Calculation Of Radiative Corrections Research Articles

Electroweak radiative corrections at high energies

We discuss the progress in the calculation of the high-order electroweak radiative corrections to high-energy processes.

Radiative corrections beyond the ultra relativistic limit in unpolarized ep elastic and Møller scatterings for the PRad Experiment at Jefferson Laboratory

The clear 7σ discrepancy between measurements of the proton charge radius from muonic hydrogen Lamb shifts and those from hydrogen Lamb shift and electron scattering lead to both intense theoretical and experimental efforts to understand and explain this difference. In this regard, a new experiment (PRad) based on unpolarized ep elastic scattering cross section measurements normalized to Møller scattering is underway at Jefferson Laboratory to extract the proton charge radius based on new proton electric form factor down to values of momentum transfer squared Q 2, as low as 10−4 GeV/c)2. To reach the precision of the experiment in such a small Q 2 region requires reliable knowledge of radiative corrections. In this paper, we present a complete calculation of radiative corrections for unpolarized elastic ep and Møller scatterings performed within a covariant formalism resulting in the set of explicit formulas beyond the ultra relativistic approximation (m 2 ≪ Q 2), and numerical results for the kinematics of the PRad experiment.

Analysis of approximations used in calculations of radiative corrections to electron-proton scattering cross section

An analysis of approximations used in calculations of radiative corrections to electron-proton scattering cross section is presented. We investigate the difference between the relatively recent Maximon and Tjon result and the Mo and Tsai result, which was used in the analysis of experimental data. We also discuss the proton form factors ratio dependence on the way we take into account radiative corrections.

Towards finite field theory: the Taylor-Lagrange regularization scheme

We recall a natural framework to deal with local field theory in which bare amplitudes are completely finite. We first present the main general properties of this scheme, the so-called Taylor-Lagrange regularization scheme. We then investigate the consequences of this scheme on the calculation of perturbative radiative corrections to the Higgs mass within the Standard Model. Important consequences for the renormalization group equations are finally discussed.

Radiative corrections to real and virtual muon Compton scattering revisited

We calculate in closed analytical form the one-photon loop radiative corrections to muon Compton scattering μ − γ → μ − γ . Ultraviolet and infrared divergences are both treated in dimensional regularization. Infrared finiteness of the (virtual) radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off λ. We find that the anomalous magnetic moment α / 2 π provides only a very small portion of the full radiative corrections. Furthermore, we extend our calculation of radiative corrections to the muon–nucleus bremsstrahlung process (or virtual muon Compton scattering μ − γ 0 ∗ → μ − γ ). These results are particularly relevant for analyzing the COMPASS experiment at CERN in which muon–nucleus bremsstrahlung serves to calibrate the Primakoff scattering of high-energy pions off a heavy nucleus with the aim of measuring the pion electric and magnetic polarizabilities. We find agreement with an earlier calculation of these radiative corrections based on a different method.

Complete calculation of electroweak corrections for polarized Møller scattering at high energies

A complete calculation of electroweak radiative corrections to observables of polarized Moller scattering at high energies was performed. This calculation took explicitly into account contributions caused by hard bremsstrahlung. A FORTRAN code that permitted including radiative corrections to high-energy Moller scattering under arbitrary electron-detection conditions was written. It was shown that the electroweak corrections caused by hard bremsstrahlung were rather strongly dependent on the choice of experimental cuts and changed substantially the polarization asymmetry in the region of high energies and over a broad interval of scattering angles.

Functional equations for one-loop master integrals for heavy-quark production and Bhabha scattering

The method for obtaining functional equations, recently proposed by one of the authors [O.V. Tarasov, Phys. Lett. B 670 (2008) 67, arXiv:0809.3028 [hep-ph]], 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 functions admitting one-fold integral representations is derived. The hypergeometric representation of a master integral for heavy-quark production follows from the functional equation.

