Text Box: Figure 1. An artists impression of a time line from the moment of the Big Bang13.Does Antimatter Matter?

By Sadie Jones

 

At the very beginning of the Universe, when it was extremely hot ~  K it is predicted that matter and antimatter were created in equal amounts in the Big Bang, as the universe cooled the matter and antimatter would have been annihilated in pairs. Had the symmetry before the cooling been exact then the universe would not exist because all the matter and anti-matter particles would have annihilated each other. Thankfully, a small asymmetry between matter and antimatter, called the CP violation resulted in the dominance of matter. “In fact, if one was to work out what the universe was like one billionth of a second after it began, it turns out that for every billion particle-antiparticle pairs there was just one extra particle. To that particle we and the stars owe our existence 8”. It is very difficult for scientists to determine when the asymmetry in particles occurred, in the early stages of the universe, growing evidence suggests there was a period of extreme inflation to the order~ e60. This Inflation is likely to have taken place well below the scale of quantum gravity, so that any baryon number produced in the plank era (up to 10-34 seconds after the big bang) was diluted to a negligible level19 i.e it would be very hard for particles to exist. Scientists are currently trying to unravel this mystery, asking firstly why one extra particle was created for every billion in the first place, and secondly, why was it a matter particle as opposed to an anti-matter particle.

 

Antimatter itself was predicted in 1928 by Paul Dirac, 4 years before it was detected by Carl Anderson21. Anderson was looking at cosmic ray tracks and noticed that some supposed electron tracks bent the ‘wrong way’ in the magnetic field, this suggested these particle had an opposite charge; he had discovered the positron (anti-electron). Antimatter is the same as matter in every way but with opposite charge, the concept of antimatter was derived from the Dirac Equation. The equation combines quantum theory and special relativity to describe the behaviour of the fermions, spin ½ particles, Equation 1.1.

 

                 Dirac Equation (Equation 1.1)

 

The Dirac Equation comes from rewriting the free particle non-relativistic Schrodinger equation, see Equation 1.2.

 

                                     (Equation 1.2) where Dirac defined the Hamiltonian, to bewhere;

 

   Since     (Equation 1.3)

The wave equation for a Dirac particle has 4 components;

                                                                                                                                                                                                                                                        

                       (Equation 1.4) rewriting Equation 1.1 in terms of 1.4 gives;

 

     (Equation 1.5)

For a particles at rest (, Dirac realised that  had to have to be a solution of the form in Equation 1.6 for all states to have. Other possible solutions gave negative energy states, which are not allowed by classical physics.

 

                        (Equation 1.6) 

 

in the form of Equation 1.6 represents 2 particles, one propagating forward in time, the other going backward in time. These particles must have the same mass, but opposite charge, which meant Dirac had theoretically shown the existence of anti-particles.

 

Anti-particles do exist naturally on Earth, for example, when a high energy electron in a solar flare collides with carbon it can form a type of nitrogen that has too many protons relative to its number of neutrons, this makes its nucleus unstable, and a positron is emitted to stabilize the situation3. Anti-particles do not exist for very long on Earth however, because there is so much matter for the antimatter particles to collide with, such a collision will destroy both particles, transforming the entire mass of both particles into energy. The excess of matter we notice around us everyday was caused by the asymmetry at the beginning of the universe.

 

Symmetries and asymmetries are very important in particle physics; the CPT Theory describes the importance of particular symmetries. CPT Theory suggests that if one was able to take a particle, replace it with its antiparticle, look in the mirror and then reverse its direction in time, the result would be a particle indistinguishable from the original1. CPT stands for Charge, Parity and Time which are the 3 symmetries of particle interactions. Charge conjugation represents the replacement of matter with the antimatter counterpart, Parity corresponds to reversing all 3 co-ordinates i.e. ones image in a mirror appears back-to-front, right-to-left and upside-down and T is time reversal.

 

Text Box: Figure 2.  Cronin and Fitch experiment which detected 1 in 500 events at the end of the bean line when none were expected. This revealed the asymmetry of the decay which leads to CP Violation7.

