+++ /dev/null
-<chapter name="Spacelike Showers">
-
-<h2>Spacelike Showers</h2>
-
-The PYTHIA algorithm for spacelike initial-state showers is
-based on the article <ref>Sjo05</ref>, where a
-transverse-momentum-ordered backwards evolution scheme is introduced,
-with the extension to fully interleaved evolution covered in
-<ref>Cor10a</ref>.
-This algorithm is a further development of the virtuality-ordered one
-presented in <ref>Sj085</ref>, with matching to first-order matrix
-element for <ei>Z^0</ei>, <ei>W^+-</ei> and Higgs (in the
-<ei>m_t -> infinity</ei> limit) production as introduced in
-<ref>Miu99</ref>.
-
-<p/>
-The normal user is not expected to call <code>SpaceShower</code>
-directly, but only have it called from <code>Pythia</code>,
-via <code>PartonLevel</code>. Some of the parameters below,
-in particular <code>SpaceShower:alphaSvalue</code>,
-would be of interest for a tuning exercise, however.
-
-<h3>Main variables</h3>
-
-The maximum <ei>pT</ei> to be allowed in the shower evolution is
-related to the nature of the hard process itself. It involves a
-delicate balance between not doublecounting and not leaving any
-gaps in the coverage. The best procedure may depend on information
-only the user has: how the events were generated and mixed (e.g. with
-Les Houches Accord external input), and how they are intended to be
-used. Therefore a few options are available, with a sensible default
-behaviour.
-
-<modepick name="SpaceShower:pTmaxMatch" default="0" min="0" max="2">
-Way in which the maximum shower evolution scale is set to match the
-scale of the hard process itself.
-<option value="0"><b>(i)</b> if the final state of the hard process
-(not counting subsequent resonance decays) contains at least one quark
-(<ei>u, d, s, c ,b</ei>), gluon or photon then <ei>pT_max</ei>
-is chosen to be the factorization scale for internal processes
-and the <code>scale</code> value for Les Houches input;
-<b>(ii)</b> if not, emissions are allowed to go all the way up to
-the kinematical limit.
-The reasoning is that in the former set of processes the ISR
-emission of yet another quark, gluon or photon could lead to
-doublecounting, while no such danger exists in the latter case.
-</option>
-<option value="1">always use the factorization scale for an internal
-process and the <code>scale</code> value for Les Houches input,
-i.e. the lower value. This should avoid doublecounting, but
-may leave out some emissions that ought to have been simulated.
-(Also known as wimpy showers.)
-</option>
-<option value="2">always allow emissions up to the kinematical limit.
-This will simulate all possible event topologies, but may lead to
-doublecounting.
-(Also known as power showers.)
-</option>
-<note>Note 1:</note> These options only apply to the hard interaction.
-Emissions off subsequent multiparton interactions are always constrainted
-to be below the factorization scale of the process itself.
-<note>Note 2:</note> Some processes contain matrix-element matching
-to the first emission; this is the case notably for single
-<ei>gamma^*/Z^0, W^+-</ei> and <ei>H^0</ei> production. Then default
-and option 2 give the correct result, while option 1 should never
-be used.
-</modepick>
-
-<parm name="SpaceShower:pTmaxFudge" default="1.0" min="0.25" max="2.0">
-In cases where the above <code>pTmaxMatch</code> rules would imply
-that <ei>pT_max = pT_factorization</ei>, <code>pTmaxFudge</code>
-introduces a multiplicative factor <ei>f</ei> such that instead
-<ei>pT_max = f * pT_factorization</ei>. Only applies to the hardest
-interaction in an event, cf. below. It is strongly suggested that
-<ei>f = 1</ei>, but variations around this default can be useful to
-test this assumption.
-</parm>
-
-<parm name="SpaceShower:pTmaxFudgeMPI" default="1.0" min="0.25" max="2.0">
-A multiplicative factor <ei>f</ei> such that
-<ei>pT_max = f * pT_factorization</ei>, as above, but here for the
-non-hardest interactions (when multiparton interactions are allowed).
-</parm>
-
-<modepick name="SpaceShower:pTdampMatch" default="0" min="0" max="2">
-These options only take effect when a process is allowed to radiate up
-to the kinematical limit by the above <code>pTmaxMatch</code> choice,
-and no matrix-element corrections are available. Then, in many processes,
-the fall-off in <ei>pT</ei> will be too slow by one factor of <ei>pT^2</ei>.
