Anisotropic electron damping and energy gap in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Bi</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Sr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Ca

The many-body electron-electron interaction in cuprates causes broadening of the electronic bands in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi mathvariant="bold-italic">k</a:mi></a:math> space, leading to a deviation from the standard Fermi liquid. While a <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi mathvariant="bold-italic">k</c:mi></c:math>-dependent anisotropic electronic scattering (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi mathvariant="bold-italic">k</e:mi></e:math>-DAES) has been assessed by photoemission, its fingerprint in <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mi mathvariant="bold-italic">Q</g:mi></g:math> space has been scarcely considered. Here, we explore the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mi mathvariant="bold-italic">Q</i:mi></i:math>-dependent electron dynamics in optimally doped <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:msub><k:mi>Bi</k:mi><k:mn>2</k:mn></k:msub><k:msub><k:mi>Sr</k:mi><k:mn>2</k:mn></k:msub><k:msub><k:mi>CaCu</k:mi><k:mn>2</k:mn></k:msub><k:msub><k:mi mathvariant="normal">O</k:mi><k:mrow><k:mn>8</k:mn><k:mo>+</k:mo><k:mi>δ</k:mi></k:mrow></k:msub></k:mrow></k:math> through the evolution of low-energy charge excitations as measured by resonant inelastic x-ray scattering (RIXS). In the normal state, the RIXS spectra display a continuum of excitations down to 0 meV, while the superconducting state features a spectral weight suppression below 80 meV without any enhancement at higher energies. To interpret the energy and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mi mathvariant="bold-italic">Q</m:mi></m:math> evolution of our data, we introduce a phenomenological expression of the charge susceptibility by including the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:mi mathvariant="bold-italic">k</o:mi></o:math>-DAES. We show that only the charge susceptibility with <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"><q:mi mathvariant="bold-italic">k</q:mi></q:math>-DAES captures the RIXS data, highlighting the importance of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"><s:mi mathvariant="bold-italic">k</s:mi></s:math>-DAES when describing the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"><u:mi mathvariant="bold-italic">Q</u:mi></u:math> dependence of charge excitations from 0 to a few eV scale. Furthermore, we also find that the inclusion of <w:math xmlns:w="http://www.w3.org/1998/Math/MathML"><w:mi mathvariant="bold-italic">k</w:mi></w:math>-DAES is essential when quantitative parameters such as the electronic energy gap are extracted from RIXS data.