# When the Universe Broke a Rule

*Physics often tells us that our universe strictly obeys well-defined laws. But what happens when it unexpectedly defies a rule that appears to be followed by countless observed phenomena?*

Suppose one routine day you wake up to find another living being who is an identical copy of your mirror image. That is, this mysterious creature behaves and moves exactly the way you do but for his body being a laterally inverted version of yours. However, if you both bump into each other, you get killed instantaneously! Bizarre, isn’t it?

While we currently know nothing that even remotely hints at the existence of such alien beings, we are aware of a similar phenomenon in the realm of particles, owing to the Nobel Prize winning inferences of the renowned physicist Paul Dirac and several other studies that were founded upon his seminal work. Interestingly, Dirac combined Einstein’s special relativity and the theory of Quantum Physics into an equation that yielded two solutions – one associated with positive energy and another with ‘negative energy’. He conjectured that for every class of charged particles, there exists a class of ‘antiparticles’ – particles with the same mass but opposite charge. For example, the antiparticles corresponding to electrons (a class of matter particles) are particles called *positrons*. Equivalently, for every class of electrically neutral matter particles, there exists a class of electrically neutral antiparticles having the same mass. Thus, for every entity of matter we are familiar with, there exists a corresponding ‘antimatter’ entity. Several experiments that ensued from Dirac’s postulates proved the existence of such antiparticles. It was also learnt that when a particle collides with its antiparticle, both of them get annihilated and release energy in the process, regardless of whether they are charged or neutral. Thanks to years of toil of physicists all over the world, today we can understand and appreciate antimatter and its relationship with matter much better.

But there is one thing we still do not comprehend: **If matter and antimatter are exactly equal and opposite, why does the universe contain much more matter than antimatter?** Many explanations have been proposed so far, but none of them is fully convincing.

Nevertheless, we *do *know that certain conditions called *Sakharov conditions *must be satisfied for there to be an imbalance between matter and antimatter. One such fascinating condition is the existence of a phenomenon called *Charge Parity Violation *(CP Violation) during the first few seconds following the Big Bang. It turns out that the most enduring theory of particle physics, known as ‘The Standard Model’, provides some explanation for CP Violation.

However, whether the Standard Model describes CP Violation correctly or not is not known with certainty. This is currently an area of active research and Dr. Libby has been engrossed in it for the pas seven years at IIT Madras. Before we move on to Dr. Libby’s specific interests within this area, let us see

what the Standard Model itself has to offer.

Developed throughout the latter half of the 20th century, this exhaustive theory seeks to explain the characteristics of the vast multitude of subatomic particles and their complex interactions with the help of only three kinds of particles – six *quarks*, six* leptons *and *force carrier particles*.

Quarks are constituents of the familiar protons and neutrons that make up most of the matter that we see around us. They do not have an independent existence; they exist only with other quarks in composite particles (particles composed of other particles). Scientists are currently aware of three pairs of quarks: the *up-down*, the *charm-strange *and the *top-bottom *pairs. Among these, up, charm and top quarks carry positive electric charge whereas the other three carry negative electric charge. On a lighter note, the characteristics of these quarks are as weird as their names.

Leptons are solitary matter particles and thus have an independent existence. The six kinds of leptons are *electrons*, *muons*, *tau particles *and three kinds of *neutrinos*. All leptons except neutrinos carry electric charge.

The third category of particles in the Standard Model is that of force carrier particles which give rise to three fundamental forces: the *strong force*, the *weak force *and the *electromagnetic force*. The strong force holds quarks together, the weak force causes the decay of massive quarks and leptons into heavier quarks and leptons, and the electromagnetic force causes electrically charged particles to repel or attract each other.

These forces in turn give rise to three kinds of interactions: the strong, the weak and the electromagnetic interactions. These interactions include particle decays and annihilations and can be represented pretty much like chemical reactions characterized by reactants and products. Furthermore, their most vital properties are described by quantum mechanics. Two such properties are the familiar electric charge (denoted by *C*) and *parity *(denoted by *P*).

Before asking what ‘parity’ means, it would be worth recalling two laws of Physics that you studied in high school: the law of conservation of linear momentum and the law of conservation of angular momentum. If you wrack your brain long enough, and if you have the genius of the great German mathematician Emmy Noether, you might gain one of the most precious insights into physics: **Every conservation law is associated with a symmetry inherent in nature.**

For example, linear momentum is conserved because of spatial symmetry – there is no particular location in space that is preferred to other locations. In the case of angular momentum, there is no preferred direction in space. Likewise, the initial assumption that nature was unbiased and thus treated matter and antimatter identically, or that there was a symmetry between antimatter and matter, reinforced the classical hypothesis that the total parity of a system is always conserved in a particle interaction. In essence, this means that an interaction and its mirror image can be represented by the same particle equation.

