CP violation

Under CP violation ( C for English charge , charge 'or charge conjugation , charge conjugation '; P for parity , parity ') is understood to mean the violation of the CP invariance . The latter says that the physical relationships and laws in a system should not change if all particles are replaced by their antiparticles and all spatial coordinates are mirrored at the same time .

Discovery and prehistory

Apparent P-invariance and parity violation

According to normal everyday experience, the physics in a mirror world should not differ from its original. This means that every process that is observed in a mirror should also be able to be realized in the normal world through a suitable experimental arrangement (P-invariance).

As early as 1956, however, Tsung-Dao Lee and Chen Ning Yang postulated that the weak interaction to which beta decay is subject violates point symmetry . In the same year, this parity violation was confirmed by Chien-Shiung Wu in the Wu experiment . The weak interaction favors left- handedness (means the "left-handed direction" of the spin of elementary particles ) over right-handedness. Only left-handed particles and right-handed antiparticles participate in it. Left- and right-handed particles participate in the electromagnetic and the strong interaction with equal strength.

The parity violation can be illustrated well with neutrinos , which only interact weakly and can only occur as left-handed neutrinos and right-handed antineutrinos. Under the parity transformation ("point reflection"), however, a left-handed neutrino becomes a right-handed neutrino.

Apparent C-invariance and C-violation

Physicists have known since the 1930s that there is an antiparticle for every elementary particle. Originally, the theory and observations suggested that all interactions and decays of antiparticles take place in exactly the same way as with normal particles, i.e. that they are invariant under charge conjugation, or C-invariant for short. The electromagnetic and the strong interaction maintain C. For example, Coulomb's law is invariant under charge conjugation. The weak interaction, on the other hand, violates C, which can also be illustrated by neutrinos . Under charge conjugation, a left-handed neutrino becomes a left-handed antineutrino, which is not observed experimentally.

Apparent CP invariance

If, in addition to the reflection, one also swaps particles with antiparticles (C + P), there is no longer a contradiction to the above situation, because a left-handed neutrino becomes a right-handed antineutrino under the CP transformation ( Lew Landau 1957).

Discovery of CP violation

In 1964 the American physicists James Christenson , James Cronin , Val Fitch and René Turlay ( Nobel Prize in Physics for Cronin and Fitch 1980) discovered a tiny irregularity in the decay of heavy neutral K mesons ( kaons ), which indicate a violation of the combined CP symmetry closed. When investigating the decays of mesons (the L stands for long-lived) in an experiment at the Alternating Gradient Synchrotron of the Brookhaven National Laboratory , the CP-violating decays of the meson into two charged mesons ( Pions ) observed. ${\displaystyle K_{L}^{0}}$ ${\displaystyle K_{L}^{0}}$ ${\displaystyle \pi }$

By mixing in the system of neutral kaons, i. That is, a ( ) can change into its antiparticle ( ), forming mass eigenstates with different masses and lifetimes. The difference in mass is extremely small, whereas the difference in service life is very large. A distinction is made between the short-lived and the long-lived , whose lifetimes differ by a factor of approximately 600. ${\displaystyle K^{0}}$ ${\displaystyle {\bar {K}}^{0}}$ ${\displaystyle {\bar {K}}^{0}}$ ${\displaystyle K^{0}}$ ${\displaystyle K_{S}^{0}}$ ${\displaystyle (\tau (K_{S}^{0})\approx 0{,}9\cdot 10^{-10}\,\mathrm {s} )}$ ${\displaystyle K_{L}^{0}}$ ${\displaystyle (\tau (K_{L}^{0})\approx 5{,}1\cdot 10^{-8}\,\mathrm {s} )}$

${\displaystyle K^{0}}$( ) can decay into the same end states, whereby end states with 2 pions and a CP eigenvalue of +1 and with 3 pions and a CP eigenvalue of −1 are of particular importance: and . ${\displaystyle {\bar {K}}^{0}}$ ${\displaystyle CP|\pi \pi \rangle =+|\pi \pi \rangle }$ ${\displaystyle CP|\pi \pi \pi \rangle =-|\pi \pi \pi \rangle }$

