_{1}

^{*}

The actual value of Higgs boson mass is difficult to determine theoretically due to lack of knowledge on the exact value of Higgs self coupling constant
l. The purpose of this paper is to obtain an upper bound on the Higgs mass in the Standard Model on the basis of one-loop effective potential in the ’t Hooft-Landau gauge and MS scheme. The condition of positivity of mass matrix at
ф =
ф
_{0} (where
ф
_{0} is the absolute minimum of the effective potential) of the scalar field gives an upper bound on the Higgs self coupling as
l ≤ 0.881. This condition yields an upper bound on the Higgs mass as
m_{H} ≤ 229.48 GeV.

The Standard Model (SM) [_{C} × SU(2)_{L} × U(1)_{Y} gauge group. The Higgs mechanism has been introduced in order to give masses to fermions and gauge bosons without violating gauge principles. The introduction of a weak isodoublet of scalar fields gives rise to a physical particle, the Higgs boson. The self-interac- tion of the scalar field leads to a non-zero field strength in the ground state. Through the interaction with the non-zero Higgs field in the ground state, the electro-weak gauge bosons and the fundamental matter particles acquire their masses. The Higgs boson gives the mechanism by which the particles can acquire mass. To confirm these ideas more rigorously it is important to find first hand evidence for the Higgs field. We still have only vague ideas and speculations about the properties of Higgs, which is a hypothetical particle, and the search for Higgs boson is one of the main goals of present and future high energy colliders. On the one hand, the experimental verification of the Standard Model cannot be considered complete until the structure of the Higgs sector is not established by experiment. On the other hand, the Higgs is directly related to most of the major open problems of particle physics, like the flavour problem or the hierarchy problem, the latter strongly suggesting the need for new physics near the weak scale, which can also clarify the dark matter identity. The detection of the Higgs particle [

The Standard Model Higgs is trusted to be an effective theory, only valid up to a cut off energy

The paper is organized as follows. The theory is given in Section 2. The results and discussions are given in Section 3. The conclusions are given in Section 4.

The one-loop effective potential of the Standard Model in the ’t Hooft-Landau gauge and the MS scheme is [

where

where

Here

For the EP of the minimal SM, the squared eigenmasses are

(1 º Higgs, 2 º Goldstone, 3 º W, 4 º Z and 5 º Top).

Where m is the mass parameter and

Using the technique of ref. [

So, the conditions

This is the exact necessary condition that must be satisfied so that all eigenmasses are real at the physical point

The effective potential

This leads to the following equation

We introduce a function p such that

and using this function p Equation (3) becomes

The reality condition (2) suggests that

Thus the limiting value

where we have taken

The limiting value of Higgs coupling

Using Equations (1) and (3) we get the expression of Higgs mass for p = 1 as

Choosing the following numerical values [

We obtain _{t} = top quark mass = 175 GeV [

In the neighborhood of

Using

Now, in the study of renormalization group evolution of the Higgs self coupling ^{14} GeV)]. Interestingly, this higher bound on l is approximately of the order of the higher bound on l calculated in this paper. The bounds on Higgs mass as calculated in [

On the basis of the above studies, I come to the following conclusions:

1) The upper bound of Higgs self coupling constant is

2) This bound on Higgs self coupling constant lies within the perturbative limit of the scalar self coupling constant. So, the calculation of upper bounds on Higgs mass and the parameters chosen in this work satisfy the perturbative validity.

3) As far as the selection of appropriate range of energy for the purpose of detection of Higgs mass is concerned, this result will help the LHC experimentalists.

This study suggests that there is still a scope for a renewed interest in the evaluation of Higgs mass until the Higgs is discovered in the LHC experiment.

Partha PratimPal， (2015) An Upper Bound on the Higgs Self-Coupling and Higgs Boson Mass from the Positivity Condition of the Mass Matrix。 Journal of Modern Physics，06，369-373. doi: 10.4236/jmp.2015.64039