However, as is the fate of most scientific theories that for a long time enjoy an unquestionable presence as *truths *even in the most critical of minds, the theory of parity conservation was proved to be incorrect. Physicists learnt through reluctantly performed experiments that parity is not conserved in weak interactions.

Usually, when a promising hypothesis is refuted by experimental evidence, scientists understandably try to modify it or extend it to a more general case rather than discarding it altogether. That is exactly what happened in this case too – physicists tried to find another quantity Q such that the combination QP of this quantity and parity would remain symmetric even in weak interactions. The renowned physicist Lev Landau proposed that in this case Q is nothing but C, the charge. Parity conservation thus came to be replaced by CP Symmetry. This meant that a process in which all the particles are exchanged with their antiparticles was assumed to be equivalent to its mirror image.

Although CP Symmetry succeeded to an extent in explaining weak decays, history was destined to repeat – this extended notion of symmetry too was found to be violated in decays of particles called *neutral kaons*. It was observed that even the combination of charge-parity was not conserved in these decays which again happened to be weak interactions. This phenomenon came to be known as *CP Violation*. To comprehend this more clearly, consider the decay *B*^{−} *→ **DK** ^{−}*. We now perform a CP operation on this decay, i.e,. we laterally invert the decay in the 3-dimensional space (or convert it into its mirror image)and then invert the signs of the charges of the particles involved. We thus arrive at the decay

*B*

^{+}*→*

*DK*

*, which is a charge-conjugated version of the mirror image of the original decay. Experiments have shown that the rates at which these two decays occur differ by a remarkable amount. In other words, the total amount of CP on the reactant’s side of the combination of the two decays*

^{+}*B*

^{±}*→*

*DK*

*doesn’t equal its total amount on the products’ side. This is how charge-parity conservation (or CP symmetry) is violated in this decay. The overall significance of this symmetry violation for particle physics can be gleaned from the fact that its discoverers, Cronin and Fitch, were awarded the Nobel Prize in 1980.*

^{±}At this juncture, the following question arises: **How should the Standard Model account for CP Violation?** The answer lies in the properties of the *Cabibbo-Kobayashi-Maskawa matrix *(CKM matrix), a square array of numbers that is central to the Standard Model. In order to get an idea about this matrix, we must first note that there are weak decays in which negatively charged quarks (bottom, down and strange) get converted into positively charged ones(top, up and charm). This gives rise to 9 possible decays. The CKM matrix, having 3 rows and 3 columns, contains information on the strengths of each of these decays. CP Violation is incorporated into the Standard Model by allowing this matrix to have complex number entries.

However, there is a crucial constraint: for the CKM matrix to make physical sense, the Standard Model requires it to have a mathematical property called *unitarity*. This property can be expressed as a set of equations which the matrix must satisfy.

**“These equations involve 18 variables!**”, says Prashanth, a student of Dr. Libby, as he laughs at the sheer complexity of the whole thing. Fortunately, the unravelling of a few relationships between the variables reduced their number by an alarming difference – from eighteen to just four! These 4 parameters are comprised of 3 *Euler angles *and 1 phase variable. The unitarity of the CKM matrix now reduces to fewer constraints, of which one states that the Euler angles should be the angles of a triangle, i.e., they must sum up to 180 degrees. The triangle formed by them is called the *unitarity triangle*. As can be seen from the figure below, its angles are denoted by *α*, *β *and *γ*. Although the phase variable is the one responsible for CP Violation, the area of the unitarity triangle indicates the degree of violation. This triangle is unique in terms of its lengths and angles. It therefore has the potential to indicate how accurately the Standard Model describes this symmetry violation.

Many physicists thus shifted their focus to the determination of the values of *α*, *β *and *γ*, the Euler angles or the angles of the unitarity triangle. They have been able to determine *α *and *β *with a reasonable accuracy by studying the interference between various decays involving particles called *mesons*, but *γ *remains elusive. You may naturally ask, “Why can’t they determine *γ *solely from their knowledge of the other two angles simply because the three angles form a triangle?” Note that such a method of determining *γ *would rest on the unitarity assumption, the constraint on the CKM matrix that in fact gave rise to the three Euler angles. In order to test this assumption, it is necessary to determine *γ *from other measurements. Moreover, “the current world average precision on *γ* is significantly worse than that of the other angles of the unitarity triangle”, says a paper recently authored by Dr. Libby. So the next question is: how must one go about enhancing this precision?

This is where Dr. Libby’s research enters the picture. His aim so far has been to improve our knowledge of *γ *by studying how certain observable quantities violate CP symmetry in *B^{±} → DK^{±} *decays. These quantities are called

*CP-violating observables*. Dr. Libby’s focus has been on a special h: 0px; “> class of these observables – observables associated with particle states called CP eigenstates. These states are the products of certain kinds of

*B*decays. Two kinds of CP eigenstates have been of greater interest:

^{±}*→**DK*^{±}*CP-even*eigenstates and

*CP-odd*eigenstates. Another way of saying that a CP eigenstate is CP-even is:

*η*= +1. Similarly,

*η*=

*−*1 implies that the state is CP-odd.

