g_P: Goldberger-Treiman and the ADW correction

[Tom Banks <tbanks@socrates.berkeley.edu>]

The original Goldberger-Treiman expression for g_p, derived in terms of
pionic constants using dispersion relation techniques, is from reference:

  @Article{Goldberger:1958vp,
       author    = "Goldberger, M. L. and Treiman, S. B.",
       title     = "Form-factors in Beta decay and muon capture",
       journal   = "Phys. Rev.",
       volume    = "111",
       year      = "1958",
       pages     = "354-361",
       SLACcitation  = "%%CITATION = PHRVA,111,354;%%"
  }
  % URL: http://link.aps.org/abstract/PR/v111/p354
  % DOI: 10.1103/PhysRev.111.354

(Incidentally, their similarly derived expression for the axial form
factor g_A is the more famous "Goldberger-Treiman relation"; see
reference:

  @Article{Goldberger:1958tr,
       author    = "Goldberger, M. L. and Treiman, S. B.",
       title     = "Decay of the pi meson",
       journal   = "Phys. Rev.",
       volume    = "110",
       year      = "1958",
       pages     = "1178-1184",
       SLACcitation  = "%%CITATION = PHRVA,110,1178;%%"
  }
  % URL: http://link.aps.org/abstract/PR/v110/p1178
)

The current algebra approaches of the 1960s enabled Adler and Dothan
as well as Wolfenstein (ADW) to identify a small correction to the
G--T expression for $g_P$; see references

  @Article{Adler:1966,
       author    = "Adler, S. L. and Dothan, Y.",
       title     = "Low-Energy Theorem for the Weak Axial-Vector Vertex",
       journal   = "Phys. Rev.",
       volume    = "151",
       year      = "1966",
       pages     = "1267"
  }
  % URL: http://link.aps.org/abstract/PR/v151/p1267
  % DOI: 10.1103/PhysRev.151.1267

  @Book{Wolfenstein:1970,
       author    = "Wolfenstein, L.",
       editor    = "S. Devons",
       title     = "High Energy Physics and Nuclear Structure",
       publisher = "Plenum",
       address   = "New York",
       year      = "1970",
       pages     = "661"
  }

Of course, ChPT just reproduces these exact results as part of a
systematic order-by-order expansion, but the ChPT people assert that their
results are founded on more fundamental principles (that is, they are not
ad hoc), and are therefore more robust.

Tom