Bottomoniumlike states in proton collisions: Fragmentation and resummation

We study the semi-inclusive hadroproduction of doubly bottomed tetraquarks (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>X</a:mi><a:mrow><a:mi>b</a:mi><a:mover accent="true"><a:mi>b</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mi>q</a:mi><a:mover accent="true"><a:mi>q</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:mrow></a:msub></a:math>) as well as fully bottomed ones (<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>b</g:mi></g:mrow></g:msub></g:math>), to which we collectively refer as “bottomoniumlike” states. We rely upon the variable-flavor number-scheme fragmentation at leading power, where a single parton perturbatively splits into the corresponding Fock state, which then hadronizes into the color-neutral, observed tetraquark. To this end, we build new sets of /-evo consistent, hadron-structure oriented collinear fragmentation functions, which we name and parametrizations. They extend and supersede the corresponding versions recently derived in previous works. The first family describes the fragmentation of doubly heavy tetraquarks and is based on an improved version of the Suzuki model for the heavy-quark channel. The second family depicts the fragmentation of fully heavy tetraquarks and embodies initial-scale inputs for gluon and heavy-quark channels, both of them calculated by the hands of potential nonrelativistic QCD. As a phenomenological application, we provide novel predictions for tetraquark-plus-jet high-energy distributions, computed within the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>NLL</i:mi><i:mo>/</i:mo><i:msup><i:mrow><i:mi>NLO</i:mi></i:mrow><i:mrow><i:mo>+</i:mo></i:mrow></i:msup></i:mrow></i:math> hybrid factorization from (sym), at 14 and 100 TeV FCC.