Hadron Vertex Information
It is not trivial to define where in space-time that the primary
hadrons are produced by the string fragmentation machinery.
The basic strategy is well-defined in a 1+1-dimensional picture,
as represented by a single straight string stretched between massless
q and qbar endpoints [And83]. Even so there
is no unique definition of the production vertex of the hadron
straddling two adjacent breakup vertices, and the transverse width
of the string adds a further smearing. Some of that ambiguity is
reflected in the options below. The major step in complexity comes
with the introduction of more convoluted string topologies, however.
Here the momentum-space description contains a number of ambiguities,
notably for those hadrons that straddle two or more different string
regions, that were only overcome by a set of reasonable simplifications
[Sjo84]. The space-time picture introduced here
[Fer18] inherits all these problems, and thus many of the
same prescriptions, but also require a few further simplifications
Below the main switches and parameters of this picture are described.
When on, the machinery assigns space-time production vertices to all
primary hadrons, i.e. those that are produced directly from the string
breakups. These vertices can be read out by the
method. Note that the length unit is mm, and mm/s for time. To study
the hadronization process it is natural to cnvert to fm. The conversion
FM2MM = 10^12 and
= 10^-12 are defined inside the
available in user programs that include
By default all partons start out from the origin and the strings are
expandong accordingly. For a more realistic picture, the
Parton Vertex Information
allows MPI production vertices to be spread across the transverse
area of the collision. All of these separate vertices are still
assumed to occur at t = z = 0. The transverse displacements
are then inherited by the final hadrons. An interpolation is applied
in case of strings stretched between partons from different vertices.
In the context of the
framework, the secondary collision vertices can be the starting points
for new outgoing partonic systems. Since such lower-energy collisions
are handled without invoking MPIs there is (currently) no corresponding
initial transverse spread as there is for the primary collision.
Secondary vertices are set in decays, but by default only for scales
of the order of mm or above. That is, decays on the fm scale, like for
rho mesons, then are not considered. When the machinery in this
section is switched on, also such displacements are considered, see
HadronVertex:rapidDecays below. Do note that the factor
10^12 separation between fm and mm scales means that the two do
not mix well, i.e. any contribution of the latter kind would leave
little trace of the former when stored in double-precision real numbers.
For this reason it is also not meaningful to combine studies of hadron
production vertices with displaced pp collision vertices from
the profile of the incoming bunches.
default = off)
Normally primary hadron production vertices are not set, but if
on they are. In the latter case the further switches and parameters
below provide more detailed choices.
default = 0;
minimum = -1;
maximum = 1)
The definition of hadron production points is not unique, and here
three alternatives are considered: one early, one late and one in the
middle. Further expressions below are written for a hadron i
produced between two string vertices i and i+1.
option 0 : A hadron production point is defined as the middle
point between the two breakup vertices,
vhi = (vi + vi+1)/2.
option -1 : An "early" hadron production, counted backwards to the
point where a fictitious string oscillation could have begun that would
have reached the two string breakup vertices above. Given the hadronic
four-momentum ph and the string tension kappa,
this vertex would be
vhi = (vi + vi+1)/2
- phi / (2 kappa). With this prescription is
is possible to obtain a negative squared proper time, since the
ph contains a transverse-momentum smearing that
does not quite match up with longitudinal-momentum string picture.
In such cases the negative term is scaled down to give a vanishing
option 1 : A "late" hadron production, defined as the point
where the two partons that form the hadron cross for the first time.
The hadron momentum contribution then shifts sign relative to the previous
vhi = (vi + vi+1)/2
+ phi / (2 kappa),
and there is no problem with negative squared proper times.
default = 1.;
minimum = 0.5;
maximum = 10.)
The string tension kappa in units of GeV/fm, i.e. how much
energy is stored in a string per unit length.
default = on)
When on, the space--time location of breakp points is smear in transverse
space accordingly to the value of xySmear given.
default = 0.5;
minimum = 0.;
maximum = 2.)
Transverse smearing of the hadron production vertices in units of fm.
This is initially assigned as a Gaussian smearing of the string breakup
vertices in the plane perpendicular to the string direction.
The xySmear parameter is picked such that a breakup vertex
should have a smearing <x^2 + y^2> = xySmear^2 for a
simple string along the z direction. The initial default
value of 0.7 was picked roughly like sqrt(2/3) of the proton
radius, to represent two out of three spatial directions. For a hadron
this is then averaged, as described above in vhi
= (vi + vi+1)/2 and its variants, giving a
width reduction of 1/sqrt(2). When now a transverse spread of MPI
vertices has been introduced, partly to cover the same aspects,
the default value has been reduced somewhat.
default = 0.2;
minimum = 0.;
maximum = 10.)
Limit the smearing defined above from giving large shifts of vertices,
by reducing the net shift to be this fraction of the original value.
(Technically the quantity studied is a quadratic combination of space
and time shifts, additionally in quadrature with the xySmear
default = off)
The transverse smearing can change either the time coordinate or
the invariant time of the breakup points with respect to the origin.
Normally, the time coordinate is kept constant and the invariant time
is modified by the smearing. If on, the tau is kept constant
and the time coordinate is recalculated to compensate the effect of
the smearing. Empirically, the former prescription gives fewer problems
on the hadron level.
default = 40.;
minimum = 1.;
maximum = 100.)
In cases of complicated string topologies the reconstruction of a
string breakup vertex can fail occasionally. Usually this translates
into a large (positive or negative) production invariant (squared)
time for the adjacent hadrons (using the middle definition), here
expressed in units of fm. This cut rejects fragmented systems where
such a large tau is found, and a new try to hadronize is made. If this
variable is set too low then also many correct vertices will be rejected.
Notably this would happen in heavy-ion collisions, where the collision
region at t = 0 can be spread transversely up to order 20 fm.
default = on)
The decay products of particles with short lifetimes, such as rho, should be
displaced from the production point of the mother particle. When on, the
corresponding displacement is included in the space--time location of the
daughter production points. More specifically, the width stored for these
particles are inverted to give the respective lifetimes. (Even more
specifically, the width must be above
10^-6 GeV.) Particles that by default already have a nonvanishing
lifetime (in the database or set by the user) are always given a displaced
vertex based on that value, so for them this flag makes no difference.
See below for unstable particles that have neither a known width nor a
known lifetime. Note that, if
HadronLevel:Rescatter is on, this
setting is ignored and decay vertices will always be set.
default = 1e-9;
minimum = 1e-12;
maximum = 1e-3)
Average lifetime c * tau_0, expressed in mm, assigned to particle
species which are unstable, but have neither been assigned a nonvanishing
lifetime nor a non-negligible (above
For such cases an intermediate scale is chosen, such that the decays happen
well separated from the primary vertex, and yet not as far away as to give
rise to an experimentally discernible secondary vertex. The default
10^-9 mm = 1000 fm meets this requirement, and is additionally
a reasonable value for the particles that mainly decay electromagnetically.
The value is also used for a few rare particles that probably have a
non-negligible width, but are so poorly known that no width is listed
in the Review of Particle Physics.