# Bounds on 2HD potential

• Safinaz

#### Safinaz

Hi all,

I found that any two Higgs doublets potential should be bounded from below - at ## V \to - \infty ##. I want to know why this bound is assumed or what does it mean ?

Also are there any textbooks to learn how to make this bound on any other general potential and so to constrain the potential's parameters ?

Best.

If the potential is not bounded from below, your theory has no ground state.

The bounds are obtained just by looking at the potential...
For example $V=a |\phi|^2$ is bounded for $a>0$ and unbound for $a<0$. If you draw the potential you will see that.
In case you have more than one fields, I guess one has to look at each direction independently ... So the potential for two Higgses could be described by a sheet $V(\phi_1, \phi_2)$ on the space of $\phi_1, \phi_2$, if it's bounded it means that it can't go to $-\infty$ anywhere.

If there was no bound then even if you had a vacuum at some potential's minimum, this vacuum would not be stable. At some point the field would "escape" the well, and then start rolling down forever.

## 1. What is a 2HD potential and why do we need bounds on it?

A 2HD potential is a mathematical representation of the interaction between two particles in a three-dimensional space. It is used to study the behavior and dynamics of particles in various physical systems, such as atoms, molecules, and nuclei. Bounds on 2HD potentials are important because they help us understand the limitations and constraints of these interactions, allowing us to make more accurate predictions and models.

## 2. How do scientists determine the bounds on 2HD potentials?

Bound on 2HD potentials are determined through a combination of theoretical calculations and experimental measurements. Theoretical methods, such as quantum mechanics and statistical mechanics, are used to develop mathematical models of the interactions. These models are then compared to experimental data to validate their accuracy and refine the bounds.

## 3. Can the bounds on 2HD potentials change over time?

Yes, the bounds on 2HD potentials can change over time as new experimental data becomes available and theoretical models are improved. As our understanding of physics and the behavior of particles advances, the bounds on 2HD potentials may also change to reflect this new knowledge.

## 4. How do bounds on 2HD potentials affect our understanding of the universe?

The bounds on 2HD potentials play a crucial role in our understanding of the universe, as they help us predict and explain the behavior of particles in a wide range of physical systems. By studying and refining these bounds, scientists are able to make more accurate predictions and develop a deeper understanding of the fundamental laws of nature.

## 5. What are some potential applications of bounds on 2HD potentials?

The bounds on 2HD potentials have many practical applications, such as in materials science, chemistry, and nuclear physics. They are also used in the design and development of new technologies, such as computer chips, pharmaceuticals, and energy sources. Additionally, understanding the bounds on 2HD potentials is crucial for studying and manipulating particles in fields such as quantum computing and particle accelerators.