QCD Radiation off Heavy Particles

TL;DR

The paper addresses how QCD radiation from heavy particle decays depends on the production process, mass, spin, and parity. It develops a matrix-element corrected parton shower that preserves a mass-aware, process-dependent description at all shower stages, using a novel choice of evolution variables and ME/PS matching factors to connect shower branchings with matrix elements. The authors compute extensive LO matrix elements, compare radiation patterns across multiple processes, and apply the approach to bottom production, Higgs decay, top production/decay, SUSY processes, and gluon splitting to heavy quarks, demonstrating improved agreement with data and revealing significant spin- and parity-dependent effects, especially in jet topologies and energy flow. The work shows that while soft-gluon emission tends toward universality, energetic gluons and heavy-quark masses introduce sizable process dependence, advocating a hybrid ME/shower framework for precision predictions in current and future colliders.

Abstract

We study QCD radiation in decay processes involving heavy particles. As input, the first-order gluon emission rate is calculated in a number of reactions, and comparisons of the energy flow patterns show a non-negligible process dependence. To proceed further, the QCD parton shower language offers a convenient approach to include multi-gluon emission effects, and to describe exclusive event properties. An existing shower algorithm is extended to take into account the process-dependent mass, spin and parity effects, as given by the matrix element calculations. This allows an improved description of multiple gluon emission effects off b and t quarks, and also off nonstandard particles like squarks and gluinos. Phenomenological applications are presented for bottom production at LEP, Higgs particle decay to heavy flavours, top production and decay at linear colliders, and some simple supersymmetric processes.

Figures (15)

• Figure 1: Example of showers, with the notations used in the text. (a) A generic shower. (b) A shower giving a three-jet event.
• Figure 2: The gluon emission rate as a function of emission angle $\theta_{13} = \theta_{\mathrm{q}\mathrm{g}}$, for a 10 GeV gluon energy at $E_{\mathrm{CM}} = 91$ GeV, and with $m_b = 4.8$ GeV. All curves are normalized to the massless matrix-element expression, eq. (\ref{['MEmassless']}), here thus represented by the small-dotted line at unity. Dashed: the massless shower before correction, $N_{\mathrm{PS}}(x_1,x_2,0)/N_{\mathrm{ME}}(x_1,x_2,0) = 1/R_{\mathrm{ME/PS}}(x_1,x_2,0)$. Full: the rate from massive matrix elements, $N_{\mathrm{ME}}(x_1,x_2,r)/N_{\mathrm{ME}}(x_1,x_2,0)$. Dash-dotted: the rate from massive parton shower, $N_{\mathrm{PS}}(x_1,x_2,r)/N_{\mathrm{ME}}(x_1,x_2,0)$. Large dots: the new rate from massive parton showers, $N'_{\mathrm{PS}}(x_1,x_2,r)/N_{\mathrm{ME}}(x_1,x_2,0)$.
• Figure 3: The gluon emission rate as a function of the emission angle $\theta_{13}$. Specifically, the vertical axis gives $(1/\sigma_0) \mathrm{d} \sigma / \mathrm{d} x_1 \, \mathrm{d} x_2$ with a normalization factor $(\alpha_{\mathrm{s}}/2\pi)C_F$ removed. This three-jet phase space density differs from $\mathrm{d} \sigma / \mathrm{d} \theta_{13} \, \mathrm{d} x_3$ by a simple Jacobian. A variety of different processes are compared: decay of a colour singlet to a triplet plus an antitriplet full curves, ditto in the eikonal approximation dotted, decay of a triplet to a triplet plus singlet dashed, and gluino processes dash-dotted. The four frames differ in the scaled masses $r_i = m_i/E_{\mathrm{CM}}$ of the two decay products, and in the gluon energy fraction $x_3$. Further explanations are given in the text.
• Figure 4: Test of the additivity of gluon emission rates, $\mathrm{d} \sigma / \mathrm{d} x_1 \, \mathrm{d} x_2$ with a normalization factor $\sigma_0 \, C_F \, \alpha_{\mathrm{s}}/2\pi$ removed. The dotted curves show two processes with colour flow $3 \to 3 + 1$ and $3 \to 1 + 3$, respectively (and spin $1/2 \to 1/2 + 1$). The upper and lower full curves give the complete expressions for $1 \to 3 + \overline{3}$ (spin $1 \to 1/2 + 1/2$) and $8 \to 3 + \overline{3}$ (spin $1/2 \to 1/2 + 0$) processes, respectively. The two dashed curves, almost completely hidden by the full ones, are the same processes according to the additive approximations in eq. (\ref{['addradiation']}).
• Figure 5: $\langle Q \rangle (r_1,r_2)$, eq. (\ref{['eq:Qdef']}), with $r_1$ fixed, $r_2$ fixed, or $r=r_1=r_2$. The processes are grouped according to spin structure.