This story happened when I was rather young (in 1987-88 - I was 16 years old). At that time I was a memeber of the team of school #542 participating in the Young Physicists Tournament organized by Moscow State University, Physics Faculty. It was a very interesting competition: there was some list of the problems to be solved and several teams (from the best schools of the USSR). We had a half a year to prepair our presentations about these problems.That's the background.
One of the problem was the problem of the "Nineth Wave". According to the sailor's legends the Nineth Wave is the biggest one and therefore might destroy the ship. (Actually russian sailors think that the nineth wave is the most dangenrous, dutch think that this is the fifth wave, and so and so. Hence, the Nineth Wave is a purely psychological phenomenon.)
We have developed a stochastic approach. My father bought Oceanology textbook with very useful information including the distribution of ocean waves by height. Denis Pospelov (he graduated from our school in 1987 and was a first year student at that time - he is extremely gifted person!) inveneted the following trick. Suppose we have X-Y axis. Using wave height distribution we can plot the curve Y(X) (Curve 1) where X is the average distance between two waves that Y times higher than average wave amplitude. We can also plot the curve Y(X) (Curve 2) where X is the average distance between any given wave and the wave that Y times higher than this given wave. It appeares that Curve 1 and Curve 2 have only one intersection - of course,near X=9.
This intersecton became the cornerstone for our speculations. Look, if X<9, than (from the viewpoint of sailor in the ship) next X waves may be large with respect to the current wave but not large with respect to average wave amplitude. On the contrary, if X>9 than waves larger than average but not large with respect to their neighbours. Finally, for X about 9 the waves are both large with respect to their neighbours and with respect to average amplitude. Therefore (according to our speculations) the Nineth Wave seems the biggest.
I've made the presentation about the 'Nineth Wave' several times including presentation at the closing ceremony of the Young Physicists Tournament. I (and my team) have got a lot of points. It was a really impressive presentation - it included computer simulation of ocean surface (1-dimension) and other stuff.
After my examination (in order to enter the Moscow Engineering Physics Institute - the MEPhI) I went to Black Sea to have a rest before the first year at college. Of course, I wanted to check my theory by experiment. I made a 3-meter yardstick (with scale) and fixed it on the sea floor not far from the coast. I sat on the boat (frankly speaking, it was not a boat - but it doesn't matter) and wrote the wave amplitudes as the waves came - one after another. All my records I entered into database files in my home computer and I plotted the wave amplitude series.
What was the conclusion? The conclusion was that my theory about Nineth Wave was wrong from the very beginning!!! I discovered for myself (I guess, it is well-known for experts) that waves in the ocean propagate in the groups (soliton waves). But my theory was based on the assumption that two neighbour waves independent from each other!!! Illustrations for my presentations contained no any wave group! All waves were represented as a superposition of linear waves and there was no any nonlinear wave interaction.
So, I've got a lot of points presenting completely wrong theory! Some persons said me that I am wrong in my theory - but I insisted that I'm right and I won! It means that if the scientific society believe that some theory is right - it doesn't mean that theory is indeed valid.
That was my diploma work. The resulting paper was entitled as 'Hadronic shift and spin-spin forces in Charmonium P-levels' [1].
What does it mean - 'Hadronic shift'? The idea is evident - like the polarization operator in Quantum ElectroDynamics. Suppose we have some particle - say, meson. It can decay into some intermediary states and these virtual decays lead to some shift of initial (bare) mass. But we have no perturbation theory in the hadronic physics - we have no even exact model for hadronic decays! So, there is a vast space for speculations, approximations, phenomenology, etc.
The most popular model for hadronic decay is the 3P0 model where quark pair with quantum numbers of vacuum is created spontaneously and you can calculate the overlap and appropriate decay amplitude. This model was checked by Isgur and Co [6] and the results are rather reasonable.
The problem for my diploma work was proposed by my scientific supevisor - Yulia Sergeevna Kalashnikova. Initially we planned to calculate hadronic shift for various light mesons - but suddenly E760 collaboration in CERN discovered 1P1 state of charmonium. From the theoretical point of view it was especially interesting because the mass of 1P1 can be easily expressed through matrix element of spin-spin forces. Charmonium itself is almost nonrelativistic system (because c-quark is rather heavy) and theoriticians treat it as a probe for their theories and assumptions.
The main idea of my supervisor (regarding my scientific career) was to participate in the international workshop on the Nucleon-AntiNucleon interactions which was held in the ITEP in 1993. Of course, it was very important for me to make a poster presentation there. At that moment there was an opinion that fine splitting of charmonium P-levels can be described via purely perturbative effects. Therefore our work might to be interesting for the charmonium people.
So, we considered virtual decays of charmonium P-states into lowest meson pairs. We used the simplest oscillators wave functions in order to simplify the calculations. I made all computational work by means of my home computer - fortunately, all numerical calculations were rather simple. But there were two important and elegant points which I would like to mention.
