Resummed azimuthal decorrelation and transverse momentum imbalance of dijets at the LHC

Abstract

We present a theoretical study of the azimuthal decorrelation $δφ$ and transverse momentum imbalance $q_T$ in dijet production at the LHC, offering intriguing insights into the dynamics of quantum chromodynamics. We define the jet axes using the recoil-free winner-take-all (WTA) recombination scheme. For the azimuthal decorrelation $δφ$, this axis choice eliminates non-global logarithms (NGLs) entirely. For the transverse momentum imbalance $q_T$, NGLs emerge specifically in the small jet radius limit ($R \ll 1$). In this regime, the WTA scheme simplifies the theoretical framework by restricting jet radius logarithms to the soft sector. We derive factorization formulae for both observables within soft-collinear effective theory. To address the small-$R$ NGLs in the $q_T$ distribution, we refactorize the soft function into global soft, collinear-soft, and ultra-collinear-soft modes. We perform the resummation of global large logarithms $\ln(δφ)$ and $\ln(q_T/Q)$ up to next-to-next-to-leading logarithmic accuracy. For the $q_T$ distribution, this is combined with a leading-logarithmic resummation of the non-global $\ln R$ terms. We match our predictions to leading fixed-order $O(α_s^3)$ calculations. We also numerically investigate the structure of the first subleading power corrections. Comparisons with PYTHIA8 simulations demonstrate that the observables we consider are robust against non-perturbative multi-parton interactions and hadronization effects.

Figures (9)

• Figure 1: Kinematics of the $pp \to$ dijet process in the transverse plane. For simplicity, the $x$-axis is aligned with the first jet, such that $\delta \phi$ corresponds to $q_y= p_{2,y}$. For the factorization theorem, it is more natural to consider a reference frame where the $x$-axis lies along the direction of the two back-to-back partons that initiate the jets. In this frame, the jet functions encode the offset between these parton directions and the jet axes, while the soft and beam functions capture the recoil induced by soft and initial-state collinear radiation. This choice of frame does not alter the factorization structure.
• Figure 2: Schematic representation of the relevant modes in the $q_T$ factorization for $pp\to$ dijets in the small-$R$ limit. Left: Standard modes (hard, beam, and soft), where the soft mode represents the global soft function. Right: Modes required in the small-$R$ limit, showing the separation of the standard collinear sector into jet, collinear-soft, and ultra-collinear-soft modes. Here $n_i = n_1$ or $n_2$.
• Figure 3: Pictorial representation of the factorization formula for the function $S_i$. The green lines correspond to the collinear-soft radiation, and the red lines represent ultra-collinear-soft emissions. Although the ultra-collinear-soft radiation contributes to the measurement only when it falls outside the jet cone, the radiation itself is not geometrically constrained and can also occur inside the jet.
• Figure 4: Theoretical uncertainties for the resummed $\delta\phi$ (top row) and $q_T$ (bottom row, $R=0.5$) distributions. The blue and red bands represent NLL and NNLL predictions, respectively. The left column (a, c) shows the uncertainty derived from varying the hard scale $\mu_h$ by factors of 2 and 0.5 around its central value $2p_T$. The right column (b, d) displays the scale uncertainties from the factorization scale $\mu_f$ (for $\delta\phi$) and the simultaneous variation of factorization, collinear-soft and ultra-collinear-soft scales (for $q_T$).
• Figure 5: The impact of the resummation of NGLs on the $q_T$ distribution for a jet radius of $R=0.5$. The solid red curve represents the full NNLL result including the non-global resummation factor $U_{\mathrm{NG}}$, while the dashed orange curve shows the "purely global" NNLL prediction where the contribution from $U_{\mathrm{NG}}$ is turned off.