO) a major challenge is therefore to find a stable implementation of numerically delicate real-virtual matrix elements. In the case of Bhabha scattering this has so far prevented the development of a fixed-order Monte Carlo at NNLO accuracy. In this paper we present a new method for stabilising the real-virtual matrix element. It is based on the expansion for soft photon energies inc…
The cross-section of (quasi-)elastic large-angle electron-positron scattering at high energies is calculated. Radiative corrections of the orders O(α^2 L^2) and O(α^2 L), besides pure two-loop box contributions, are explicitly calculated. In the second order we considered the following sources of corrections: 1) Virtual photonic corrections coming from squares of 1-loop level amplitudes and their relevant interferences (vertex-type and box-type Feynman diagrams). 2) Double soft photon emission and one-loop corrections to single soft photon emission. The results are presented in an analytical f…
The accurate knowledge of luminosity at e^+ e^- flavour factories requires the precision calculation of the Bhabha cross section at large scattering angles. In order to achieve a theoretical accuracy at the 0.1% level, the relevant effect of QED radiative corrections is taken into account in the framework of the Parton Shower method, which allows exclusive event generation. On this scheme, a Monte Carlo event generator (BABAYAGA) is developed for data analysis. To test the reliability of the approach, a benchmark calculation, including exact O(alpha) corrections and higher-order leading logari…
In this paper we present a numerical implementation of the one-loop QED corrections to the hard-bremsstrahlung process e- e+ \to e- e+ gamma. These corrections can be included in the Monte Carlo event generators employed for simulating Bhabha scattering events at low-energy high-luminosity electron-positron colliders. The calculation is performed by employing the reduction method developed by Ossola, Papadopoulos and Pittau. Our results are implemented in a modular code for the numerical evaluation of the scattering amplitudes for any given phase-space point. In a similar way, we also evaluate…
We present the exact O(alpha) correction to the process e+ e- -> e+ e- + gamma in the low angle luminosity regime at SLC/LEP energies. We give explicit formulas for the completely differential cross section. As an important application, we illustrate the size of the respective corrections of O(alpha^2) to the SLC/LEP luminosity cross section. We show explicitly that our results have the correct infrared limit, as a cross-check. Some comments are made about the implementation of our results in the framework of a Monte Carlo event generator. This latter implementation will appear elsewhere.
Contributions from the reaction e+e- --> pi+pi- e+e- to the pion form factor measurement via radiative return method are discussed basing on the results of a Monte Carlo generator (EKHARA). The generator contains contributions from the initial and final state emission of a e+e- pair from e+e- --> pi+pi- production diagrams and the pi+pi- pair production from space-like and time-like Bhabha diagrams. A detailed study is performed for the Phi- factory energy. Tests of the generation procedure are also presented.
In this thesis exact results on O(alpha^2) single bremsstrahlung corrections to low angle Bhabha scattering at LEP/SLC energies are given. The calculation represents the last outstanding theoretical second order subleading electroweak contribution for that process, needed to determine the experimental luminosity at second generation LEP detectors below the 0.1% precision threshold. The exact, fully differential result is obtained by employing analytical as well as computer-algebraic methods and includes terms up to O(0.05%) relative to the Born cross section. The initial output of over 20,000 …
The luminosity determination of electron-positron colliders operating in the region of low-lying hadronic resonances (E_cm ~ 1-10 GeV), such as BEPC/BES, DAPHNE, KEKB, PEP-II and VEPP-2M, requires the precision calculation of the Bhabha process at large scattering angles. In order to achieve a theoretical accuracy at a few 0.1% level, the inclusion of radiative corrections is mandatory. The phenomenologically relevant effect of QED corrections is taken into account in the framework of the Parton Shower (PS) method, which is employed both for cross section calculation and event generation. To t…
This work deals with the computation of electron pair correction to small angle Bhabha scattering, in order to contribute to the improvement of luminometry precision at LEP/SLC below 0.1% theoretical accuracy. The exact QED four-fermion matrix element for $e^+e^-\to e^+e^-e^+e^-$, including all diagrams and mass terms, is computed and different Feynman graph topologies are studied to quantify the error of approximate calculations present in the literature. Several numerical results, obtained by a Monte Carlo program with full matrix element, initial-state radiation via collinear structure func…
Virtual fermionic N_f = 1 and N_f = 2 contributions to Bhabha scattering are combined with realistic real corrections at next-to-next-to-leading order in QED. The virtual corrections are determined by the package bha_nnlo_hf, and real corrections with the Monte Carlo generators Bhagen-1Ph, Helac-Phegas and Ekhara. Numerical results are discussed at the energies of and with realistic cuts used at the Phi factory DAFNE, at the B factories PEP-II and KEK, and at the charm/tau factory BEPC II. We compare these complete calculations with the approximate ones realized in the generator BabaYaga@NLO u…
A comparison of theoretical results on NNLO leptonic and hadronic corrections to Bhabha scattering with the Monte Carlo generator BabaYaga@NLO used at meson factories is given. Complete NLO virtual corrections to the $e^+e^- \to μ^+ μ^- γ$ process are discussed.
Recently, various cross sections of e+e- annihilation into hadrons were accurately measured in the energy range from 0.37 to 1.39 GeV with the CMD-2 detector at the VEPP-2M collider. In the pi+pi- channel a systematic uncertainty of 0.6% has been achieved. A Monte-Carlo Generator Photon Jets (MCGPJ) was developed to simulate events of the Bhabha scattering as well as production of two charged pions, kaons and muons. Based on the formalism of Structure Functions, the leading logarithmic contributions related to the emission of photon jets in the collinear region are incorporated into the MC gen…
We have used YFS Monte Carlo techniques to obtain per-mil level accuracy for the Bhabha scattering cross section used in the luminosity monitor in electro-weak scattering experiments. We will describe techniques for extending these methods for use in the W production luminosity cross section for hadron colliders.