-That is, while showers have an approximate <ei>dpT^2/pT^2</ei> shape, often
-it should become more like <ei>dpT^2/pT^4</ei> at <ei>pT</ei> values above
-the scale of the hard process. Whether this actually is the case
-depends on the particular process studied, e.g. if <ei>t</ei>-channel
-gluon exchange is likely to dominate. If so, the options below could
-provide a reasonable high-<ei>pT</ei> behaviour without requiring
-higher-order calculations.
-<option value="0">emissions go up to the kinematical limit,
-with no special dampening.
-</option>
-<option value="1">emissions go up to the kinematical limit,
-but dampened by a factor <ei>k^2 Q^2_fac/(pT^2 + k^2 Q^2_fac)</ei>,
-where <ei>Q_fac</ei> is the factorization scale and <ei>k</ei> is a
-multiplicative fudge factor stored in <code>pTdampFudge</code> below.
-</option>
-<option value="2">emissions go up to the kinematical limit,
-but dampened by a factor <ei>k^2 Q^2_ren/(pT^2 + k^2 Q^2_ren)</ei>,
-where <ei>Q_ren</ei> is the renormalization scale and <ei>k</ei> is a
-multiplicative fudge factor stored in <code>pTdampFudge</code> below.
-</option>
-<note>Note:</note> These options only apply to the hard interaction.
-Emissions off subsequent multiparton interactions are always constrainted
-to be below the factorization scale of the process itself.
-</modepick>
-
-<parm name="SpaceShower:pTdampFudge" default="1.0" min="0.25" max="4.0">
-In cases 1 and 2 above, where a dampening is imposed at around the
-factorization or renormalization scale, respectively, this allows the
-<ei>pT</ei> scale of dampening of radiation by a half to be shifted
-by this factor relative to the default <ei>Q_fac</ei> or <ei>Q_ren</ei>.
-This number ought to be in the neighbourhood of unity, but variations
-away from this value could do better in some processes.
-</parm>
-
-<p/>
-The amount of QCD radiation in the shower is determined by
-<parm name="SpaceShower:alphaSvalue" default="0.137" min="0.06" max="0.25">
-The <ei>alpha_strong</ei> value at scale <code>M_Z^2</code>.
-Default value is picked equal to the one used in CTEQ 5L.
-</parm>
-
-<p/>
-The actual value is then regulated by the running to the scale
-<ei>pT^2</ei>, at which it is evaluated
-<modepick name="SpaceShower:alphaSorder" default="1" min="0" max="2">
-Order at which <ei>alpha_strong</ei> runs,
-<option value="0">zeroth order, i.e. <ei>alpha_strong</ei> is kept
-fixed.</option>
-<option value="1">first order, which is the normal value.</option>
-<option value="2">second order. Since other parts of the code do
-not go to second order there is no strong reason to use this option,
-but there is also nothing wrong with it.</option>
-</modepick>
-
-<p/>
-QED radiation is regulated by the <ei>alpha_electromagnetic</ei>
-value at the <ei>pT^2</ei> scale of a branching.
-
-<modepick name="SpaceShower:alphaEMorder" default="1" min="-1" max="1">
-The running of <ei>alpha_em</ei>.
-<option value="1">first-order running, constrained to agree with
-<code>StandardModel:alphaEMmZ</code> at the <ei>Z^0</ei> mass.
-</option>
-<option value="0">zeroth order, i.e. <ei>alpha_em</ei> is kept
-fixed at its value at vanishing momentum transfer.</option>
-<option value="-1">zeroth order, i.e. <ei>alpha_em</ei> is kept
-fixed, but at <code>StandardModel:alphaEMmZ</code>, i.e. its value
-at the <ei>Z^0</ei> mass.
-</option>
-</modepick>
-
-<p/>
-The natural scale for couplings and PDFs is <ei>pT^2</ei>. To explore
-uncertainties it is possibly to vary around this value, however, in
-analogy with what can be done for
-<aloc href="CouplingsAndScales">hard processes</aloc>.
-
-<parm name="SpaceShower:renormMultFac" default="1." min="0.1" max="10.">
-The default <ei>pT^2</ei> renormalization scale is multiplied by
-this prefactor. For QCD this is equivalent to a change of
-<ei>Lambda^2</ei> in the opposite direction, i.e. to a change of
-<ei>alpha_strong(M_Z^2)</ei> (except that flavour thresholds
-remain at fixed scales). Below, when <ei>pT^2 + pT_0^2</ei> is used
-as scale, it is this whole expression that is multiplied by the prefactor.
