# The Higgs Mechanism 1

The spin reasoning. It is always told that the graviton has spin +2 or -2 and that the Higgs particle has spin 0. Let's for the moment propose the vacuum that is *gravity* to consists of a superposition of a glue2ball field gl gl (spin +2) and a glue2ball field gl gl (spin -2). The vacuum that is *gravitation* is taken to consist of gravitons made of two gluons each. The vacuum that is *the hadronic Higgs field* consists of a glue2ball field gl gl and a glue2ball field gl gl (spin 0). The vacuum that is the hadronic Higgs field is taken to consist of Higgs particles, also made of two gluons.

Here “gl” means “gluon” and a glue2ball is a glueball made of 2 gluons; here “” means “spin +1” and “” means “spin -1”.

I tried to work out the concept of gluNons in page 7 of the storyline QCD.

Suppose one of the two gluons from the graviton gl gl absorbs a graviton gl gl . Three gluons merge easier than two gluons, as is argued at page 7 of the QCD storyline.

( gl , spin +1) + ( gl gl , spin -2) --> ( gl , spin -1) (3.1)

The other gluon from the pair gl gl remains unaffected. The disappeared graviton leaves an empty spot at the place it had occupied. So the two gravitons change into one empty spot and one Higgs particle of same volume (is assumed) as the graviton:

gl gl + gl gl --> gl gl + empty spot (3.2)

Then the Higgs particle gl gl is absorbed at the coupling of some particle in the course of renormalization, leaving another empty place there.

So finally 2 gravitons converted to 2 empty spots and 1 Higgs absorption. (3.3)

This process rules out the possibility of taking e.g. the gl gl as vacuum particle while the other, gl gl , could be real. We need them both as vacuum particles.

If two gravitons gl gl and gl gl would just swap a gluon, one gets gl gl and gl gl . Now there are two Higgs particles in one single strike to be absorbed in the course of renormalization.

So then 2 gravitons convert to 2 empty spots and 2 Higgs absorptions. (3.4)

If this yields a heavier particle then, is this mechanism a candidate for one of the extra generations of elementary particles? One absorption at the spot isn't enough, the mechanism should work for quite a time all over the track of the heavy particle, isn't it? And where is the third generation?

In (3.1) and (3.2) graviton 1, to give them names, had absorbed vacuum marble graviton 2 and in doing so acquires the energy of graviton 2 added to its own energy. It is not precisely the Higgs mechanism because it had absorbed a graviton and not a Higgs particle. So it is in doubt whether the absorbing graviton gains mass. But it has caused one empty spot that will be filled in from the outside and this is one bit of gravitation. A vacuum locally acquiring energy, a local excited state of the vacuum, is not yet defined, maybe even not possible. So we conclude this reaction will not take place in empty space. But it does occur in the neighborhood of a quark ready to give that quark its mass. (3.5)

Then there doesn't have to be a separate Higgs field in empty space. There don't have to be two fields, a gravitational field AND a Higgs field. When a Higgs vacuum marble emerges, it is absorbed immediately thereafter. The hadronic vacuum then is one single grid of gravitons. The Higgs field, the Higgs particle, only does exist as a short-living intermediate state between the gravitational field and any coupling anywhere. The link between space and matter. (3.6)

The quaternion consideration. A vacuum marble like ( i -i ) consists of two gluons, i and -i. We start with two neighboring vacuum marbles, e.g.

( i -i ) ( i -i ) (3.7)

Now we assume the right gluon of the first vacuum marble ( -i ) to absorb the entire second vacuum marble ( i -i ). The left gluon of that first vacuum marble is unaffected.

If we rename ( i -i ) ( i -i ) as ( i a ) ( b c ) then there are 6 multiplication orders: abc, acb, bac, bca, cab, cba. In gluon-gluon reactions there is no preferred multiplication order and so the 6 possible outcomes superpose. In this case they all give same outcome -i, so the superposed possibilities merge to one possibility again.

-i * i * -i = -i * -i * i = i * -i * -i = i * -i * -i = -i * i * -i = -i * -i * i = -i (3.8)

The result is, as far as the colors are concerned, that the first vacuum marble is unchanged and the second vacuum marble is absorbed, leaving behind a hole in the vacuum, in accordance with the spin consideration.

(Quaternion multiplication has the *associative property*. As long as you don't change the order of multiplication, it doesn't matter whether you first multiply the last two gluons and then multiply by the first gluon, or multiply the first and second gluon and then multiply with the third one.)

The vacuum now is a superposition of ( i -i ), ( j -j ), ( k -k ) and ( 1 1 ) from (2.8), each in spin state gl gl or gl gl . So 8 fields altogether. (3.9)

## The Higgs mechanism 2

Suppose, at the spot of a quark in a baryon two gravitons from the vacuum - four gluons altogether - couple as follows.

(gl gl ) graviton 1

(gl gl ) graviton 2

+

(gl gl ) Higgs particle -->

(gl ) (gl ) two independent gluons (3.10)

Two gluons of opposite spin merge, one gluon from graviton 1 and one gluon from graviton 2. Then the remaining two gluons, also of opposite spin, merge too. There are two possibilities for this, | | and X (one above the other or crosswise). To end up with spin1 gluons we need to assume “one spin from one gluon from graviton 1 to annihilate with one spin from one gluon from graviton 2”. This is thought to take place at the location of a quark, the quark mediates this spin conversion. Take in mind a baryon, three quarks together. If this conversion also detaches the gluons from each other, then you have two independent gluons of opposite color. Then one gluon can go to the second quark and the other to the third quark.

So 2 gravitons disappear from the vacuum, reducing it by their volume, and 2 gluons appear. Vacuum converts into matter. (3.11)

The quaternion approach of Higgs mechanism 1.

( i -i ) is a vacuum particle consisting of the gluons i and -i.