By Philipp Gubler

The writer develops a singular research approach for QCD sum ideas (QCDSR) through utilising the utmost entropy approach (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 principles of a number of channels: the light-quark meson within the vector channel, the light-quark baryon channel with spin and isospin 0.5, and a number of other quarkonium channels at either 0 and finite temperatures. This novel means of combining QCDSR with MEM is utilized to the examine of quarkonium in sizzling topic, that is a big probe of the quark-gluon plasma at present 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 ideas and Its Ambiguities

1.3 Hadrons in a scorching and/or Dense Environment

1.4 Motivation and objective of this Thesis

1.5 define of the Thesis

bankruptcy 2 easy 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 middle 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 sensible 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 better 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 building of the Sum Rules

o 3.4.4 normal research of the Sum ideas for Three-Quark Baryons

bankruptcy four the utmost Entropy Method

4.1 easy Concepts

o 4.1.1 the possibility functionality and the earlier Probability

o 4.1.2 The Numerical Analysis

o 4.1.3 blunders Estimation

4.2 pattern MEM research of a Toy Model

o 4.2.1 building 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 info and the Corresponding Errors

o 5.2.2 number of a suitable Default Model

o 5.2.3 research of the steadiness of the got Spectral Function

o 5.2.4 Estimation of the Precision of the ultimate Results

o 5.2.5 Why it really is Difficul to correctly 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 ideas 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 ideas 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 information 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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**Extra resources for A Bayesian Analysis of QCD Sum Rules**

**Sample text**

3. Here we notice that in the limit of vanishing quark mass, the quark propagator with two attached gluons vanishes (Ioffe et al. 2010) and is therefore strongly suppressed for light quarks. Therefore, we only have to calculate the graph on the left side of Fig. 3. (Note, however, that for heavy quarks, all three graphs give contributions of comparable size and thus have to be taken into account (Novikov et al. ) The concrete evaluation of the relevant diagram of Fig. 3 is then quite simple. One substitutes the third term of Eq.

33) and take the traces, which leads to 0|T[ j μ (x) jμ† (0)]|0 = leading pert. 6 1 . 34) To calculate the first order αs correction of the perturbative term, one needs to calculate the diagrams shown in Fig. 2. This calculation has to be done in momen- Fig. 2 More on the Operator Product Expansion 37 tum space and is quite involved. Therefore, we do not discuss it here and refer the reader to literature (Colangelo and Khodjamirian 2001; Schwinger 1998) for details. The next term would in principle be the one with the quark condensate with mass dimension 3.

34) To calculate the first order αs correction of the perturbative term, one needs to calculate the diagrams shown in Fig. 2. This calculation has to be done in momen- Fig. 2 More on the Operator Product Expansion 37 tum space and is quite involved. Therefore, we do not discuss it here and refer the reader to literature (Colangelo and Khodjamirian 2001; Schwinger 1998) for details. The next term would in principle be the one with the quark condensate with mass dimension 3. This term, however vanishes due to chiral symmetry.