On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

14 Chapter 1. Introduction: Problems beyond the Standard Model
large amount of symmetry of a conformal theory allows to extract information on
the bounds on the scaling dimension ∆ ¯ QQ in dependence of ∆ ( ¯ QQ) 2 numerically. The
progress made over the last years in these studies leads to the blue curve plotted in
Figure 1.4, corresponding to a fit function from [30, Sec. 3.2]. The blue shaded region
corresponds to the numerically excluded region. The result is, that there exists no
conformal field theory in the phenomenologically preferred region, indicated by the
red shaded rectangle. Additional assumptions, like minimal flavor violation, are thus
necessary to find a viable CTC theory. Nevertheless, CTC may be the only way to
implement strongly coupled EWSB without introducing composite fermions.
Partial Compositeness
The concept of partial compositeness was introduced in 1991 by Kaplan [31]. It
is based on the fact that there may be a fourth kind of dimension six operators not
included in (1.11), if the strongly coupled sector allows for fermionic bound states with
the same quantum numbers as the SM fermions, build from three technifermions,
dij
qT i Q QT j Q
Λ 2 ETC
. (1.21)
This bound state will appear as a composite Dirac-fermion and leads to a novel mechanism
to generate fermion masses. The basic idea is, that the elementary SM fermions
are massless and do not couple directly to the technicolor condensate, i.e. the TC
condensate has a small or even a negative anomalous dimension, so that the b-terms
are irrelevant. The composite fermions however may have a marginal Yukawa coupling
with the TC condensate (suggestively called H in this section), because the Yukawa
operator does now only contain composites and its scaling dimension is therefore not
the sum of the scaling dimensions of its constituents. 13 Only through the linear mixing
generated by the operator (1.21) will EWSB be communicated to the SM fermions.
Kaplan first developed his idea in upscaled QCD TC and therefore he considered the
techniquarks to form technibaryons Q ¯ QQ → |ψ(0)| 2 B, with |ψ(0)| 2 the wavefunctions
overlap of the techniquarks in the technibaryon, measuring the coupling strength.
Naive dimensional analysis tells us |ψ(0)| 2 ∼ Λ3 TC , which can be supported by comparison
with the QCD analogue, see [32, eq. (2.12) and (2.13)].
Denoting the left/right-handed Lorentz-chirality of the SU(2)L-doublet composite by
BL and BR and the SU(2)L-singlet with components Bc L and Bc R , one can write down
an effective Lagrangian,
L ∋ Λ3 TC
Λ2 (
ETC
˜ d qRB c L + d qLBR) − mBBB − �mBB c B c + BL (λHB c R) + h.c. . (1.22)
Here, d and ˜ d denote the mixing parameters from (1.21) and its analogue involving a
right-handed SM-quark, λ is an O(1) Yukawa coupling in the composite sector, and
13 In the original paper, a coupling to a composite Higgs was not considered and only explicit mass
terms for the composite fermions were introduced.