Deuteron Production
- Main parameters
- Technical parameters
After the final state particles of an event are produced, protons and
neutrons are selected and combined into pairs which may form
deuterons. A generalized version of the model in [Dal15] is
implemented here. The cross-sections used to determine if a combination
binds into a deuteron are differential in
k ≡ |p1 - p2| where
pi are the momenta of the binding combination in
the center-of-mass frame of the combination. Here all notation is used
to specify deuteron production, but anti-deuteron production is also
provided where the anti-particles for all relevant particles are used.
To ensure conservation of momentum and energy, the final state for
each deuteron production channel is required to have at least two
final products, where one product is a deuteron. This is in contrast
to the traditional coalescence model of [Scd63] and
[Kap80] where typically only a deuteron is produced from a
two-body initial state and so momentum and energy are not
conserved. Here, a modified coalescence model can be used where the
final state can be specified as a deuteron and a photon.
The default deuteron production setup is taken from [Dal15],
where 8 production channels are defined:
- p+ n0 → gamma 2H
- p+ n0 → pi0 2H
- p+ n0 → pi0 pi0 2H
- p+ n0 → pi+ pi- 2H
- p+ p+ → pi+ 2H
- p+ p+ → pi+ pi0 2H
- n0 n0 → pi- 2H
- n0 n0 → pi- pi0 2H
These channels, and the models used to calculate their differential
cross-sections, can be fully specified by the user as detailed below. The
DeuteronProduction class performs the deuteron
production, first building all valid two-particle combinations, then
determining whether the combinations bind, and finally performing an
isotropic decay of the bound state into the specified final state.
Main parameters
Assuming you have set HadronLevel:DeuteronProduction = on,
you can regulate the detailed behaviour with the following settings.
Warning: changed mvec and wvec values
must be provided as a comma-separated list enclosed in braces,
{...}.
parm DeuteronProduction:norm
(default = 119.6; minimum = 1)
An overall unitless multiplicative normalization scale to increase the
maximum used when sampling the differential cross-sections. Increasing
this scale decreases the cross-section for deuteron production. Using
the default model, the maximum differential cross-section is 3.2
mb with the n0 n0 → pi- 2H and p+ p+ → pi+
2H channels. To convert the fit values from table VIII of
[Dal15] into this multiplicative normalization factor, take
1/(value from table * maximum cross-section). For example,
the ALICE 7 TeV deuteron fit with a 1/σ0 of
2.63 inverse barn, the multiplicative normalization is 119.6.
wvec DeuteronProduction:channels
(default = {2212 2112 > 22, 2212 2112 > 111, 2212 2112 > 111 111, 2212 2112 > 211 -211, 2212 2212 > 211, 2212 2212 > 211 111, 2112 2112 > -211, 2112 2112 > -211 111})
List of the deuteron production channels to include of the form
initial states > final states where initial
states are the PDG particle IDs of the initial state particles to
combine (there must be two), and final states are the PIDs of
the final state particles, excluding the deuteron. There must be one
or more final state particles in addition to the deuteron. The
products of each channel are space separated, while the channels are
comma separated.
mvec DeuteronProduction:models
(default = {1, 2, 3, 3, 2, 3, 2, 3})
List of the parameterization mode for each deuteron production channel
specified by DeuteronProduction:channels. The parameters
for each of the channels is specified with
DeuteronProduction:parms. The length of this vector must
be the same as DeuteronProduction:channels.
option 0 : the coalescence model, p1
θ(p0 - k), a step function with two
parameters: p0 the cut-off of the step function
and p1 the normalization of the step
function.
option 1 : the differential cross-section model in
κ is given by the piece-wise function
∑i=112 pi
κi-2 for κ < p0,
otherwise exp(-p13 κ - p14
κ2). A total of 15 parameters are required: the
function split followed by 12 polynomial coefficients for the first
function, and 2 polynomial coefficients for the second exponential
function. The function is fixed below 0.1 GeV to its value
at this κ where κ is defined as
k/GeV.
option 2 : the differential cross-section model in
η is given by p0
ηp1/((p2 - exp(p3
η))2 + p4). A total of 5 parameters is
required. Here, η is the momentum of the non-deuteron
final state divided by its mass in the COM. This model is intended for
two-body final states containing a deuteron and a pion.
option 3 : the differential cross-section model in
κ is given by ∑i=0 p5*i+0
κp5*i+1/((p5*i+2 -
exp(p5*i+3 κ))2 + p5*i+4)
where the number of parameters can be any multiple of 5 and
κ is defined as k/GeV.
wvec DeuteronProduction:parms
(default = {1.28 2.3034605532591175 -93.663463313902028 2565.3904680353621 -25594.100560137995 143513.10872427333 -503572.89020794741 1149248.0196165806 -1723683.9119787284 1679348.7891145353 -1019888.5470232342 349840.35161061864 -51662.760038375141 -5.1885266705385051 2.9195632726211609, 85 1.34 1.77 0.38 0.096, 2.85519622e+06 1.31114126e+01 2.96145497e+03 5.57220777e+00 1.46051932e+06, 6.46455516e+06 1.05136338e+01 1.97924778e+03 5.36301369e+00 6.04534114e+05 2.54935423e+15 1.65669163e+01 2.32961298e+07 1.11937373e+01 2.86815089e+16, 170 1.34 1.77 0.38 0.096, 5.09870846e+15 1.65581228e+01 2.33337076e+07 1.13304315e+01 2.86815089e+16, 170 1.34 1.77 0.38 0.096, 5.09870846e+15 1.65581228e+01 2.33337076e+07 1.13304315e+01 2.86815089e+16})
The parameters needed for the model of each channel. The parameters
for each channel are space separated, while the channels are separated
by commas. The length of this vector must be the same as
DeuteronProduction:channels. Note, to match the parameters
of [Dal15] these parameters give differential cross-sections in
μb not mb.
Technical parameters
The maximum cross-section for each deuteron production channel is
calculated using an initial grid search followed by the simplex algorithm.
Assuming parameters similar to the default parameters above are used, the
following technical parameters should not need to be changed. However, if
the maximum finding fails for a given configuration, the following can be
modified to ensure appropriate determination of the cross-section maximums.
parm DeuteronProduction:kMin
(default = 1e-1)
The minimum bracketing value of k (in GeV) when maximum
finding. For the default p n → gamma 2H production model
the cross-section diverges at low k, but the probability of
producing two nucleons with low k suppresses this divergence.
parm DeuteronProduction:kMax
(default = 5)
The maximum bracketing value of k (in GeV) when maximum
finding.
parm DeuteronProduction:kTol
(default = 1e-4)
The minimum relative tolerance in k required when maximum
finding.
mode DeuteronProduction:kSteps
(default = 100)
The number of steps to sample in k when calculating the
initial grid for maximum finding.