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A rather simple question: Starting from an electrically neutral state, pairs of top quarks are produced as top and anti-top, and denoted as $t\bar t$.

Now the production of pairs of scalar top quarks, the supersymmetric partners of the top quarks, seems to be commonly denoted as $\tilde t \tilde t^*$ (e.g. 1, 2), rather than $\tilde t \bar{\tilde t}$. Why this notational difference? What is $\tilde t^*$?

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up vote 4 down vote accepted

There are two aspects. One is sort of trivial and comprehensible; the other is a bit technical.

The trivial reason is that $\tilde t \bar{\tilde t}$ has two "accents" on top of each other and the symbol therefore occupies too much vertical space which is undesirable because we may get overlapping characters and/or non-uniform spacing between lines. The asterisk in $\tilde t \tilde t^*$ is horizontally shifted so the vertical space is saved.

However, there also exists a more technical reason. The bar $\bar t$ is not "just" the complex conjugation or a symbol of antiparticles. This bar is a symbol for the Dirac conjugate spinor, $\bar t = t^\dagger \gamma_0$. And indeed, the top quark is described by the Dirac spinor $t$ and $\bar t$ is the most natural form of its complex (plus other operations) conjugation which makes the construction of Lorentz-covariant express more intuitive.

On the other hand, the top squark $\tilde t$ isn't a Dirac spinor; it is a scalar field. It's more usual to denote complex conjugate scalar fields by the asterisk.

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Good answer, now the distinction makes sense to me. – fuenfundachtzig Apr 24 '13 at 9:47
The asterisk still isn't typographically ideal, because it runs into the other convention of using an asterisk to denote off-shell particles. To try to minimize confusion, I was using ${\tilde t}^\dagger$ in the draft of one paper about stops but my coauthors didn't like it so we reverted to asterisk in the end.... – Matt Reece Apr 24 '13 at 13:29
Yes, I guess many people will think of an off-shell particle when seeing the asterisk next to the stop. – fuenfundachtzig Apr 25 '13 at 13:32

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