<chapter name="Beam Parameters"> 
 
<h2>Beam Parameters</h2> 
 
The settings on this page relate to the beam identities and energies, 
to a beam momentum spread and to a beam interaction spot. 
As always, momenta and energies are to be given in units of GeV, 
and of space and time in mm. 
 
<h3>Incoming beams</h3> 
 
The identities and energies of the two incoming beam particles 
should be specified using the settings in this section. 
Note that, if nothing is done, you will default to LHC at 14 TeV. 
 
<p/> 
Currently the beam particles must be either a hadron pair, a lepton 
pair, a photon pair, a lepton and a hadron or a photon and a hadron. 
In the first category <ei>p p</ei> and <ei>pbar p</ei> 
combinations dominate, but it is also possible to combine with 
<ei>pi^+</ei>, <ei>pi^-</ei> and <ei>pi^0</ei>. In the second 
<ei>e^+ e^-</ei> and <ei>mu^+ mu^-</ei> would be the most useful 
combinations, but also others should work if combined with an 
appropriate hard process. 
 
<modeopen name="Beams:idA" default="2212"> 
The PDG <code>id</code> code for the first incoming particle. 
Allowed codes include 
<br/><ei>2212 = p</ei>, <ei>-2212 = pbar</ei>, 
<br/><ei>2112 = n</ei>, <ei>-2112 = nbar</ei>, 
<br/><ei>211 = pi^+</ei>, <ei>-211 = pi^-</ei>, <ei>111 = pi^0</ei>, 
<br/><ei>990 = Pomeron</ei> (used in diffractive machinery; 
here mainly for debug purposes), 
<br/><ei>22 = gamma</ei> (for <ei>gamma-gamma</ei> and <ei>gamma-hadron</ei> 
interactions, more info <aloc href="Photoproduction">here</aloc>), 
<br/><ei>11 = e^-</ei>, <ei>-11 = e^+</ei>, 
<br/><ei>13 = mu^-</ei>, <ei>-13 = mu^+</ei>, 
<br/>and a few more leptons/neutrinos in a few combinations. 
<br/>Recently <aloc href="HeavyIons">heavy-ion collisions</aloc> have 
been implemented in PYTHIA. Therefore a handful of nuclei have been 
added as allowed incoming beams, using PDG codes of the format 
<code>100ZZZAAAI</code>: 
1000020040 = <sup>4</sup>He , 1000030060 = <sup>6</sup>Li, 
1000060120 = <sup>12</sup>C, 1000080160 = <sup>16</sup>O, 
1000290630 = <sup>63</sup>Cu, 1000791970 = <sup>197</sup>Au, and 
1000822080 = <sup>208</sup>Pb. More can be added using the function 
<code>ParticleData::addParticle</code>. 
</modeopen> 
 
<modeopen name="Beams:idB" default="2212"> 
The PDG <code>id</code> code for the second incoming particle. 
</modeopen> 
 
<modepick name="Beams:frameType" default="1" min="1" max="5"> 
Choice of frame for the two colliding particles. For options 
1 - 3 the beam identities are specified above, while they are 
obtained by the Les Houches information for options 4 and 5. 
<option value="1">the beams are colliding in their CM frame, 
and therefore only the CM energy needs to be provided, see 
<code>Beams:eCM</code> below. 
</option> 
<option value="2">the beams are back-to-back, but with different energies, 
see <code>Beams:eA</code> and <code>Beams:eB</code> below. 
This option could also be used for fixed-target configurations. 
</option> 
<option value="3">the beams are not back-to-back, and therefore the 
three-momentum of each incoming particle needs to be specified, see 
<code>Beams:pxA</code> through <code>Beams:pzB</code> below. 
</option> 
<option value="4">the beam and event information is stored in a 
<aloc href="LHEF">Les Houches Event File</aloc>, 
see <code>Beams:LHEF</code> below. 
</option> 
<option value="5">the beam and event information is obtained by a 
pointer to an <code><aloc href="LHA">LHAup</aloc></code> 
class instance. 
</option> 
</modepick> 
 