Due to the larger phase space, the decay into 2 pions has a significantly larger partial decay width. If CP is preserved, then both mass eigenstates in the system of neutral kaons must also be CP eigenstates. The short-lived state would therefore have to decay into the 2-pion end state and the long-lived into the 3-pion end state. Decays of the type or can only occur if the CP symmetry is violated. In the experiment, neutral kaons are first generated, which form a superposition of and mesons. Due to the large difference in lifespan, the -component disappears after a while and only -Mesons remain . In order to achieve this, the kaons were generated at a certain distance from the detector, so that, due to the required flight time, they could only get into the detector and disintegrate there. The observation of the decay was the first evidence of the CP violation. ${\displaystyle K_{L}^{0}\rightarrow \pi \pi }$ ${\displaystyle K_{S}^{0}\rightarrow \pi \pi \pi }$ ${\displaystyle K_{S}^{0}}$ ${\displaystyle K_{L}^{0}}$ ${\displaystyle K_{S}^{0}}$ ${\displaystyle K_{L}^{0}}$ ${\displaystyle K_{L}^{0}}$ ${\displaystyle K_{L}^{0}\rightarrow \pi ^{+}\pi ^{-}}$

Charged kaons that cannot mix with their antiparticles can also decay into 2 and 3 pions. With that one would naively expect that the charged kaons and the have similar lifetimes. However, charged kaons are much more durable . Obviously, the partial decay width for is many times greater than for . Since the 2-pion wave function must be symmetrical in relation to the exchange of the two pions, the 2-pion end state for decays of the charged kaons can only have the isospin , whereas the end states with isospin and are possible for the decay . Since the weak interaction in kaon decays clearly favors the final state with isospin , the 2-pion decay is so dominant in the neutral kaons. However, the fact that final states can also be reached with an isospin in decays is important with regard to direct CP violation, i.e. H. CP violation upon decay. ${\displaystyle K_{S}^{0}}$ ${\displaystyle (\tau (K^{\pm })\approx 1{,}2\cdot 10^{-8}\,\mathrm {s} )}$ ${\displaystyle K_{S}^{0}\rightarrow \pi \pi }$ ${\displaystyle K^{\pm }\rightarrow \pi \pi }$ ${\displaystyle I=2}$ ${\displaystyle K_{S}^{0}}$ ${\displaystyle I=0}$ ${\displaystyle I=2}$ ${\displaystyle I=0}$ ${\displaystyle K_{S}^{0}}$ ${\displaystyle I=2}$

The CP violation observed by Christenson, Cronin, Fitch, and Turlay essentially originated from a CP violation in the mix. If one does not transition into one with the same strength as one does into one , i.e. H. , then the mass eigenstates no longer consist of equal parts and , which means that they can no longer be CP eigenstates. However, direct CP violation can also lead to disintegrating into 2 pions if and with different strengths disintegrating into 2 pions. Obviously, only a measurement of the decay rate does not allow a statement to be made about the contribution of the direct CP violation. The observation of the direct CP violation in this system thus required a complex and lengthy measurement program in which the partial decay widths for the decays ${\displaystyle K^{0}}$ ${\displaystyle {\bar {K}}^{0}}$ ${\displaystyle {\bar {K}}^{0}}$ ${\displaystyle K^{0}}$ ${\displaystyle \Gamma (K^{0}\rightarrow {\bar {K}}^{0})\neq \Gamma ({\bar {K}}^{0}\rightarrow K^{0})}$ ${\displaystyle K^{0}}$ ${\displaystyle {\bar {K}}^{0}}$ ${\displaystyle K_{L}^{0}}$ ${\displaystyle K^{0}}$ ${\displaystyle {\bar {K}}^{0}}$ ${\displaystyle K_{L}^{0}\rightarrow \pi \pi }$

• ${\displaystyle K_{L}^{0}\rightarrow \pi ^{+}\pi ^{-}}$
• ${\displaystyle K_{L}^{0}\rightarrow \pi ^{0}\pi ^{0}}$
• ${\displaystyle K_{S}^{0}\rightarrow \pi ^{+}\pi ^{-}}$
• ${\displaystyle K_{S}^{0}\rightarrow \pi ^{0}\pi ^{0}}$

were measured with precision.

Conservation of CPT invariance

In contrast to ( "dual-combined") CP violation is for a fundamental theorem of Wolfgang Pauli and Lueders Gerhart of all events quantum field theory , the ( "triple combination") CPT symmetry in all circumstances invariant (T = time reversal, ie Reversal of the direction of movement, the orbital and spin angular momentum and transition to the conjugate complex, ). This CPT invariance together with CP violation means a violation of the time symmetry ( T violation ). This could be confirmed experimentally. ${\displaystyle i\rightarrow -i}$

Link to the standard model

In the standard model of particle physics, the cause of the CP violation in the quark sector is linked to the generation of the quark masses. Quarks get their mass by coupling to the Higgs field , whereby a mass mixing matrix necessarily occurs, which is named after the physicists Nicola Cabibbo , Makoto Kobayashi and Toshihide Masukawa ( CKM matrix ). In 1972 Kobayashi and Maskawa showed that this matrix is ​​complex when there are three or more quark families in nature. In three families, according to the theory, there is exactly one complex phase in the unitary CKM matrix. In the standard model, this phase is responsible for the CP violation, since it changes its sign during the CP operation. Since a partial decay width or an effective cross-section only contains the square of the amount of the underlying amplitude, certain requirements must be met so that CP violation can occur in particle reactions. There must be at least two competing processes that lead from the same initial state to the same final state, so that interference occurs. Three types of CP violation are known:

