Basic ideas of Particle Physics.. A Klong Meson

What did I know about K-long mesons a decade ago … 16th October 2002

A set of slides of my research from the year 2002. These were the initial years of my studying K-long meson at Belle, KEK, Japan. This is a very interesting toy MC study I had performed. I had developed a c++ program to do this simulation. Here are the slides. Klong meson

The particle physics laboratories are one of the prime locations for scientific research in the world. These labs consists of apart from large structures over and below the earth’s surface, huge computational facilities spread across the world, data-collection and monitoring systems on-site and in member-research-institutions spread around the globe and the intellectual analysis of the data which follows layers and layers of sparsing, filtration and size reduction and the final analysis to extract meaningful physical phenomena.

Its after this last step any new result from such studies are given out to the outside world and is celebrated or criticized in the scientific world depending upon these are results of vast implication or a spurious uplifted piece of work.

The very famous Higgs Boson called a God-particle from its condenscending name-sake God-damn particle for its notorious difficulty towards its discovery is one example of studies in particle physics labs. I rather name it a gauge-particle because God is a linguistically closer phonetics to Gauge given that you realize that “d” is accented like a “g/z” of Godzila and also in Soldier. In that sense there is no harm doen to the scientific integrity of scientific-naming by even as powerful a theological term as God. No harm done and also technical-experts and the students of science know that “Gauge-Symmetry” is the attribute of elementary particles like Higgs-Boson. **This is here that over-enthused internet racoons can initiate a tradition of calling it “God-Symmetry”. Don’t be surprised if you hear such a thing in 10 years from now.

Its not the responsibility of scientists to keep a watch on each and every malice that goes in the world today. The very fact that Higgs-Boson was called a God-Particle was also taken to its most negative bottom by the media recently {Circa 2012}. These are  unethical commercial practice. Such a trend is a formulaic approach. The same was last in action when Hawking’s Grand Design was out of press.

Another example of importance of Particle Physics as is understood by the general public is Blackhole. Well see blackhole is not a particle-phyics idea but the general public knows LHC is a particle-physics lab which produces blackholes that can engulf the world. Such was the paranoia in the year 2008 before LHC had started banging its protons into protons at the speed of light. In roughly 4 years the Higgs-like has been discovered. Why I say its a Higgs-like and not a Higgs? Because the Scientists are not perfectly sure that Higgs is that which they have found. If you want to remember Higgs here is a hint: it sounds like Eggs. {like in my eggs-girlfriend, My Higgs-girlfriend and my ex-girlfriend don’t they all sound the same?}

But talking about importance of particle physics one can write and write and write and forget that the general audience is zzzring .. in hindsight you were sounding all … nne nne nne neutrino … gggu gggu ggu gluino uppp uppp uppp uppp down down down bottom beauty anti beauty .. Its so beautiful really they felt like they are in papa’s lap.

Yesterday there was a news that a Kerala political leader of the “opposition party” wants the only and first international particle physics lab in India known as INO **Indian Neutrino Observatory** slated to come soon to be stopped on the pretext of Environment. Scientists from India and perhaps abroad have worked painstakingly for this lab for a decade now and like in all particle physics labs around the world there are several hundred scientists directly working for this project. Its like the size of the Indian parliament but the later was never stopped for environment.

Particle Physics must be brought to India at any cost and before even we talk about “Sojourn to Mars”. Particle Physics is the most fundamental and most advanced branch of Physics, today. Einstein and Feynman are its most famous fathers. If we are to honor Rutherford, Openheimer, Bethe and Fermi there would be no better way than to have a particle Physics lab’s inauguration in India by next month and have it in commission by a year or two.

Now that I have done some necessary advocacy of science through importance of particle physics in India we should be back to understanding some basic particle physics.

At the internationally famed laboratory of science in Tsukuba city of Ibaraki state of Japan where I lived for my research for 3 years over a period of 5 years and made numerous trips when I didn’t live, I started my career as a particle physicist by studying the Klong Mesons among other things. This laboratory is called KEK. [In Japanese: 高 エネルギ 加速器 研究 機構. High Energy Accelerator Research Organization is written “kō enerugi kasokuki kenkyū kikō” in Japanese, in short KEK for KEKKK. In Japanese short is kou-en, it also equates to Japanese: kouen = park/garden]

So whats a Klong Meson? And what are Mesons. A meson is literally a me-s-on which means “intermittent-oscillation”. Mesons are intermediary particles that consists of two quarks .. You can see it this way. meson is me-s-on. me is multilingually {eg in Japanese and in Indian} in/between/internal. on is similarly multilingually {originally Japanese} “oscillation/sound/vibration“. s is for sa/se which means “of”, “like” “as-if” etc. me-s-on is intermittent-oscillation, particles that are produced in the middle of other studied processes. When two quarks bind with each other they must be each-other’s anti-particle. One is called a quark and the other the anti-quark and vice-a-versa. anti-quarks are denoted by a “bar” on the top of the quark-particle’s name. eg if you have a “top” quark-particle you also have an “anti-top” quark-particle which is a bar on the top-of-top’s symbol. Like this; top-quark: t, anti-top-quark = top-bar = t-bar =  .