<parm name="Beams:eCM" default="14000." min="0."> 
Collision CM energy, to be set if <code>Beams:frameType</code> = 1. 
</parm> 
 
<parm name="Beams:eA" default="7000." min="0."> 
The energy of the first incoming particle, moving in the 
<ei>+z </ei>direction, to be set if <code>Beams:frameType</code> = 2. 
If the particle energy is smaller than its mass 
it is assumed to be at rest. 
</parm> 
 
<parm name="Beams:eB" default="7000." min="0."> 
The energy of the second incoming particle, moving in the 
<ei>-z</ei> direction, to be set if <code>Beams:frameType</code> = 2. 
If the particle energy is smaller than its mass 
it is assumed to be at rest. 
</parm> 
 
<parm name="Beams:pxA" default="0."> 
The <ei>p_x</ei> component of the first incoming particle, 
to be set if <code>Beams:frameType</code> = 3. 
</parm> 
 
<parm name="Beams:pyA" default="0."> 
The <ei>p_y</ei> component of the first incoming particle, 
to be set if <code>Beams:frameType</code> = 3. 
</parm> 
 
<parm name="Beams:pzA" default="7000."> 
The <ei>p_z</ei> component of the first incoming particle, 
to be set if <code>Beams:frameType</code> = 3. 
</parm> 
 
<parm name="Beams:pxB" default="0."> 
The <ei>p_x</ei> component of the second incoming particle, 
to be set if <code>Beams:frameType</code> = 3. 
</parm> 
 
<parm name="Beams:pyB" default="0."> 
The <ei>p_y</ei> component of the second incoming particle, 
to be set if <code>Beams:frameType</code> = 3. 
</parm> 
 
<parm name="Beams:pzB" default="-7000."> 
The <ei>p_z</ei> component of the second incoming particle, 
to be set if <code>Beams:frameType</code> = 3. 
</parm> 
 
<word name="Beams:LHEF" default="void"> 
The name of a Les Houches Event File, 
to be set if <code>Beams:frameType</code> = 4. 
</word> 
 
<word name="Beams:LHEFheader" default="void"> 
As some information in a Les Houches Event File init block is only known 
at the end of generation, some programs choose to output this as a 
separate file. If <code>Beams:LHEFheader</code> is given, information up 
till the end of the init block is read from this file, with 
the events themselves read as usual from the file given in 
<code>Beams:LHEF</code>. 
</word> 
 
<flag name="Beams:newLHEFsameInit" default="off"> 
Allow to begin reading events from a new LHEF or or a new 
<code>LHAup</code> instance without a completely new initialization. 
Only useful when <code>Beams:frameType</code> = 4 or 5. 
</flag> 
 
<flag name="Beams:readLHEFheaders" default="on"> 
Read in LHEF header blocks and store them in the 
<aloc href="EventInformation">Info</aloc> class. See also 
<aloc href="LHA">LHAupLHEF</aloc> 
and the <aloc href="LHEF">Les Houches Event files</aloc> 
section for more information. 
</flag> 
 
<mode name="Beams:nSkipLHEFatInit" default="0"> 
Skip the first <ei>nSkip</ei> events of the input stream 
(cf. the <code>LHAup::skipEvent(nSkip)</code> method). 
Only used when <code>Beams:frameType</code> = 4 or 5. 
</mode> 
 
<flag name="Beams:strictLHEFscale" default="off"> 
Always use the <code>SCALUP</code> value read from LHEF 
as production scale for particles, also including particles 
coming from resonance decays. By default, the production scale 
of resonance decay products (W-, Z-, H-bosons, top quarks) will 
be set to <ei>M/2</ei>, where <ei>M</ei> is the mass of the resonance. 
</flag> 
 
