15252744
Precise Numerical Evaluation of the Scalar One-Loop Integrals with the Infrared Divergence
We present a new approach for obtaining very precise integration results for infrared vertex and box diagrams, where the integration is carried out directly without performing any analytic integration of Feynman parameters. Using an appropriate numerical integration routine with an extrapolation method, together with a multi-precision lib rary, we have obtained integration results which agree with the analytic results to 10 digits even for such a very small photon mass as 10 150 GeV in the infrared vertex diagram.
117897043
Automatic calculations in high energy physics and GRACE at one-loop
Abstract We describe the main building blocks of a generic automated package for the calculation of Feynman diagrams. These blocks include the generation and creation of a model file, the graph generation, the symbolic calculation at an intermediate level of the Dirac and tensor algebra, implementation of the loop integrals, the generation of the matrix elements or helicity amplitudes, methods for the phase space integrations and eventually the event generation. The report focuses on the fully automated systems for the calculation of physical processes based on the experience in developing GRACE-loop which is a general purpose code applicable to one-loop corrections in the Standard Model. As such, a detailed description of the renormalisation procedure in the Standard Model is given emphasizing the central role played by the non-linear gauge fixing conditions for the construction of such automated codes. These new gauge-fixing conditions are used as a very efficient means to check the results of large scale automated computations in the Standard Model. Their need is better appreciated when it comes to devising efficient and powerful algorithms for the reduction of the tensorial structures of the loop integrals and the reduction of the N > 4 point-function to lower rank integrals. A new technique for these reduction algorithms is described. Explicit formulae for all two-point functions in a generalised non-linear gauge are given, together with the complete set of counterterms. We also show how infrared divergences are dealt with in the system. We give a comprehensive presentation of some systematic test-runs which have been performed at the one-loop level for a wide variety of two-to-two processes to show the validity of the gauge check. These cover fermion–fermion scattering, gauge boson scattering into fermions, gauge bosons and Higgs bosons scattering processes. Comparisons with existing results on some one-loop computation in the Standard Model show excellent agreement. These include e + e - → t t ¯ , W + W - , ZH ; γ γ → t t ¯ , W + W - ; e γ → eZ , ν W and W + W - → W + W - . We also briefly recount some recent development concerning the calculation of one-loop corrections to 3 body final states cross sections in e + e - with the help of an automated system.
28368514
Numerical computation of two-loop box diagrams with masses
Abstract A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass configurations. As an example, the computation of two-loop planar and non-planar box diagrams is shown. The results are confirmed by comparisons with other techniques, including the reduction method, and by a consistency check using the dispersion relation.
15585002
Full one-loop electroweak radiative corrections to single photon production in e+e-
Abstract Large-scale calculations for the radiative corrections required for the current and future collider experiments can be done automatically using the GRACE-LOOP system. Here several results for e + e - → 3-body processes are presented including e + e - → e + e - H and e + e - → ν ν ¯ γ .
15312798
Monte Carlo Approach to Radiative Corrections in Bhabha Scattering
§ 1. lntroduction It has become a common understanding that detailed theoretical predictions for e+ e- experiments should include the radiative corrections with multi-photon contribu­ tion. A well-known example is the significant modification of the apparent cross section around the Z-boson pole at LEP.ll The study of inclusive processes with multi-photon emission has led some authors to propose several kinds of Monte Carlo generators. 2 l In a pre~ious paper 3 l we have reported a new method for the Monte Carlo generator of multi-photon and have shown some results obtained via a computer progam written for muon pair production in e+ e- annihilation. This is a QED version of the parton shower model which has been studied extensively in QCD. In this paper we generalize this method to the Bhabha scattering by employing essen­ tially the same algorithm as that for muon pair production. It will be convenient to summarize the main features of the algorithm to generate photons. We rely on the technique to sum up all the collinear singularities, which plays an essential role in the parton shower model. 4 J The present model is limited to the leading logarithmic approximation, though there is no difficulty in principle to include the next-to-leading corrections. 5 l This approximation is reasonable as the QED coupling a is very small compared with that in QCD. Another remarkable feature is that the transverse momentum distribution of produced photons is derived correctly once one imposes the four-momentum conservation at each of branching vertices. 4 l This is a consequence of the branching, e±--> e±y, being aprocess of 1--> 2 bodies.
