By Philipp Gubler

The writer develops a unique research approach for QCD sum ideas (QCDSR) by means of utilizing the utmost entropy procedure (MEM) to reach at an research with much less synthetic 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 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 learn of quarkonium in scorching topic, that's a massive 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 sizzling and/or Dense Environment

1.4 Motivation and goal 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 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 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 formed" 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 easy 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 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 number 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 adequately make sure 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 facts 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 info for A Bayesian Analysis of QCD Sum Rules**

**Sample text**

As was pointed out in Kondo et al. (2006), it is not entirely clear whether this prescription is justifiable. Therefore, in this study, we implement two essential improvements as compared to Jido et al. (1996): (1) We do not use the time ordered correlator, but derive all results directly from the “old fashioned” correlator of Eq. 53). (2) We do not restrict the region of integration of the OPE side of Eq. 60) to positive values and therefore remove the ambiguities that might occur for higher order OPE terms.

For a more detailed discussion of this issue, see Chap. 6 of Yagi et al. (2005). Finally, let us consider more realistic cases, which lie close to the physical point, indicated by the black dot in Fig. 3. Even though still challenging due to the light u and d quark masses, lattice simulations are now at the stage of becoming possible in 22 2 Basic Properties of QCD such a regime. Most of these simulations employ the staggered fermions (Susskind 1977; Sharatchandra et al. 1981), while some also use the Wilson fermion formalism (Wilson 1975).

3. Even though still challenging due to the light u and d quark masses, lattice simulations are now at the stage of becoming possible in 22 2 Basic Properties of QCD such a regime. Most of these simulations employ the staggered fermions (Susskind 1977; Sharatchandra et al. 1981), while some also use the Wilson fermion formalism (Wilson 1975). Recent results of such studies suggest that the transition at the physical point is smooth crossover (Aoki et al. 2006). Furthermore, the value of the critical temperature has been evaluated by various groups, the latest results giving an averaged value of roughly 170 MeV, with a scatter of about 20 MeV (Aoki et al.