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Title: | Radiative corrections and accuracy tests of Monte Carlo generators used at meson factories |

Authors: | Gunia, Michał |

Advisor: | Czyż, Henryk |

Keywords: | cząstki elementarne; Metoda Monte Carlo; analiza numeryczna; informatyka |

Issue Date: | 2013 |

Publisher: | Katowice : Uniwersytet Śląski |

Abstract: | The amazing progress of research in the field of elementary particles in the second half of the twentieth century led to the formulation of the theory known as the Standard Model (SM). With this theory it was possible to connect in one model three of the four known fundamental interactions [1], At the same time, technological developments had allowed experimental methods to be improved. The accelerators used in experiments reached ever higher energies of accelerated particles while increasing the precision of the detectors. On the other hand, significant progress was made in the field of theoretical research and calculations. The predictions of the SM were confirmed by experiments, but the SM cannot be treated as a full theory of particle physics. First of all, the SM treats particle masses as parameters - they cannot be obtained by theoretical predictions. Furthermore, the SM does not describe particle physics phenomena such as dark matter or matter antimatter asymmetry, etc. This means that the SM should be considered as an effective theory. This is one of the reasons that suggest the need for searching for so called new physics or physics beyond the SM. Research conducted at high energies in the large hadron collider (LHC) could answer some of this question. However, there is a possibility of a parallel search for evidences of new physics. It is possible to test known parameters of the SM like for example the anomalous magnetic moment. This kind of test requires the comparison between the experimental measurement and the theoretical prediction done with extremely high precision. Thus, this advance of theoretical calculation and experimental methods has resulted in today’s tests of the SM requiring an inclusion of higher order effects. In an era of high energy measurements at the TeV level in the LHC, calculations and experiments conducted for low energy particle physics could play a crucial role in searching for traces of physics beyond the SM [2]. The hadronie contribution to the anomalous magnetic moment of the muon a^ld is an example of a quantity that depends strongly on low energy data. The low energy hadronie contributions are not calculable in the quantum chromodynamics (QCD) perturbation theory and the calculations require use of phenomenological models and the precise experimental data studies. The hadronie contribution to the anomalous magnetic moment of the muon a^ad is divided into three parts: the leading-order (LO) a^ad,LO and higher-order (HO) ah“d'HO vacuum polarisation contributions, and the lightby- light scattering contribution The leading order contribution can be obtained from the data for the processes e+e~ —> hadrons and using the dispersion integral it can be presented in the following form [3]: l o = / dsK{s)rTlutd{s) ( 1 .! ) ^ J where a had{s) is the total hadronie cross section (without the vacuum polarisation corrections). The K (s) function is called kernel function and is calculated within quantum electrodynamics (QED). The behaviour of this function shows that it decreases monotonically with increasing value of s. Therefore the a^ld'LO integrand is dominated by the hadron production below a few GeV. The hadron part of the anomalous magnetic moment of the muon obtained from e+e~ data is [4]: a had = (6 9 5 5 ± 4 9 ) . 1 0 - i i ( 1 2 ) Where: ahad,LO = (6 9 4 9 x ± 4 2 . 7 ) . i q - 11 (1 .3 ) a had,HO = ( _ 9 8 4 ± 0 .7 ) . l o - 11 (1 .4 ) ahadW = (1Q5 ± 26) . 10-11 ( j 5) The error for the leading order contribution is the biggest one. The sum of all contributions to the value of the anomalous magnetic moment of the muon obtained for the SM prediction is equal to: a lM = 116591828(50) • 1CT11 (1.6) The errors were added in quadrature. This value also contains ah“d. The value taken from the experiment gives: a™p = 116592089(63) • 10“n (1.7) A careful comparison of these two values gives the difference equal to 3.3 standard deviation: = a^p - a lM = 261(80) • l(Tn (1.8) This discrepancy could suggest the existence of some unknown effects, so it is very important to improve the accuracy of the experimental and theoretical value of to check if it is true. The uncertainty of theoretical calculations depends strongly on the hadronie contribution at low energies. The error of a^M is equal to 50 • 10~n , while the error of a^d,LO is equal to 42.7 • 10-11. So the biggest contribution to the error of aSM comes from the prediction of the leading-order hadronie contribution ,L°. The biggest contribution to the value of a^ad'LO comes from the region between 0.32 and 1.43 GeV and is equal to (6065±34)- 10~u [4]. The second in order is the region between 2 and 11.09 GeV where the contribution is equal to (411.9 ± 8.2) • 10-11. Here, for the region between 2.6 and 3.73 GeV for some channels, perturbative QCD (pQCD) was used. The contribution for energies above 11.09 GeV (obtained with pQCD) is equal to 0.211 • 10-11 and gives the error below 10-14. So the error of a^ad'LO is dominated by the low energy hadron production. This example shows the importance of results obtained for low energies where the use of perturbation methods for hadrons is not possible. A similar influence of low-energy data occurs for the hadronie part of the fine structure constant Aa had(Mz). The dispersion relation gives the following form of this magnitude [5]: £ } a»> Here the R(s) function depends on the total cross section ahad of the process e+e~ —> hadrons(muons) + 7 : = <L10> The error of A a had(Mz), at the level of about one percent, comes mainly from the process at the scale of about a few GeV [4], The precise determination of the value of Aa had(Mz) is, for example, necessary for the better determination of the Higgs mass . To increase accuracy of the theoretical value of ah“d or Aa had(Mz), it is necessary to improve the determination of the hadronie cross section. It is connected with the accuracy of the Monte Carlo (MC) generators used for the analysis of the experimental data. Generators like BabaYaga@NLO, MCGPJ and PHOKHARA are examples of generators that include NLO. |

URI: | http://hdl.handle.net/20.500.12128/5461 |

Appears in Collections: | Rozprawy doktorskie (WNŚiT) |

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