Lorentz invariance in heavy particle effective theories

Abstract

Employing induced representations of the Lorentz group (Wigner's little group construction), formalism for constructing heavy particle effective Lagrangians is developed, and Lagrangian constraints enforcing Lorentz invariance of the S matrix are derived. The relationship between Lorentz invariance and reparameterization invariance is established and it is shown why a standard ansatz for implementing reparameterization invariance in heavy fermion effective Lagrangians breaks down at order 1/M 4 . Formalism for fields of arbitrary spin and for self-conjugate fields is presented, and the extension to effective theories of massless fields is discussed.

Standard Model anatomy of WIMP dark matter direct detection. II. QCD analysis and hadronic matrix elements

“…where S = iσ 2 for fermions and S = 1 for scalars [33]. In this formulation of the self-conjugate parity, the action of discrete symmetries transforms fields, but leaves the reference vector v µ unchanged.…”

“…We may further simplify the matrix (33). By dimensional analysis, the gauge invariant operator m qq q matches onto (G A µν ) 2 with power suppression, ∼ m q /m Q , and hence M gq ≡ 0.…”

“…A heavy fermion has two degrees of freedom which may be embedded in a Dirac spinor, χ v , with constraint v / χ v = χ v (see, e.g., Ref. [33] and Sec. 2 of Ref.…”

Effective field theory for large logarithms in radiative corrections to electron proton scattering

“…For a discussion of general heavy particle e↵ective theories see Ref. [14]. At the same time, we introduce formalism and notation that will carry over to the more complicated case of relativistic electron scattering (i.e., Q 2 m 2 ) considered later.…”

“…(8), where only a single, soft, momentum mode is present). 14 We proceed by direct evaluation of the diagrams.…”