By Philipp Gubler

ISBN-10: 4431543171

ISBN-13: 9784431543176

The writer develops a singular research technique for QCD sum principles (QCDSR) by means of utilizing the utmost entropy procedure (MEM) to reach at an research with much less man made assumptions than formerly held. it is 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 learn of quarkonium in sizzling topic, that's a huge 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 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 uncomplicated 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 levels 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 larger 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 formed" 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 simple Concepts

o 4.1.1 the possibility functionality and the earlier Probability

o 4.1.2 The Numerical Analysis

o 4.1.3 mistakes 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 information and the Corresponding Errors

o 5.2.2 selection of a suitable Default Model

o 5.2.3 research of the soundness of the received Spectral Function

o 5.2.4 Estimation of the Precision of the ultimate Results

o 5.2.5 Why it's Difficul to effectively ascertain 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 specialty of the utmost of P[.|GH]

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

**Example text**

4 Phases of QCD The phases of QCD at various values of temperature and density continue to be intensively studied both theoretically and experimentally. For a recent review of the current statues in theory, see Fukushima and Hatsuda (2011). However, despite of these efforts, there are still many open questions and fully established facts are rather rare. In this short introduction, we will not discuss all open issues in detail, but can only give a broad overview about what is known about the properties of QCD in a hot or dense medium.

As one can see in the above equation, we are seemingly running into problems for terms with dimension 7 and higher, as the limit q2 → 0 leads to a divergence for these terms. However, as we will see below, after substituting Eq. 63) into Eq. 60) and evaluating the integral over q0 , these divergences in fact vanish, leaving only finite expressions for the final form of the sum rules. Let us now carry out this last step and calculate the right hand side of Eq. 60). For this, we consider two classes of weight functions W (q0 ), one which is an even function of q0 , We (q0 ) = F(q02 ), the other being an odd function, Wo (q0 ) = q0 F(q02 ).

Essentially, the idea is that the simple expression of Eq. 3) is in fact not completely correct, but should be written down including a scale μ, specifying the energy at which one separates the high- and low-energy contributions: Π (q 2 ) = Cd (q 2 , μ) 0|Od |0 (μ). 20) d Here, both the Wilson coefficients Cd (q 2 , μ) and the condensates 0|Od |0 (μ) depend on the factorization scale μ. However, as a whole, this expression should not depend on μ and hence these dependencies of the different parts cancel.

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