Dihadron correlations in small-$x$ DIS at NLO: transverse momentum dependent fragmentation
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arXiv
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| Format: | Preprint |
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2024
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| author | Caucal, Paul Salazar, Farid |
| author_facet | Caucal, Paul Salazar, Farid |
| contents | We compute 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 $-\frac{α_s}{2π}\left[C_F+\frac{N_c}{2}\right]$ instead of $-\frac{α_s N_c}{4π}$ 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 $\overline{\rm MS}$-scheme. These results pave the way towards numerically calculating dihadron correlations at small $x$ at the future Electron-Ion Collider with full NLO accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19404 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dihadron correlations in small-$x$ DIS at NLO: transverse momentum dependent fragmentation Caucal, Paul Salazar, Farid High Energy Physics - Phenomenology Nuclear Theory We compute 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 $-\frac{α_s}{2π}\left[C_F+\frac{N_c}{2}\right]$ instead of $-\frac{α_s N_c}{4π}$ 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 $\overline{\rm MS}$-scheme. These results pave the way towards numerically calculating dihadron correlations at small $x$ at the future Electron-Ion Collider with full NLO accuracy. |
| title | Dihadron correlations in small-$x$ DIS at NLO: transverse momentum dependent fragmentation |
| topic | High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2405.19404 |