The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory

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might be responsible for solving the Ay problem in the elastic nd scattering at low energies. For more discussion on that see ref. [196J. We also point out that problems related to renormalization of the effective Hamiltonian after eliminating the pionic degrees of freedom have to be investigated more carefully than it has been done in sec. 3.8.2. In particular, one should include also the zero- and one-body operators in order to perform a complete renormalization at NLO and NNLO. Furthermore, it would be interesting to study the problem of carrying out the renormalization at an arbitrary order in the moment um expansion. As far as we know, the problem of renormalization within the Hamiltonian approach has never been worked out in detail (also in the context of an effective field theory). Last not least we have shown that isospin violation can be systematically included in the effective field theory approach to the two-nucleon system in the KSW formulation. For that, one has to construct the most general isospin violating effective Lagrangian and extend the power counting sehe me accordingly. We have shown that this framework allows one to syste�atically classify the various contributions to charge indepedence and charge symmetry breaking (CIB and CSB). In particular, the power counting combined with dimensional analysis allows one to understand the suppression of contributions from a possible charge-dependence in the pion-nucleon coupling constants. It would be interesting to extend this formalism to other partial waves and to higher energies so as to investigate e.g. isospin violation in pion production. 171
Appendix A Dimensional analysis of the projected decoupling equation (3.206) In this appendix, we work out the chiral power of various terms appearing in eq. (3.206). Any one of these can be characterized by a counting index v, i.e. it is proportional to QV. This index should not be confused with the one giving the chiral dimension of the matrix-elements (w i IAI
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The Nucleon-Nucleon Interaction in
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11 vom ursprünglichen wesentlich u
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IV Ordnung des Potentials besteht a
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VI sagen für die Schwerpunktsimpul
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Vlll betrachten, um eine komplette
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x 5 Isospin violation in the two-nu
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2 1. Introduction nuclear force of
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4 1. Introduction the Thcson-Melbou
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6 1. Introduction pion-nucleon syst
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8 1. Introduction completely domina
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10 1. Introduction such interaction
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12 2. Low-momentum effective theori
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28 2. Low-momentum efIective theori
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36 2 o -2 -4 -6 -8 -10 � -12 t-
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38 (Eq - Ep )A(p, q) [GeV-2] 2 1.6
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42 -3 -5 -7 -9 2. Low-momentum effe
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Chapter 3 The derivation of nuclear
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50 3. The derivation of nuc1ear for
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52 and for the SU(Nf h x SU(Nf)R [Q
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54 3. The derivation of nuclear for
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66 3. The derivation o{ nuclear {or
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74 3. The derivation o{ nuc1ear {or
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84 .... . - - .... \ . • A .... .
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94 , , , , , , , , , , , , , , , ,
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96 _ . . -.:;: " :,,,_ ._ . . _. 3.
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98 3. The derivation o{ nuc1ear {or
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100 3. The derivation o{ nuc1ear {o
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102 3. The derivation o{ nuclear {o
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104 3. The derivation of nuclear fo
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114 / / / / / / / 5 / / \ \ \ \ I I
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116 3. The derivation o{ nuc1ear {o
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Page 131 and 132: 120 4. The two-nuc1eon system: nume
Page 145 and 146: 134 10 8 4 2 o o • Nijmegen PSA N
Page 147 and 148: 136 4. The two-nucleon system: nume
Page 151 and 152: 140 4. The two-nucleon system: nume
Page 157 and 158: 146 --- .... . � - --- .... . ...
Page 159 and 160: 148 � .... --- � � .... --- :
Page 162 and 163: 4.5. Results for the NNLO-ß approa
Page 164 and 165: 5.1 Isospin violating effective Lag
Page 166 and 167: 5.1 Isospin violating effective Lag
Page 168 and 169: 5.2 Brief introduction into the KSW
Page 170 and 171: 5.3 The leading eIB and eSB effects
Page 172 and 173: 5.3 The leading CIB and CSB effects
Page 174 and 175: 5.5 Classification scheme 163 scatt
Page 176 and 177: Chapter 6 Summary and outlook In th
Page 178 and 179: 2. Secondly, we considered the real
Page 180 and 181: NNLO, this range is larger and exte
Page 184 and 185: derivative. Further helpful equalit
Page 186 and 187: Appendix B Operators contributing t
Page 188 and 189: Appendix C Small scale expansion wi
Page 190 and 191: 179 (C.16) l�r-2. (C.17) h + l2 =
Page 192 and 193: Appendix E Anti-symmetrization of t
Page 194 and 195: Consequently, only four of the eigh
Page 196 and 197: where qJ-! is chosen to satisfy (v
Page 198 and 199: To keep the presentation self-conta
Page 200 and 201: - i�03{ [(NtVN) . (VNt x ifN) + (
Page 202 and 203: Consequently, it is not possible to
Page 204 and 205: (j ± 1, 1jIVIJ =f 1, 1j) Here, Pj
Page 206 and 207: Bibliography [1] E. Rutherford, Phi
Page 208 and 209: [62] J. Goldstone, A. Salam and S.
Page 210 and 211: [137] V. Bernard, N. Kaiser and Ulf
Page 212: [204] J.M. Blatt and L.C. Biedenhar
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The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory

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