Holographic study of the scalar meson $$K_0^*(1430)$$ with dynamical longitudinal confinement

Abstract Within the framework of light-front holographic QCD, where transverse confinement is inherently realized through holography, the structure and mass spectrum of the light scalar meson $$K_0^{*}(1430)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mmultiscripts> <mml:mi>K</mml:mi> <mml:mn>0</mml:mn> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:mmultiscripts> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1430</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> are investigated by employing the invariant mass ansatz and enhancing the model with a longitudinal confinement potential (specifically, the ’t Hooft equation and the analytically solvable LMZV potential). The combined transverse and longitudinal confinement dynamics lead to more reliable calculations of key observables, including decay constants, parton distribution function, $$\xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ξ</mml:mi> </mml:math> -moments, and twist-2 and twist-3 distribution amplitudes. Transition form factors for the semileptonic decay $$B \rightarrow K_0^{*} \ell ^+ \ell ^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>→</mml:mo> <mml:mmultiscripts> <mml:mi>K</mml:mi> <mml:mn>0</mml:mn> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:mmultiscripts> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> are computed from these amplitudes, yielding predictions for differential branching ratios and longitudinal lepton polarization asymmetries as functions of $$q^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> . The results are compared with other theoretical models, offering valuable insights into the non-perturbative dynamics of QCD. The predicted observables provide theoretically motivated benchmarks for future experimental investigations of $$B\rightarrow K_0^*(1430)\ell ^+\ell ^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>→</mml:mo> <mml:msubsup> <mml:mi>K</mml:mi> <mml:mn>0</mml:mn> <mml:mo>∗</mml:mo> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1430</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>ℓ</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> decays at LHCb and Belle II.