Effective Field Theories

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

The student will aquire the necessary knowledge to build effective field theories, compute Wilson coefficients, renormalize them, solve renormalization group equations and compute observables in principle at any order in the expansion parameter(s). In practice we will work out one loop calculations for non-relativistic effective field theories in QED and QCD.

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

Lectures will be given on a blackboard. Many physical examples will be presented and worked out in all details. Exercises are suggested and will be discussed as requested. Discussions and feedbacks during the lectures  are strongly encouraged.

blackboard,
accompanying website http://users.ph.tum.de/gu32tel/Lectures/SS18-EFT.html

Literature

• Principles of EFTs
  • Books: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
  • Review papers and lecture notes: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
  • A founding paper:S. Weinberg, Phenomenological Lagrangians, Physica A96:327,1979
  • EFTs courses:School on Flavor Physics, Centro de Ciencias de Benasque (2008)
    Effective field theory course (2013) at MIT by Iain Stewart (with emphasis on SCET)

• Heavy quark effective theory
• Books:A.V. Manohar, M.B. Wise, Heavy quark physics, Cambridge University Press 2000
• • Review papers and lecture notes: 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
  • Related papers: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

• Applications to atomic physics
  • Related papers: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

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

• Typical questions will include: how to construct an EFT, how to match it, how to write an RG equation,
• how to write an RG equation. Specific physical examples presented during the lecture (HQET,NRQED,pNRQED, etc.) may be also discussed.