1. Introduction

In the quest for the predicted Higgs boson Atlas[1,2] and CMS[3] collaborations have found a light narrow resonance with a mass of about 126 GeV. This very important finding has also been supported by data from the Tevatron[4]. However, some properties of the newly found boson differ from those of the predicted Higgs boson. In particular, D0 and CDF collaborations have reported an excess of [5,6] which is the top quark forward-backward asymmetry, and also an increase in the channel[4], while the LHC has observed an excess in the diphoton channel[7,8]. Moreover, a detailed fitting to the available data up to the end of 2012[9] has shown that “In short, significant deviations from the SM values are preferred by the currently available data and should be considered viable”.

Therefore, it is very important to identify the Higgs couplings to quarks to determine the true nature of the recently found Higgs-like boson. On the other hand, theoretically, only SUSY models identify the Higgs boson couplings to quarks, as discussed in the article by Blum et al.[10]. Considering the work presented in reference[11], which presented Higgs-like bosons in the framework of a composite quark model, we identify all couplings of the Higgs-like bosons to quarks.

2. Calculation of all Higgs-like Bosons Couplings to Quarks

The calculation is based on the quark compositeness model described in detail in reference[11]. The model considers that each quark is composed of two primons (prequarks) and, thus, we need 4 primons to describe the 6 quarks. It is assumed that primons should have the baryon number B=1/6, of course. As to electric charges has charge equal to +5/6 and primons have each charge equal to -1/6. Using the modified Gell-Mann and Nishijima relation

(1)

for a system of primons (a quark), where, , for primon , and for the other primons, we obtain,

(2)

for quarks u,c,t, and

(3)

for quarks d,s,b.

As quarks quarks and have isospins equal to and , respectively, we have to have for primons, and Using the modified Gell-Mann—Nishijima relation

(4)

for primons, we obtain

(5)

for primon , and

(6)

for and assuming that has also . Therefore, can assume the values and and, thus, these values can be considered as the projections of (Table 1).

Table 1. Projections of the isospin I and of the quantum number

In terms of and a quark has the four possible states (described in detail in ref.[11]):

Organizing the values of and for quarks on a table we obtain Table 2 below.

Table 2. Assignments of the values of       and       for quarks

Taking into account the charges of primons and the assignments of for primons from Table 1 we obtain that there should exist the Higgs-like bosons for generating quark masses, as shown on Table 3 below.

Table 3. The generators of quark masses

With the values of for quarks from Table 2 and making use of the Higgs-like bosons identifications in terms of the quarks we obtain Table 4 below.

Table 4. The quantum numbers of the Higgs-like bosons

According to Table 4 the neutral Higgs-like boson is a triplet in which each member belongs to one of three possible values of which are . Because of this feature let us use a subscript for assigning the different values of , and thus, there are for the Higgs-like with , for the Higgs-like with , and for the Higgs-like with . For simplifying matters further, let us call both and by . This way we can say that as a proton and a neutron exchange a pion by means of a strong interaction, primons and exchange a and form quark , yielding its mass, that is,

.

According to the above reasoning, there are the charged bosons , , , and also , , , . We can simplify the notation and designate both and by and and by . And for each we can drop the plus and minus signs and consider, for example, that the interaction of and by means of produce the quark , that is,

.

This symbolizes

and

which in terms of the electric charges are, respectively,

and

and in terms of the charges are, respectively,

and

.

2.1. Interactions with Equal Quarks

Let us begin with the interactions. For example, the quark is the combination , and thus between two quarks there are two interactions involving . Between two quarks there are two interactions by means of . Doing the same for the other quarks we obtain Table 5.

Table 5. Interactions involving equal quarks

2.2. Interactions between two Different Quarks

Since there are too many interactions between two different quarks, we classify them keeping one quark fixed, avoiding repetitions. For example, between quarks and there are interactions mediated by the bosons and . Doing the same for the other quarks we obtain Tables 6, 7, 8, 9 and 10.

Table 6. Interactions involving the       quark

Table 7. Interactions involving the       quark, excluding

Table 8. Interactions involving the       quark, excluding       and

Table 9. Interactions involving the       quark, excluding      ,       and

Table 10. Interaction involving the       quark, excluding       and

2.3 Most Intense Interactions with

As we see from the above tables, the most intense interactions involving are those of the quark with the quark and the quark, and the interaction of the quark with the quark because they are mediated by one and two . This is an important result from the experimental point of view because we can compare one of these three interactions with an interaction mediated by only one . For example, comparing the interaction with the interaction , we obtain a factor of 3 for the relative strength,

.

And we should also have the ratios

.

2.4. Medium Intensity Interactions with

We obtain from the above tables, that there are interactions involving two ’s which are the interactions , , , , and . We can compare them with those of section 2.3 and obtain the important relation (just one of the several ratios)

.

And we should also have the ratios (just some of the ratios)

2.5. Less Intense Interactions with

From the above tables we obtain that there are interactions involving just one which are the interactions , , , , , , , and . We can compare them with those of section 2.3 and 2.4 and obtain the important relation (just some of several ratios)

.

And we should also have the ratios (just some of the ratios)

2.6. Interactions without

We also obtain from the above tables that there are exactly three suppressed interactions involving which are the interactions , and . This is an important prediction that can be experimentally tested.

2.7. Interactions with the Charged Bosons

With respect to the charged bosons we notice that there is no interaction involving three bosons, that is, the most intense interactions involve two charged bosons. There are 15 of these interactions that are listed on Table 11. It is important to observe that there are interactions that do not involve the charged bosons. These are the six interactions , , , , and .

Table 11. Interactions involving 2 charged bosons

3. Conclusions

All couplings of the Higgs-like bosons to quarks have been identified. With them we are able to evaluate the relative strengths of the interactions among quarks as well as the suppressed interactions. A very important result is that the search for the charged Higgs-like bosons should not involve the interactions , , , , and because they are suppressed for the charged Higgs-like bosons.