So Klong is a meson, this means Klong is an elementary particle and has two quark-pairs in it, one of which is a quark-particle and the other an anti-quark-particle. Klong is the name of a meson which has a “strange” or “s” quark and a “d” or “down” quark. This is the reason why Klong and its quark-pair look-alikes are called strange mesons. See, quarks are found to be of 6-types. They are named as {u,d}, {t,b} and {s,c} and stand for up, down, top, bottom, strange and charm. That means all the elementary particles in the world consists of either a pair of these quarks or a triplet {three} of these, the triplet of quarks is always called a Baryon. There is a slight exception to this because apart from quarks there are only two more types of fundamental/elementary building blocks of all matter called leptons and force-carrier-particles known as vector-bosons or gauge-bosons.

The Klong is a strange-meson because it has a “s” or strange-quark in it. Kshort is its look-alike. I say look-alike because their quark-content is the same. The Klong and the Kshort have the same quark content: {s,d} or their anti-quarks   actually the combination of these with one quark and one antiquark; so we have {s, }, {, d} which are: one of them a Klong and the other the Kshort. Actually the wavefunctions of these mesons Klong and Kshort decide how the quark-particles {s, , d} will mix with each other but they will mix only in two ways Kshort and Klong. Collectively these are called the Kzero mesons because eventually the charge of the meson after mixing of the quark-particles will be zero. But even after that there are two ways this can happen. The Kzero and its anti-particle the anti-Kzero written as a Kzero-bar []. The charged K-mesons [K+ or K-] or the K-resonances [K* etc] are also called strange mesons because they must have a strange or s-quark in their wavefunction. So the 4 possible combinations of the above 4 quarks produce 4 different wavefunctions for neutral Kmeson. The masses of the Kshort [which can now come in two ways: Kzero or anti-Kzero] and the Klong [which also comes from either Kzero or anti-Kzero] are same. The masses are same in all 4 cases. But the lifetime or the time for which these 4 wavefunctions exist is not the same. In otherwords Klong irrespective of whether it comes from Kzero or anti-Kzero and Kshort irrespective of its release from Kzero or anti-Kzero have different lifetimes. The Kshort and Klong have same mass but have different lifetimes because of how the wavefunctions mixes the inherent quarks of {s, , d}. Which is why the naming short and long, short: lives for short time, long: lives for long time. The Kshort lives for {} and the Klong lives for {}. The other difference between Kshort and Klong arises in the fact how profusely tehy are produced from their parents. In other words are the Klong and Kshort produced in equal numbers from say the combined wavefunction of {Kzero + anti-Kzero}? The answer is NO. And its not unequal because the lifetime is unequal which is a misconception I have addressed in another description of the properties of particles in the elementary world. One can safely say its the mixing of the quark-contents which decides that their mass is same, lifetime is different. But also its the wavefunction which due to mixing/intereference with other particle’s wavefunctions decides how profusely the Kshort and Klong will be produced. Such intereference of wavefunctions [as opposed to how mixing of the inherent quark-particles decided the lifetime difference] decides the so called branching-rate of production of Kshort and Klong mesons. The interference of wavefunctions is due to phase and amplitude mixing/intereference. Basically the amplitude gives the probability or rate at which the branchings will occur and phase gives the angles at which which these wavefunctions gets mixed. The angles are not physical angle in the sense of direction we see everyday but the angular or geometric/trigonometric quantities in spaces which are not ordinary. They are necessary to bring consistency in what rates of branchings are to occur from a particular reaction. [amount of a specified channel, eg is a Klong channel 30% or 45%? 30 or 45 %? is rate and Klong or Kshort channel?  is branching because such comes out as a branch from the tree of its parent-particles. The tree of parents and siblings is called a topography. ]

So the mixing of wavefunctions of different particles and processes is responsible for the difference in the amount or rate of Kshort and Klong meson and the mixing of the quark-content is responsible for the difference of lifetime of Kshort and Klong mesons. The masses are still the same because its the same particle. Kshort and Klong are the same particle. A particle is defined by among other variables “its rest-mass”. Life times can be arbitrary. Usually because the processes in nature can be limited for a particular channel we do not see much variety of lifetime. I have described the nature of eg different kind of neutrinos [solar or atmospheric neutrino etc] and how they differ in their lifetime based on their source-energy.  Masses of particles are not arbitrary by definition. If its a different mass its a different particle, we have never seen an exception to that .. The rest-mass of Kshort and Klong, together a Kzero {and anti-Kzero} is same: 0.496 GeV. Its a little less than 1000 times heavier than the electron. Since proton is ~2000 times heavier than electron it simply means the Kzero mesons are half as light as the proton. Hence Hydrogen gas about is twice as heavy as the Kzero mesons. If the hydrogen hits you, you better wish the Kzero mesons had hit you, then you will have half as much damage to your sunken face.

