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J/$\psi$ and other Hidden Heavy Flavours

86 $\mathrm{g}\mathrm{g}\to \mathrm{J}/\psi \mathrm{g}$
87 $\mathrm{g}\mathrm{g}\to \chi_{0 \c } \mathrm{g}$
88 $\mathrm{g}\mathrm{g}\to \chi_{1 \c } \mathrm{g}$
89 $\mathrm{g}\mathrm{g}\to \chi_{2 \c } \mathrm{g}$
104 $\mathrm{g}\mathrm{g}\to \chi_{0 \c }$
105 $\mathrm{g}\mathrm{g}\to \chi_{2 \c }$
106 $\mathrm{g}\mathrm{g}\to \mathrm{J}/\psi \gamma$
107 $\mathrm{g}\gamma \to \mathrm{J}/\psi \mathrm{g}$
108 $\gamma \gamma \to \mathrm{J}/\psi \gamma$

MSEL = 61,62,63
$\c\overline{\mathrm{c}}$ $\b\overline{\mathrm{b}}$  
421 461 $\mathrm{g}\mathrm{g}\to \mathrm{Q}\overline{\mathrm{Q}}[^3S_1^{(1)}] \, \mathrm{g}$
422 462 $\mathrm{g}\mathrm{g}\to \mathrm{Q}\overline{\mathrm{Q}}[^3S_1^{(8)}] \, \mathrm{g}$
423 463 $\mathrm{g}\mathrm{g}\to \mathrm{Q}\overline{\mathrm{Q}}[^1S_0^{(8)}] \, \mathrm{g}$
424 464 $\mathrm{g}\mathrm{g}\to \mathrm{Q}\overline{\mathrm{Q}}[^3P_J^{(8)}] \, \mathrm{g}$
425 465 $\mathrm{g}\mathrm{q}\to \mathrm{q}\, \mathrm{Q}\overline{\mathrm{Q}}[^3S_1^{(8)}]$
426 466 $\mathrm{g}\mathrm{q}\to \mathrm{q}\, \mathrm{Q}\overline{\mathrm{Q}}[^1S_0^{(8)}]$
427 467 $\mathrm{g}\mathrm{q}\to \mathrm{q}\, \mathrm{Q}\overline{\mathrm{Q}}[^3P_J^{(8)}]$
428 468 $\mathrm{q}\overline{\mathrm{q}}\to \mathrm{g}\, \mathrm{Q}\overline{\mathrm{Q}}[^3S_1^{(8)}]$
429 469 $\mathrm{q}\overline{\mathrm{q}}\to \mathrm{g}\, \mathrm{Q}\overline{\mathrm{Q}}[^1S_0^{(8)}]$
430 470 $\mathrm{q}\overline{\mathrm{q}}\to \mathrm{g}\, \mathrm{Q}\overline{\mathrm{Q}}[^3P_J^{(8)}]$
431 471 $\mathrm{g}\mathrm{g}\to \mathrm{Q}\overline{\mathrm{Q}}[^3P_0^{(1)}] \, \mathrm{g}$
432 472 $\mathrm{g}\mathrm{g}\to \mathrm{Q}\overline{\mathrm{Q}}[^3P_1^{(1)}] \, \mathrm{g}$
433 473 $\mathrm{g}\mathrm{g}\to \mathrm{Q}\overline{\mathrm{Q}}[^3P_2^{(1)}] \, \mathrm{g}$
434 474 $\mathrm{g}\mathrm{q}\to \mathrm{q}\, \mathrm{Q}\overline{\mathrm{Q}}[^3P_0^{(1)}]$
435 475 $\mathrm{g}\mathrm{q}\to \mathrm{q}\, \mathrm{Q}\overline{\mathrm{Q}}[^3P_1^{(1)}]$
436 476 $\mathrm{g}\mathrm{q}\to \mathrm{q}\, \mathrm{Q}\overline{\mathrm{Q}}[^3P_2^{(1)}]$
437 477 $\mathrm{q}\overline{\mathrm{q}}\to \mathrm{g}\, \mathrm{Q}\overline{\mathrm{Q}}[^3P_0^{(1)}]$
438 478 $\mathrm{q}\overline{\mathrm{q}}\to \mathrm{g}\, \mathrm{Q}\overline{\mathrm{Q}}[^3P_1^{(1)}]$
439 479 $\mathrm{q}\overline{\mathrm{q}}\to \mathrm{g}\, \mathrm{Q}\overline{\mathrm{Q}}[^3P_2^{(1)}]$

In PYTHIA one may distinguish between three main sources of $\mathrm{J}/\psi $ production.