122420983
Monte Carlo Approach to Radiative Processes in e+ e- Annihilation
We present a new approach to radiative processes in e+ e- annihilation based on a Monte Carlo method. This is nothing but the QED version of the parton shower model studied extensively in QCD. It is applicable to both initial and final state radiation but without the interference between these two. To examine the validity of the model, we compare it with the results of the exact calculations up to OCa) and OCa 2 ). Comparison of several distributions shows that the model can give reliable results for practical use. Study of radiative corrections in e+ e- collisions has a long history!) since its importance was recognized in the discovery of ]/CP.2) Until now, most efforts have concentrated on the calculation of O(a) corrections to weak interactions. Precise measurements of properties of the ZO boson, however, required the detailed study of higher order QED corrections. Techniques of calculating some contributions in all order have been developed, such as soft photon summation 3 ) and collinear photon summation. 4 ) Generally speaking, these are methods suitable only for inclusive distributions, and they can hardly be applied to exclusive processes or event genera­ tions. It is obvious that the collinear photon summation has an exact correspondence with the collinear parton summation based on the Altarelli-Parisi equation in pertur­ bative quantum chromodynamics (QCD). The parton shower model was originally proposed to deal with exclusive processes in QCD. 5 ) In this paper we apply this technique to QED and examine its validity for radiative processes. We shall call this new model QED parton shower (QEDPS). Although the development of the model is not difficult in the technical sense, study of its validity is a nontrivial task because a much higher accuracy of calculation is required than in QCD. Recently one of the authors calculated exact O(a 2 ) QED corrections to the initial state of e+ e- annihila­ tion. 6 ) With the help of this calculation, we are able to test the validity of QEDPS in a systematic and quantitative way. The purposes of this paper are to present the formulation of QEDPS in a Monte Carlo method and to show that it is really a practical method to describe radiative processes. Since the parton shower model is applied to the final q, q and gluon system in e+ e- annihilation, QEDPS can also be used to estimate QED radiative corrections to the charged particles in the final state. Thus it is equally applicable to both initial and final state radiation, though the interference between these two states cannot be included at present. In the next section we will give the algorithm of QEDPS. In § 3, comparison will
119265355
Tetrahedral symmetry in Zr nuclei: calculations of low-energy excitations with Gogny interaction
We report on the results of the calculations of the low energy excitation patterns for three Zirconium isotopes, viz 80Zr40, 96Zr56 and 110Zr70, reported by other authors to be doubly-magic tetrahedral nuclei (with tetrahedral magic numbers Z = 40 and N = 40, 56 and 70). We employ the realistic Gogny effective interactions using three variants of their parametrization and the particle-number, parity and the angular-momentum projection techniques. We confirm quantitatively that the resulting spectra directly follow the pattern expected from the group theory considerations for the tetrahedral symmetric quantum objects. We also find out that, for all the nuclei studied, the correlation energy obtained after the angular momentum projection is very large for the tetrahedral deformation as well as other octupole deformations. The lowering of the energies of the resulting configurations is considerable, i.e. by about 10 MeV or even more, once again confirming the significance of the angular-momentum projections techniques in the mean-field nuclear structure calculations.
16491530
Diabatic Mean-Field Description of Rotational Bands in Terms of the Selfconsistent Collective Coordinate Method
Diabatic description of rotational bands provides a clear-cut picture for understanding the back-bending phenomena, where the internal structure of the yrast band changes dramatically as a function of angular momentum. A microscopic framework to obtain the diabatic bands within the mean-field approximation is presented by making use of the selfconsistent collective coordinate method. Applying the framework, both the ground state rotational bands and the Stockholm bands are studied systematically for the rare-earth deformed nuclei. An overall agreement has been achieved between the calculated and observed rotational spectra. It is also shown that the inclusion of the double-stretched quadrupole-pairing interaction is crucial to obtain an overall agreement for the even-odd mass differences and the rotational spectra simultaneously.
121954152
The role of spin-orbit potential in nuclear prolate-shape dominance
Abstract It is confirmed, in terms of the Woods–Saxon–Strutinsky method, that the spin–orbit potential plays a decisive role in the predominance of prolate deformation, which has been a long standing problem in nuclear physics. It is originated from the combined effects of the spin–orbit coupling and the diffused surface of the potential, in agreement with the previous work based on a more schematic Nilsson–Strutinsky method. The degree of prolate-shape dominance exhibits an oscillatory behavior with respect to the strength of spin–orbit potential and, the prolate-shape dominance is realized at the proper strength of the spin–orbit potential together with the standard surface diffuseness; this oscillatory behavior disappears in case of small diffuseness corresponding to ellipsoidal cavity. The calculated energy differences between oblate and prolate minima in this Letter are consistent with those of our extensive self-consistent calculations of the Hartree–Fock + BCS method with the Skyrme interaction.
120353160
Forward photon energy spectrum at LHC 7 TeV p-p collisions measured by LHCf
Abstract The LHCf experiment is one of the LHC forward experiments. The aim is to measure the energy and the transverse momentum spectra of photons, neutrons and π 0 's at the very forward region (the pseudo-rapidity range of η > 8.4 ), which should be critical data to calibrate hadron interaction models used in the air shower simulations. LHCf successfully operated at s = 900 GeV and s = 7 TeV proton–proton collisions in 2009 and 2010. We present the first physics result, single photon energy spectra at s = 7 TeV proton–proton collisions and the pseudo-rapidity ranges of η > 10.94 and 8.81 η 8.9 . The obtained spectra were compared with the predictions by several hadron interaction models and the models do not reproduce the experimental results perfectly.
119098407
Microscopic Calculation of the Wobbling Excitations Employing the Woods-Saxon Potential as a Nuclear Mean-Field
The wobbling excitations of the triaxial superdeformed (TSD) bands in the Lu and Hf region are studied by the microscopic framework of the cranked mean-field and the randomphase approximation (RPA). In contrast to the previous works, where the Nilsson potential was used, the more realistic Woods-Saxon potential is employed as a nuclear mean-field. It is pointed out that the original formulation should be slightly modified for general meanfield like the Woods-Saxon potential. The wobbling-like RPA solutions have been found systematically in the nuclei studied and their characteristic properties are investigated in detail. This confirms the wobbling phonon excitations in TSD nuclei from the microscopic calculations. The result of B(E2) values indicates that the triaxial deformation is increasing as a function of spin in the observed TSD bands in 163 Lu. Subject Index: 210, 211, 212