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Physics Letters B 737 (2014) 172–177

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Ultraviolet ﬁxed point and massive composite particles in TeV scales

She-Sheng Xue

a,b,∗

ICRANeT, Piazzale della Repubblica, 10-65122, Pescara, Italy

Physics Department, University of Rome “La Sapienza”, Rome, Italy

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

Article history:

Received

12 May 2014

Received

in revised form 24 July 2014

Accepted

13 August 2014

Available

online 15 August 2014

Editor:

A. Ringwald

We present a further study of the dynamics of high-dimension fermion operators attributed to the

theoretical inconsistency of the fundamental cutoff (quantum gravity) and the parity-violating gauge

symmetry of the standard model. Studying the phase transition from a symmetry-breaking phase to

a strong-coupling symmetric phase and the β-function behavior in terms of four-fermion coupling

strength, we discuss the critical transition point as a ultraviolet-stable ﬁxed point where a quantum

ﬁeld theory preserving the standard model gauge symmetry with composite particles can be realized.

The form-factors and masses of composite particles at TeV scales are estimated by extrapolating the

solution of renormalization-group equations from the infrared-stable ﬁxed point where the quantum

ﬁeld theory of standard model is realized and its phenomenology including Higgs mass has been

experimentally determined. We discuss the probability of composite-particle formation and decay that

could be experimentally veriﬁed in the LHC by measuring the invariant mass of relevant ﬁnal states and

their peculiar kinetic distributions.

(http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP

1. Introduction

The parity-violating (chiral) gauge symmetries and sponta-

neous/explicit

breaking of these symmetries for the hierarchy of

fermion masses have been at the center of a conceptual elab-

oration

that has played a major role in donating to mankind

the beauty of the standard model (SM) for particle physics. The

Nambu–Jona-Lasinio model (NJL) [1] of four-fermion interactions

at high energies and its effective counterpart, the Higgs model [2]

fermion–boson Yukawa interactions at low energies, provide an

elegant description for the electroweak symmetry breaking and in-

termediate

gauge boson masses. After a great experimental effort

for many years, the ATLAS [3] and CMS [4] experiments have re-

cently

shown the ﬁrst observations of a 126 GeV scalar particle in

the search for the Standard Model Higgs boson at the LHC. This

far-reaching result begins to shed light on this most elusive and

fascinating arena of fundamental particle physics.

is an important issue to study the dynamics at high-energy

scale that originates the high-dimensional operators of fermion

ﬁelds.

The strong technicolor dynamics of extended gauge theo-

ries

at the TeV scale was invoked [5,6] to have a natural scheme

incorporating the relevant four-fermion operator (1) of the NJL

type. We here present a brief introduction that the origin of high-

Correspondence to: ICRANeT, Piazzale della Repubblica, 10-65122, Pescara, Italy.

E-mail

address: xue@icra.it.

dimensional operators of all fermion ﬁelds is due to the quan-

tum

gravity at the Planck length (a

∼ 10

−33

cm, Λ

= π /a

∼

GeV). Studying the quantum Einstein–Cartan theory in the

framework of Regge calculus, we calculated [7] the minimal length

(≈1.2a

) of discrete space–time, which provides a natural regu-

lator

for local quantum ﬁeld theories of particles and gauge in-

teractions.

On the other hand, based on low-energy observations

of parity violation, the SM Lagrangian was built in such a way

as to preserve the exact chiral-gauge-symmetries SU

(2) ⊗ U

(1)

that are accommodated by elementary left-handed fermions and

right-handed fermions. However, a profound result, in the form

of a generic no-go theorem [8], tells us that there is no consis-

tent

way to straightforwardly transpose on a discrete space–time

the bilinear fermion Lagrangian of the continuum SM theory in

such a way as to exactly preserve the chiral gauge symmetries.

We are led to consider at least quadrilinear fermion interactions

to preserve the chiral gauge symmetries. As an example, the four-

fermion

operator in the Einstein–Cartan theory can be obtained

by integrating over static torsion ﬁelds at the Planck scale [9].

The very-small-scale structure of space–time and high-dimensional

operators of fermion ﬁelds must be very complex as functions

of the space–time spacing

a and the gravitational gauge-coupling

grav

between fermion ﬁelds and quantum gravity at the Planck

scale. As the running gravitational gauge-coupling g

grav

(

a) is ap-

proaching

to its ultraviolet (UV) stable critical point g

crit

grav

for

a →

[10], the physical scale Λ = Λ[g

grav

(

a),

a] (Λ

−1



a) satisﬁes

http://dx.doi.org/10.1016/j.physletb.2014.08.031

0370-2693/

SCOAP

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