Hadron Form Factors-From Basic Phenomenology to QCD Sum Rules

313 Pages·2020·6.047 MB·\313

by  Alexander Khodjamirian (Author)

Hadron Form Factors
From Basic Phenomenology to
QCD Sum Rules

Hadron Form Factors
From Basic Phenomenology to
QCD Sum Rules
Alexander Khodjamirian
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Contents
Preface xi
Introduction xv
hapter
C 1(cid:4) QCD, QUARK CURRENTS, AND HADRONS 1
1.1 BASICELEMENTSOFQCD 1
1.1.1 QCD Lagrangian 1
1.1.2 Perturbative QCD, the running coupling, and quark mass 2
1.1.3 Nonperturbative regime, confinement, and hadrons 5
1.1.4 Quark-gluon coupling and quark masses 7
1.2 QUARKELECTROMAGNETICCURRENT 8
1.3 QUARKWEAKCURRENTS 9
1.4 EFFECTIVECURRENTS 11
1.5 ISOSPINANDSU(3)-FLAVORSYMMETRIES 13
1.6 CHIRALSYMMETRYANDITSVIOLATION 15
1.7 HADRONSANDTHEIRSPECTROSCOPY 17
1.7.1 Mesons and baryons 17
1.7.2 Hadronic state in QCD 18
1.7.3 Exotic hadrons and hadronic molecules 19
1.7.4 Basics of hadron spectroscopy 20
1.7.5 Varying the quark flavors 23
1.7.6 Hadrons are not alike 25
1.7.7 Mixing of light isoscalar mesons 26
1.7.8 Unstable hadrons 28
1.8 HEAVYQUARKSYMMETRIESANDEFFECTIVETHEORY 31
hapter
C 2(cid:4) MESON FORM FACTORS 39
2.1 HADRONICMATRIXELEMENTOFTHEELECTRON-PIONSCATTERING 39
2.2 PIONELECTROMAGNETICFORMFACTOR 42
2.3 SIMPLERTHANAFORMFACTOR:THEPIONDECAYCONSTANT 46
2.4 THEFORMFACTORSOFWEAKπ DECAY 49
e3
2.5 VARYINGFLAVORS:K-,D-,ANDB-MESONFORMFACTORS 54
2.6 FORMFACTORSINHQET 65
vii
viii (cid:4) Contents
hapter
C 3(cid:4) BARYON FORM FACTORS 71
3.1 ELECTROMAGNETICFORMFACTORSOFTHENUCLEON 71
3.2 WEAKFORMFACTORSOFTHENUCLEONANDβ DECAY 73
3.3 VARYINGFLAVORS:FORMFACTORSOFΛ,Λ ,ANDΛ BARYONS 75
C B
3.4 IOFFECURRENTANDBARYONDECAYCONSTANTS 77
hapter
C 4(cid:4) HADRONIC RADIATIVE TRANSITIONS 79
4.1 THEρ πγ DECAYANDVECTORDOMINANCE 79
→
4.2 D∗ Dγ ANDB∗ Bγ DECAYS 84
→ →
4.3 RADIATIVETRANSITIONSINHEAVYQUARKONIUM 85
4.4 B K∗γ DECAY 87
→
hapter
C 5(cid:4) FORM FACTORS IN THE TIMELIKE REGION 89
5.1 CROSSINGTRANSFORMATIONANDANALYTICITY 89
5.2 UNITARITYANDDISPERSIONRELATION 92
5.3 PION FORM FACTOR IN THE ELASTIC REGION AND THE WATSON
THEOREM 96
5.4 OMNESREPRESENTATION 99
5.5 RESONANCESINTHEPIONFORMFACTOR 101
5.6 KAONFORMFACTORSANDτ DECAYS 111
5.7 B ππ(cid:96)ν DECAYS 117
(cid:96)
→
hapter
C 6(cid:4) NONLOCAL HADRONIC MATRIX ELEMENTS 125
6.1 π0 2γ DECAY 125
→
6.2 PHOTOLEPTONICWEAKDECAYS 130
6.3 THEANATOMYOFB K(∗)(cid:96)+(cid:96)− AMPLITUDES 135
→
hapter
C 7(cid:4) FORM FACTOR ASYMPTOTICS 143
7.1 CANWECALCULATEHADRONFORMFACTORSINQCD? 143
7.2 ASYMPTOTICSOFTHEPIONFORMFACTORINQCD 144
hapter
C 8(cid:4) QCD SUM RULES 153
8.1 TWO-SIDEDUSEOFTHECORRELATIONFUNCTION 153
8.2 SHORTDISTANCEDOMINANCE 157
8.3 PERTURBATIVECONTRIBUTIONS 159
8.4 VACUUMCONDENSATESANDOPERATOR-PRODUCTEXPANSION 160
8.5 CALCULATINGATWO-POINTCORRELATIONFUNCTION 162
8.5.1 Perturbative loop 162
8.5.2 Condensate terms 166
8.6 VARIOUSAPPLICATIONSOFQCDSUMRULES 174
8.6.1 The s-quark mass determination 174
Contents (cid:4) ix
8.6.2 Pion decay constant 176
8.6.3 Heavy quarkonium 181
8.6.4 Decay constants of heavy mesons 187
8.7 THREE-POINTSUMRULESFORHADRONFORMFACTORS 192
hapter
C 9(cid:4) LIGHT-CONE EXPANSION AND DISTRIBUTION
AMPLITUDES 205
9.1 THEγ∗γ∗ π0 AMPLITUDE 205
→
9.2 LIGHT-CONEDOMINANCE 207
9.3 EXPANSIONNEARTHELIGHT-CONE 208
9.4 THEPIONDISTRIBUTIONAMPLITUDE 211
hapter
C 10(cid:4) QCD LIGHT-CONE SUM RULES 223
10.1 QUARKPROPAGATORNEARTHELIGHT-CONE 223
10.2 CALCULATIONOFTHEPIONFORMFACTOR 226
10.3 THEPHOTON-PIONTRANSITIONFORMFACTOR 235
10.4 VARYINGFLAVORS:HEAVY-TO-LIGHTFORMFACTORS 239
10.5 SUMRULESWITHB-MESONDISTRIBUTIONAMPLITUDES 244
ppendix
A A(cid:4) Collection of useful formulas 251
ppendix
A B(cid:4) Decay amplitudes and widths 265
Appendix C(cid:4) Parameterization and z-expansion of form factors 275
ppendix
A D(cid:4) The pion light-cone distribution amplitudes 279
Bibliography 283
Index 291