# LHC t shirt formula

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1. Jun 10, 2010

### rhenretta

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.

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

Last edited by a moderator: May 4, 2017
2. Jun 10, 2010

### cristo

Staff Emeritus
3. Jun 10, 2010

### Pinu7

Please note that, in general, a fancy L in physics usually represents something called a "Lagrangian density."

4. Jun 11, 2010

### bapowell

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:

$$-\frac{1}{4}F^{\mu \nu}F_{\mu \nu}$$

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

Second term:

$$i\bar{\psi}D\psi$$

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 $$D$$ term). So, in QED, these would be electrons, and the gauge fields they interact with are photons.

Third term:

$$\psi_i y_{ij}\psi_j \phi$$

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

Last terms:

$$|D_\mu\phi|^2 - V(\phi)$$

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.

Last edited: Jun 11, 2010
5. Jun 11, 2010

### Kevin_Axion

Last edited: Jun 11, 2010
6. May 1, 2012

### physstud

Hey all,

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

thx in advance for some elucidation

7. May 1, 2012

### kurros

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. May 9, 2012

### physstud

that is exactly what I thought. OK, thanks for the confirmation ;-)

9. Jul 9, 2012

### 3m0k177y

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. Jul 9, 2012

### bapowell

There are many fields described by this Lagrangian, not just the Higgs. For example, the gauge boson Lagrangian, $f^{\mu \nu}F_{\mu \nu}$ would be there Higgs or no Higgs.

11. Jul 9, 2012

### kurros

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. Jul 9, 2012

### 3m0k177y

Oh, I get it all now. Thanks.

13. Jul 10, 2012

### 3m0k177y

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. Jul 10, 2012

### bapowell

By 2nd and 3rd terms, do you mean the $\psi_i y_{ij} \psi_j \phi$ and the $|D_\mu \phi|^2$ terms?

15. Jul 10, 2012

### 3m0k177y

I mean the Yukawa coupling and the term that describes the fermions in the theory.

16. Jul 11, 2012

### Coin

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.