In particle physics, CP violation is a violation
of CP-symmetry (or charge conjugation parity
symmetry): the combination of C-symmetry (charge
conjugation symmetry) and P-symmetry (parity
symmetry). CP-symmetry states that the laws
of physics should be the same if a particle
is interchanged with its antiparticle (C symmetry)
while its spatial coordinates are inverted
("mirror" or P symmetry). The discovery of
CP violation in 1964 in the decays of neutral
kaons resulted in the Nobel Prize in Physics
in 1980 for its discoverers James Cronin and
Val Fitch.
It plays an important role both in the attempts
of cosmology to explain the dominance of matter
over antimatter in the present Universe, and
in the study of weak interactions in particle
physics.
== CP-symmetry ==
CP-symmetry, often called just CP, is the
product of two symmetries: C for charge conjugation,
which transforms a particle into its antiparticle,
and P for parity, which creates the mirror
image of a physical system. The strong interaction
and electromagnetic interaction seem to be
invariant under the combined CP transformation
operation, but this symmetry is slightly violated
during certain types of weak decay. Historically,
CP-symmetry was proposed to restore order
after the discovery of parity violation in
the 1950s.
The idea behind parity symmetry is that the
equations of particle physics are invariant
under mirror inversion. This leads to the
prediction that the mirror image of a reaction
(such as a chemical reaction or radioactive
decay) occurs at the same rate as the original
reaction. Parity symmetry appears to be valid
for all reactions involving electromagnetism
and strong interactions. Until 1956, parity
conservation was believed to be one of the
fundamental geometric conservation laws (along
with conservation of energy and conservation
of momentum). However, in 1956 a careful critical
review of the existing experimental data by
theoretical physicists Tsung-Dao Lee and Chen-Ning
Yang revealed that while parity conservation
had been verified in decays by the strong
or electromagnetic interactions, it was untested
in the weak interaction. They proposed several
possible direct experimental tests. The first
test based on beta decay of cobalt-60 nuclei
was carried out in 1956 by a group led by
Chien-Shiung Wu, and demonstrated conclusively
that weak interactions violate the P symmetry
or, as the analogy goes, some reactions did
not occur as often as their mirror image.
Overall, the symmetry of a quantum mechanical
system can be restored if another symmetry
S can be found such that the combined symmetry
PS remains unbroken. This rather subtle point
about the structure of Hilbert space was realized
shortly after the discovery of P violation,
and it was proposed that charge conjugation
was the desired symmetry to restore order.
Simply speaking, charge conjugation is a symmetry
between particles and antiparticles, and so
CP-symmetry was proposed in 1957 by Lev Landau
as the true symmetry between matter and antimatter.
In other words, a process in which all particles
are exchanged with their antiparticles was
assumed to be equivalent to the mirror image
of the original process.
=== CP violation in the Standard Model ===
"Direct" CP violation is allowed in the Standard
Model if a complex phase appears in the CKM
matrix describing quark mixing, or the PMNS
matrix describing neutrino mixing. A necessary
condition for the appearance of the complex
phase is the presence of at least three generations
of quarks. If fewer generations are present,
the complex phase parameter can be absorbed
into redefinitions of the quark fields. A
popular rephasing invariant whose vanishing
signals absence of CP violation and occurs
in most CP violating amplitudes is the Jarlskog
invariant,
J
=
c
12
c
13
2
c
23
s
12
s
13
s
23
sin
⁡
δ
≈
3
10
−
5
.
{\displaystyle J=c_{12}c_{13}^{2}c_{23}s_{12}s_{13}s_{23}\sin
\delta \approx 3~10^{-5}.}
The reason why such a complex phase causes
CP violation is not immediately obvious, but
can be seen as follows. Consider any given
particles (or sets of particles)
a
{\displaystyle a}
and
b
{\displaystyle b}
, and their antiparticles
a
¯
{\displaystyle {\bar {a}}}
and
b
¯
{\displaystyle {\bar {b}}}
. Now consider the processes
a
→
b
{\displaystyle a\rightarrow b}
and the corresponding antiparticle process
a
¯
→
b
¯
{\displaystyle {\bar {a}}\rightarrow {\bar
{b}}}
, and denote their amplitudes
M
{\displaystyle M}
and
M
¯
{\displaystyle {\bar {M}}}
respectively. Before CP violation, these terms
must be the same complex number. We can separate
the magnitude and phase by writing
M
=
|
M
|
e
i
θ
{\displaystyle M=|M|e^{i\theta }}
. If a phase term is introduced from (e.g.)
the CKM matrix, denote it
e
i
ϕ
{\displaystyle e^{i\phi }}
. Note that
M
¯
{\displaystyle {\bar {M}}}
contains the conjugate matrix to
M
{\displaystyle M}
, so it picks up a phase term
e
−
i
ϕ
{\displaystyle e^{-i\phi }}
.
