My T-shirt and the Standard Model

  • #1
This T-shirt I bought at a physics conference displays the following equation. It looks like the Lagrangian of the Standard Model of particle physics but I only recognise lines 1 (electroweak) and 3 (Higgs mechanism). What are lines 2 and 4 and what is/isn't included? eg. are quarks, gluons, Fadeev-Popov ghosts and Higgs ghosts all included? What about neutrino mass?
ParticlePhysics_zpsvus9erah.jpg
 

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  • #2
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Line ##2## is a so-called kinetic term that describes the interaction of the different leptons and quarks amongst themselves. A kinetic term is a term with the derivative ##\partial## or the covariant derivative ##D##.

Line ##4## is a so-called interaction term that describes the interaction of the leptons and quarks with the Higgs field. Interaction terms add richness to the theory. In this case, spontaneous symmetry breaking occurs within the interaction terms.

Let me know if you'd like more details. I do not know your background, but I presume you are a newbie to the standard model of particle physics, so I have given a high-level overview without going into the details of what each term in lines ##2## and ##4## mean.

P.S.: Gluon self-interaction is the third term in line ##1##. Neutrinos are massless in the standard model.
 
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  • #3
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Line ##2## is a so-called kinetic term that describes the interaction of the different leptons and quarks amongst themselves. A kinetic term is a term with the derivative ##\partial## or the covariant derivative ##D##.
It is worth pointing out that the derivative needs to be covariant in order for the Lagrangian to be gauge invariant. The covariant derivative also contains a coupling to the gauge fields, which gives the minimal coupling of the fermions to the gauge fields.

Line ##4## is a so-called interaction term that describes the interaction of the leptons and quarks with the Higgs field. Interaction terms add richness to the theory. In this case, spontaneous symmetry breaking occurs within the interaction terms.
I would add that this particular type of interaction term are Yukawa couplings. It would also be more appropriate to say that the spontaneous symmetry breaking occurs in the gauge sector and does not necessarily have anything to do with the Yukawa couplings to fermions. However, upon SSB, the Yukawa couplings give rise to mass terms for the fermions.

Let me know if you'd like more details. I do not know your background, but I presume you are a newbie to the standard model of particle physics, so I have given a high-level overview without going into the details of what each term in lines ##2## and ##4## mean.
This is what the thread level indicator is for. In this case the A would mean that the reader has an understanding of the topic at graduate student level or higher. I believe the OP has used it incorrectly. (It is supposed to reflect the OP's level of knowledge, not the level of the topic itself.)

P.S.: Gluon self-interaction is the third term in line ##1##. Neutrinos are massless in the standard model.
It is worth pointing out that the gauge part contains both kinetic and self-interaction terms for all gauge fields.

Fadeev-Popov ghosts and Higgs ghosts all included?
There are no ghosts included here. They appear once you look at gauge fixing and integrating out the redundant degrees of freedom that comes with gauge transformations.

What about neutrino mass?
Indeed, as stated in #2, there are no neutrino masses in the standard model and consequently not in your Lagrangian.
 
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  • #4
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It is worth pointing out that the derivative needs to be covariant in order for the Lagrangian to be gauge invariant. The covariant derivative also contains a coupling to the gauge fields, which gives the minimal coupling of the fermions to the gauge fields.



I would add that this particular type of interaction term are Yukawa couplings. It would also be more appropriate to say that the spontaneous symmetry breaking occurs in the gauge sector and does not necessarily have anything to do with the Yukawa couplings to fermions. However, upon SSB, the Yukawa couplings give rise to mass terms for the fermions.



This is what the thread level indicator is for. In this case the A would mean that the reader has an understanding of the topic at graduate student level or higher. I believe the OP has used it incorrectly. (It is supposed to reflect the OP's level of knowledge, not the level of the topic itself.)



It is worth pointing out that the gauge part contains both kinetic and self-interaction terms for all gauge fields.


There are no ghosts included here. They appear once you look at gauge fixing and integrating out the redundant degrees of freedom that comes with gauge transformations.


Indeed, as stated in #2, there are no neutrino masses in the standard model and consequently not in your Lagrangian.
Thank you for the clarification. I was not fully qualified to reply to the post.
 
  • #5
Brilliant answers, both. Thank you.

> I do not know your background, but I presume you are a newbie to the standard model of particle physics, so I have given a high-level overview without going into the details of what each term means.

Yes, I'm a complete novice when it comes to the standard model, my expertise is Navier-Stokes and I'm self taught in quantum field theory.
 

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