Decays of $\mathrm{B}$ mesons and baryons.
Parton-shower evolution, wherein a $\c $ and a $\overline{\mathrm{c}}$ quark produced in adjacent branchings (e.g. $\mathrm{g}\to \mathrm{g}\mathrm{g}\to \c\overline{\mathrm{c}}\c\overline{\mathrm{c}}$) turn out to have so small an invariant mass that the pair collapses to a single particle.
Direct production, where a $\c $ quark loop gives a coupling between a set of gluons and a $\c\overline{\mathrm{c}}$ bound state. Higher-lying states, like the $\chi_c$ ones, may subsequently decay to $\mathrm{J}/\psi $.

The first two sources are implicit in the production of $\b $ and $\c $ quarks, although the forcing specifically of $\mathrm{J}/\psi $ production is difficult. In this section are given the main processes for the third source, intended for applications at hadron colliders.

The traditional `colour singlet' approach is encapsulated in the above processes in the range 86 - 108. Processes 104 and 105 are the equivalents of 87 and 89 in the limit of $p_{\perp}\to 0$; note that $\mathrm{g}\mathrm{g}\to \mathrm{J}/\psi $ and $\mathrm{g}\mathrm{g}\to \chi_{1 \c }$ are forbidden and thus absent. As always one should beware of double-counting between 87 and 104, and between 89 and 105, and thus use either the one or the other depending on the kinematic domain to be studied. The cross sections depend on wave function values at the origin, see PARP(38) and PARP(39). A review of the physics issues involved may be found in [Glo88] (note, however, that the choice of $Q^2$ scale is different in PYTHIA).

While programmed for the charm system, it would be straightforward to apply these processes instead to bottom mesons, i.e. for the production of $\Upsilon$.One needs to change the codes of states produced, which is achieved by KFPR(ISUB,1) = KFPR(ISUB,1) + 110 for the processes ISUB above, and changing the values of the wave functions at the origin, PARP(38) and PARP(39).

It is known that the above sources are not enough to explain the full $\mathrm{J}/\psi $ rate, and further production mechanisms have been proposed, extending on the more conventional treatment here [Can97]. The most common extension is the `colour octet' production mechanism, in the framework of nonrelativistic QCD (NRQCD) [Bod95]. In this language, production in part proceeds via intermediate colour octet states that collapse to singlet states by the emission of soft (and thus nonperturbative) gluons. In the current implementation [Wol02], three new colour octet states are introduced for each of the $\c\overline{\mathrm{c}}$ and $\b\overline{\mathrm{b}}$ systems, with spectroscopic notation $\mathrm{Q}\overline{\mathrm{Q}}[^{2S+1}L_J^{(8)}]$, where the $(8)$ is a reminder of the colour octet nature of these states. These new `particles' are assumed to `decay' exclusively to $\mathrm{J}/\psi + \mathrm{g}$ or $\Upsilon + \mathrm{g}$, respectively. Their masses have been chosen to allow this, without too much excess phase space, so that the emitted gluon is always very soft.

Unlike the first set of processes above, the NRQCD processes have been explicitly duplicated for the $\c\overline{\mathrm{c}}$ and $\b\overline{\mathrm{b}}$ sectors. Further, several processes already present in the colour singlet framework are repeated here, only differing by the way wave function and matrix element normalization factors are defined, so as to provide a coherent framework. For this reason, obviously the processes above 420 should not be combined with the lower-number ones, or else one would doublecount.

The rates for these new processes are regulated by 10 new NRQCD matrix element values, PARP(141) - PARP(150). The switches MSTP(145) - MSTP(149) can be used to modify the behaviour of the processes, but are mainly intended for experts.

next up previous contents
Next: Minimum bias Up: QCD Processes Previous: Heavy flavours   Contents
Stephen Mrenna 2007-10-30