<flag name="Beams:setProductionScalesFromLHEF" default="off"> 
If enabled, production scales for all particles in an input Les Houches 
event will be set by using auxiliary information provided in the 
input event. Depending on which LHEF version is used, different 
information will be read. For LHEF 1.0, scale information can be 
transferred by including a line starting with the hashtag 
(#) character at the end of the event. The hashtag should be 
followed by the sequential scale values of the particles with status 1. 
For LHEF 3.0, the standardised <ei>&lt;scales&gt;</ei> tag is used 
instead. In this case, please ensure that production scale of 
the final state particle with position <ei>i</ei> in the input event 
will be transferred as the value of a scales tag attribute which contains 
<ei>i</ei> at the end of the attribute name, separated from the rest of 
the name by an underscore (_). An example <ei>&lt;scales&gt;</ei> tag 
would be <ei>&lt;scales muf="100" pt_start_3="100" pt_start_4="50"&gt; 
&lt;/scales&gt;</ei>. This could be used to set the production scales 
of particles three and four to 100 GeV and 50 GeV, respectively, provided 
that these particles have status 1. 
</flag> 
 
<h3>Variable collision energy</h3> 
 
There are two different machineries that can provide an event-by-event 
spread of collision energies. The one in this section is intended 
to allow for very large variations in collision energy, more-or-less 
from threshold to the highest LHC/FCC/cosmic-ray energies. This is made 
possible by interpolation in a grid of CM energies. Such a strategy 
requires the processes to have a smooth and well-understood energy 
dependence. In practice this limits us to the soft QCD processes 
betweeen two incoming hadrons. Thus the framework is convenient e.g. 
for studies of cosmic-ray cascades, or for secondary collisions in 
general. 
 
<p/> 
The core extension in this option is that the multiparticle interactions 
(MPI) machinery is initialized over a (logarithmically spaced) grid of 
collision energies, from the maximal energy provided at the 
initialization down to a lower cutoff (see <code>eMinPert</code> below). 
For each new event, with a new CM energy, a suitable interpolation is 
then performed among the generation coefficients determined at 
initialization. The MPI framework is what is needed to simulate 
hadronic nondiffractive events (<code>SoftQCD:nonDiffractive</code>). 
Pretty much the same strategy is already used for diffraction, to handle 
MPIs inside the variable-mass diffractive systems. Thus all the 
<aloc href="QCDSoftProcesses">Soft QCD processes</aloc> can be used 
within this framework. Below the minimal energy for a perturbative 
description (see below) instead the simplified 
<aloc href="QCDLowEnergyProcesses">Low-energy QCD processes</aloc> 
can be used. It is not possible to generate other processes 
with the variable-energy framework, however, and the program will abort 
if you try. 
 
<p/> 
The initialization involves setting up optimal coefficients for 
the kinematics selection in the subsequent MPI generation, and 
finding the associated maximum of the differentialcross section. 
At a fixed energy this typically takes less than a second, and so 
normally is not noticeable.It is a major fraction of the full PYTHIA 
initialization time, however. Thus the initialization over a grid of 
energies raises the total initialization time appreciable, to the order 
of ten seconds. Initialization of diffraction contributes comparable 
numbers, when switched on. You should therefore not be surprised that 
the startup time is longer than usual. The subsequent event generation 
should not become noticeably slower, however. 
 
<p/> 
There are three main settings in this framework. 
 
<flag name="Beams:allowVariableEnergy" default="off"> 
Master switch to allow collision energies below the initialization one, 
as described above. 
</flag> 
 
<parm name="Beams:eMinPert" default="10." min="10."> 
The lowest CM energy that collisions are allowed to have. The highest 
is set by the full energy at initialization, as calculated in the 
respective options above. If you do not want to generate events with 
a higher collision energy than this you can save some initialization 
time by raising this number accordingly, so that fewer grid energies need 
to be used. You should not lower the value below the default one, however, 
since the perturbative MPI machinery cannot be made to work at lower 
energies. If you do want to generate events with lower energies, it 
is possible in a nonperturbative framework, see next. 
</parm> 
 
<parm name="Beams:eWidthPert" default="10." min="1."> 
A simpler low-mass description can be used for energies below the 
threshold energy <ei>e_min</ei> = <code>eMinPert</code> above, with 
only longitudinally stretched strings. A gradual switch-over between 
the simple low-energy and perturbative high-energy regimes is then 
natural. The probability for the latter picture is parametrized as 
<eq> 
P_pert = 1 - exp( (e_CM - e_min) / e_width ) 
</eq> 
which vanishes for the CM energy <ei>e_CM &lt; e_min</ei>, and is 
<ei>1 - 1/e = 0.632</ei> for <ei>e_CM = e_min + e_width</ei>. 
The current parameter is this <ei>e_width.</ei> 
</parm> 
 
<p/> 
To input the variable energy, the normal argument-less 
<code>Pythia::next()</code> method has three siblings that take 
relevent arguments as required by the <code>Beams:frameType</code>. 
 