It was my PhD thesis to determine experimentally, how much difference exists between the Kshort and the Klong production. These mesons are produced from a {Kzero+anti-Kzero} wavefunction and that in turn is produced from a {Dzero+anti-Dzero} wavefunction. The latter is called a neutral charm meson. Because the meson is neutral  and there is a charm {c} quark-particle in it.  Due to such a production channel {neutral D+antiD; in-to; Kzero+antiKzer0 + anything else } two types of internal-channels are observed for such a reaction. One is called a Cabibbo-Favored [CF] and the other a twice Cabibbo-Suppressed channel called as Doubly-Cabibbo-Suppressed channel [DCS]. These are the modes or intermittent-channels. I also called them internal-channels. Each of these channels are a superposition of wavefunctions. Wavefunctions are superpositions of Quarks of different kinds, in other words quarks are themselves wavefunction. Which is why I had said Higgs is simply a differential equation. The wavefunctions are complex number functions hence each of them has two parts: Phase and Amplitude. The Phase as I explained above gives an angle in a non-ordinary space. The Amplitude gives the amount of the probability of this wavefunction being found in a particular situation. These wavefunctions satisfy something called a Schrodinger’s equation which is a wave-particle-equation of motion. We have particle equations of motion that describe motion of particles such as Tenis balls. Then we have wave-equations of motion which are description of waves such as satelite communication. In the elementary particles level [such as atoms and molecules and quarks and mesons] these equations fail to satisfy the motion properties of the particles because these are not exclusively particles or waves. They are both. In other words the waves and particles interfere or mix and their description must come from an equation which has properties of equation of motion of both wave and particles. These equations of motion for particles or waves separately are differential equation of various types. An equation of motion which explains both waves and particles due to their interference and mixing is called a wave-equation although wave-equation means in the Physics of ordinary phenomena just wave-properties, in quantum mechanics it naturally means wave-particle equation. Particles produce waves and waves produce particles and all other possibilities of such are together describable by a wavefunction equation known as Schrodinger’s equation or simply Schrodinger’s wave-equation.

So the intermittent-channels of CF and DCS have their superpositions of the wavefunctions. A wavefunction is a solution to a differential equation known as, as explained above, Schrodinger wave-equation. Hence CF channel of Kshort and Klong production from neutral charm meson {Dzero+antiDzero} wavefunction is a different mix/superposition of wavefunctions from DCS channel of Kshort and Klong production from neutral charm meson {Dzero+antiDzero} wavefunction. It was my purpose to measure the asymmetry that arised out of such a difference of wavefunction-mixing. The difference of wavefunction-mixing is called an interference of CF and DCS modes. That is: due to such mixing only a term that has both CF and DCS factors survive in the definition of asymmetry between Kshort and Klong production. Asymmetry A= (Klong-Kshort)/(Klong+Kshort) = some {CF+DCS} wavefunction. This latter + is not a simple additon but could also be a product of wavefunctions of CF and DCS. Also note that if Klong+Kshort = 100, Klong-Kshort = 10, then there is 10% difference or asymmetry in such production. So Kshort rate = 30% and Klong rate = 70% would means A = 40%. Kshort rate = 45% and Klong rate = 55% would means A = 10%. Its something like this in nature. The earlier phenomenological studies of particle physicists had produced a prediction of about atleast 5%. This came from a cabibbo angle of theta = {13 deg!!!} where the asymmetry was tan-of-theta. My results were almost complete by November 2006 whence I was invited to some important conferences to talk about my results. But an ambition from the collaboration people to have a starkingly shocking result to the community meant my result was slated to be studied more and I got to talk about other 5 important results. By 2008 CLEO collaboration had come up with a measurement of this asymmetry although their result was a good analysis it didn’t have the details of my analysis. Theirs was also a very different technique. My analysis constituted of atleast 30 modes of particle-reactions whilst theirs only about 10 if I recall. Theirs was dedicated to some other study from where they extracted such an asymmetry but mine was exclusively directed to this Asymmetry. They obtained about 10% asymmetry and mine was roughly 13%. Since due to discontinuity of my analysis work due to the decision making of senior scientists in the community I could not estimate or augment the analysis for an exact value of this asymmetry. Since then I have tried to put important pieces of my work on my website so someday in the future this can be accomplished. If I devoted 7 years for an important work and the authorities funded such a work its only imminent that such a work is not stopped in various pretexts. Scientific practices has in it much different views than one is ready often to see immediately ..