On the Flavor Problem in Strongly Coupled Theories - THEP Mainz

2 Chapter 1. Introduction: Problems beyond the Standard Model
as described by the SM, the coefficient of the Higgs mass operator has to be of the
order of the electroweak scale, i.e. ΛEW ≈ 1 TeV. This introduces a large unexplained
hierarchy in scales, unless there is new physics at ΛEW or the dimensionless coefficient
c2 is tuned to be of the order c2 ≈ Λ2 EW /Λ2 UV . Even more severe is the problem of the
cosmological constant, which is indirectly measured at c0 ≈ � 10−12 GeV �4 /Λ4 UV [2],
and either calls for a UV completion at the millielectronvolt scale or a fine-tuning of
hundreds of orders of magnitude if one assumes that ΛUV is of the order of the Planck
scale MPl = 1019 GeV.
Both hierarchies become a problem if one expects the theory to be natural, for which
we will adopt the definition of ’t Hooft,
The naturalness criterion states that one such [dimensionless and
measured in units of the cut-off] parameter is allowed to be much
smaller than unity only if setting it to zero increases the symmetry
of the theory. If this does not happen, the theory is unnatural.[3]
A good measure to judge the attractiveness of a physical theory is therefore the absence
of these small parameters, or equivalently the absence of large hierarchies between
scales. However, since the cosmological constant is not directly relevant for
the physics of the SM , we will ignore this problem and concentrate on the hierarchy
problem of the SM in Part 1.1 of this chapter.
This hierarchy problem becomes even more puzzling if one considers higher dimensional
operators. If it can be explained by new physics at the electroweak scale, one
would expect from the EFT ansatz (1.1), that also the suppression scale of the irrelevant
operators are of the order ΛUV = ΛEW. However, if not prevented by some
mechanism in the new physics sector, bounds from measurements on flavor changing
processes involving quarks will enforce at least
ΛUV � 10 3 TeV . (1.2)
A UV completion of the SM should therefore not only be able to explain why the
electroweak scale is stabilized against radiative corrections, but also why higher dimensional
operators are absent or suppressed by orders of magnitude compared to
ΛEW.
The question of how both of these requirements can be brought in agreement is one
of the most pressing issues for models of physics beyond the SM. Further, while the
marginal operators in LGauge all have natural coefficients , 3 the Yukawa couplings in
LYukawa exhibit hierarchical structures which are not explained by SM physics either,
and although these parameters are not radiatively unstable, the question what sets
the masses and mixings of quarks and leptons is also to be answered by physics beyond
the SM. Part 1.2 of this chapter will describe models which aim to explain the
hierarchies of the Yukawa sector and mechanisms which generate a hierarchy between
the coefficients of higher dimensional operators relevant for flavor changing processes
3 With the exception of operators allowing for strong CP violation.