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Photon physics at all virtualities

ISUB =
direct$\times$direct: 137, 138, 139, 140
direct$\times$resolved: 131, 132, 135, 136
DIS$\times$resolved: 99
resolved$\times$resolved, high-$p_{\perp}$: 11, 12, 13, 28, 53, 68
resolved$\times$resolved, low-$p_{\perp}$: 91, 92, 93, 94, 95

where `resolved' is a hadron or a VMD or GVMD photon.

At intermediate photon virtualities, processes described in both of the sections above are allowed, and have to be mixed appropriately. The sets are of about equal importance at around $Q^2 \sim m_{\rho}^2 \sim 1$ GeV$^2$, but the transition is gradual over a larger $Q^2$ range. The ansatz for this mixing is given by eq. ([*]) for $\gamma^*\mathrm{p}$ events and eq. ([*]) for $\gamma^*\gamma^*$ ones. In short, for direct and DIS processes the photon virtuality explicitly enters in the matrix element expressions, and thus is easily taken into account. For resolved photons, perturbation theory does not provide a unique answer, so instead cross sections are suppressed by dipole factors, $(m^2/(m^2 + Q^2))^2$, where $m = m_V$ for a VMD state and $m = 2 k_{\perp}$ for a GVMD state characterized by a $k_{\perp}$ scale of the $\gamma^*\to \mathrm{q}\overline{\mathrm{q}}$ branching. These factors appear explicitly for total, elastic and diffractive cross sections, and are also implicitly used e.g. in deriving the SaS parton distributions for virtual photons. Finally, some double-counting need to be removed, between direct and DIS processes as mentioned in the previous section, and between resolved and DIS at large $x$.

Since the mixing is not trivial, it is recommended to use the default MSTP(14) = 30 to obtain it in one go and hopefully consistently, rather than building it up by combining separate runs. The main issues still under your control include, among others

$\bullet$
The CKIN(61) - CKIN(78) should be used to set the range of $x$ and $Q^2$ values emitted from the lepton beams. That way one may decide between almost real or very virtual photons, say. Also some other quantities, like $W^2$, can be constrained to desirable ranges.
$\bullet$
Whether or not minimum-bias events are simulated depends on the CKIN(3) value, just like in hadron physics. The only difference is that the initialization energy scale $W_{\mathrm{init}}$ is selected in the allowed $W$ range rather than to be the full c.m. energy.
For a high CKIN(3), CKIN(3) $> p_{\perp\mathrm{min}}(W_{\mathrm{init}}^2)$, only jet production is included. Then further CKIN values can be set to constrain e.g. the rapidity of the jets produced.
For a low CKIN(3), CKIN(3) $< p_{\perp\mathrm{min}}(W_{\mathrm{init}}^2)$, like the default value CKIN(3) = 0, low-$p_{\perp}$ physics is switched on together with jet production, with the latter properly eikonalized to be lower than the total one. The ordinary CKIN cuts, not related to the photon flux, cannot be used here.
For a low CKIN(3), when MSEL = 2 instead of the default = 1, also elastic and diffractive events are simulated.
$\bullet$
The impact of resolved longitudinal photons is not unambiguous, e.g. only recently the first parameterization of parton distributions appeared [Chý00]. Different simple alternatives can be probed by changing MSTP(17) and associated parameters.
$\bullet$
The choice of scales to use in parton distributions for jet rates is always ambiguous, but depends on even more scales for virtual photons than in hadronic collisions. MSTP(32) allows a choice between several alternatives.
$\bullet$
The matching of $p_{\perp}$ generation by shower evolution to that by primordial $k_{\perp}$ is a general problem, for photons with an additional potential source in the $\gamma^*\to \mathrm{q}\overline{\mathrm{q}}$ vertex. MSTP(66) offer some alternatives.
$\bullet$
PARP(15) is the $k_0$ parameter separating VMD from GVMD.
$\bullet$
PARP(18) is the $k_{\rho}$ parameter in GVMD total cross sections.
$\bullet$
MSTP(16) selects the momentum variable for an $\mathrm{e}\to \mathrm{e}\gamma^*$ branching.
$\bullet$
MSTP(18) regulates the choice of $p_{\perp\mathrm{min}}$ for direct processes.
$\bullet$
MSTP(19) regulates the choice of partonic cross section in process 99, $\gamma^*\mathrm{q}\to \mathrm{q}$.
$\bullet$
MSTP(20) regulates the suppression of the resolved cross section at large $x$.
The above list is not complete, but gives some impression what can be done.


next up previous contents
Next: Electroweak Gauge Bosons Up: Physics with Incoming Photons Previous: Deeply Inelastic Scattering and   Contents
Stephen_Mrenna 2012-10-24