First insight into transverse-momentum-dependent fragmentation physics at photon-photon colliders

Future planned lepton colliders, both in the circular and linear configurations, can effectively work as virtual and quasireal photon-photon colliders and are expected to stimulate an intense physics program in the next few years. In this paper, we suggest to consider photon-photon scattering as a useful source of information on transverse-momentum-dependent fragmentation functions (TMD FFs), complementing semi-inclusive deeply inelastic scattering and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>e</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>e</a:mi><a:mo>−</a:mo></a:msup></a:math> annihilation processes, which provide most of the present phenomenological information on TMD FFs. As a first illustrative example, we study two-hadron azimuthal asymmetries around the jet thrust axis in the process <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msup><c:mrow><c:mo>ℓ</c:mo></c:mrow><c:mrow><c:mo>+</c:mo></c:mrow></c:msup><c:msup><c:mrow><c:mo>ℓ</c:mo></c:mrow><c:mrow><c:mo>−</c:mo></c:mrow></c:msup><c:mo stretchy="false">→</c:mo><c:msup><c:mrow><c:mi>γ</c:mi></c:mrow><c:mrow><c:mo>*</c:mo></c:mrow></c:msup><c:mi>γ</c:mi><c:mo stretchy="false">→</c:mo><c:mi>q</c:mi><c:mover accent="true"><c:mrow><c:mi>q</c:mi></c:mrow><c:mrow><c:mo stretchy="false">¯</c:mo></c:mrow></c:mover><c:mo stretchy="false">→</c:mo><c:msub><c:mrow><c:mi>h</c:mi></c:mrow><c:mrow><c:mn>1</c:mn></c:mrow></c:msub><c:msub><c:mrow><c:mi>h</c:mi></c:mrow><c:mrow><c:mn>2</c:mn></c:mrow></c:msub><c:mo>+</c:mo><c:mi>X</c:mi></c:mrow></c:math>, in which in a circular lepton collider one tagged, deeply virtual photon scatters off an untagged quasireal photon, both originating from the initial lepton beams, producing inclusively an almost back-to-back light-hadron pair with large transverse momentum, in the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msup><j:mi>γ</j:mi><j:mo>*</j:mo></j:msup><j:mi>γ</j:mi></j:math> center-of-mass frame. Similar processes, in a more complicated environment due to the presence of initial hadronic states, can also be studied in ultraperipheral collisions at the LHC and the planned future hadron colliders.