Bottom-up reconstruction scenarios for (un)constrained MSSM parameters at the CERN LHC

We consider some specific inverse problem or "bottom-up" reconstruction strategies at the LHC for both general and constrained MSSM parameters, starting from a plausibly limited set of sparticle identification and mass measurements, using mainly gluino/squark cascade decays, plus eventually the lightest Higgs boson mass. For the three naturally separated sectors of: gaugino/Higgsino, squark/slepton, and Higgs parameters, we examine different step-by-step algorithms based on rather simple, entirely analytical, inverted relations between masses and basic MSSM parameters. This includes also reasonably good approximations of some of the relevant radiative correction calculations. We distinguish the constraints obtained for a general MSSM from those obtained with universality assumptions in the three different sectors. Our results are compared at different stages with the determination from more standard "top-down" fit of models to data, and finally combined into a global determination of all the relevant parameters. Our approach gives complementary information to more conventional analysis, and is not restricted to the specific LHC measurement specificities. In addition, the bottom-up renormalization group evolution of general MSSM parameters, being an important ingredient in this framework, is illustrated as a new publicly available option of the MSSM spectrum calculation code "SuSpect".

Ward-Takahashi identities in the description of electroweak transitions of nucleons and pions

For nucleons and pions, the relations between the propagators and vertex functions that describe the vector electroweak transitions have been derived directly as a natural consequence of the symmetries of the strong and electroweak interactions of hadrons. Significantly, the system under study includes various strongly interacting hadrons. The electromagnetic corrections to the vertex functions and propagators of the hadrons are taken into account to within e2. The results obtained are discussed in connection with the calculation of radiative corrections in the description of electroweak transitions of nucleons and pions.

Calculation of radiative corrections to hyperfine splitting inp3∕2states

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Improved calculation of the isospin-symmetry-breaking corrections to superallowed Fermi β decay

We report new shell-model calculations of the isospin-symmetry-breaking correction ${\ensuremath{\delta}}_{C}$ to superallowed ${0}^{+}\ensuremath{\rightarrow}{0}^{+}$ nuclear \ensuremath{\beta} decay. The most important improvement is the inclusion of core orbitals, which are demonstrated to have a significant impact on the mismatch in the radial wave functions of the parent and daughter states. We determine which core orbitals are important to include from an examination of measured spectroscopic factors in single-nucleon pickup reactions. In addition, where new sets of effective interactions have become available since our last calculation, we now include them; this leads to small changes in ${\ensuremath{\delta}}_{\mathrm{NS}}$ as well. We also examine the new radiative-correction calculation by Marciano and Sirlin and, by a simple reorganization, show that it is possible to preserve the conventional separation into a nucleus-independent ``inner'' radiative term, ${\ensuremath{\Delta}}_{R}^{V}$, and a nucleus-dependent ``outer'' term, ${\ensuremath{\delta}}_{R}^{'}$. We tabulate the new values for ${\ensuremath{\delta}}_{C},{\ensuremath{\delta}}_{\mathrm{NS}}$, and ${\ensuremath{\delta}}_{R}^{'}$ for 20 superallowed transitions, including the 13 currently well-studied cases. With these new correction terms, the corrected $\mathcal{F}t$ values for the 13 cases are statistically consistent with one another, and the anomalousness of the $^{46}\mathrm{V}$ result disappears. These new calculations lead to a lower average $\overline{\mathcal{F}t}$ value and a higher value for ${V}_{\mathrm{ud}}$. The sum of squares of the top-row elements of the Cabibbo-Kobayashi-Maskawa matrix now agrees exactly with unitarity.

Wavelet-Based Quantum Field Theory

The Euclidean quantum field theory for the fields x(x), which depend on both the positionx and the resolution x, constructed in SIGMA 2 (2006), 046, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments.

Two-loop formfactors in theories with mass gap and Z-boson production

The non-factorizable two-loop corrections to the formfactor both for a U ( 1 ) × U ( 1 ) and a SU ( 2 ) × U ( 1 ) gauge theory with massive and massless gauge bosons respectively are evaluated at arbitrary momentum transfer q 2 . The asymptotic behaviour for q 2 → ∞ is compared to a recent calculation of Sudakov logarithms. The result is an important ingredient for the calculation of radiative corrections to Z-boson production at hadron and lepton colliders.