Since 1957 scientists have been aware that weak interactions violate both C and P symmetries. CP is defined as the product of charge and parity, if CP is conserved then every reaction that produces a particle will be accompanied by a reaction which produces its antiparticle at the exact same rate, so no baryon number can be generated19. It was thought that C and P were always violated together so as to respect the CP combination, but this was not the case. James Cronin and Val Fitch at the US Brookehaven Laboratory discovered that CP was not conserved in the decay of neutral kaons (K Mesons); they named the effect CP Violation. Figure 2 shows a graphic of the of the beam experiment Cronin and Fitch used. They measured the decay of pions from the 2 types of neutral kaon species at the end of 57ft beam. The two kaon species have different lifetimes; this means one expects to see only the long lived pions at the end of the beam line. However, 1 in 500 events at the end of the tube were detected as the short lived pions. For any expected particle velocity all short lived pions should have decayed long before the end of the tube. The reason for short lived pions being detected is as a result of the asymmetry in the kaon decay which leads to the CP violation theory7.

 

The kaon decay to pions and electrons, as apposed to pions alone reveals the CP Violation more simply. The majority of kaons will decay in the following way:

 

 (Equation 2.3)

 
    (Equation 2.1)

    (Equation 2.2)

Equation 2.3 details the CP Operation; by operating CP on the decay products of Equation 2.1 the result is the decay products of 2.2. This suggests there should be an identical probability of each type of decay occurring. Experimental evidence disproves this, it reveals that positron decay happens more often, the excess is only tiny but is great enough to prove a violation of CP.

 

CP violation became the basis of 3 conditions devised by Andrei Sakharov in 1967 to explain the matter excess of the universe. Sakharov first revealed that in order to produce a baryon excess, there must be a process first that changes baryon number; the second that violations of C and CP could cause the exact antimatter–matter configuration of the big bang to be unbalanced resulting in mass excess and the third that the universe had to undergo a rapid expansion so that antimatter and matter was not in thermal equilibrium8. In equilibrium the antibaryons and baryons would pair up and nullify the baryon number leaving nothing2.However, proving that the universe was not initially at thermal equilibrium is challenging. The CMBR is the most perfect blackbody spectrum measured in nature, which means 105 years after the big bang the universe is certain to have been in thermodynamic equilibrium19. Sakharov’s landmark ideas provided the framework for generating a matter universe but it has fallen to other scientists to discover the causes of the CP violation and think of new ways to detect and understand it. At present CP Violation has only been detected in the decay of kaons, several particle accelerators have been built since the 1960’s with the purpose of finding other reactions which violate CP, Fermilab is currently looking into the possibility of observing CP Violation in B decay20. CERN and SLAC also play an important part in recent experiments with several new accelerators such as KEK and the CESR at Cornell University expected to make an important contribution to unravelling the mystery of CP Violation2.

 

Text Box: Figure 3. CP Violation Parameter plane, with results from CERN and SLAC in rainbow colours where red=max, highest probability of parameter values and the unitarity triangle from previous experiments with B Mesons11.

Many ideas have been put forward to explain CP, Cabbibo hypothesised in 1963 that the violation was based on quark mixing, however as this time only 4 quarks had been discovered, this meant  the rotation matrix to transform the quark states was restricted by real numbers and could therefore not accommodate CP Violation. Thankfully in 1973 Kobayashi and Maskawa deduced that CP Violation followed automatically if there were not 4, but 6 quark flavours. Their theory uses a unitary matrix called the CabbiboKobashyiMaskawa Matrix which contains information on the strength of the flavour-changing weak decays. The matrix specifies the mismatch of quantum states of quarks when they propagate freely and when they take part in weak interactions, the matrix can have a physical phase that is a complex number and it is this phase that would account for CP. The Kobayashi and Maskawa theory has become the favoured theory in the understanding of the CP Violation since all 6 quarks have now been discovered10.

 

The rainbow colours in Figure 3 detail the findings of the NA48 experiment at CERN and the Babar experiment at SLAC in the CP Violation plane,, where red represents the highest probability of parameter values. The black triangle represents a unitarity triangle, which is a graphical representation of the CabbiboKobashyiMaskawa (CKM) Matrix; the size of the sides of the triangle can be deduced by B Meson decay rates. The fact that the apex of the triangle coincides with the red area of recent experiments at CERN and SLAC shows that recent measurements correlate well with the older measurements of B Mesons.

The CP Violation parameter, the angle  is important because if quark mixing were symmetric then  and there would be no unitarity triangle, and no universe. Therefore, measuring this angle was a very important step in understanding CP violation, CERN and SLAC can now measure  to 10% accuracy.  Deducing the angles and is a lot more challenging both experimentally and theoretically11. For example, An effect known as Penguin Contribution is a non-negligible effect and can hide information on angle , calculations of the penguin-induced shifts requires much complex analysis18 .Other experiments into antimatter include one carried out by CERN with the intention of making anti-atoms. CERN were able to create the first anti-atom by pairing together positrons and antiprotons. They created nine anti-hydrogen atoms each lasting about 40 ns. As of 1998 CERN researches were able to produce 2,000 anti-hydrogen atoms per hour16.

