|NET FORCES IN QCD|
In the previous page we used the names glu1on (which is an ordinary gluon), glu2on and glu3on for composites of respectively 1, 2 and 3 gluons. Any number of N gluons can always couple to each other to form a composite, a gluNon (pronounce glu-en-on) of net spin 1. The gluons then orbit each other with an impulse momentum that can have specific values (Ö, -2, -1, 0 1, 2, Ö). When the gluNon is white this is a glueNball (glue-en-ball).
Since gluons can emit and absorb each other, a gluNon can always vary between all possible Nís, provided the impulse momentum can adapt somehow. And if the energy is sufficient. And if the whole gluNon concept isnít beside the point.
In page 5 of this storyline, especially paragraph Meson exchange and Four quarks in the shell, is argued the gluon consists of a quark and an antiquark that are so near to each other they coincide to masslessness. So gluons are massless. Also the gluons can approach each other “within their time borders” but this is not necessary for their existence as gluons. (For the time border, see paragraph The calculation of the time border at page 2 of storyline EXPANSION OF THE UNIVERSE) The gluon does not really have a time border. The two quarks it consists of, they have time borders. Are two gluons allowed to near each other within the time borders of their 4 constituting quarks, the 4 quarks all within their respective time borders? Yes, why not? If so it would be a fundamental under the gluNon concept.
Maybe there is a kind of bottleneck for the composing quarks of gluNon states. When the 4 quarks are not near enough to each other they will not be all within their time borders and masslessness is not achieved. Why should the quarks be not near enough to each other? For gluon-gluon interactions we adopt the force being proportional to distance like between quarks, zero force at zero distance and maximum force at about 0.9 fm, see The proton at page 5 of this storyline. So when the quarks are too near to each other they hardly will interact. They will pass each other by, at least try to do so. If they would, they are soon outside the reach of their time borders. But at the moment they are near enough, they form a gluon. So the chances are largest gluons are formed, just normal gluons. But once in a while it will happen all four quarks are near enough and when within their time borders the composing quarks achieve masslessness, gain lightspeed and are frozen in a glu4on.
In case you might try to calculate something, don't forget to read page 9 of the QQD storyline, where gluon colors as quaternion units are represented as matrices.
Letís now pay more attention to the impulse momentum of the gluNon, orbital momentum as well as spin.
Consider a gluNon with N going 2-->1, which means the two gluons of a glu2on merge to one gluon, formerly named gluon-absorption. (Nobody knows if gluon 1 absorbs gluon 2 or that it is the other way around. They just merge and split.)
Can 2 gluons merge to 1 gluon easily?
For a gluon to act as a vector-boson its spin must be +1 or -1. If two single gluons meet and merge, their spins add up to 0 (opposite spins, 2 possibilities and ) or +2 or -2 (aligned spins, also 2 possibilities and ) which is not possible when the gluon has to stay a gluon. And the quark has to end up with spin +1/2 or spin -1/2, so nor can a spin2-glu2on nor a spin-2-glu2on be absorbed by a quark.
To get rid of extra spin or shortage of spin an extra particle can be added to the interaction. The actual Feynman diagram then in fact shifts to a different diagram that depicts another possibility. Apart from that, a quark-to-meet to scatter along (to convey a +1 orbital impulse momentum to a spin -1/2 quark, or convey a -1 orbital impulse momentum if the quark happens to have a +1/2 spin - but what if that wasnít the suitable impulse momentum the glu2on needs to convey) is not always available in time. And if the glu2on becomes absorbed by the quark, the merging has not been accomplished - there hasnít been no merging. And if they meet a third gluon we encounter the next situation: can 3 gluons change into 1 gluon easily, N going 3 --> 1?
Better is the meeting gluons do not hit each other head-on, but a little ”off line” precisely that much the desired orbital impulse momentum is created in the glu2on from the beginning. When the spins counteract to 0 the orbital impulse momentum will be +1 or -1. And when they line up to +2 or -2 the orbital impulse momentum shall be -1 or +1 respectively. Then the glu2on has a spin like a normal gluon and will easily merge to 1 gluon.