However, this does not mean that no efforts were made in this direction previously in order to know more about the Euler angle. Four kinds of *B^{±} → DK^{±} *decays had already been studied. Essentially, each of these is a decay of a D meson to a unique CP eigenstate. Furthermore, in each decay, only a fraction of D mesons decays to the desired eigenstate. This fraction is known as the branching ratio (BR) of the decay. With this background in mind, we can represent the end results of these four decays through the table below:

As can be seen from this table, only a very minute fraction of the D mesons decays to a given CP eigenstate. Measurements on these states are thus limited because not many samples are available for study. So the challenge facing Dr. Libby and his team of students was to identify more easily available eigenstates to which these mesons decay. And they did. They used the following critical observation made in a separate study: the branching ratio for the decay *D*^{0} *→ **π*^{+}*π*^{−}*π*^{0} is 1*.*43%, a fraction significantly greater than the ones listed in the table above. This implied that the state *π*^{+}*π*^{−}*π*^{0} was certainly more useful than the four states studied earlier. But it was not known whether it was a CP-even or a CP-odd eigenstate. As it turns out, the answer to this question facilitated a more precise determination of *γ*.

The data pertaining to the CP observables associated with the decays described above as well as several other decays has been collected by a giant particle detector called CLEO-c. **“CLEO is the granddaddy of flavour physics, with a history of achievement dating back over 30 years”**, says Dr. Libby. This machine of monumental importance was designed way back in 1977 to collide electrons with their antiparticles called positrons at an energy of approximately 10 GeV, an amount sufficient to accelerate 10,000,000,000 electrons through a potential difference of one volt. Of particular interest is the Cornell Electron-positron Storage Ring (CESR), the part of CLEO where these collisions take place. It has a circumference of 768 metres and is located 12 metres below the ground level! Since its initial construction, CLEO has been upgraded several times for various purposes. Its final version, CLEO-c, has been tailored to the study of charm quarks such as D mesons. CLEO-c has so far collected 3 million pairs of D mesons.

Dr. Libby and his team thus set out to analyse the data gathered by CESR that contains information on the CP-content of the previously mentioned D decay. You may have correctly guessed that the data concerned was extremely vast – so vast that even after the physicists concerned analysed all the data using the methods they had planned to employ, they felt compelled to use an altogether different class of methods just to validate their analysis. This class of methods, known as the *Monte Carlo *methods, involves generating random numbers and performing repeated simulations on the acquired data using these random numbers as inputs for the simulations.

The next part of the analysis was to determine whether the state *π*^{+}*π*^{−}*π*^{0} was CP-even or CP-odd. Results indicated that the state was in fact in between these two extremes; a quantity called *CP** fraction *(denoted by *F*^{+}) that was determined for* D **→ **π*^{+}*π*^{−}*π*^{0} revealed that it was almost a pure CP-even eigenstate (with the “purity” being close to 96.8%). This key observation was examined further in order to understand its various implications. As far as *γ *was concerned, Dr. Libby and his team showed that further investigation of the decay mode *D **→ **π*^{+}*π*^{−}*π*^{0} could enhance the precision on *γ*. What is more, they were also able to propose an exact analytical method for the determination of this Euler angle. It is just a matter of time before this method is implemented in the near future. So it is safe to say that in the worldwide efforts to unravel the most intriguing mysteries of matter and antimatter, Dr. Libby and his team, and hence IIT Madras, have taken a step forward.

However, the story is not over yet. “The formalism needs to be adjusted to incorporate *F*^{+} to account for the small CP-odd component in the final state”, as per a recent paper of Dr. Libby’s. Another massive particle collider named Beijing Spectrometer III could supply the data necessary for this purpose. Analysing this data would then contribute to our knowledge of *γ *and push us closer to solving the larger questions involving matter and antimatter. Undoubtedly, this means that there is a long way to go and that innumerable exciting discoveries are in store for us.

**Dr. Jim Libby **is an experimental particle physicist working at IITM since 2009. Dr. Libby received his undergraduate and postgraduate degrees from the University of Oxford. His PhD work was with the DELPHI experiment at the Large Electron-Positron Collider at CERN. Since completing his PhD in 1999, he has worked with accelerator experiments at CERN, Stanford, Cornell and KEK (Japan). He also participates in studies related to the Indian-based Neutrino Observatory (INO).

**Rohit Parasnis **is a final year Dual Degree student pursuing his B.Tech. in Electrical Engineering and M.Tech. in Biomedical Engineering at IIT Madras. One of his long-term goals is to make science more interesting and more accessible to all. Some of his past endeavours include generation of video content for familiarising school students with experimental science, translation of scientific and social scientific Wikipedia articles into regional languages and performing a managerial role for the National Service Scheme (NSS) at IIT Madras. He can be reached at rohityparasnis@gmail.com.

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