5.4 Excited Third Generation Quarks
173
5.4 Excited Third Generation Quarks
In models of compositeness, SM particles are built from strongly bound constituents,
which obey more fundamental equations of motion. The strong force binding the
constituents would induce contact interactions at scales lower than the compositeness scale [944, 945]. For quarks, contact interactions change the distribution
of the scattering angle in qq → qq scattering [946], which can be probed in pp
collisions [947–956]. Another consequence of the internal structure of quarks is the
existence of excited states, only possible for composite objects. While all quarks
might be composite particles, the large masses of third generation quarks suggests
that excited quarks couple primarily to b and t, which can be realised in RandallSundrum [957, 958] or composite Higgs models [898, 959]. Especially the large
mass of the top quark has initiated studies of consequences from a possible top quark
compositeness [960–963]. In some models of warped extra dimensions, the top and
bottom quark excitations, t
∗ and b
∗ , can be spin-3/2 states, with dominant decays
t
∗
→ t + g [964–966] and b
∗
→ b + g [967]. The phenomenology of excited third
generation quarks is also related to VLQs, where the absence of mixing with SM
quarks can lead to vanishing branching fractions into final states involving W , Z and
H bosons. Instead, in models with an additional scalar S, loop-induced contributions
can lead to dominant decays T → tg, T → tγ and T → t S [968]. In these models,
the dominant channel is the decay T → tg with a branching fraction of about 97%
in a large part of the parameter space [969].
The dominant production and decay processes of excited quarks in pp collisions is
through qg → q
∗
→ qg, if the coupling to light quarks q = {u, d, s, c} is sufficiently
large. These would lead to resonant structures in the dijet mass spectrum at high
p T [970]. Recent searches by ATLAS and CMS with the total available 13 TeV data,
collected in the years 2015–2018 and corresponding to an integrated luminosity
of about 140 fb
−1 , exclude excited quarks with masses below 6.7 TeV [971, 972].
The mass limits for a b
∗ , obtained for the process bg → b
∗
→ bg, are reduced to
3.2 TeV because of b tagging efficiencies and the smaller production cross section
due to the smallness of the b PDF. If the b
∗ has weak couplings in addition to the
chromomagnetic bgb
∗ coupling, the decay b
∗
→ W t is possible with a branching
fraction up to 40% [973]. The weak coupling is introduced in models where the heavy
particle stabilises the Higgs boson mass at the electroweak scale [974, 975], or in
so-called beautiful mirror models [976, 977], resolving the observed discrepancy
of the forward-backward asymmetry in Z → bb decays [107]. The most general
Lagrange density describing the interaction of a heavy bottom quark with gluons
is [970, 973, 978]
L =
g s
2
G μν bσ
μν
(κ L P L + κ R P R ) b
∗
+ h.c.,
(5.4)
where g s is the strong coupling constant, is the scale of compositeness which is
usually set to the mass of the b
∗ , G μν is the gluon field strength tensor and σ
μν
are the relativistic spin matrices. The left- and right-handed coupling strengths are
173
5.4 Excited Third Generation Quarks
In models of compositeness, SM particles are built from strongly bound constituents,
which obey more fundamental equations of motion. The strong force binding the
constituents would induce contact interactions at scales lower than the compositeness scale [944, 945]. For quarks, contact interactions change the distribution
of the scattering angle in qq → qq scattering [946], which can be probed in pp
collisions [947–956]. Another consequence of the internal structure of quarks is the
existence of excited states, only possible for composite objects. While all quarks
might be composite particles, the large masses of third generation quarks suggests
that excited quarks couple primarily to b and t, which can be realised in RandallSundrum [957, 958] or composite Higgs models [898, 959]. Especially the large
mass of the top quark has initiated studies of consequences from a possible top quark
compositeness [960–963]. In some models of warped extra dimensions, the top and
bottom quark excitations, t
∗ and b
∗ , can be spin-3/2 states, with dominant decays
t
∗
→ t + g [964–966] and b
∗
→ b + g [967]. The phenomenology of excited third
generation quarks is also related to VLQs, where the absence of mixing with SM
quarks can lead to vanishing branching fractions into final states involving W , Z and
H bosons. Instead, in models with an additional scalar S, loop-induced contributions
can lead to dominant decays T → tg, T → tγ and T → t S [968]. In these models,
the dominant channel is the decay T → tg with a branching fraction of about 97%
in a large part of the parameter space [969].
The dominant production and decay processes of excited quarks in pp collisions is
through qg → q
∗
→ qg, if the coupling to light quarks q = {u, d, s, c} is sufficiently
large. These would lead to resonant structures in the dijet mass spectrum at high
p T [970]. Recent searches by ATLAS and CMS with the total available 13 TeV data,
collected in the years 2015–2018 and corresponding to an integrated luminosity
of about 140 fb
−1 , exclude excited quarks with masses below 6.7 TeV [971, 972].
The mass limits for a b
∗ , obtained for the process bg → b
∗
→ bg, are reduced to
3.2 TeV because of b tagging efficiencies and the smaller production cross section
due to the smallness of the b PDF. If the b
∗ has weak couplings in addition to the
chromomagnetic bgb
∗ coupling, the decay b
∗
→ W t is possible with a branching
fraction up to 40% [973]. The weak coupling is introduced in models where the heavy
particle stabilises the Higgs boson mass at the electroweak scale [974, 975], or in
so-called beautiful mirror models [976, 977], resolving the observed discrepancy
of the forward-backward asymmetry in Z → bb decays [107]. The most general
Lagrange density describing the interaction of a heavy bottom quark with gluons
is [970, 973, 978]
L =
g s
2
G μν bσ
μν
(κ L P L + κ R P R ) b
∗
+ h.c.,
(5.4)
where g s is the strong coupling constant, is the scale of compositeness which is
usually set to the mass of the b
∗ , G μν is the gluon field strength tensor and σ
μν
are the relativistic spin matrices. The left- and right-handed coupling strengths are