By Philipp Gubler

ISBN-10: 4431543171

ISBN-13: 9784431543176

The writer develops a singular research procedure for QCD sum principles (QCDSR) via using the utmost entropy strategy (MEM) to reach at an research with much less synthetic assumptions than formerly held. this can be a first-time accomplishment within the box. during this thesis, a reformed MEM for QCDSR is formalized and is utilized to the sum ideas of numerous channels: the light-quark meson within the vector channel, the light-quark baryon channel with spin and isospin half, and several other quarkonium channels at either 0 and finite temperatures. This novel means of combining QCDSR with MEM is utilized to the research of quarkonium in scorching topic, that's a major probe of the quark-gluon plasma at the moment being created in heavy-ion collision experiments at RHIC and LHC.

Table of Contents

Cover

A Bayesian research of QCD Sum Rules

ISBN 9784431543176 ISBN 9784431543183

Supervisor's Foreword

Acknowledgments

Contents

Part I creation and Review

bankruptcy 1 Introduction

1.1 Describing Hadrons from QCD

1.2 QCD Sum principles and Its Ambiguities

1.3 Hadrons in a sizzling and/or Dense Environment

1.4 Motivation and objective of this Thesis

1.5 define of the Thesis

bankruptcy 2 simple houses of QCD

2.1 The QCD Lagrangian

2.2 Asymptotic Freedom

2.3 Symmetries of QCD 2.3.1 Gauge Symmetry

o 2.3.2 Chiral Symmetry

o 2.3.3 Dilatational Symmetry

o 2.3.4 heart Symmetry

2.4 stages of QCD

bankruptcy three fundamentals of QCD Sum Rules

3.1 Introduction

o 3.1.1 The Theoretical Side

o 3.1.2 The Phenomenological Side

o 3.1.3 useful models of the Sum Rules

3.2 extra at the Operator Product Expansion

o 3.2.1 Theoretical Foundations

o 3.2.2 Calculation of Wilson Coefficient

3.3 extra at the QCD Vacuum

o 3.3.1 The Quark Condensate

o 3.3.2 The Gluon Condensate

o 3.3.3 The combined Condensate

o 3.3.4 greater Order Condensates

3.4 Parity Projection for Baryonic Sum Rules

o 3.4.1 the matter of Parity Projection in Baryonic Sum Rules

o 3.4.2 Use of the "Old shaped" Correlator

o 3.4.3 development of the Sum Rules

o 3.4.4 common research of the Sum principles for Three-Quark Baryons

bankruptcy four the utmost Entropy Method

4.1 uncomplicated Concepts

o 4.1.1 the chance functionality and the earlier Probability

o 4.1.2 The Numerical Analysis

o 4.1.3 errors Estimation

4.2 pattern MEM research of a Toy Model

o 4.2.1 development of the Sum Rules

o 4.2.2 MEM research of the Borel Sum Rules

o 4.2.3 MEM research of the Gaussian Sum Rules

o 4.2.4 precis of Toy version Analysis

Part II Applications

bankruptcy five MEM research of the . Meson Sum Rule

5.1 Introduction

5.2 research utilizing Mock Data

o 5.2.1 producing Mock facts and the Corresponding Errors

o 5.2.2 selection of a suitable Default Model

o 5.2.3 research of the soundness of the got Spectral Function

o 5.2.4 Estimation of the Precision of the ultimate Results

o 5.2.5 Why it's Difficul to thoroughly confirm the Width of the . Meson

5.3 research utilizing the OPE effects 5.3.1 The . Meson Sum Rule

o 5.3.2 result of the MEM Analysis

5.4 precis and Conclusion

bankruptcy 6 MEM research of the Nucleon Sum Rule

6.1 Introduction

6.2 QCD Sum principles for the Nucleon

o 6.2.1 Borel Sum Rule

o 6.2.2 Gaussian Sum Rule

6.3 research utilizing the Borel Sum Rule

o 6.3.1 research utilizing Mock Data

o 6.3.2 research utilizing OPE Data

6.4 research utilizing the Gaussian Sum Rule

o 6.4.1 research utilizing Mock Data

o 6.4.2 research utilizing OPE Data

o 6.4.3 research of the � Dependence

6.5 precis and Conclusion

bankruptcy 7 Quarkonium Spectra at Finite Temperature from QCD Sum principles and MEM

7.1 Introduction

7.2 Formalism

o 7.2.1 formula of the Sum Rule

o 7.2.2 The Temperature Dependence of the Condensates

7.3 result of the MEM research for Charmonium 7.3.1 Mock info Analysis

o 7.3.2 OPE research at T= 0

o 7.3.3 OPE research at T = 0

o 7.3.4 precis for Charmonium

7.4 result of the MEM research for Bottomonium

o 7.4.1 Mock information Analysis

o 7.4.2 OPE research at T= 0

o 7.4.3 OPE research at T = 0

o 7.4.4 precis for Bottomonium

Part III Concluding Remarks

bankruptcy eight precis, end and Outlook

8.1 precis and Conclusion

8.2 Outlook

Appendix A The Dispersion Relation

Appendix B The Fock-Schwinger Gauge

Appendix C The Quark Propagator

Appendix D Non-Perturbative Coupling of Quarks and Gluons

Appendix E Gamma Matrix Algebra

Appendix F The Fourier Transformation

Appendix G Derivation of the Shannon-Jaynes Entropy

Appendix H forte of the utmost of P[.|GH]

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**Additional info for A Bayesian Analysis of QCD Sum Rules**

**Example text**

This disagreement between the results of these two approaches certainly needs further investigation. 41) in our calculations. The mixed condensate for the strange quarks qgσ Gq is parametrized similarly to Eq. 42) ≡ m 21 . 1) GeV2 . 4 Higher Order Condensates There are two sorts of condensates with mass dimension six. Firstly there is the bλ cμ three-gluon condensate g 3 f abc G aν μ G ν G λ , where f abc are the structure constants 40 3 Basics of QCD Sum Rules of the SU(3) group. The value of this condensate is not very well known and only a crude estimate based on the dilute instanton gas model exists (Novikov et al.

We thus have to rely on the analytic properties of Π ± (q0 ), which allows us to extract information on the spectral functions via certain sum rules, that we will discuss in the next subsection. 3 Construction of the Sum Rules We now use the analyticity of the functions Π ± (q0 ) to construct the sum rules. To do that, we first have to remember that there are two distinct ways of expressing Π ± (q0 ). The first expression uses the OPE and is written down in the language of the elementary degrees of freedom of QCD.

68) has the potential to be more reliable. To establish which sum rule is more useful, a detailed study of both Eqs. 68) is certainly necessary. Also note that if one employs the maximum entropy method (to be discussed in the next chapter) to analyze the sum rules, it even becomes possible to study both sum rules at the same time. As a last point of this section, we briefly touch on the issue of what function should be chosen for the weight function F(q02 ). The traditionally favored choice has been the Borel weight function, given as F(q02 , M) = e−q0 /M .

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