Structure function method applied to polarized and unpolarized electron-proton scattering: A solution of theGE(p)/GM(p)discrepancy

The cross section for polarized and unpolarized electron-proton scattering is calculated taking into account radiative corrections in leading and next-to leading logarithmic approximation. The expression of the cross section is formally similar to the cross section of the Drell-Yan process, where the structure functions of the electron play the role of Drell-Yan probability distributions. The interference of the Born amplitude with the two photon exchange amplitude (box-type diagrams) is expressed as a contribution to K-factor and it is larger when the momentum is equally shared between the two photons, assuming that proton form factors decrease rapidly with the momentum transfer squared. The calculation of the box amplitude is done when the intermediate state is a proton or the Delta-resonance. The results of numerical estimations show that the present calculation of radiative corrections can bring into agreement the conflicting experimental results on proton electromagnetic form factors an that the two photon contribution is very small.

Weak boson emission in hadron collider processes

The $\mathcal{O}(\ensuremath{\alpha})$ virtual weak radiative corrections to many hadron collider processes are known to become large and negative at high energies, due to the appearance of Sudakov-like logarithms. At the same order in perturbation theory, weak boson emission diagrams contribute. Since the $W$ and $Z$ bosons are massive, the $\mathcal{O}(\ensuremath{\alpha})$ virtual weak radiative corrections and the contributions from weak boson emission are separately finite. Thus, unlike in QED or QCD calculations, there is no technical reason for including gauge boson emission diagrams in calculations of electroweak radiative corrections. In most calculations of the $\mathcal{O}(\ensuremath{\alpha})$ electroweak radiative corrections, weak boson emission diagrams are therefore not taken into account. Another reason for not including these diagrams is that they lead to final states which differ from that of the original process. However, in experiment, one usually considers partially inclusive final states. Weak boson emission diagrams thus should be included in calculations of electroweak radiative corrections. In this paper, I examine the role of weak boson emission in those processes at the Fermilab Tevatron and the CERN LHC for which the one-loop electroweak radiative corrections are known to become large at high energies (inclusive jet, isolated photon, $Z+1$ jet, Drell-Yan, di-boson, $\overline{t}t$, and single top production). In general, I find that the cross section for weak boson emission is substantial at high energies and that weak boson emission and the $\mathcal{O}(\ensuremath{\alpha})$ virtual weak radiative corrections partially cancel.

Two-photon contributions toe+e−→ηγande+e−→η′γ

Motivated by recent BABAR measurements of the {gamma}*{yields}{gamma}{eta} and {gamma}*{yields}{gamma}{eta}{sup '} transition form factors, we estimate two-photon exchange contributions to the corresponding cross sections. By using a phenomenological model, based on the vector meson dominance, it is argued that the expected contributions are small enough not to effect the BABAR results. As a by product we predict Br({eta}{sup '}{yields}{mu}{sup +}{mu}{sup -})=(1.4{+-}0.2)x10{sup -7}. Our results might be useful also in high precision calculations of radiative corrections to the Dalitz decays of pseudoscalar mesons.

QCD radiative corrections to Higgs boson production at the Tevatron and the LHC

We consider Higgs boson production, through gluon fusion, in hadron collisions at the Tevatron and the LHC. We briefly summarize the calculations of QCD radiative corrections to this process. We show theoretical predictions for the total cross section and the transverse-momentum ( q T ) distribution of the Standard Model (SM) Higgs boson. The perturbative QCD uncertainty on these predictions is discussed.

ZFITTER: a semi-analytical program for fermion pair production in [formula omitted] annihilation, from version 6.21 to version 6.42

