Jet fragmentation functions in proton-proton collisions using soft-collinear effective theory

TL;DR

This work develops a soft-collinear effective theory (SCET) framework for jet fragmentation functions in proton-proton collisions, expressing the observable as a ratio of the fragmenting jet function to the unmeasured jet function and enabling simultaneous resummation of large logarithms in the jet radius $R$ and in $1-z$. The fragmenting jet function is matched onto standard fragmentation functions with algorithm-dependent coefficients, and both functions share the same RG evolution, making their ratio RG-invariant. Phenomenologically, the authors achieve excellent agreement with LHC data for light hadrons, while heavy-meson production within jets is underpredicted unless the gluon-to-heavy-meson fragmentation function is enhanced, highlighting its strong sensitivity and potential as a constraint. The results underscore the utility of SCET for precision jet substructure studies and point to future extensions to heavy-ion collisions and improved heavy-mavor fragmentation function determinations.

Abstract

The jet fragmentation function describes the longitudinal momentum distribution of hadrons inside a reconstructed jet. We study the jet fragmentation function in proton-proton collisions in the framework of soft-collinear effective theory (SCET). We find that, up to power corrections, the jet fragmentation function can be expressed as the ratio of the fragmenting jet function and the unmeasured jet function. Using renormalization group techniques, we are able to resum large logarithms of jet radii R in the perturbative expansion of the cross section. We use our theoretical formalism to describe the jet fragmentation functions for light hadron and heavy meson production measured at the Large Hadron Collider (LHC). Our calculations agree very well with the experimental data for the light hadron production. On the other hand, although our calculations for the heavy meson production inside jets are consistent with the PYTHIA simulation, they fail to describe the LHC data. We find that the jet fragmentation function for heavy meson production is very sensitive to the gluon-to-heavy-meson fragmentation function.

Figures (7)

• Figure 1: Illustration of the $N$-jet production in $e^+e^-$ collisions, where a hadron is measured in the jet labeled by $J_1$ with rapidity $y$ and transverse momentum $p_T$. $z$ is the fraction of the jet momentum carried by the hadron. Jets are reconstructed using a jet algorithm with radius $R$. We impose an energy cutoff $\Lambda$ outside the jets to ensure the $N$-jet configuration. $\Lambda$ is a low energy scale constraining the soft radiation (red lines). The green lines represent the collinear splittings.
• Figure 2: Comparison of our theoretical calculations with the ATLAS experimental data Aad:2011sc in proton-proton collisions at $\sqrt{s} = 7$ TeV. Jets are reconstructed using the anti-k$_{\rm T}$ algorithm with $R=0.6$ within the rapidity range $|y|<1.2$. The numbers in the square brackets correspond to different jet transverse momentum bins, e.g. [25, 40] means $25 < p_T < 40$ GeV. The blue solid curves are the "nominal" theoretical calculations, where we make the scale choice of $\mu=p_T$, and $\mu_{\mathcal{G}} = \mu_J = 2p_T\tan\left(R/2\right)\equiv p_{TR}$. The green bands are the estimated uncertainties of our theoretical calculations from scale variations, see the discussion in the text.
• Figure 3: Comparison of our theoretical calculations with the LHC data from proton-proton collisions at $\sqrt{s} = 2.76$ TeV. The solid red circles are the ATLAS preliminary data ATLAS:2015mla, while the magenta triangles are the CMS data Chatrchyan:2012gw. The blue solid curves are the "nominal" theoretical calculations, with the green bands representing the theoretical uncertainties estimated from scale variations.
• Figure 4: Upper panel: Jet fragmentation function $F(z, p_T)$ for light charged hadrons plotted as a function of $z$ for jets with $60<p_T<80$ GeV, $|y| < 1.2$, $R=0.6$) at $\sqrt{s} = 7$ TeV, as an example. We choose the scales $\mu= p_T$ and $\mu_{\mathcal{G}} = \mu_J = p_{TR}$. The solid red curve is for anti-k$_{\rm T}$ jets, while the dashed blue curve is for cone jets. Lower panel: the ratio of the jet fragmentation functions $F(z, p_T)_{\rm cone}/F(z, p_T)_{\rm k_T}$ for cone and anti-k$_{\rm T}$ jets.
• Figure 5: Jet fragmentation functions plotted as a function of $z$ for four different jet radii $R=0.2$ (solid red), $R=0.4$ (dashed blue), $R=0.6$ (dotted black), and $R=0.8$ (dash-dotted magenta) for jets with $60<p_T<80$ GeV, $|y| < 1.2$) at $\sqrt{s} = 7$ TeV as an example. We choose the scales $\mu = p_T$ and $\mu_{\mathcal{G}} =\mu_J = p_{TR}$.