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Small-$x$ factorisation in the target fragmentation region

Paul Caucal, Farid Salazar

Abstract

We consider the differential cross-section for single-inclusive jet production with transverse momentum $P_\perp$ in Deep Inelastic Scattering (DIS) at small Bjorken $x_{\rm Bj}$, mediated by a virtual photon with virtuality $Q^2$. Unlike most studies at small $x$, which focus on particle production in the current fragmentation region, we investigate the kinematic regime where the jet is produced in the target fragmentation hemisphere of the Breit frame, and with $P_\perp \ll Q$. For a longitudinally polarised photon, we demonstrate that this cross-section is not power suppressed in $P_\perp/Q$ and we derive a factorised expression in terms of extended quark and gluon jet fracture functions. Our formula, valid at next-to-leading order in $α_s$ at small $x$, is akin to the Altarelli-Martinelli identity for the longitudinal DIS structure function. Numerical estimates show that the extended quark jet fracture function is the most sensitive to saturation effects in large nuclei.

Small-$x$ factorisation in the target fragmentation region

Abstract

We consider the differential cross-section for single-inclusive jet production with transverse momentum in Deep Inelastic Scattering (DIS) at small Bjorken , mediated by a virtual photon with virtuality . Unlike most studies at small , which focus on particle production in the current fragmentation region, we investigate the kinematic regime where the jet is produced in the target fragmentation hemisphere of the Breit frame, and with . For a longitudinally polarised photon, we demonstrate that this cross-section is not power suppressed in and we derive a factorised expression in terms of extended quark and gluon jet fracture functions. Our formula, valid at next-to-leading order in at small , is akin to the Altarelli-Martinelli identity for the longitudinal DIS structure function. Numerical estimates show that the extended quark jet fracture function is the most sensitive to saturation effects in large nuclei.

Paper Structure

This paper contains 9 sections, 69 equations, 3 figures.

Table of Contents

  1. Supplemental material
  2. A. Leading twist contribution to $F_L$ from the LO structure function $F_{UU,L}^{\rm LO}$ for semi-inclusive DIS jet production
  3. The sea quark contribution to $F_L$.
  4. B. Proof of Eq. (9) in the main text
  5. C. Proof of Eqs. (11)-(12) in the main text
  6. The NLO-4 contribution
  7. The NLO-1 contribution
  8. The NLO-0+NLO-3 contributions
  9. Final result for the NLO gluon-jet contribution at leading power

Figures (3)

  • Figure 1: Feynman graphs for the $\gamma^*_L+A\to \textrm{jet}+X$ sub-process at small $x_{\rm Bj}$. Top: LO (left) and LP NLO diagram (right) for a quark jet measurement. Bottom: examples of LP NLO diagrams for gluon jet production ($q\leftrightarrow\bar{q}$ exchanged and interference graphs are not displayed but contribute at LP).
  • Figure 2: Breit frame views of the LP jet produced in $\gamma_L^*$-$A$ collision at small $x$ in the quark (left) and gluon (right) channels.
  • Figure 3: Small-$x$ quark and gluon extended fracture functions at LO for a proton and a nucleus with $A^{1/3}=5$ (normalized by the transverse area $S_\perp$ of the target). The lower panel shows the nucleus/proton ratio times $A^{-1/3}$.