-</parm>
-
-<parm name="SpaceShower:factorMultFac" default="1." min="0.1" max="10.">
-The default <ei>pT^2</ei> factorization scale is multiplied by
-this prefactor.
-</parm>
-
-<p/>
-There are two complementary ways of regularizing the small-<ei>pT</ei>
-divergence, a sharp cutoff and a smooth dampening. These can be
-combined as desired but it makes sense to coordinate with how the
-same issue is handled in multiparton interactions.
-
-<flag name="SpaceShower:samePTasMPI" default="off">
-Regularize the <ei>pT -> 0</ei> divergence using the same sharp cutoff
-and smooth dampening parameters as used to describe multiparton interactions.
-That is, the <code>MultipartonInteractions:pT0Ref</code>,
-<code>MultipartonInteractions:ecmRef</code>,
-<code>MultipartonInteractions:ecmPow</code> and
-<code>MultipartonInteractions:pTmin</code> parameters are used to regularize
-all ISR QCD radiation, rather than the corresponding parameters below.
-This is a sensible physics ansatz, based on the assumption that colour
-screening effects influence both MPI and ISR in the same way. Photon
-radiation is regularized separately in either case.
-<note>Warning:</note> if a large <code>pT0</code> is picked for multiparton
-interactions, such that the integrated interaction cross section is
-below the nondiffractive inelastic one, this <code>pT0</code> will
-automatically be scaled down to cope. Information on such a rescaling
-does NOT propagate to <code>SpaceShower</code>, however.
-</flag>
-
-<p/>
-The actual <code>pT0</code> parameter used at a given CM energy scale,
-<ei>ecmNow</ei>, is obtained as
-<eq>
- pT0 = pT0(ecmNow) = pT0Ref * (ecmNow / ecmRef)^ecmPow
-</eq>
-where <ei>pT0Ref</ei>, <ei>ecmRef</ei> and <ei>ecmPow</ei> are the
-three parameters below.
-
-<parm name="SpaceShower:pT0Ref" default="2.0"
-min="0.5" max="10.0">
-Regularization of the divergence of the QCD emission probability for
-<ei>pT -> 0</ei> is obtained by a factor <ei>pT^2 / (pT0^2 + pT^2)</ei>,
-and by using an <ei>alpha_s(pT0^2 + pT^2)</ei>. An energy dependence
-of the <ei>pT0</ei> choice is introduced by the next two parameters,
-so that <ei>pT0Ref</ei> is the <ei>pT0</ei> value for the reference
-cm energy, <ei>pT0Ref = pT0(ecmRef)</ei>.
-</parm>
-
-<parm name="SpaceShower:ecmRef" default="1800.0" min="1.">
-The <ei>ecmRef</ei> reference energy scale introduced above.
-</parm>
-
-<parm name="SpaceShower:ecmPow" default="0.0" min="0." max="0.5">
-The <ei>ecmPow</ei> energy rescaling pace introduced above.
-</parm>
-
-<parm name="SpaceShower:pTmin" default="0.2"
-min="0.1" max="10.0">
-Lower cutoff in <ei>pT</ei>, below which no further ISR branchings
-are allowed. Normally the <ei>pT0</ei> above would be used to
-provide the main regularization of the branching rate for
-<ei>pT -> 0</ei>, in which case <ei>pTmin</ei> is used mainly for
-technical reasons. It is possible, however, to set <ei>pT0Ref = 0</ei>
-and use <ei>pTmin</ei> to provide a step-function regularization,
-or to combine them in intermediate approaches. Currently <ei>pTmin</ei>
-is taken to be energy-independent.
-</parm>
-
-<parm name="SpaceShower:pTminChgQ" default="0.5" min="0.01">
-Parton shower cut-off <ei>pT</ei> for photon coupling to a coloured
-particle.
-</parm>
-
-<parm name="SpaceShower:pTminChgL" default="0.0005" min="0.0001">
-Parton shower cut-off mass for pure QED branchings.
-Assumed smaller than (or equal to) <ei>pTminChgQ</ei>.
-</parm>
-
-<flag name="SpaceShower:rapidityOrder" default="off">
-Force emissions, after the first, to be ordered in rapidity,
-i.e. in terms of decreasing angles in a backwards-evolution sense.
-Could be used to probe sensitivity to unordered emissions.
-Only affects QCD emissions.
-</flag>
-
-<h3>Further variables</h3>
-
-These should normally not be touched. Their only function is for
-cross-checks.