CP violation in the particle-antiparticle mixture, also known as indirect CP violation

Neutral kaons , D mesons, and B mesons can mix with their antiparticles; that is, they can merge into one another ("oscillate"), e.g. B. and ( oscillations). CP violation in the mixture occurs when e.g. B. the rate is different from . The CP violation observed in the neutral kaon system in 1964 can essentially be traced back to this. ${\displaystyle B^{0}\rightarrow {\bar {B}}^{0}}$ ${\displaystyle {\bar {B}}^{0}\rightarrow B^{0}}$ ${\displaystyle B^{0}{\bar {B}}^{0}}$ ${\displaystyle \Gamma (K^{0}\rightarrow {\bar {K}}^{0})}$ ${\displaystyle \Gamma ({\bar {K}}^{0}\rightarrow K^{0})}$

Decay CP violation, also known as direct CP violation

Direct CP violation occurs when the partial decay width for the decay of a particle into a final state is different from that of its antiparticle, i.e. H. . Direct CP violation in the kaon system was first observed in 1999 with the experiments KTEV at Fermilab and NA48 (the successor to NA31 ) at CERN . They confirmed a measurement of the NA31 experiment at CERN from 1988 (publication 1993), which, however, as a three-sigma event, was not statistically significant enough to be considered an unambiguous observation. In the B meson system, the direct CP violation was first found in 2004 through the BaBar experiment at SLAC . Direct CP violation can only occur if there are at least two competing processes (amplitudes) that have different weak phases that change sign under the CP operation, but also different other phases that do not change their sign under the CP operation, wear. Such phases are due to interactions such as the strong interaction, which are invariant under the CP operation. Therefore, one speaks of strong phases in this context. The interpretation of measurements for direct CP violation is difficult due to problems in the calculation of the large phase differences. Nevertheless, especially in the kaon sector, there was an intensive search for direct CP violation, since it enabled models of the so-called super-weak interaction, as proposed by Lincoln Wolfenstein in 1964, to be excluded. ${\displaystyle T}$ ${\displaystyle E}$ ${\displaystyle (\Gamma (T\rightarrow E))}$ ${\displaystyle \Gamma (T\rightarrow E)\neq \Gamma ({\bar {T}}\rightarrow {\bar {E}})}$

CP violation in the interference between mixing and decay

This type of CP violation can occur when a particle and its associated antiparticle can decay into the same final state. Such a particle is thus subject to the particle-antiparticle mixture, so that the final state can be reached directly or via the detour of conversion into the antiparticle and its decay. In the kaon system the phenomenon is well known; In the B meson system, the examination enables a sensitive test of the standard model to determine the origin of the CP violation. Due to the structure of the CKM matrix, the CP violation should be most pronounced at transitions between quarks of the third ( bottom and top quark ) and the first generation ( down and up quark ). B mesons , which contain both a light and a heavy bottom quark , are therefore the ideal candidates for testing the theory. They have about five times the proton mass and have a lifespan of about In meson decays into a meson and a neutral kaon . This type of CP violation was first possible for B mesons through the BaBar experiment and the Belle experiment to be watched. It is now known with great precision and is in excellent agreement with the predictions of the Standard Model. After confirming Kobayashi and Maskawa's prediction, they were both awarded the 2008 Nobel Prize in Physics . ${\displaystyle 1{,}5\cdot 10^{-12}\,\mathrm {s} .}$ ${\displaystyle B^{0}}$ ${\displaystyle J/\psi }$ ${\displaystyle B^{0}\rightarrow J/\psi K_{S}^{0}}$

CP violation remains an extremely active area of ​​research, as numerous other channels allow tests of the Standard Model with great sensitivity to the presence of new physics. Research into CP violation in the system of neutral mesons offers such perspectives. Precision measurements of CP violation in the system of B and B _s mesons are a focus of the physics program of the LHCb experiment at the Large Hadron Collider at CERN . The Super- KEKB accelerator at KEK is currently under construction in Japan , and the successor to the Belle experiment, Belle II, is expected to start taking data in 2019. ${\displaystyle B_{s}^{0}}$

In principle, CP violation should also be possible in the strong interaction. B. would lead to a relatively large electric dipole moment of the neutron . However, there is no experimental evidence of such a CP violation. This discrepancy is also known as the “strong CP problem”.

