The spread of the gluon k_t-distribution and the determination of the saturation scale at hadron colliders in resummed NLL BFKL

TL;DR

This paper compares the gluon kt-distribution along high-energy evolution predicted by resummed NLL BFKL with LO DGLAP, focusing on the unintegrated gluon distribution and its implications for the underlying event and saturation. By implementing a resummation approach that preserves the LO DGLAP splitting function and enforces energy-momentum constraints, the authors show that the NLL BFKL intercept becomes close to DGLAP for most of the relevant γ-range, mitigating the large NLL corrections. Numerical studies of kt-evolution reveal that NLL BFKL predictions for intermediate gluon kt distributions resemble DGLAP results, with modest broadening due to inverse kt-ordering. The analysis of saturation yields a slower growth of Q_s(x) under NLL BFKL, with Q_s at LHC energies remaining perturbative and indicating that LO BK-based saturation predictions may be unreliable in this regime.

Abstract

The transverse momentum distribution of soft hadrons and jets that accompany central hard-scattering production at hadron colliders is of great importance, since it has a direct bearing on the ability to separate new physics signals from Standard Model backgrounds. We compare the predictions for the gluonic k_t-distribution using two different approaches: resummed NLL BFKL and DGLAP evolution. We find that as long as the initial and final virtualities (k_t) along the emission chain are not too close to each other, the NLL resummed BFKL results do not differ significantly from those obtained using standard DGLAP evolution. The saturation momentum Q_s(x), calculated within the resummed BFKL approach, grows with 1/x even slower than in the leading-order DGLAP case.

Figures (8)

• Figure 1: The comparison of the approximation of Eqs. (\ref{['eq:ht']}-\ref{['eq:X1equals']}) for the characteristic function with the exact NLL result. The upper diagram shows $X_1/X_0$ as a function of $\gamma$ with Im $\gamma =0$, whereas lower diagram shows the deviation, $\Delta X_1$, suitably normalised, of our approximation of $X_1$ from the exact result for various values of Im $\gamma$. Recall that $\omega = \bar{a} X_0 + \bar{a}^2 X_1$, where $\bar{a} =3\alpha_s/\pi$.
• Figure 2: The 'Pomeron' intercept, $\omega_s$, obtained by solving Eq. (\ref{['eq:solution']}), in the following four approximations: LO BFKL; DL; NLL BFKL and LO DGLAP; as described in the text. We include quark-loop corrections, with $n_F=4$.
• Figure 3: As for Fig. \ref{['fig:w1']}, but for pure gluodynamics, with $n_F=0$.
• Figure 4: A schematic sketch of the 'cigar-like' kinematic domain in $x'$ and $k_t$ covered by the possible paths from the initial to the final evolution points. Note that the scales for $k_t$ and $x'_+$ are both logarithmic, as indicated by the exponential factors. Also note that the + subscript on $x'$ indicates a light cone variable, which is only introduced to ensure that the fixed $\eta$ curve is a straight line. Figs. \ref{['fig:fixed']} and \ref{['fig:running']}a,b show the gluon $k_t$ distribution at fixed values of $y'$, whereas Fig. \ref{['fig:running']}c,d show the distributions at fixed $\eta$.
• Figure 5: The $k'^2_t\, dN/d k'^2_t$ distributions of the intermediate gluons as a function of $\ln k'^2_t$ at intermediate $y'=4$, for fixed $\alpha_s=0.2$. We show the four distributions corresponding to using LO BFKL, resummed NLL BFKL, DGLAP and DL, labelled just as in Figs. \ref{['fig:w1']} and \ref{['fig:w2']}. The four plots show the distributions for different choices of the input distributions.