Now the formula becomes:
M
=
|
M
|
e
i
θ
e
i
ϕ
{\displaystyle M=|M|e^{i\theta }e^{i\phi }}
M
¯
=
|
M
|
e
i
θ
e
−
i
ϕ
{\displaystyle {\bar {M}}=|M|e^{i\theta }e^{-i\phi
}}
Physically measurable reaction rates are proportional
to
|
M
|
2
{\displaystyle |M|^{2}}
, thus so far nothing is different. However,
consider that there are two different routes:
a
⟶
1
b
{\displaystyle a{\overset {1}{\longrightarrow
}}b}
and
a
⟶
2
b
{\displaystyle a{\overset {2}{\longrightarrow
}}b}
or equivalently, two unrelated intermediate
states:
a
→
1
→
b
{\displaystyle a\rightarrow 1\rightarrow b}
and
a
→
2
→
b
{\displaystyle a\rightarrow 2\rightarrow b}
. Now we have:
M
=
|
M
1
|
e
i
θ
1
e
i
ϕ
1
+
|
M
2
|
e
i
θ
2
e
i
ϕ
2
{\displaystyle M=|M_{1}|e^{i\theta _{1}}e^{i\phi
_{1}}+|M_{2}|e^{i\theta _{2}}e^{i\phi _{2}}}
M
¯
=
|
M
1
|
e
i
θ
1
e
−
i
ϕ
1
+
|
M
2
|
e
i
θ
2
e
−
i
ϕ
2
{\displaystyle {\bar {M}}=|M_{1}|e^{i\theta
_{1}}e^{-i\phi _{1}}+|M_{2}|e^{i\theta _{2}}e^{-i\phi
_{2}}}
Some further calculation gives:
|
M
|
2
−
|
M
¯
|
2
=
−
4
|
M
1
|
|
M
2
|
sin
⁡
(
θ
1
−
θ
2
)
sin
⁡
(
ϕ
1
−
ϕ
2
)
{\displaystyle |M|^{2}-|{\bar {M}}|^{2}=-4|M_{1}||M_{2}|\sin(\theta
_{1}-\theta _{2})\sin(\phi _{1}-\phi _{2})}
Thus, we see that a complex phase gives rise
to processes that proceed at different rates
for particles and antiparticles, and CP is
violated.
From the theoretical end, the CKM matrix is
defined as VCKM =Uu．Ud﹢, where Uu and
Ud are unitary transformation matrices which
diagonalize the fermion mass matrices Mu and
Md, respectively.
Thus, there are two necessary conditions for
getting a complex CKM matrix:
At least one of Uu and Ud is complex, or the
CKM matrix will be purely real.
Even both of them are complex, Uu and Ud mustn’t
be the same, i.e., Uu≠Ud , or CKM matrix
will be an identity matrix which is also purely
real.
== Experimental status ==
=== Indirect CP violation ===
In 1964, James Cronin, Val Fitch and coworkers
provided clear evidence from kaon decay that
CP-symmetry could be broken. This work won
them the 1980 Nobel Prize. This discovery
showed that weak interactions violate not
only the charge-conjugation symmetry C between
particles and antiparticles and the P or parity,
but also their combination. The discovery
shocked particle physics and opened the door
to questions still at the core of particle
physics and of cosmology today. The lack of
an exact CP-symmetry, but also the fact that
it is so nearly a symmetry, created a great
puzzle.
Only a weaker version of the symmetry could
be preserved by physical phenomena, which
was CPT symmetry. Besides C and P, there is
a third operation, time reversal T, which
corresponds to reversal of motion. Invariance
under time reversal implies that whenever
a motion is allowed by the laws of physics,
the reversed motion is also an allowed one
and occurs at the same rate forwards and backwards.
