Revisiting the role of grooming in DIS

We introduce a novel grooming procedure, which is an extension of the modified MassDrop tagging algorithm, tailored to the needs of deep inelastic scattering (DIS). The new algorithm, which grooms the event as a whole, takes advantage of the natural separation of current and target fragmentation in the Breit frame, in order to eliminate radiation in the beam and central rapidity regions. We study the groomed invariant mass in DIS and within soft-collinear effective theory we construct a factorization theorem for the cross section in the back-to-back limit. In this limit we show that, up to a normalization factor, the cross section does not depend on the incoming hadronic matrix element and we propose this measurement at HERA and the future electron-ion collider (EIC) as a probe to hadronization, precision QCD, and cold nuclear matter effects. We also give an event based definition of the winner-take-all axis and comment on possible applications.

Figure 1

Diagrammatic illustration of the Born level process in deep inelastic quark scattering in the Breit frame.

Figure 2

Visualization of three pythia 8 events at $\sqrt{s}=63\mathrm{GeV}$ and $Q\sim 10\mathrm{GeV}$ before and after grooming. The particles in this events are represented by disks on the unfolded sphere. Green disks represent particles that pass grooming where grayed-out particles are removed from the event by the grooming procedure. For the grooming parameter we use here $z_{\mathrm{cut}}=0.1$

Figure 3

pythia 8 groomed invariant mass (GIM) spectrum for EIC kinematics. We present three different values of the grooming parameter $z_{\mathrm{cut}}=0.2$, 0.1, and 0.05 from left to right. We compare the GIM distributions before and after imposing rapidity cutoff at $|\eta |<3.5$ in the Laboratory frame.

Figure 4

The modes contributing to the factorization theorem of the groomed-invariant-mass spectrum in region 1 (top-panel) and region 2 (bottom panel). The modes are represented by locations on the energy and polar-angle plane, here $\overline{\theta }\equiv \pi -\theta$. The shaded area correspond to regions of phase-space failing grooming.

Figure 5

GIM for two values of $Q>30$ and 60 GeV for HERA beam energies: 27.5 GeV electron on 920 GeV proton. We find that for small values of the GIM spectrum the normalized distributions merge. This confirms what is anticipated from the form of the factorized cross section as discussed in the main text.

Figure 6

The relative size of power corrections as a function of $m_{\mathrm{gr}.}^2$ and $z_{\mathrm{cut}}$ for different values of $x-Q^2$. The orange shaded area denotes the nonperturbative region for which $m_{\mathrm{gr}.}^2{z}_{\mathrm{cut}}\le 1.5{\mathrm{GeV}}^2$.

Figure 7

Comparing the NLL predictions (dashed) against the partonic shower pythia 8 (solid) for three different values of the grooming parameter $z_{\mathrm{cut}}=0.2$, 0.1, and 0.05.

Figure 8

NNLL prediction including theoretical uncertainties. The theory band is constructed by varying all scales in the factorization theorem by a factor 2 and $1/2$.

Figure 9

Hadronic pythia simulations for GIM distribution compared against NLL convolved with shape function $f_{\text{mod}.}$ for EIC ($\sqrt{s}=140\mathrm{GeV}$) kinematics. To emphasize the role of the shape function we also included the NLL distribution without including the model for hadronization.

Figure 10

Diagrams contributing at next-to-leading order in the perturbative calculation of the u-soft function. Mirror diagrams not shown in this figure.