Due to the observation of neutrino oscillations and the associated knowledge that neutrinos are not massless, there must also be a mixing matrix, the PMNS matrix (sometimes just MNS matrix), which according to Bruno Pontecorvo , Ziro Maki , Masami Nakagawa and Shoichi Sakata is named. As with the CKM matrix, this could also be a source of CP violation, but it has not yet been clearly observed. In the T2K experiment, however, there were clear indications of such an injury in muon neutrinos (2017).

Cosmological necessity

Andrei Sakharov noted in the 1960s that the CP violation is one of the prerequisites for the observed great dominance of matter over antimatter in the universe ( baryon asymmetry ). Our current understanding of the Big Bang assumes that it produced particles and antiparticles in equal quantities. In the baryogenesis the now observed imbalance arose. What the exact mechanism is, however, is disputed. Experiments must clarify the origin of the CP violation and whether it is large enough to be able to generate sufficient matter.

See also

• B factory

literature

• Alban Kellerbauer: 50 years of CP violation. In: Physics in Our Time. 45 (July 2014) 168, doi : 10.1002 / piuz.201401371 .
  Direct download from the author: Article (PDF; 874 kB) .
• J. Beringer et al. (Particle Data Group): Review of particle physics. In: Physical Review. D86, 010001 (2012).
• Michael Peskin : High-energy physics: The matter with antimatter. In: Nature. Volume 419, 2002, pp. 24-27.
• Marcel Kunze, Klaus R. Schubert, Bernhard Spaan: The BABAR experiment. In: Physical sheets. Volume 55, Issue 5, 1999, p. 27.
• GC Branco, L. Lavoura, JP Silva: CP Violation. Oxford University Press, 1999, ISBN 0-19-850399-7 .
• Makoto Kobayashi , Toshihide Maskawa : CP Violation in the Renormalizable Theory of Weak Interaction. In: Progress of Theoretical Physics Volume 49, 1973, pp. 652-657.
• AD Sakharov : Violation of CP Invariance, c Asymmetry, and Baryon Asymmetry of the Universe. In: JETP Letters. Volume 5, 1967, pp. 24-27.
• JH Christenson , JW Cronin , VL Fitch , R. Turlay : Evidence for the 2π Decay of the K ₂ ⁰ Meson. In: Physical Review Letters. Volume 13, 1964, pp. 138-140.

Web links

• Brigitte Röthlein: Mirrored world . In: Wissenschaft.de . December 1, 1999.
• Flavor physics and CP violation . University of Karlsruhe. January 29, 2003.
• Hendrik van Hees: The neutral K mesons and CP violation . Bielefeld University. July 17, 2003.
• Particle Data Group: The Review of Particle Physics .
• KTEV: Kaons at the Tevatron .
• CERN : LHCb sees a new flavor of matter – antimatter asymmetry , press release from March 21, 2019. In
  addition: Robert Gast: New puzzle piece in the antimatter riddle , on: Spektrum.de from March 21, 2019

Individual evidence

1. ↑ BaBar makes first direct measurement of time-reversal violation. November 21, 2012, accessed December 18, 2017 . 
2. ↑ A. Alavi-Harati et al. (KTEV): Observation of Direct CP Violation in K _{S, L} → π π Decays. In: Phys. Rev. Lett. 83, 22 (1999).
3. ^ V. Fanti et al. (NA48): A new measurement of direct CP violation in two pion decays of the neutral kaon. In: Phys. Lett. B 465, 335 (1999).
4. ^ Theresa Harrison: NA31 / 48: the pursuit of direct CP violation. In: CERN.Courier.com. 23rd July 2014.
5. ↑ GD Barr et al. (NA31): A new measurement of direct CP violation in the neutral kaon system. In: Phys. Lett. B 317, 233 (1993).
6. ↑ B. Aubert et al. (BABAR): Direct CP Violating Asymmetry in B ⁰ → K ⁺ π ^- Decays. In: Phys. Rev. Lett. 93, 131801 (2004).
7. ^ L. Wolfenstein: Violation of CP Invariance and the Possibility of Very Weak Interactions. In: Phys. Rev. Lett. 13, 562 (1964).
8. ↑ B. Aubert et al. (BABAR): Observation of CP violation in the B ⁰ meson system. In: Phys. Rev. Lett. 87, 091801, (2001).
9. ↑ K. Abe et al. (Belle): Observation of Large CP Violation in the Neutral B Meson System. In: Phys. Rev. Lett. 87, 091802 (2001).
10. ^ Belle II detector rolled-in. In: belle2.jp. June 26, 2017. Retrieved November 7, 2017 . 
11. ↑ U. Bern: CP symmetry violated for neutrinos. August 11, 2017, accessed February 4, 2018.