The combination of CPT is thought to constitute
an exact symmetry of all types of fundamental
interactions. Because of the CPT symmetry,
a violation of the CP-symmetry is equivalent
to a violation of the T symmetry. CP violation
implied nonconservation of T, provided that
the long-held CPT theorem was valid. In this
theorem, regarded as one of the basic principles
of quantum field theory, charge conjugation,
parity, and time reversal are applied together.
=== Direct CP violation ===
The kind of CP violation discovered in 1964
was linked to the fact that neutral kaons
can transform into their antiparticles (in
which each quark is replaced with the other's
antiquark) and vice versa, but such transformation
does not occur with exactly the same probability
in both directions; this is called indirect
CP violation.
Despite many searches, no other manifestation
of CP violation was discovered until the 1990s,
when the NA31 experiment at CERN suggested
evidence for CP violation in the decay process
of the very same neutral kaons (direct CP
violation). The observation was somewhat controversial,
and final proof for it came in 1999 from the
KTeV experiment at Fermilab and the NA48 experiment
at CERN.In 2001, a new generation of experiments,
including the BaBar Experiment at the Stanford
Linear Accelerator Center (SLAC) and the Belle
Experiment at the High Energy Accelerator
Research Organisation (KEK) in Japan, observed
direct CP violation in a different system,
namely in decays of the B mesons. A large
number of CP violation processes in B meson
decays have now been discovered. Before these
"B-factory" experiments, there was a logical
possibility that all CP violation was confined
to kaon physics. However, this raised the
question of why CP violation did not extend
to the strong force, and furthermore, why
this was not predicted by the unextended Standard
Model, despite the model's accuracy for "normal"
phenomena.
In 2011, a hint of CP violation in decays
of neutral D mesons was reported by the LHCb
experiment at CERN using 0.6 fb−1 of Run
1 data. However, the same measurement using
the full 3.0 fb−1 Run 1 sample was consistent
with CP symmetry.In 2013 LHCb announced discovery
of CP violation in strange B meson decays.
== Strong CP problem ==
There is no experimentally known violation
of the CP-symmetry in quantum chromodynamics.
As there is no known reason for it to be conserved
in QCD specifically, this is a "fine tuning"
problem known as the strong CP problem.
QCD does not violate the CP-symmetry as easily
as the electroweak theory; unlike the electroweak
theory in which the gauge fields couple to
chiral currents constructed from the fermionic
fields, the gluons couple to vector currents.
Experiments do not indicate any CP violation
in the QCD sector. For example, a generic
CP violation in the strongly interacting sector
would create the electric dipole moment of
the neutron which would be comparable to 10−18
e·m while the experimental upper bound is
roughly one trillionth that size.
This is a problem because at the end, there
are natural terms in the QCD Lagrangian that
are able to break the CP-symmetry.
L
=
−
1
4
F
μ
ν
F
μ
ν
−
n
f
g
2
θ
32
π
2
F
μ
ν
F
~
μ
ν
+
ψ
¯
(
i
γ
μ
D
μ
−
m
e
i
θ
′
γ
5
)
ψ
{\displaystyle {\mathcal {L}}=-{\frac {1}{4}}F_{\mu
\nu }F^{\mu \nu }-{\frac {n_{f}g^{2}\theta
}{32\pi ^{2}}}F_{\mu \nu }{\tilde {F}}^{\mu
\nu }+{\bar {\psi }}(i\gamma ^{\mu }D_{\mu
}-me^{i\theta '\gamma _{5}})\psi }
For a nonzero choice of the θ angle and the
chiral phase of the quark mass θ′ one expects
the CP-symmetry to be violated. One usually
assumes that the chiral quark mass phase can
be converted to a contribution to the total
effective
θ
~
{\displaystyle \scriptstyle {\tilde {\theta
}}}
angle, but it remains to be explained why
this angle is extremely small instead of being
of order one; the particular value of the
θ angle that must be very close to zero (in
this case) is an example of a fine-tuning
problem in physics, and is typically solved
by physics beyond the Standard Model.
There are several proposed solutions to solve
the strong CP problem. The most well-known
is Peccei–Quinn theory, involving new scalar
particles called axions. A newer, more radical
approach not requiring the axion is a theory
involving two time dimensions first proposed
in 1998 by Bars, Deliduman, and Andreev.
