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Physics Letters B 747 (2015) 541–544

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Scalar coupling evolution in a non-perturbative QCD resummation

scheme

J.D. Gomez

, A.A. Natale

a,b,∗

Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 09210-170, Santo André, SP, Brazil

Instituto de Física Teórica, UNESP, Rua Dr. Bento T. Ferraz, 271, Bloco II, 01140-070, São Paulo, SP, Brazil

a r t i c l e i n f o a b s t r a c t

Article history:

Received

2 June 2015

Received

in revised form 17 June 2015

Accepted

19 June 2015

Available

online 22 June 2015

Editor:

M. Cveti

Keywords:

Other

nonperturbative techniques

General

properties of QCD

We compute the Standard Model scalar coupling (λ) evolution in a particular QCD resummation scheme,

where the QCD coupling becomes infrared ﬁnite due to the presence of a dynamically generated gluon

mass, leading to the existence of a non-perturbative infrared ﬁxed point. We discuss how this scheme

can be ﬁxed taking recourse to phenomenological considerations in the infrared region. The QCD β

function associated to this non-perturbative coupling when introduced into the SM renormalization group

equations increases the λ values at high energies.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

One of the techniques to study QCD at low energies are the

Schwinger–Dyson Equations (SDE). This is an analytic method but

with the complication of dealing with an inﬁnite tower of cou-

pled

integral equations. Because of this, when using the SDE, one

have to make a truncation in the system of equations, which has

to be done in a way that the symmetries of the theory are not

broken, in particular, a rough truncation in the SDE can cause a vi-

olation

of the gauge symmetry. In the recent years an enormous

progress has been made in solving SDE in a gauge invariant way

using the so-called Pinch Technique [1], as a result it has been

found the existence of a dynamical gluon mass in the propaga-

tor

of the gluon ﬁeld, as suggested many years ago by Cornwall

[2]. Another non-perturbative technique is Lattice QCD [3], which

implies heavy numerical calculations requiring a considerably high

amount of computer power. Results obtained in QCD lattice simu-

lations

are in agreement with the SDE in what concerns dynamical

gluon mass generation [4,5].

The

infrared QCD coupling turns out to be infrared ﬁnite when

gluons develop a dynamically generated mass. This point was al-

ready

emphasized in Ref. [2]; was also discussed at length in

Refs. [6,7], and leads to an infrared ﬁxed point, which is a prop-

erty

of dynamical mass generation in non-Abelian theories [8]. The

phenomenological consequences of such infrared ﬁnite coupling,

Corresponding author at: Instituto de Física Teórica, UNESP, Rua Dr. Bento T.

Ferraz, 271, Bloco II, 01140-070, São Paulo, SP, Brazil.

E-mail

addresses: jgomez@ufabc.edu.br (J.D. Gomez), natale@ift.unesp.br

(A.A. Natale).

or non-perturbative ﬁxed point, have been discussed in Ref. [9],

and recently we have discussed how this non-perturbative ﬁxed

point can change the local minimum of a renormalization group

improved effective potential [10]. This change of minimum state

may produce noticeable modiﬁcations in the physical properties of

the model studied in Ref. [10].

view of the results of Ref. [10] we will study the effect of

the non-perturbative ﬁxed point present in QCD with dynamically

massive gluons in the scalar coupling evolution of the Standard

Model (SM). It should be noticed that we shall be dealing with a

very particular QCD resummation scheme, provided by the results

of the Pinch Technique applied to the SDE, which have been ar-

gued

that can lead to off-shell Green’s functions that are locally

gauge invariant and renormalization group invariant [11]. The QCD

coupling that we shall consider will not depend on the renor-

malization

point μ but on the dynamical gluon mass m

) and,

of course, on the QCD characteristic scale 

QCD

≡ . This coupling

contains the effect of summation of several loops according to the

calculations detailed in Refs. [1,2,6,7], and the free parameter in

this particular scheme, namely the infrared value of the dynamical

gluon mass, will be ﬁxed by taking recourse to phenomenological

considerations about the coupling constant IR behavior.

The

ﬁrst calculation of the IR frozen QCD coupling in the pres-

ence

of a dynamically generated gluon mass was obtained in

Ref. [2], leading to the following coupling:

) =



+4·m



QCD



4πα

), (1)

http://dx.doi.org/10.1016/j.physletb.2015.06.047

0370-2693/

SCOAP

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