LHC T-Shirt Formula: Unravel the Mystery

In summary, the conversation discusses a t-shirt with a formula on it that represents the electroweak part of the standard model Lagrangian in a concise way. The shirt highlights some important ingredients of the standard model of particle physics, including the gauge bosons, fermions, Higgs boson, and kinetic and potential energy terms. The Lagrangian describes the equations of motion for all the fields in the standard model and is considered a fancy version of F=ma. There is also a discussion about the possibility of finding flaws or extensions in the standard model through the LHC.
  • #1
rhenretta
66
0
I went to see the LHC (my version of a pilgrimage to Mecca). I bought a tshirt with a formula on it, but I can't find any information on what the formula describes.


http://www.facebook.com/photo.php?pid=4005975&l=cc76e7a9d7&id=529304037 [Broken]

hopefully, that link works, if not I can tell you it is a formula describing L. I doubt in this case L is referring to angular momentum.

I am only on my iPhone, so unfortunately I can't transcribe the formula. I want to wear it, but I refuse until I understand the formula, lest I misrepresent myself.
 
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  • #3
Please note that, in general, a fancy L in physics usually represents something called a "Lagrangian density."
 
  • #4
This is a Lagrangian density -- it contains all the dynamics of the theory (ie the equations of motion are derived from it). The first term:

[tex]-\frac{1}{4}F^{\mu \nu}F_{\mu \nu}[/tex]

describes the gauge bosons (force carriers). In electromagnetism, the [tex]F^{\mu \nu}[/tex] is just the familiar field strength tensor (you can derive Maxwell's equations from this part of the Lagrangian!).

Second term:

[tex]i\bar{\psi}D\psi[/tex]

describes the fermions in the theory. These fermions are interacting with the gauge fields (you don't see this directly here -- it's hidden in the [tex]D[/tex] term). So, in QED, these would be electrons, and the gauge fields they interact with are photons.

Third term:

[tex]\psi_i y_{ij}\psi_j \phi[/tex]

is a Yukawa coupling between the fermions and a scalar field, [tex]\phi[/tex]. This scalar is the elusive Higgs boson, and this term is responsible for giving the fermions masses. Very important ingredient!

Last terms:

[tex]|D_\mu\phi|^2 - V(\phi)[/tex]

describes the Higgs boson. The first term is the kinetic energy (the field theory analog of half mv^2), and the second term is the potential energy of the field.

So, the shirt highlights some of the important ingredients of the standard model of particle physics.

EDIT: I shouldn't say this describes all the dynamics of the standard model -- the full SM Lagrangian is a monster. Rather, the t shirt displays some well known parts of it.
 
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  • #6
Hey all,

I have a question concerning the Yukawa coupling terms... Shouldn't the first [tex]\psi[/tex] rather wear a bar such that the terms look like [tex]\bar{\psi}_i y_{ij}\psi_j\phi[/tex]?? This keeps on confusing me (wearing the same T-Shirt and being asked from time to time... ;) )

thx in advance for some elucidation
 
  • #7
physstud said:
Hey all,

I have a question concerning the Yukawa coupling terms... Shouldn't the first [tex]\psi[/tex] rather wear a bar such that the terms look like [tex]\bar{\psi}_i y_{ij}\psi_j\phi[/tex]?? This keeps on confusing me (wearing the same T-Shirt and being asked from time to time... ;) )

thx in advance for some elucidation

I should think yes it should have a bar, otherwise the spinors don't contract properly. It is only schematic and lots of other things are suppressed so I wouldn't worry too much, except it is a bit inconsistent to put the bar and D-slash in the fermion kinetic energy/interaction term if you aren't going to bother with those details in the yukawa term.
 
  • #8
that is exactly what I thought. OK, thanks for the confirmation ;-)
 
  • #9
I'm still confused about one thing. That is; what does the lagrangian describe?
When I look at this explanation, I just think that all this does is describe the higgs field. But, whenever I hear about this lagrangian, someone will say that it describes just about all of particle physics, but I don't see how it does that. Can someone please explain?
Thank you.
 
  • #10
There are many fields described by this Lagrangian, not just the Higgs. For example, the gauge boson Lagrangian, [itex]f^{\mu \nu}F_{\mu \nu}[/itex] would be there Higgs or no Higgs.
 
  • #11
3m0k177y said:
I'm still confused about one thing. That is; what does the lagrangian describe?
When I look at this explanation, I just think that all this does is describe the higgs field. But, whenever I hear about this lagrangian, someone will say that it describes just about all of particle physics, but I don't see how it does that. Can someone please explain?
Thank you.

From that Lagrangian you can compute the equations of motion for all the fields in the Standard Model. It is like a fancy version of F=ma.
 
  • #12
Oh, I get it all now. Thanks.
 
  • #13
Well, I get it all except for two things: the second and third terms. I din't quite understand them well, can someone go in depth on them please.
Thanks, once again.
 
  • #14
3m0k177y said:
Well, I get it all except for two things: the second and third terms. I din't quite understand them well, can someone go in depth on them please.
Thanks, once again.
By 2nd and 3rd terms, do you mean the [itex]\psi_i y_{ij} \psi_j \phi[/itex] and the [itex]|D_\mu \phi|^2[/itex] terms?
 
  • #15
I mean the Yukawa coupling and the term that describes the fermions in the theory.
 
  • #16
I got one of these shirts! There is an older thread with some people attempting to answer this same question.

My daydream is that someday the LHC will find a flaw or extension of the standard model, and then I can sew a patch onto the t-shirt correcting the lagrangian.

bapowell, thank you for your exhaustive post.
 

1. What is the "LHC T-Shirt Formula"?

The "LHC T-Shirt Formula" is a mathematical equation that was created by scientists at the Large Hadron Collider (LHC) in Switzerland. It is a complex formula that describes the behavior of subatomic particles and their interactions within the LHC.

2. Why is it called a "T-Shirt" formula?

The name "T-Shirt formula" was given to this equation because it is short and simple enough to fit on the front of a t-shirt. It was meant to be a fun and catchy way to explain the complex science behind the LHC to the general public.

3. What is the significance of the "LHC T-Shirt Formula"?

The "LHC T-Shirt Formula" is significant because it helps scientists understand the behavior of subatomic particles and their interactions, which is crucial in studying the fundamental laws of nature. It also helps in the search for new particles and understanding the origins of the universe.

4. Can anyone understand the "LHC T-Shirt Formula"?

While the "LHC T-Shirt Formula" may seem intimidating, it was designed to be accessible to the general public. With some basic knowledge of physics and mathematics, anyone can understand the components of the equation and its significance.

5. How does the "LHC T-Shirt Formula" contribute to our understanding of the universe?

The "LHC T-Shirt Formula" helps scientists answer some of the biggest questions about the universe, such as the origin of mass and the existence of dark matter. By studying the behavior of subatomic particles through this equation, we can gain a deeper understanding of the fundamental laws that govern our universe.

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