So the answer is no, 2 gluons donít merge easily to 1 gluon. A suiting quark is seldom available in time and only a small fraction of the gluons will have the necessary precise approaching-angle to each other in time.
In the previous page we assumed the glu2ons and glu3ons act like gluons, spin-1 particles (we mean a spin +1 or spin -1). So if we speak about a glu2on, glu3on or gluNon we just assume its spin to be 1 (+1 or -1). A spin-1 glu2on - already formed somehow - will easily merge to 1 gluon. A gluon can easily shift between the states glu1on and spin-1 glu2on. But 2 sole gluons will not easily merge to a glu2on or a gluon. And a glu2on will not easily decay in 2 sole gluons.
This means a building block of QCD, the emission or absorption of gluons by gluons, is not an easy process. Relative to the color-unit of time, 10 exp -23 seconds, it will be a rather slow process with low abundance.
In the previous page we allowed the creation of glu2ons and glue2balls. Spin1-glu2ons or spin1-glue2balls are difficult to create. Should we leave them out of count?
Can 3 gluons change into 1 gluon easily, N going 3 --> 1?
The next table is about orbital momentum of gluNons. All numbers are gluon spins, except for the last number in a row, after the space, which is the total orbital impulse momentum of the gluNon.
As you see, when the 3 quarks of a baryon all emit a gluon in concord - or anyway 3 gluons were created - and the gluons form a glu3on, then there are 8 possibilities for the spin and orbital momentum to be gluon-like, +1 or -1. Six of them are groundstate (orbital impulse momentum = 0) and so yes, in these 6 cases 3 gluons merge into 1 gluon easily. Two cases have the significant higher orbital impulse momentum of 2 or -2, making them to cost more energy.
Mark the striking resemblance of this situation with 8 gluons from which 2 are the energetic more expensive glueballs. Is it possible a mismatch has taken place here? The accepted 8 gluon-states being composites of gluons?
When the energy is sufficient for 3 gluons to come to existence and the actual reaction is unobserved then the reaction sets off as a superposition of all possible ways it can happen up to 3 gluons participating. And then the 3-gluon-reaction outnumbers the 2-, 1- and 0-gluon-reactions together by 186 - 58 - 13 - 1 = 186 - 72 = 114. Consider 186 + 58 + 13 + 1 = 258 and regard 86, 172, 258. The number of 3-gluon-reactions is more than 2/3 of the other reactions together.
There is the notorious ďspin-puzzleĒ stating the spin of the proton can only for 30 % be attributed to the spin of the quarks.
So 3 --> 1 is easy while 2 --> 1 is slower and less frequently. A gluon will split in rather 3 than 2 gluons (a gluon will rather emit 2 gluons than 1). Merging of 3 gluons is more abundant than the merging of 2 gluons (a gluon will rather absorb 2 gluons than 1).
In the antibaryon
Spin has features like color. It is impossible to enter a spins world with an elementary particle without changing the spin. The spin-0 Higgs boson in my theory of gravitation, see page 2 of the QG storyline, is a composite and a short living intermediate state only. Otherwise there are no elementary particles with zero spin. E.g. the spin-0 mesons always consist of 2 quarks.
A spin +1/2 quark emits a spin +1 gluon, leaving the emitting quark with spin -1/2. The spin +1 gluon is absorbed by a spin -1/2 quark that turns into a spin +1/2 quark. In a single gluon reaction the quark spins interchange, just like the colors of the quarks. Interacting quarks swap their spins.
To the outside observer it is unknown which quark has which color. If a quark in the antibaryon emits a gluon one has to consider the whole antibaryon. There are 6 possibilities for the 3 colors to be divided over the 3 quarks:
The antibaryon (given here as quark 1, quark 2, quark 3) is in a superposition of all its possible quark-spin configurations:
(As a whole this gives the impression of a spin-0 baryon, but when we enter, none of these 8 possibilities have spin 0.)