Last month had the unique pleasure of making my first trip to CERN (more on that in a later post). I made a point to stop by the CERN gift shop to pick up a snazzy mug to show off to my colleagues back in the US, and am now the proud owner of a new vessel for my tea:

The equation above is the **Standard Model Lagrangian**, which you can think of as the origin of all of the Feynman rules that I keep writing about. Each term on the right-hand side of the above equation actually encodes several Feynman rules. Roughly speaking, terms with an *F* or a *D* contain gauge fields (photon, *W*, *Z*, gluon), terms with a *ψ* include fermions, and terms with a ϕ include the Higgs boson. Some representative diagrams coming from each of the terms are depicted below:

But alas, there’s a bit of a problem with the design. It appears that there’s an extra term which isn’t included in the usual parametrization of the Standard Model:

I won’t go so far as to call this a mistake because *technically *it’s not wrong, but I suspect that whoever designed the mug didn’t mean to write this term. Let me put it this way: if *I *had written the above expression, my adviser would pretend he didn’t know me. The “h.c.” means Hermitian conjugate, which is a generalization of the complex conjugate of a complex number. In terms of Feynman diagrams, this “+h.c.” term means “the same diagram with antiparticles.”

The problem is that the term above,

*
already *includes its Hermitian conjugate. In physics-speak, we say that the kinetic term is

*self-conjugate*(or

*Hermitian,*or

*self-adjoint*). This just means that there is no additional “+h.c.” necessary. In fact, including the “+h.c.” means that you are writing the same term twice and the equation is no longer “canonically normalized.” This just means that you ought to rescale some of your variables.

I was mulling over this not-quite-correct term on my mug while looking over photos from CERN when I discovered the *same *‘error’ in a chalkboard display in the “Universe of Particles” exhibit:

The “+h.c.” on the top right is the same ‘error’ as printed on the CERN mug. I wonder who wrote this?

To be clear: this expression *does *summarize the basic structure of the Standard Model in the sense that it does give all of the correct Feynman rules. However, the extra “+h.c.” introduces a factor of two that needs to be accounted for by weird conventions elsewhere (that would not match any of the usual literature or textbooks).

**Nit picky remarks for experts.**It is worth noting that the above expression does get one thing absolutely right: it writes everything in terms of

*Weyl*(two-component) fermions, as appropriate for a chiral theory like the Standard Model. One can see that these as Weyl fermions because the Yukawa term contains two un-barred fermions (the “+h.c.” gives two barred fermions). Note that even for Weyl fermions, one shouldn’t have a “+h.c.” on the kinetic term. In fact, I would typically write the

*D*-slash with a bar since it contains a barred Pauli matrix, but this is a matter of personal convention. The “+h.c.” is

*not*“personal convention” since it means the kinetic term is not canonically normalized.

Anyone who has done tedious physics calculations is familiar with the frequent agony of being off by a factor of 2. Now when people make remarks about this ‘error’ on my mug, I’m quick to tell them that the factor of 2 mistake just makes it more authentic.

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