Flavor Constraints from Unitarity and Analyticity

Abstract

We use unitarity and analyticity of scattering amplitudes to constrain fermionic operators in the standard model effective field theory. For four-fermion operators at mass dimension 8, we scatter flavor superpositions in fixed standard model representations and find the Wilson coefficients to be constrained so that their contraction with any pair of pure density matrices is positive. These constraints imply that flavor-violating couplings are upper bounded by their flavor-conserving cousins. For instance, LEP data already appears to preclude certain operators in upcoming μ → 3e measurements.

Sum rules in the standard model effective field theory from helicity amplitudes

“…Such relations, often denoted as sum rules, can be classified in terms of the energy expansion of the amplitudes analogous to the EFT operator expansion. In previous works, the main focus has been at the level of dimension-8 operators for which the sum rules can be interpreted as positivity bounds on certain operator coefficients (or combinations of them) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. This remarkable finding suggests that the possible parameter space in an EFT is already constrained by the fundamental properties of quantum field theory, i.e.…”

“…A recent study on the flavor constraints from dimension-8 four-fermion operators can be found in ref. [16]. Given that we are working in the massless limit with no EWSB, we will parameterize the Higgs doublet as H = φ + φ 0…”

“…[47]) and keep only the parts proportional to y 2 t . This gives the running of c T as 16) where c T (µ 0 ) is the value of c T evaluated at a reference scale µ 0 . In the BM model, we have c Hq…”

“…One important feature of an on-shell 3-point amplitude is that it is composed of either only angle brackets or only square brackets. 16 Its form is thus fixed by the little group scaling, given by…”

Low-Energy Effective Field Theory below the Electroweak Scale: dimension-8 operators

“…Furthermore, many dimension-8 operators are subject to positivity bounds arising from fundamental principles of quantum field theory including unitarity and analyticity, see [20][21][22][23][24][25][26][27][28][29] for some recent applications. The LEFT is a valid EFT in its own right, independent of whatever its UV completion may be.…”