ZFITTER is a Fortran program for the calculation of fermion pair production and radiative corrections at high energy e + e − colliders; it is also suitable for other applications where electroweak radiative corrections appear. ZFITTER is based on a semi-analytical approach to the calculation of radiative corrections in the Standard Model. We present a summary of new features of the ZFITTER program version 6.42 compared to version 6.21. The most important additions are: (i) some higher-order QED corrections to fermion pair production, (ii) electroweak one-loop corrections to atomic parity violation, (iii) electroweak one-loop corrections to ν ¯ e ν e production, (iv) electroweak two-loop corrections to the W boson mass and the effective weak mixing angle. Program summary Title of program: ZFITTER version 6.42 (18 May 2005) Catalogue identifier:ADMJ_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADMJ_v2_0 Authors of original program: D. Bardin, P. Christova, M. Jack, L. Kalinovskaya, A. Olshevski, S. Riemann, T. Riemann Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Reference for ZFITTER version 6.21: D. Bardin et al., Comput. Phys. Comm. 133 (2001) 229–395 Operating system: UNIX/LINUX, program tested under, e.g., HP-UX and PC/Linux Programming language used: FORTRAN 77 High speed storage required: <2 MB No. of lines in distributed program, including test data, etc.:29 164 No. of bytes in distributed program, including test data, etc.:185 824 Distribution format:tar.gz Does the new version supersede the previous version:Yes Nature of the physical problem: Fermion pair production is an important reaction for precision tests of the Standard Model, at LEP/SLC and future linear colliders at higher energies. For this purpose, QED, electroweak and QCD radiative corrections have to be calculated with high precision, including higher order effects. Multi parameter fits used to extract model parameters from experimental measurements require a program of sufficient flexibility and high calculational speed. ZFITTER combines these two aspects by employing analytical integrations of matrix elements and at most one-dimensional numerical integration, as well as a variety of flags defining the physics content used. The calculated predictions are typically at the per mille precision level, sometimes better. Method of solution: Numerical integration of analytical formulae. Reasons for new version:Addition of substantial material into the code: covering of more reactions; more accurate description of existing reactions. Summary of revisions:New parts for predicting atomic parity violation and for neutrino pair production; more accurate higher order QED corrections for fermion pair production; two-loop corrections to the predictions of W mass and of the weak mixing angle. Restrictions on the complexity of the problem: Fermion pair production is described below the top quark pair production threshold. Photonic corrections are taken into account with simple cuts on photon energy, or the energies and acollinearity of the two fermions, and one fermion production angle. The treatment of Bhabha scattering is less advanced. Typical running time: On a Pentium IV PC installation (2.8 GHz) using g77 under Linux 2.4.21, approximately 23 s are needed to run the standard test of subroutine ZFTEST. This result is for a default/recommended setting of the input parameters, with all corrections in the Standard Model switched on. ZFTEST computes 12 cross-sections and cross-section asymmetries for 8 energies with 5 interfaces, i.e. about 360 cross-sections in 23 s.

The Dalitz decay π0 → e + e – γ revisited

The amplitude of the Dalitz decay pi0 -> e+ e gamma is studied and its model-independent properties are discussed in detail. A calculation of radiative corrections is performed within the framework of two-flavour chiral perturbation theory, enlarged by virtual photons and leptons. The lowest meson dominance approximation, motivated by large N\_C considerations, is used for the description of the pi0 - gamma* - gamma* transition form factor and for the estimate of the NLO low energy constants involved in the analysis. The two photon reducible contributions is included and discussed. Previous calculations are extended to the whole kinematical range of the soft-photon approximation, thus allowing for the possibility to consider various experimental situations and observables.

Radiative potential and calculations of QED radiative corrections to energy levels and electromagnetic amplitudes in many-electron atoms

We derive an approximate expression for a "radiative potential" which can be used to calculate QED strong Coulomb field radiative corrections to energies and electric dipole (E1) transition amplitudes in many-electron atoms with an accuracy of a few percent. The expectation value of the radiative potential gives radiative corrections to the energies. Radiative corrections to E1 amplitudes can be expressed in terms of the radiative potential and its energy derivative (the low-energy theorem): the relative magnitude of the radiative potential contribution is ~alpha^3 Z^2 ln(1/(alpha^2 Z^2)), while the sum of other QED contributions is ~alpha^3 (Z_i+1)^2, where Z_i is the ion charge; that is, for neutral atoms (Z_i=0) the radiative potential contribution exceeds other contributions ~Z^2 times. The advantage of the radiative potential method is that it is very simple and can be easily incorporated into many-body theory approaches: relativistic Hartree-Fock, configuration interaction, many-body perturbation theory, etc. As an application we have calculated the radiative corrections to the energy levels and E1 amplitudes as well as their contributions (-0.33% and 0.42%, respectively) to the parity non-conserving (PNC) 6s-7s amplitude in neutral cesium (Z=55). Combining these results with the QED correction to the weak matrix elements (-0.41%) we obtain the total QED correction to the PNC 6s-7s amplitude, (-0.32 +/- 0.03)%. The cesium weak charge Q_W=-72.66(29)_{exp}(36)_{theor} agrees with the Standard Model value Q_W^{SM}=-73.19(13), the difference is 0.53(48).