Physics Letters B 795 (2019) 644–649
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Perturbative unitarity bounds for effective composite models
S. Biondini
a,∗
, R. Leonardi
b
, O. Panella
b
, M. Presilla
c,d
a
Van Swinderen Institute, University of Groningen, Nijenborgh 4, NL-9747 AG Groningen, Netherlands
b
Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Via A. Pascoli, I-06123 Perugia, Italy
c
Dipartimento di Fisica e Astronomia “Galileo Galielei”, Università degli Studi di Padova, Via Marzolo, I-35131, Padova, Italy
d
Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Via Marzolo, I-35131, Padova, Italy
a r t i c l e i n f o a b s t r a c t
Article history:
Received
5 April 2019
Received
in revised form 7 June 2019
Accepted
18 June 2019
Available
online 20 June 2019
Editor:
G.F. Giudice
Keywords:
Perturbative
unitarity
Composite
models
Composite
fermions
LHC
Run 2
High-Luminosity
and High-Energy LHC
In this paper we present the partial wave unitarity bound in the parameter space of dimension-5 and
dimension-6 effective operators that arise in a compositeness scenario. These are routinely used in
experimental searches at the LHC to constraint contact and gauge interactions b etween ordinary Standard
Model fermions and excited (composite) states of mass M. After deducing the unitarity bound for the
production process of a composite neutrino, we implement such bound and compare it with the recent
experimental exclusion curves for Run 2, the High-Luminosity and High-Energy configurations of the
LHC. Our results also applies to the searches where a generic single excited state is produced via contact
interactions. We find that the unitarity bound, so far overlooked, is quite compelling and significant
portions of the parameter space (M, ) become ex cluded in addition to the standard request M ≥ .
© 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
It is well known that partial wave unitarity is a powerful tool to
estimate the perturbative validity of effective field theories (EFTs).
It has been used in the past to provide useful insights both in
strong and electroweak interactions [1]as well as in quantum
gravity [2]. Perhaps the best known example is the bound on the
Higgs mass derived from an analysis of WW → WW scattering
within the Standard Model (SM) [1,3]. On the other end, unitar-
ity has
also been applied to a number of approaches beyond the
Standard Model (BSM). For instance in composite Higgs models [4],
in searches of scalar di-boson resonances [5,6], searches for dark
matter effective interactions [7] and on generic dimension-6 oper-
ators [8].
One
possible BSM alternative, widely discusses in literature and
routinely pursued in high-energy experiments, is a composite-
fermions
scenario which offers a possible solution to the hierar-
chy
pattern of fermion masses [9–15]. In this context [14–20], SM
quarks “q” and leptons “” are assumed to be bound states of some
as yet not observed fundamental constituents generically referred
as preons. If quarks and leptons have an internal substructure, they
are expected to be accompanied by heavy excited states
∗
, q
∗
of
*
Corresponding author.
E-mail
address: s.biondini@rug.nl (S. Biondini).
masses M that should manifest themselves at an unknown energy
scale, the compositeness scale .
As
customary in an EFT approach, the effects of the high-energy
physics scale, here , are captured in higher dimensional opera-
tors
that describe processes within a lower energy domain, where
the fundamental building blocks of the theory cannot show up.
Hence, the heavy excited states may interact with the SM ordi-
nary
fermions via dimension-5 gauge interactions of the SU(2)
L
⊗
U(1)
Y
SM gauge group of the magnetic-moment type (so that the
electromagnetic current conservation is not spoiled by e.g.
∗
γ
processes [18]). In addition, the exchange of preons and/or bind-
ing
quanta of the unknown interactions between ordinary fermions
( f ) and/or the excited states ( f
∗
) results in effective contact in-
teractions
(CI) that couple the SM fermions and heavy excited
states [19–22]. In the latter case, the dominant effect is expected
to be given by the dimension-6 four-fermion interactions scaling
with the inverse square of the compositeness scale :
L
6
=
g
2
∗
2
1
2
j
μ
j
μ
, (1a)
j
μ
=η
L
¯
f
L
γ
μ
f
L
+η
L
¯
f
∗
L
γ
μ
f
∗
L
+η
L
¯
f
∗
L
γ
μ
f
L
+h.c.
+(
L → R), (1b)
where g
2
∗
= 4π and the η’s factors are usually set equal to unity.
In this work the right-handed currents will be neglected for sim-
https://doi.org/10.1016/j.physletb.2019.06.042
0370-2693/
© 2019 The Author(s). Publishe d by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
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