We describe packages for the calculation of radiative corrections to two-fermion production at colliders. The packages use DIANA, and also QGRAF, FORM, Fortran, and further unix/linux tools. The one-loop calculations in the Standard Model are highly automatized with the package aITALC. Further, the automatic determination of all the matrix elements for two-loop corrections to massive Bhabha scattering in QED and the classification of their topologies and prototypes is done with DIANA. A generalization to the Standard Model is straightforward.
For high precision measurements of K decays, the presence of radiated photons cannot be neglected. The Monte Carlo simulations must include the radiative corrections in order to compute the correct event counting and efficiency calculations. In this paper we briefly describe a method for simulating such decays.
The Monte Carlo generator MERADGEN 1.0 for the simulation of radiative events in parity conserving doubly-polarized Moller scattering has been developed. Analytical integration wherever it is possible provides rather fast and accurate generation. Some numerical tests and histograms are presented.
A new Monte-Carlo generator including real radiated photons in DIS on polarized and unpolarized targets is presented. Analytical and numerical tests are performed and discussed in details.
The structure and algorithms of the Monte-Carlo generator ELRADGEN 2.0 designed to simulate radiative events in polarized ep-scattering are presented. The full set of analytical expressions for the QED radiative corrections is presented and discussed in detail. Algorithmic improvements implemented to provide faster simulation of hard real photon events are described. Numerical tests show high quality of generation of photonic variables and radiatively corrected cross section. The comparison of the elastic radiative tail simulated within the kinematical conditions of the BLAST experiment at MIT…
We discuss the theoretical approach and practical algorithms for simulation of radiative events in elastic ep-scattering. A new Monte Carlo generator for real photon emission events in the process of elastic electron-proton scattering is presented. We perform a few consistency checks and present numerical results.
We analyse the possibility of detecting visible photons from a hypothetical radiative decay of solar neutrinos. Our study is focused on the simulation of such measurements during total solar eclipses and it is based on the BP2000 Standard Solar Model and on the most recent experimental information concerning the neutrino properties.
Bhabha scattering is one of the processes at the ILC where high precision data will be expected. The complete NNLO corrections include radiative loop corrections, with contributions from Feynman diagrams with five external legs. We take these diagrams as an example and discuss several features of the evaluation of pentagon diagrams. The tensor functions are usually reduced to simpler scalar functions. Here we study, as an alternative, the application of Mellin-Barnes representations to 5-point functions. There is no evidence for an improved numerical evaluation of their finite, physical parts.…
A new version of Monte Carlo generator ELRADGEN for simulation of real photon emission in elastic electron-proton scattering is presented. The extensions in the new version include opportunity to deal with polarized particles: longitudinally polarized electron and arbitrary polarized proton. Simulation strategy, specifications of used kinematics, structure of the contributions to the observed cross section, cross-checks, and numerical results for BLAST experimental setup are presented and briefly discussed.
Extending the use of Monte Carlo (MC) event generators to jets in nuclear collisions requires a probabilistic implementation of the non-abelian LPM effect. We demonstrate that a local, probabilistic MC implementation based on the concept of formation times can account fully for the LPM-effect. The main features of the analytically known eikonal and collinear approximation can be reproduced, but we show how going beyond this approximation can lead to qualitatively different results.
In this paper we present a new Monte Carlo event generator ReneSANCe for simulation of processes at electron-positron colliders. In the current release of the generator the Bhabha scattering ($e^+e^- \to e^-e^+$) and Higgs-strahlung ($e^+e^- \to ZH$) process are implemented. Based on the SANC (Support for Analytic and Numeric Calculations for experiments at colliders) modules, the new generator takes into account complete one-loop and some higher-order electroweak radiative corrections with finite particle masses and polarizations. The new generator effectively operates in the collinear region…
We present the Monte Carlo event generator {\tt WOPPER} for pair production of $W$'s and their decays at high energy $e^+e^-$ colliders. {\tt WOPPER} includes the effects from finite $W$ width and focusses on the calculation of higher order electromagnetic corrections in the leading log approximation including soft photon exponentiation and explicit generation of exclusive hard photons.
The status and accuracy of the precision Monte Carlo generators used for luminosity measurements at flavour factories is reviewed. It is shown that, thanks to a considerable, long-term effort in tuned comparisons between the predictions of independent programs, as well as in the validation of the generators against the presently available calculations of the next-to-next-to-leading order QED corrections to Bhabha scattering, the theoretical accuracy reached by the most precise tools is of about one per mille. This error estimate is valid for realistic experimental cuts, appears to be quite rob…
This work is devoted to a theoretical description of polarized Møller scattering. Complete one-loop electroweak radiative corrections are calculated in the helicity amplitude approach with allowance for the exact dependence on the muon mass. Numerical results are presented for integrated unpolarized and polarized cross sections as well as angular differential distributions. Calculations are performed using ReneSANCe Monte Carlo generator and MCSANC Monte Carlo integrator.
We present the LL final state radiative effects for the exact O(alpha) YFS exponentiated (un)stable WW pair production at LEP2/NLC energies using Monte Carlo event generator methods. The respective event generator, version 1.12 of the program YFSWW3, wherein both Standard Model and anomalous triple gauge boson couplings are allowed, generates n(γ) radiation both from the initial state and from the intermediate W+ W- and generates the LL final state W decay radiative effects. Sample Monte Carlo data are illustrated.
