The full set of polarized deep inelastic scattering structure functions at NNLO accuracy
Ignacio Borsa, Daniel de Florian, Iván Pedron
Abstract
Abstract We present the second order contributions to the coefficient functions for the parity violating polarized structure functions $$g_L$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>g</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:math> and $$g_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>g</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> , thus completing the $${\mathcal {O}}(\alpha _S^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>S</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> knowledge on DIS structure functions. We obtain the missing $${\mathcal {O}}(\alpha _S^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>S</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> pieces from the known parity conserving unpolarized coefficient functions. We also present a phenomenological analysis for the phase space region the future Electron-Ion Collider is set to explore.