Gauge contribution to the 1/NF expansion of the Yukawa coupling beta function

Abstract

We provide a closed analytical form for the gauge contribution to the beta function of a generic Yukawa coupling in the limit of large N F , where N F is the number of heavy vector-like fermions charged under an abelian or non-abelian gauge group. The resummed expression is finite and for the abelian case presents a pole at the same location as for the corresponding gauge beta function. When applied to new physics scenarios characterized by large Yukawa couplings, the contribution calculated here can cure their pathological UV behavior and make the couplings asymptotically free.

Abelian gauge-Yukawa β -functions at large Nf

“…The function ξ E (p 2 , t, 0) = lim n→0 ξ E (p 2 , t, n) has to be independent of p 2 for the consistency of the computation. This is indeed the case: we checked that corresponds to the result of Refs [11,12], and we have checked that our result agrees with those.…”

“…We recently computed the O(1/N f ) β-function for Yukawa-theory [10] inspired by the earlier works [11,12]. The Yukawa-theory is closely related to the Gross-Neveu model, which has been extensively studied in the past using a different approach; see e.g.…”

“…The gauge contribution to the Yukawa β-function was computed in the abelian case in Ref. [11] and later generalised to non-abelian and semi-simple gauge groups in Ref. [12] assuming that only one flavour of fermions couples to the scalar via Yukawa interaction.…”

The β-function for Yukawa theory at large Nf

“…Recently, a further step towards a more complete understanding of these models was achieved by working out the leading 1/N f contribution from the gauge sector to a Yukawa coupling [13]; an extension to semi-simple gauge groups was discussed in ref. [14].…”

Safe glueballs and baryons

“…This was first studied in Abelian gauge theory in [1] and in the non-Abelian case in [2]. Recently, there has been a revived interest in asymptotically safe four-dimensional quantum field theories, with particular emphasis on pure fermionic gauge theories, chiral gauge theories, gauge-Yukawa theories involving both scalars and fermions and theories with or without supersymmetry [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”