Fully charmed tetraquark production in forward rapidity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>p</mml:mi> <mml:mi>p</mml:mi> </mml:math> collisions at LHC and FCC energies

In this paper, we investigate the production of a fully charmed tetraquark state <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>T</a:mi> <a:mrow> <a:mn>4</a:mn> <a:mi>c</a:mi> </a:mrow> </a:msub> </a:math> in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>p</c:mi> <c:mi>p</c:mi> </c:math> collisions at forward rapidities through the fragmentation mechanism considering the color glass condensate formalism and the solution of the running coupling Balitsky-Kovchegov equation. The contributions of gluon- and charm-initiated processes are taken into account, and the impact of an intrinsic charm component in the proton’s wave function is estimated. Predictions for the transverse momentum distribution of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>T</e:mi> <e:mrow> <e:mn>4</e:mn> <e:mi>c</e:mi> </e:mrow> </e:msub> </e:math> state are presented assuming different rapidities, distinct quantum numbers of the state and center-of-mass energies. Our results indicate that the higher cross section is associated with the production of a tensor state <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>T</g:mi> <g:mrow> <g:mn>4</g:mn> <g:mi>c</g:mi> </g:mrow> </g:msub> <g:mo stretchy="false">(</g:mo> <g:msup> <g:mn>2</g:mn> <g:mrow> <g:mo>+</g:mo> <g:mo>+</g:mo> </g:mrow> </g:msup> <g:mo stretchy="false">)</g:mo> </g:math> , which is dominated by the gluon-initiated process. In contrast, the production of the axial-vector state <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>T</k:mi> <k:mrow> <k:mn>4</k:mn> <k:mi>c</k:mi> </k:mrow> </k:msub> <k:mo stretchy="false">(</k:mo> <k:msup> <k:mn>1</k:mn> <k:mrow> <k:mo>+</k:mo> <k:mo>−</k:mo> </k:mrow> </k:msup> <k:mo stretchy="false">)</k:mo> </k:math> is dominated by the charm-initiated process and is very sensitive to the presence (or not) of an intrinsic charm.