<method name="bool Pythia::next(double eCM)"> 
events created by the collision of two particles coming in along the 
<ei>+-z</ei> axis in their common rest frame, with the CM energy as 
argument, to be used for <code>Beams:frameType = 1</code>. 
</method> 
 
<method name="bool Pythia::next(double eA, double eB)"> 
events created by the collision of two particles coming in along the 
<ei>+-z</ei> axis, with the respective energies as arguments, to be 
used for <code>Beams:frameType = 2</code>. 
</method> 
 
<method name="bool Pythia::next(double pxA, double pyA, double pzA, 
double pxB, double pyB, double pzB)"> 
events created by two incoming particles with arbitrary three-momenta, 
to be used for <code>Beams:frameType = 3</code>. 
</method> 
 
 
<h3>Beam momentum spread</h3> 
 
This framework currently is intended for a modest beam spread, such as 
experienced at hadron colliders. Thus it can be safely assumed that the 
physics does not change over the CM energy range probed, so that the 
parameters of the physics initialization at the nominal energy can be 
used as is. Therefore it can be used for all processes implemented in 
PYTHIA. It can <b>not</b> be used for the more extensive energy spread, 
however, e.g. as expected at linear <ei>e^+ e^-</ei> colliders. Also, 
any attempt to combine it with external Les Houches input of 
parton-level events is at own risk. This option cannot be combined with 
the variable-collision-energy option above, but will be switced off in 
such a case. 
 
<p/> 
On this page you can set the momentum spread according to a simple 
Gaussian distribution. If you instead want a more sophisticated 
parametrization, you can write and link your own 
<code><aloc href="BeamShape">BeamShape</aloc></code> class. 
 
<flag name="Beams:allowMomentumSpread" default="off"> 
Allow the beam momenta to be smeared around their initialization 
nominal values. 
</flag> 
 
<parm name="Beams:sigmaPxA" default="0." min="0."> 
The width of a Gaussian distribution of the <ei>p_x</ei> spread of the 
first incoming particle. 
</parm> 
 
<parm name="Beams:sigmaPyA" default="0." min="0."> 
The width of a Gaussian distribution of the <ei>p_y</ei> spread of the 
first incoming particle. 
</parm> 
 
<parm name="Beams:sigmaPzA" default="0." min="0."> 
The width of a Gaussian distribution of the <ei>p_z</ei> spread of the 
first incoming particle. 
</parm> 
 
<parm name="Beams:maxDevA" default="5." min="0."> 
The triply Gaussian distribution <ei>(p_x, p_y, p_z)</ei> is restricted to 
a maximal total deviation from the nominal values <ei>(p_x0, p_y0, p_z0)</ei> 
for the first incoming particle, like 
<eq> 
(p_x - p_x0)^2/sigma_px^2 + (p_y - p_y0)^2/sigma_py^2 + 
(p_z - p_z0)^2/sigma_pz^2 &lt; maxDev^2 
</eq> 
(Note the absence of a factor 2 in the denominator, unlike the Gaussians 
used to pick <ei>(p_x, p_y, p_z)</ei>.) 
</parm> 
 
<parm name="Beams:sigmaPxB" default="0." min="0."> 
The width of a Gaussian distribution of the <ei>p_x</ei> spread of the 
second incoming particle. 
</parm> 
 
<parm name="Beams:sigmaPyB" default="0." min="0."> 
The width of a Gaussian distribution of the <ei>p_y</ei> spread of the 
second incoming particle. 
</parm> 
 
