The strong CP problem is a puzzling question in
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
: Why does
quantum chromodynamics (QCD) seem to preserve
CP-symmetry
In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge symmetry) and P-symmetry ( parity symmetry). CP-symmetry states that the laws of physics should be th ...
?
In particle physics, CP stands for the combination of
charge
Charge or charged may refer to:
Arts, entertainment, and media Films
* '' Charge, Zero Emissions/Maximum Speed'', a 2011 documentary
Music
* ''Charge'' (David Ford album)
* ''Charge'' (Machel Montano album)
* ''Charge!!'', an album by The Aqu ...
conjugation symmetry (C) and
parity symmetry (P). According to the current mathematical formulation of quantum chromodynamics, a violation of CP-symmetry in
strong interactions could occur. However, no violation of the CP-symmetry has ever been seen in any experiment involving only the strong interaction. As there is no known reason in QCD for it to necessarily be conserved, this is a "
fine tuning
In theoretical physics, fine-tuning is the process in which parameters of a model must be adjusted very precisely in order to fit with certain observations. This had led to the discovery that the fundamental constants and quantities fall into suc ...
" problem known as the strong CP problem.
The strong CP problem is sometimes regarded as an
unsolved problem in physics, and has been referred to as "the most underrated puzzle in all of physics." There are several proposed solutions to solve the strong CP problem. The most well-known is
Peccei–Quinn theory
In particle physics, the Peccei–Quinn theory is a well-known, long-standing proposal for the resolution of the strong CP problem formulated by Roberto Peccei and Helen Quinn in 1977. The theory introduces a new anomalous symmetry to the Stan ...
, involving new
pseudoscalar
In linear algebra, a pseudoscalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion while a true scalar does not.
Any scalar product between a pseudovector and an ordinary vector is a pseudoscalar. T ...
particles called
axions.
Theory
CP-symmetry states that physics should be unchanged if particles were swapped with their antiparticles and then left-handed and right-handed particles were also interchanged. This corresponds to performing a charge conjugation transformation and then a parity transformation. The symmetry is known to be broken in the
Standard Model through
weak interactions
In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction ...
, but it is also expected to be broken through
strong interactions which govern
quantum chromodynamics (QCD), something that has not yet been observed.
To illustrate how the CP violation can come about in QCD, consider a
Yang–Mills theory
In mathematical physics, Yang–Mills theory is a gauge theory based on a special unitary group SU(''N''), or more generally any compact, reductive Lie algebra. Yang–Mills theory seeks to describe the behavior of elementary particles using ...
with a single massive
quark. The most general mass term possible for the quark is a complex mass written as
for some arbitrary phase
. In that case the
Lagrangian
Lagrangian may refer to:
Mathematics
* Lagrangian function, used to solve constrained minimization problems in optimization theory; see Lagrange multiplier
** Lagrangian relaxation, the method of approximating a difficult constrained problem with ...
describing the theory consists of four terms
:
The first and third terms are the CP-symmetric
kinetic terms of the
gauge
Gauge ( or ) may refer to:
Measurement
* Gauge (instrument), any of a variety of measuring instruments
* Gauge (firearms)
* Wire gauge, a measure of the size of a wire
** American wire gauge, a common measure of nonferrous wire diameter, ...
and quark fields. The fourth term is the quark mass term which is CP violating for non-zero phases
while the second term is the so-called
θ-term, which also violates CP-symmetry.
Quark fields can always be redefined by performing a chiral transformation by some angle
as
:
which changes the complex mass phase by
while leaving the kinetic terms unchanged. The transformation also changes the θ-term as
due to a change in the
path integral measure, an effect closely connected to the
chiral anomaly
In theoretical physics, a chiral anomaly is the anomalous nonconservation of a chiral current. In everyday terms, it is equivalent to a sealed box that contained equal numbers of left and right-handed bolts, but when opened was found to have mor ...
.
The theory would be CP invariant if one could eliminate both sources of CP violation through such a field redefinition. But this cannot be done unless
. This is because even under such field redefinitions, the combination
remains unchanged. For example, the CP violation due to the mass term can be eliminated by picking
, but then all the CP violation goes to the θ-term which is now proportional to
. If instead the θ-term is eliminated through a chiral transformation, then there will be a CP violating complex mass with a phase
. Practically, it is usually useful to put all the CP violation into the θ-term and thus only deal with real masses.
In the Standard Model where one deals with six quarks whose masses are described by the
Yukawa matrices and
, the physical CP violating angle is
. Since the θ-term has no contributions to perturbation theory, all effects from strong CP violation is entirely non-perturbative. Notably, it gives rise to a
neutron electric dipole moment
The neutron electric dipole moment (nEDM), denoted ''d''n, is a measure for the distribution of positive and negative charge inside the neutron. A finite electric dipole moment can only exist if the centers of the negative and positive charge distr ...
:
Current experimental upper bounds on the dipole moment give an upper bound of
cm, which requires
. The angle
can take any value between zero and
, so it taking on such a particularly small value is a fine-tuning problem called the strong CP problem.
Proposed solutions
The strong CP problem is solved automatically if one of the quarks is massless. In that case one can perform a set of chiral transformations on all the massive quark fields to get rid of their complex mass phases and then perform another chiral transformation on the massless quark field to eliminate the residual θ-term without also introducing a complex mass term for that field. This then gets rid of all CP violating terms in the theory. The problem with this solution is that all quarks are known to be massive from experimental matching with
lattice calculations. Even if one of the quarks was essentially massless to solve the problem, this would in itself just be another fine-tuning problem since there is nothing requiring a quark mass to take on such a small value.
The most popular solution to the problem is through the Peccei–Quinn mechanism. This introduces a new global
anomalous symmetry which is then
spontaneously broken at low energies, giving rise to a
pseudo-Goldstone boson called an axion. The axion ground state dynamically forces the theory to be CP-symmetric by setting
. Axions are also considered viable candidates for
dark matter
Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not a ...
and axion-like particles are also predicted by
string theory.
Other less popular proposed solutions exist such as Nelson–Barr models.
These set
at some high energy scale where CP-symmetry is exact but the symmetry is then spontaneously broken at low energies. The tricky part of these models is to account for why
remains small at low energies while the CP breaking phase in the
CKM matrix becomes large.
See also
*
Axion
*
CP violation
In particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge symmetry) and P-symmetry ( parity symmetry). CP-symmetry states that the laws of physics should be th ...
References
{{Reflist
Particle physics
Unsolved problems in physics