First, there is a sum rule in this problem. Yulia Sergeevna pointed me that if the masses of intermediary states will be degenarate and wave functions paramaters also will be the same, than all P-levels mass shifts will be the same. It is very easy to prove this statement - if you know that it is really valid (and Yulia Sergeevna showed me by straightforward calculation that it is indeed valid - and I've proved this sume rule myself).
Second, when I made all the calculations numerically, I discovered that there is some pattern of hadronic shifts for various P-levels - and this pattern almost doesn't depend from model parameters (wave function radii). It was rather strange because it appeared that S-wave decays into intermediate states should be suppressed with respect to D-wave decays. After short consideration I've found rather simple explanation of this problem - this S-wave supression appeared from polynomial structures of decay amplitude and seemed rather obvious.
I've presented my paper at NAN'93 poster session and even distributed of about 10 (!!!) copies of my paper (E760 people took some copies when they saw that the first reference in the paper [1] points to their original paper about 1P1 level discovery - thanks to Yulia Sergeevna - she prepared references list very carefully). I was very proud that my paper was printed as ITEP preprint [1] and (later) - in the Proceedings of NAN'95 - in Yad.Fiz.
It was supposed that my Ph.D thesis will be entitled "exotic states in the QCD-motivated models". I thought that I could include calculations of hadronic shifts for hybrid states into my diploma. Unfortunately, I didn't do it. I didn't calculate the hadronic shift no more (in spite that we had some plans about this activity).
Hybrids are the states with quarks and excited (or additional) gluonic degrees of freedom. It would be very desirable to find a hybrid state (or glueball - pure glue state) - such a state is a direct evidence of gluonic degrees of freedom in hadronic physics.
I'll try to explain the main idea of our hybrid activity [2],[3],[4]. Let us consider hybrid meson with heavy (c or b) quarks. Than we have heavy (and slow) quark subsystem and light (and fast) gluonic subsystem. Usual approach is to fix heavy quarks and calculate the interquark potential - this is an adiabatic approximation (see, for example, Landau-Lifshitz textbook, part III).
An important point is the guess about possible equilibrium configurations of such a system. Isgur and Paton [6] supposed that gluonic string connecting quarks oscillates very small and can be considered as a straight line in the zeroth approximation.
The amazing discovery made by Yulia Sergeevna Kalashnikova on spring of 1994 was: for heavy quark hybrids gluonic subsystem radius should be much larger than interquark distance. It can be checked rather easy if we assume that interquark potential and quark-gluon potential are oscillator ones and appropriate gluonic values are determined through the string tension, then all unharmonic corrections should be of the next order. Indeed, as it is well-known from the adiabatic approach, the small parameter is square root from the mass ratio. Gluonic mass in such an approach is of order of square root of string tension. So, you can easily check (its really easy - and if you don't too lazy and know something about quantum oscillator) that in the main approximation quarks are in the center and gluon(s) flights far from them.
Actually if you have a c-quark with mass of about 1.8 GeV and square root from string tension is about 0.4 GeV - you see that your 'small" parameter is not small enough .Even for b-quark with mass of about 5-6GeV you have square root from the mass ratio of about 1/4. So, your perturbation series is rather doubtful. Nevertheless, I insist that if quarks are fixed (in the adiabatic approximation) - than with the same accuracy you can place them into the center and take only oscillator term of the interquark potential.
So, we had a Lagrangian based on Simonov's QCD string model and we obtained the equations for the interquark oscillator potential. Unfortunately, the main problem in the hybrid mass estimation is that you don't know actually what additional constant in the interquark potential should be used. Within our model it's easy to check that there is no balance if interquark distance much larger than gluon wave function radius. (Isgur and Co [6] obtained that in their "equilibrium" oscillations of the string are large - in contradiction with their basic assumption).
Alexey Nefediev [5] (at that time he was postgraduate student) considered baryon in the same approach. It was shown for lowest states that because of string junction dynamics there is some short-distance repulsion and the situation differs substantially from hybrid mesons. I have a strong arguments that this short-distance repulsion is the consequense of the Lagrangian used in the model but not a computational artifact.
So, that's it. Later I'll try to add references.
References
[1] Yu.S.Kalashnikova, Yu.B.Yufryakov. Hadronic shift and spin-spin forces in charmonium P-levels.Preprint ITEP-??-93
[2] Yu.S.Kalashnikova, Yu.B.Yufryakov. Hybrid excitations of the QCD string with quarks. Phys. Lett. B 359 (1995),175
[3] Yu.S.Kalashnikova, Yu.B.Yufryakov. Constituent string model for hybrid mesonic excitations. Preprint ITEP-53-95.
[4] Yu.S.Kalashnikova, Yu.B.Yufryakov. Hybrids with heavy quarks: from potential to string. Preprint ITEP-56-95.
[5] Yu.S.Kalashnikova, A.V.Nefediev. String junction as a baryonic constituent. Preprint ITEP-52-95.
[6] J.Merlin and J.Paton, J.Phys. G11, 439 (1985)
If you have comments or suggestions (or if you want to get TeX-files with one of my papers), email me at shmelyuga@hotmail.com
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