== CP violation and the matter–antimatter
imbalance ==
The universe is made chiefly of matter, rather
than consisting of equal parts of matter and
antimatter as might be expected. It can be
demonstrated that, to create an imbalance
in matter and antimatter from an initial condition
of balance, the Sakharov conditions must be
satisfied, one of which is the existence of
CP violation during the extreme conditions
of the first seconds after the Big Bang. Explanations
which do not involve CP violation are less
plausible, since they rely on the assumption
that the matter–antimatter imbalance was
present at the beginning, or on other admittedly
exotic assumptions.
The Big Bang should have produced equal amounts
of matter and antimatter if CP-symmetry was
preserved; as such, there should have been
total cancellation of both—protons should
have cancelled with antiprotons, electrons
with positrons, neutrons with antineutrons,
and so on. This would have resulted in a sea
of radiation in the universe with no matter.
Since this is not the case, after the Big
Bang, physical laws must have acted differently
for matter and antimatter, i.e. violating
CP-symmetry.
The Standard Model contains at least three
sources of CP violation. The first of these,
involving the Cabibbo–Kobayashi–Maskawa
matrix in the quark sector, has been observed
experimentally and can only account for a
small portion of the CP violation required
to explain the matter-antimatter asymmetry.
The strong interaction should also violate
CP, in principle, but the failure to observe
the electric dipole moment of the neutron
in experiments suggests that any CP violation
in the strong sector is also too small to
account for the necessary CP violation in
the early universe. The third source of CP
violation is the Pontecorvo–Maki–Nakagawa–Sakata
matrix in the lepton sector. The current long-baseline
neutrino oscillation experiments, T2K and
NOνA, may be able to find evidence of CP
violation over a small fraction of possible
values of the CP violating Dirac phase while
the proposed next-generation experiments,
Hyper-Kamiokande and DUNE, will be sensitive
enough to definitively observe CP violation
over a relatively large fraction of possible
values of the Dirac phase. Further into the
future, a neutrino factory could be sensitive
to nearly all possible values of the CP violating
Dirac phase. If neutrinos are Majorana fermions,
the PMNS matrix could have two additional
CP violating Majorana phases, leading to a
fourth source of CP violation within the Standard
Model. The experimental evidence for Majorana
neutrinos would be the observation of neutrinoless
double-beta decay. The best limits come from
the GERDA experiment. CP violation in the
lepton sector generates a matter-antimatter
asymmetry through a process called leptogenesis.
This could become the preferred explanation
in the Standard Model for the matter-antimatter
asymmetry of the universe once CP violation
is experimentally confirmed in the lepton
sector.
If CP violation in the lepton sector is experimentally
determined to be too small to account for
matter-antimatter asymmetry, some new physics
beyond the Standard Model would be required
to explain additional sources of CP violation.
Adding new particles and/or interactions to
the Standard Model generally introduces new
sources of CP violation since CP is not a
symmetry of nature.
Sakharov proposed a way to restore CP-symmetry
using T-symmetry, extending spacetime before
the Big Bang. He described complete CPT reflections
of events on each side of what he called the
"initial singularity". Because of this, phenomena
with an opposite arrow of time at t < 0 would
undergo an opposite CP violation, so the CP-symmetry
would be preserved as a whole. The anomalous
excess of matter over antimatter after the
Big Bang in the orthochronous (or positive)
sector, becomes an excess of antimatter before
the Big Bang (antichronous or negative sector)
as both charge conjugation, parity and arrow
of time are reversed due to CPT reflections
of all phenomena occurring over the initial
singularity:
We can visualize that neutral spinless maximons
(or photons) are produced at t < 0 from contracting
matter having an excess of antiquarks, that
they pass "one through the other" at the instant
t = 0 when the density is infinite, and decay
with an excess of quarks when t > 0, realizing
total CPT symmetry of the universe. All the
phenomena at t < 0 are assumed in this hypothesis
to be CPT reflections of the phenomena at
t > 0.
== See also ==
B-factory
CPT symmetry
BTeV experiment
Cabibbo–Kobayashi–Maskawa matrix
LHCb
Penguin diagram
Neutral particle oscillation
Electron electric dipole moment