-
-<p/>
-There are three flags you can use to switch on or off selected
-branchings in the shower:
-
-<flag name="SpaceShower:QCDshower" default="on">
-Allow a QCD shower; on/off = true/false.
-</flag>
-
-<flag name="SpaceShower:QEDshowerByQ" default="on">
-Allow quarks to radiate photons; on/off = true/false.
-</flag>
-
-<flag name="SpaceShower:QEDshowerByL" default="on">
-Allow leptons to radiate photons; on/off = true/false.
-</flag>
-
-<p/>
-There are some further possibilities to modify the shower:
-
-<flag name="SpaceShower:MEcorrections" default="on">
-Use of matrix element corrections; on/off = true/false.
-</flag>
-
-<flag name="SpaceShower:MEafterFirst" default="on">
-Use of matrix element corrections also after the first emission,
-for dipole ends of the same system that did not yet radiate.
-Only has a meaning if <code>MEcorrections</code> above is
-switched on.
-</flag>
-
-<flag name="SpaceShower:phiPolAsym" default="on">
-Azimuthal asymmetry induced by gluon polarization; on/off = true/false.
-</flag>
-
-<flag name="SpaceShower:phiIntAsym" default="on">
-Azimuthal asymmetry induced by interference; on/off = true/false.
-</flag>
-
-<parm name="SpaceShower:strengthIntAsym" default="0.7"
-min="0." max="0.9">
-Size of asymmetry induced by interference. Natural value of order 0.5;
-expression would blow up for a value of 1.
-</flag>
-
-<modeopen name="SpaceShower:nQuarkIn" default="5" min="0" max="5">
-Number of allowed quark flavours in <ei>g -> q qbar</ei> branchings,
-when kinematically allowed, and thereby also in incoming beams.
-Changing it to 4 would forbid <ei>g -> b bbar</ei>, etc.
-</modeopen>
-
-<h3>Technical notes</h3>
-
-Almost everything is equivalent to the algorithm in [1]. Minor changes
-are as follows.
-<ul>
-<li>
-It is now possible to have a second-order running <ei>alpha_s</ei>,
-in addition to fixed or first-order running.
-</li>
-<li>
-The description of heavy flavour production in the threshold region
-has been modified, so as to be more forgiving about mismatches
-between the <ei>c/b</ei> masses used in Pythia relative to those
-used in a respective PDF parametrization. The basic idea is that,
-in the threshold region of a heavy quark <ei>Q</ei>, <ei>Q = c/b</ei>,
-the effect of subsequent <ei>Q -> Q g</ei> branchings is negligible.
-If so, then
-<eq>
- f_Q(x, pT2) = integral_mQ2^pT2 dpT'2/pT'2 * alpha_s(pT'2)/2pi
- * integral P(z) g(x', pT'2) delta(x - z x')
-</eq>
-so use this to select the <ei>pT2</ei> of the <ei>g -> Q Qbar</ei>
-branching. In the old formalism the same kind of behaviour should
-be obtained, but by a cancellation of a <ei>1/f_Q</ei> that diverges
-at the theshold and a Sudakov that vanishes.
-<br/>
-The strategy therefore is that, once <ei>pT2 < f * mQ2</ei>, with
-<ei>f</ei> a parameter of the order of 2, a <ei>pT2</ei> is chosen
-like <ei>dpT2/pT2</ei> between <ei>mQ2</ei> and <ei>f * mQ2</ei>, a
-nd a <ei>z</ei> flat in the allowed range. Thereafter acceptance
-is based on the product of three factors, representing the running
-of <ei>alpha_strong</ei>, the splitting kernel (including the mass term)
-and the gluon density weight. At failure, a new <ei>pT2</ei> is chosen
-in the same range, i.e. is not required to be lower since no Sudakov
-is involved.
-</li>
-<li>
-The QED algorithm now allows for hadron beams with non-zero photon
-content. The backwards-evolution of a photon in a hadron is identical
-to that of a gluon, with <ei>CF -> eq^2</ei> and <ei>CA -> 0</ei>.
-Note that this will only work in conjunction with
-parton distribution that explicitly include photons as part of the
-hadron structure (such as the MRST2004qed set). Since Pythia's
-internal sets do not allow for photon content in hadrons, it is thus
-necessary to use the LHAPDF interface to make use of this feature. The
-possibility of a fermion backwards-evolving to a photon has not yet
-been included, nor has photon backwards-evolution in lepton beams.
-</li>
-</ul>
-
-</chapter>
-
-<!-- Copyright (C) 2012 Torbjorn Sjostrand -->
-
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