Scheme-independent series for anomalous dimensions of higher-spin operators at an infrared fixed point in a gauge theory

Abstract

We consider an asymptotically free vectorial gauge theory, with gauge group G and N f fermions in a representation R of G, having an infrared fixed point of the renormalization group. We calculate scheme-independent series expansions for the anomalous dimensions of higher-spin bilinear fermion operators at this infrared fixed point up to O(∆ 3 f ), where ∆ f is an N f -dependent expansion variable. Our general results are evaluated for several special cases, including the case G = SU(Nc) with R equal to the fundamental and adjoint representations.τ Oi,n = d Oi,n − j Oi,n ,(1.5) with j Oi,n = n here. Thus, among bilinear fermion operators, in addition toψγ µ1 ψ with dimension 3, spin 1, and hence τ = 2, there are the operatorsψγ µ1 D µ2 · · · D µj ψ, with dimension 3 + (j − 1) and spin j, which also have τ = 2. These are the minimum-twist bilinear fermion operators that contribute to the light-cone OPE (1.3)

Renormalization-group behavior of ϕ3 theories in d=6 dimensions

“…As N f decreases below the region near N u , the IR theory becomes more strongly coupled and higher-order terms in perturbative series expansions become more important. Although the value of the IR zero, α IR;nl , at n-loop order is scheme dependent if n ≥ 3, scheme-independent series expansions as power series in the variable Δ f ¼ N u − N f have been used to obtain scheme-independent calculations of physical quantities such as anomalous dimensions [22][23][24][25][26]. The resultant values of these anomalous dimensions have been compared with lattice simulations [22,24].…”

Strongly coupled gauge theories towards physics beyond the Standard Model

“…However, this approach becomes not only scheme dependent for ℓ ≥ 3, but also results in a severe convergence problem when the 5th order results in the MS scheme, the highest loop-order known to us so far, are concerned [6]. An alternative scheme-independent expansion in Δ 𝑁 𝑓 = 𝑁 AF 𝑓 − 𝑁 IR 𝑓 , called conformal or BZ expansion, has been proposed [7] and, for the past few years, extensively used to compute certain physical observables of IR conformal gauge theories by Ryttov and Shrock [8][9][10][11][12][13][14][15]. A particularly interesting quantity is the anomalous dimension of a fermion condensate…”

Sp(2N) Lattice Gauge Theories and Extensions of the Standard Model of Particle Physics

“…A number of recent studies [284][285][286][287][288][289][290][291][292] discuss the determination of the conformal window in terms of a (Banks-Zaks) expansion in the small physical parameter…”