Observation of spin-conserving two-spinon continuum in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:mat

We report a Cu $K$-edge resonant inelastic x-ray scattering (RIXS) study of spin excitations in the $S=1/2$ antiferromagnetic chain system ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}$. The spectral weight observed below the charge-transfer gap appears in two-spinon continuum, indicating the fractionalization of a spin-conserving ($\mathrm{\ensuremath{\Delta}}S=0$) magnetic excitation into two-spinon states. The intensity of these excitations reaches a maximum near the midpoint between the center and the boundary of the Brillouin zone, and decreases toward the zone boundary; this behavior contrasts with that of the spin-flip ($\mathrm{\ensuremath{\Delta}}S=1$) excitations typically observed via inelastic neutron scattering or Cu ${L}_{3}$-edge RIXS. The momentum dependence of the intensity is described by the spin-exchange dynamical structure factor. A phenomenological analysis of the symmetry between the polarization and the $d$ orbital explains the resonance condition for the two-spinon excitations.