 

Some scientists believe that CP Violation is only partially to blame for the mass dominance of the universe, since the current particle experiments fail to account for the entire matter-antimatter imbalance14. One theory is that during the big bang the antimatter formed small windows that link our 3D physical universe with the 5D Hyperspace. Hyperspace theories however are as a result of complex mathematics and are not proven, hyperspace theorists generally believe that higher dimensions make the laws of nature easier. The 5D hyperspace theory basically says that the antimatter has not disappeared as such, but there is a whole universe composed of antimatter that overlaps our universe of matter, and is exactly the same in every way, apart from the type of matter it is made from15. Hyperspace theories open the door to parallel universes, and seem more like the “Star Trek” science fiction than science fact, they therefore are not considered as the scientific answer to the matter dominance of our universe.

 

Antimatter in hyperspace is not the only region of particle physics where science fiction may become fact. Scientists are currently researching ways that antimatter can be used in the engines of interstellar space craft. The propulsion of such space craft is based on the fact that the annihilation of antimatter-matter pairs results in an energy release equivalent to the mass of both particles. It is believed that this energy is more than can be generated by other propulsion methods16 since they yield the highest specific impulse and jet power. Howe and Hynes suspect that propulsion involving the antiproton mass-conversion reaction offers the highest potential but the greatest problems17. However, If the problems with antimatter propulsion can be removed, it is proposed that such an engine could be used to launch manned missions to Mars and Jupiter in as little as 3.8 to 10.8 days respectively22, which is an incredibly exciting prospect.

 

To conclude, antimatter “does matter” and there are many exciting mysteries surrounding it, particularly why it exists in the first place, hopefully further particle accelerator experiments will aid in untangling its mystery. A complete understanding of CP violation and antimatter may ultimately aid in the completion of the Standard Model of Particle Physics and also show us how beings of matter, like ourselves, came to exist; the imperfection or CP Violation that caused the matter excess is definitive proof that perfection is not always paramount.

References

1.              http://lhcb-public.web.cern.ch/lhcb-public/html/symmetry.htm

2.              http://cerncourier.com/main/article/39/8/16

3.              http://www.space.com/scienceastronomy/antimatter_sun_030929.html

4.              http://livefromcern.web.cern.ch/livefromcern/antimatter/history/AM-history01.html

5.              http://www.fnal.gov/pub/inquiring/questions/cp_violations.html

6.              http://www.fnal.gov/pub/ferminews/ferminews00-08-25/standard.pdf

7.              http://hyperphysics.phy-astr.gsu.edu/hbase/particles/cronin.html#c2

8.              Sather. E, 1996,The Mystery of the Matter Asymmetry,

http://www.slac.stanford.edu/pubs/beamline/26/1/26-1-sather.pdf

9.              http://en.wikipedia.org/wiki/CKM_matrix

10.            http://cerncourier.com/main/article/39/5/14

11.            http://www-dapnia.cea.fr/Phocea/Vie_des_labos/Ast/ast_visu.php?id_ast=570

12.            http://universe-review.ca/R02-14-CPviolation.htm

13.            http://map.gsfc.nasa.gov/m_ig/060915/CMB_Timeline75nt.jpg

14.            http://www.indiadaily.com/editorial/4297.asp

15.            http://www.indiadaily.com/editorial/7643.asp

16.            http://science.howstuffworks.com/antimatter1.htm

17.            Howe, S.D, Hynes, M.V, 1986, Antimatter propulsion status and prospects, V. 2, Sect. 5, App. p 836-855

18.            Jerome Charlies, 1999, Taming the Penguin Contributions in CP Symmetry, Phys. Rev. D 59, 054007, http://prola.aps.org/abstract/PRD/v59/i5/e054007

19.            Dine. M, Kusenko. A, 2003, Origin of the matter-antimatter symmetry, 98.80.Cq, 98.80.Bp, 01.30.Rr, 12.60.Jv, 11.30.Pb, http://link.aps.org/abstract/RMP/v76/p1

20.            Cox. B, 1988, Experimental Possibilities for Observation of CP Violation in B Decay, Annals of the New York Academy of Sciences 535 (1), 224–242.

21.            http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/980330a.html

22.            Smith.D, Webb.J, 2001, The Antimatter Photon Drive, a relativisitic propulsion system, AIAA Paper, moon.pr.erau.edu