What does half sum mean?

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Just a short question: I'm reading about Newton polynomials (https://arxiv.org/abs/math/0206077) and I'm wondering, what the "half-sum of the positive roots" (page 9 'notation') is. Is it something like $$\frac{1}{2}\sum\limits_{\alpha\in R^{+}}\alpha ?$$ I can't find a definition of this term anywhere.