Quark mass dependence of nucleon observables and lattice QCD

Abstract

SummaryUnderstanding hadron structure from first principles is one of the great unsolved problems in physics. Lattice QCD on one side and chiral effective field theory on the other are progressively developing as important tools to deal with the non-perturbative nature of low-energy QCD and the structure of the nucleon. At present, however, there is a gap between the relatively large quark masses accessible in fully-dynamical lattice simulations and the small quark masses relevant for comparison with physical quantities. We combine Chiral Perturbation Theory, which predicts the quark mass dependence of nucleon observables, with lattice computations where the quark mass is a tunable parameter. We explore the feasibility of a systematic approach, based on the chiral effective Lagrangian, for the chiral extrapolation of lattice QCD data. In the framework of baryon chiral effective field theories with and without explicit ∆ (1232) degrees of freedom, we work out the quark mass dependence of the nucleon mass M N and the axialvector coupling constant g A at one-loop order and perform a numerical analysis of the relevant formulae using as input the most recent lattice QCD results. ZusammenfassungEs ist eines der großen ungelösten Probleme in der Physik, die hadronische Struktur von Anfang an zu verstehen. Gitter-QCD auf der einen Seite und chirale effektive Feldtheorie auf der anderen entwickeln sich schrittweise zu wichtigen Werkzeugen, mit der nicht-perturbativen Natur der Niederenergie-QCD und der Nukleonstruktur umzugehen. Momentan besteht jedoch eine Lücke zwischen den relativ großen Quarkmassen, die in voll-dynamischen Gittersimulationen verwendet werden müssen, und den kleinen Quarkmassen, die für den Vergleich mit physikalischen Größen relevant sind. Wir kombinieren Chirale Störungstheorie, die die Quarkmassenabhängigkeit von Nukleon-Observablen vorhersagt, mit Gitterrechnungen, in denen die Quarkmasse ein veränderbarer Parameter ist. Wir untersuchen, ob ein systematischer Zugang zur chiralen Extrapolation von Gitter-QCD-Daten, basierend auf der chiralen effektiven Lagrangedichte, möglich ist. Im Rahmen von baryonischen chiralen effektiven Feldtheorien mit und ohne explizitem ∆ (1232)-Freiheitsgrad berechnen wir die Quarkmassenabhängigkeit der Nukleonmasse M N und der Axialvektor-Kopplungskonstante g A in führender Ein-Schleifen-Ordnung und führen eine numerische Analyse der relevanten Formeln mit den neuesten Gitter-QCD-Ergebnissen als Input durch. 5 6

Leading-order hadronic contribution to the electron and muon g-2

“…Specifically: (a) HVP via a dispersion integral over e + e − → hadrons data (1 independent amplitude to be determined by one specific data channel) (see e.g. [4]) as elaborated below, by the HLS effective Lagrangian approach [5][6][7][8][9], or by lattice QCD [10][11][12][13][14][15]; (b) HLbL via a RLA together with operator product expansion (OPE) methods [16][17][18][19], by a dispersive approach using γγ → hadrons data (28 independent amplitudes to be determined by as many independent data sets in prina e-mail: fjeger@physik.hu-berlin.de ciple) [20][21][22] or by lattice QCD [23,24]; (c) EW quarktriangle diagrams are well under control, because the possible large corrections are related to the Adler-Bell-Jackiw (ABJ) anomaly which is perturbative and non-perturbative at the same time. Since VVV = 0 by the Furry theorem, only VVA (of γγZ -vertex, V=vector, A=axialvector) contributes.…”

Leading-order hadronic contribution to the electron and muong− 2

“…Specifically: (a) HVP via a dispersion integral over e + e − → hadrons data (1 independent amplitude to be determined by one specific data channel) (see e.g. [4]) as elaborated below, by the HLS effective Lagrangian approach [5][6][7][8][9], or by lattice QCD [10][11][12][13][14][15]; (b) HLbL via a RLA together with operator product expansion (OPE) methods [16][17][18][19], by a dispersive approach using γγ → hadrons data (28 independent amplitudes to be determined by as many independent data sets in prina e-mail: fjeger@physik.hu-berlin.de ciple) [20][21][22] or by lattice QCD [23,24]; (c) EW quarktriangle diagrams are well under control, because the possible large corrections are related to the Adler-Bell-Jackiw (ABJ) anomaly which is perturbative and non-perturbative at the same time. Since VVV = 0 by the Furry theorem, only VVA (of γγZ -vertex, V=vector, A=axialvector) contributes.…”

Chiral Perturbation Theory and mesons

“…These arguments, as described below were generalized and applied to a larger number of processes in [40 -43]. Some doubt on the simple arguments has been presented in [44,45].…”

“…Recently [44,45], the test done at two loops was extended to higher orders. What was found there was that the hard pion ChPT prediction held to all orders for the elastic intermediate state but failed in a three loop calculation of the inelastic four-particle-cut part.…”

“…What was found there was that the hard pion ChPT prediction held to all orders for the elastic intermediate state but failed in a three loop calculation of the inelastic four-particle-cut part. For details I refer to [44,45]. The arguments for the general method are the same as for IR divergences, SCET,.…”