Effective Field Theories

Module PH2122

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

PH2122 is a semester module in English language at Master’s level which is offered irregular.

This Module is included in the following catalogues within the study programs in physics.

  • General catalogue of special courses
  • Specific catalogue of special courses for nuclear, particle, and astrophysics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 75 h 5 CP

Responsible coordinator of the module PH2122 is Antonio Vairo.

Content, Learning Outcome and Preconditions


The lecture course will provide an introduction to effective field theories (EFTs) and renormalization techniques with applications ranging from high energy to atomic physics. The following topics will be covered:

  • Principles of EFTs
    • Scales and systems in nature
    • What is an EFT and how to construct it
    • Example: the Euler-Heisenberg Lagrangian
    • Example: the Fermi theory of weak interactions at tree level
    • Example: the Rayleigh scattering
    • Relevant, irrelevant and marginal operators
    • Quantum loops of irrelevant operators
    • Mass-dependent vs mass-independent regularization schemes
    • Dimensional regularization
    • Quantum loops of marginal operators
    • Example: β function and running coupling constant in QED and QCD
    • Decoupling theorem
    • Example: the one and two loop matching of the QCD strong-coupling constant in MSbar
    • Renormalization group equations in QFTs and EFTs
    • Anomalous dimensions
    • Mixing
    • Example: ΔS = 2 transition amplitude in the Fermi theory of weak interactions
  • Heavy quark effective theory
    • Heavy-light meson spectrum
    • Heavy-quark spin-flavour symmetry
    • Static Lagrangian
    • Spectroscopy implications
    • Heavy meson decay constants
    • Transition form factors: Isgur-Wise functions
    • Example: B → D transitions and calculation of dΓ(B → D e ν)/dq²
    • Renormalization of composite operators
    • Example: heavy-light currents and heavy-heavy currents
    • Heavy meson decay constants at LL and NLO
    • The 1/m expansion of the HQET Lagrangian
    • Reparameterization invariance
    • Chromomagnetic coupling and hyperfine splitting at LL
    • Decoupling in the HQET
    • B → D e ν and Luke's theorem
  • Applications to atomic physics
    • Bound states in QED: physical picture, scales, degrees of freedom
    • NRQED: Lagrangian, power counting, matching
    • Four-fermion operators
    • Example: matching of dimension six four-fermion operators and the positronium decay width
    • pNRQED: Lagrangian, power counting, matching
    • Example: the hydrogen atom and the Lamb shift
    • Example: the Rayleigh scattering in pNRQED

Learning Outcome

After attending the course, the attendant has become familiar with modern renormalization techniques and effective field theories. This aim is achieved by looking at how the degrees of freedom of ordinary matter (hadrons, nuclei, atoms, molecules) emerge in a systematic fashion from the elementary degrees of freedom of the Standard Model (lepton, quarks, gauge fields).


Quantum Mechanics 1 + 2 and some basic knowledge of Quantum Field Theory and the Standard Model

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 4 Effective Field Theories Vairo, A. Dienstag, 10:00–12:00
Mittwoch, 10:00–12:00

Learning and Teaching Methods

preparation and presentation of a lecture, beamer presentation, board work, discussion


complementary literature


A. Dobado, A. Gomez-Nicola, A.L. Maroto, J.R. Pelaez,  Effective Lagrangians for the Standard Model, Springer Verlag 1997

S. Weinberg, The Quantum Theory of Fields Vol. II, Cambridge University Press 1996, Chapter 19

A. Pich, Effective field theory, Les Houches 1997, Probing the standard model of particle interactions, Pt. 2* 949-1049, e-Print: hep-ph/9806303

A.V. Manohar, Effective field theories, Schladming 1996, Perturbative and nonperturbative aspects of quantum field theory* 311-362, e-Print: hep-ph/9606222

D.B. Kaplan, Effective field theories, 7th Summer School in Nuclear Physics Symmetries, Seattle, e-Print: nucl-th/9506035

H. Georgi, Effective field theory, Ann.Rev.Nucl.Part.Sci.43:209-252,1993

B.R. Holstein, Effective effective interactions, Eur.Phys.J.A18:227-230,2003

S. Weinberg,  Phenomenological Lagrangians, Physica A96:327,1979

School in  Applications of Effective Field Theories, U. Milano (2003)

School on Flavor Physics, Centro de Ciencias de Benasque (2008)

A.V. Manohar, M.B. Wise, Heavy quark physics, Cambridge University Press 2000

M. Neubert, Heavy-quark symmetry, Phys.Rept.245:259-396,1994

B. Grinstein, An introduction to heavy mesons, 6th Mexican School of Particles and Fields, Villahermosa, e-Print: hep-ph/9508227

T. Mannel, Heavy-quark effective field theory, Rept.Prog.Phys.60:1113-1172,1997

G.P. Lepage, L. Magnea, C. Nakhleh, U. Magnea, K. Hornbostel, Improved nonrelativistic QCD for heavy quark physics, Phys.Rev.D46:4052-4067,1992, e-Print: hep-lat/9205007

A.V. Manohar, The HQET/NRQCD Lagrangian to order α/m^3, Phys.Rev.D56:230-237,1997, e-Print: hep-ph/9701294

W.E. Caswell, G.P. Lepage,  Effective Lagrangians for bound state problems in QED, QCD, and other field theories, Phys.Lett.B167:437,1986

A. Pineda, J. Soto, The Lamb shift in dimensional regularization, Phys.Lett.B420:391-396,1998, e-Print: hep-ph/9711292

A. Pineda, J. Soto, Potential NRQED: the positronium case, Phys.Rev.D59:016005,1999, e-Print: hep-ph/9805424

B.R. Holstein, Blue skies and effective interactions, American Journal of Physics 67:422,1999

Module Exam

Description of exams and course work

In an oral exam the learning outcome is tested using comprehension questions and sample problems.

In accordance with §12 (8) APSO the exam can be done as a written test. In this case the time duration is 60 minutes.

Exam Repetition

There is a possibility to take the exam at the end of the semester. There is a possibility to take the exam in the following semester.

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