Estimates of the cross section at a hadron collider
The claim that the $X(3872)$ meson cannot be a charm-meson molecule because its prompt production cross section at hadron colliders is too large is based on an upper bound in terms of a cross section for producing charm-meson pairs. Assuming $$X$$ is sufficiently weakly bound, we derive an equality between the $$X$$ cross section and a charm-meson pair cross section that takes into account the threshold enhancement from the $$X$$ resonance. The cross section for producing $$X$$ is equal to that for producing $$D^{*0} \bar{D}^0$$ integrated up to a relative momentum $$k_\mathrm{max} = 7.7\,\gamma_X$$, where $$\gamma_X$$ is the binding momentum of $$X$$. We also derive an order-of-magnitude estimate of the $$X$$ cross section in terms of a naive charm-meson pair cross section that does not take into account the threshold enhancement, such as that produced by a Monte Carlo event generator. The cross section for producing $$X$$ can be approximated by the naive cross section for producing $$D^{*0} \bar{D}^0$$ integrated up to a relative momentum $$k_\mathrm{max}$$ of order $$(m_\pi^2 \gamma_X)^{1/3}$$. The estimates of the prompt $$X$$ cross section at hadron colliders are consistent with the cross sections observed at the Tevatron and the LHC.
- Research Organization:
- The Ohio State Univ., Columbus, OH (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
- Grant/Contract Number:
- SC0011726; PHY-1607190
- OSTI ID:
- 1607574
- Alternate ID(s):
- OSTI ID: 1602459
- Journal Information:
- Physical Review D, Vol. 100, Issue 9; ISSN 2470-0010
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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