Dihadron correlations in small-x DIS at NLO: transverse momentum dependent fragmentation
Paul Caucal, Farid Salazar
Abstract
A bstract We compute the inclusive dihadron cross-section in Deep Inelastic Scattering at next-to-leading order (NLO) and small x in the Color Glass Condensate. We focus on the kinematic limit where the hadrons are produced at forward rapidities (in the direction of the virtual photon) and back-to-back in the transverse plane. Our calculation demonstrates that the coefficient of the Sudakov double logarithm for this process is $$ -\frac{\alpha_s}{2\pi}\left[{C}_F+\frac{N_c}{2}\right] $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>−</mml:mo> <mml:mfrac> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>π</mml:mi> </mml:mrow> </mml:mfrac> <mml:mfenced> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>F</mml:mi> </mml:msub> <mml:mo>+</mml:mo> <mml:mfrac> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:mfenced> </mml:math> instead of $$ -\frac{\alpha_s{N}_c}{4\pi } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>−</mml:mo> <mml:mfrac> <mml:mrow> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>π</mml:mi> </mml:mrow> </mml:mfrac> </mml:math> when back-to-back jets are measured in the final state. To preserve the universality of the Sudakov soft factor associated with the Weizsäcker-Williams transverse momentum dependent (TMD) gluon distribution, we promote the collinear fragmentation functions into TMD fragmentation functions. We then perform the resummation of the Sudakov logarithms through Collins-Soper-Sterman evolution of the TMD fragmentation functions and the Weizsäcker-Williams TMD gluon distribution. Finally, analytic expressions are obtained for the NLO coefficient functions in the $$ \overline{\textrm{MS}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>MS</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> -scheme. These results pave the way towards numerically calculating dihadron correlations at small x at the future Electron-Ion Collider with full NLO accuracy.