<parm name="Beams:sigmaPzB" default="0." min="0."> 
The width of a Gaussian distribution of the <ei>p_z</ei> spread of the 
second incoming particle. 
</parm> 
 
<parm name="Beams:maxDevB" default="5." min="0."> 
The triply Gaussian distribution <ei>(p_x, p_y, p_z)</ei> is restricted to 
a maximal total deviation from the nominal values <ei>(p_x0, p_y0, p_z0)</ei>, 
for the second incoming particle, like 
<eq> 
(p_x - p_x0)^2/sigma_px^2 + (p_y - p_y0)^2/sigma_py^2 + 
(p_z - p_z0)^2/sigma_pz^2 &lt; maxDev^2 
</eq> 
(Note the absence of a factor 2 in the denominator, unlike the Gaussians 
used to pick <ei>(p_x, p_y, p_z)</ei>.) 
</parm> 
 
<h3>Beam interaction vertex</h3> 
 
On this page you can set the spread of the interaction vertex according to 
a simple Gaussian distribution. If you instead want a more sophisticated 
parametrization, you can write and link your own 
<code><aloc href="BeamShape">BeamShape</aloc></code> class. 
 
<flag name="Beams:allowVertexSpread" default="off"> 
Allow the interaction vertex of the two colliding beams to be smeared. 
If off, then the vertex is set to be the origin. 
</flag> 
 
<parm name="Beams:sigmaVertexX" default="0." min="0."> 
The width of a Gaussian distribution of the <ei>x</ei> location of the 
interaction vertex. 
</parm> 
 
<parm name="Beams:sigmaVertexY" default="0." min="0."> 
The width of a Gaussian distribution of the <ei>y</ei> location of the 
interaction vertex. 
</parm> 
 
<parm name="Beams:sigmaVertexZ" default="0." min="0."> 
The width of a Gaussian distribution of the <ei>z</ei> location of the 
interaction vertex. 
</parm> 
 
<parm name="Beams:maxDevVertex" default="5." min="0."> 
The triply Gaussian distribution of interaction vertex position 
<ei>(x, y, z)</ei> is restricted to a maximal total deviation from the 
origin, like 
<eq> 
x^2/sigma_x^2 + y^2/sigma_y^2 + z^2/sigma_z^2 &lt; maxDevVertex^2 
</eq> 
(Note the absence of a factor 2 in the denominator, unlike the Gaussians 
used to pick <ei>(x, y, z)</ei>.) 
</parm> 
 
<parm name="Beams:sigmaTime" default="0." min="0."> 
The width of a Gaussian distribution of the collision time (in units of 
mm/c). Note that, if the above space parametrization is viewed as the 
effect of two incoming beams along the <ei>+-z</ei> axis, with each beam 
having a Gaussian spread, then the spread of the time would also become 
a Gaussian with the same width as the <ei>z</ei> one (times the 
velocity of the beams, which we expect is close to unity). For flexibility 
we have not enforced any such relation, however. 
</parm> 
 
<parm name="Beams:maxDevTime" default="5." min="0."> 
The collision time is restricted to be in the range 
<ei>|t| &lt; sigma_t * maxDevTime</ei>. 
</parm> 
 
<p/> 
The distributions above are all centered at the origin. It is also 
possible to shift the above distributions to be centered around another 
nominal position. You must have <code>Beams:allowVertexSpread = on</code> 
to use this possibility. 
 
<parm name="Beams:offsetVertexX" default="0."> 
The <ei>x</ei> location of the interaction vertex is centered at this value. 
</parm> 
 
<parm name="Beams:offsetVertexY" default="0."> 
The <ei>y</ei> location of the interaction vertex is centered at this value. 
</parm> 
 
<parm name="Beams:offsetVertexZ" default="0."> 
The <ei>z</ei> location of the interaction vertex is centered at this value. 
</parm> 
 
<parm name="Beams:offsetTime" default="0."> 
The time <ei>t</ei> of the interaction vertex is centered at this value. 
</parm> 
 
</chapter> 
 
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