Dimension-5 interaction beyond the standard model

In summary, Dimension-5 interaction beyond the standard model is a theoretical framework that extends the Standard Model of particle physics by introducing additional interactions between fundamental particles. These interactions involve higher-dimensional operators and are believed to occur at a higher energy scale. Dimension-5 interactions are different from other dimensions in that they refer to the number of fields involved in an interaction rather than physical dimensions. They can involve a variety of particles, including quarks, leptons, and gauge bosons, and are being studied and tested through theoretical calculations and experiments at facilities such as the Large Hadron Collider at CERN. Although there is currently no direct evidence for their existence, Dimension-5 interactions are motivated by their potential to address unanswered questions in the Standard Model.
  • #1
spaghetti3451
1,344
33
Consider the following dimension-5 interaction:

$$\bar{\psi}D^{2}\psi.$$

Why is this interaction not consistent with either Lorentz invariance, the standard model field content or gauge invariance?
 
Physics news on Phys.org
  • #2


This interaction is not consistent with Lorentz invariance because it involves the second derivative of a fermion field, which is not a scalar quantity under Lorentz transformations. Lorentz invariance requires that all interactions be invariant under rotations and boosts, and the second derivative of a field does not transform in a consistent way under these transformations.

Additionally, this interaction is not consistent with the standard model field content because it involves a fermion field ($\psi$) and a gauge boson field (the covariant derivative $D$). The standard model only includes interactions between fermion and boson fields that are consistent with the symmetries of the theory. The inclusion of the second derivative of the fermion field breaks this symmetry and is therefore not allowed in the standard model.

Finally, this interaction is not consistent with gauge invariance, which is a fundamental principle of the standard model. Gauge invariance requires that all interactions be invariant under local gauge transformations, which are transformations that vary in space and time. The second derivative in this interaction breaks this symmetry, making it not consistent with gauge invariance.

In conclusion, this dimension-5 interaction is not consistent with Lorentz invariance, the standard model field content, or gauge invariance, and therefore it is not a valid interaction in the context of particle physics.
 

Related to Dimension-5 interaction beyond the standard model

1. What is Dimension-5 interaction beyond the standard model?

Dimension-5 interaction beyond the standard model refers to a theoretical framework that extends the Standard Model of particle physics. It introduces additional interactions between fundamental particles, beyond the four known fundamental forces (strong, weak, electromagnetic, and gravitational). These interactions are believed to occur at a higher energy scale and involve higher-dimensional operators.

2. How does Dimension-5 interaction differ from other dimensions?

Dimension-5 interactions are different from other dimensions because they are not physical dimensions in the traditional sense. In physics, dimensions refer to the parameters that describe the position and motion of an object in space and time. However, in the context of the Standard Model, "dimension" refers to the number of fields involved in an interaction. Dimension-5 interactions involve five fields, while the Standard Model interactions involve four fields.

3. What particles are involved in Dimension-5 interactions?

Dimension-5 interactions can involve a variety of particles, including quarks, leptons, and gauge bosons. These interactions can also involve the Higgs boson, which is responsible for giving mass to particles. The exact particles involved depend on the specific operators and couplings included in the theory.

4. What evidence supports the existence of Dimension-5 interaction beyond the standard model?

Currently, there is no direct evidence for Dimension-5 interaction beyond the standard model. However, there are theoretical motivations for including these interactions in our understanding of particle physics. These include addressing open questions in the Standard Model, such as the hierarchy problem and the nature of dark matter.

5. How are Dimension-5 interactions being studied and tested?

Dimension-5 interactions are being studied through various theoretical and experimental methods. Theoretical studies involve calculations and simulations to predict the expected effects of these interactions on particle interactions. Experimental tests involve colliding particles at high energies and analyzing the resulting data for any signatures of Dimension-5 interactions. The Large Hadron Collider (LHC) at CERN is currently one of the primary facilities used for these tests.

Similar threads

Replies
5
Views
1K
  • Beyond the Standard Models
Replies
0
Views
972
  • Beyond the Standard Models
Replies
3
Views
1K
  • Beyond the Standard Models
Replies
27
Views
7K
  • Beyond the Standard Models
Replies
1
Views
369
  • Beyond the Standard Models
Replies
2
Views
2K
Replies
2
Views
1K
  • Beyond the Standard Models
Replies
4
Views
2K
  • Beyond the Standard Models
Replies
1
Views
2K
  • Beyond the Standard Models
Replies
4
Views
2K
Back
Top