Kavli Affiliate: Tom Melia
| First 5 Authors: David E. Kaplan, Tom Melia, Surjeet Rajendran, ,
| Summary:
Three possible strategies have been advocated to solve the strong CP problem.
The first is the axion, a dynamical mechanism that relaxes any initial value of
the CP violating angle $bar{theta}$ to zero. The second is the imposition of
new symmetries that are believed to set $bar{theta}$ to zero in the UV. The
third is the acceptance of the fine tuning of parameters. We argue that the
latter two solutions do not solve the strong CP problem. The $theta$ term of
QCD is not a parameter – it does not exist in the Hamiltonian. Rather, it is a
property of the quantum state that our universe finds itself in, arising from
the fact that there are CP violating states of a CP preserving Hamiltonian. It
is not eliminated by imposing parity as a symmetry since the underlying theory
is already parity symmetric and that does not preclude the existence of CP
violating states. Moreover, since the value of $theta$ realized in our
universe is a consequence of measurement, it is inherently random and cannot be
fine tuned by choice of parameters. Rather any fine tuning would require a
tuning between parameters in the theory and the random outcome of measurement.
Our results considerably strengthen the case for the existence of the axion and
axion dark matter. The confusion around $theta$ arises from the fact that
unlike classical mechanics, the Hamiltonian and Lagrangian are not equivalent
in quantum mechanics. The Hamiltonian defines the differential time evolution,
whereas the Lagrangian is a solution to this evolution. Consequently, initial
conditions could in principle appear in the Lagrangian but not in the
Hamiltonian. This results in aspects of the initial condition such as $theta$
misleadingly appearing in the Lagrangian as parameters. We comment on the
similarity between the $theta$ vacua and the violations of the constraint
equations of classical gauge theories in quantum mechanics.
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