Hadron Scattering

This page describes a few simple hadron (re)scattering models. They are intended to take into account that the overlap of multiple strings at low transverse dimensions is likely to lead to some collective effects, not unlike those observed in heavy-ion collisions, even if not quite as pronounced. Specifically, it is assumed that the hadrons produced can scatter against each other on the way out, before the fragmenting system has had time to expand enough that the hadrons get free. Thereby heavier particles are shifted to higher transverse momenta, at the expense of the lighter ones.

The main switch on/off switch for rescattering is HadronLevel:HadronScatter, which by the default is off, since all models are rather simplistic and have to be used with some caution. Currently there are three different options available:

mode HadronScatter:mode (default = 0; minimum = 0; maximum = 2)
The first two options are variations of the same model, whereas option 2 respresents a different model.
option 0 : The new model, based on separation in rapidity as described in [Fis16]. Further options are found here.
option 1 : The new model, based on separation in rapidity and azimuthal angle as described in [Fis16]. Further options are found here.
option 2 : The old model. Further options are found here.
Warning: Option 2 is still at an experimental level, and should not be used unless you know what you are doing.

The New Model for Hadron Scattering

Within the new modle, there are two options available for how hadron pairs are found:

Rapidity based

This corresponds to HadronScatter:mode = 0.

Probe all hadron pairs with an invariant mass m_inv < (m²₁+p²_Max)^1/2 + (m²₂+p²_Max)^1/2 with the parameter p_Max

parm HadronScatter:pMax (default = 0.5; minimum = 0.1; maximum = 1000000.0)

If a hadron pair passes this cut, the scattering probability for hadrons of different strings is P_DS(Δy) = P^max_DS(1 - Δy/Δy^max) with rapidity difference Δy of the hadron pair and the parameters Δy^max

parm HadronScatter:yDiffMax (default = 1.0; minimum = 0.1; maximum = 10.0)

and P^max_DS, see below. If the hadrons are produced within the same string the probability is P_DS(Δy) P^max_SS if the hadrons are further apart from each other as HadronScatter:neighbourFar, 0 if they are closer together as HadronScatter:neighbourNear, and linear between the maximum HadronScatter:maxProbSS and minimum probability HadronScatter:minProbSS inbetween.

Rapidity and Azimuth based

This corresponds to HadronScatter:mode = 1.

All hadron pairs are considered. The scattering probability for hadrons of different strings is P_DS(Δy,Δφ) = P^max_DS(1 - ((Δy)² +(Δφ)²)^1/2/R^max) with rapidity difference Δy and difference in azimuth Δφ of the hadron pair and the parameters R^max

parm HadronScatter:Rmax (default = 1.0; minimum = 0.1; maximum = 10.0)

and P^max_DS, see below. The probability for hadron pairs from the same string is similar to the one before.

Common Parameters

The following paramters are used for both the above cases:

flag HadronScatter:scatterSameString (default = on)
If switched on, strings within the same string are allowed to scatter off each other. Otherwise only hadron pairs that are not produced on the same string are taken into account.

flag HadronScatter:scatterMultipleTimes (default = on)
If switched off, each hadron is only allowed to scatter at most once. By the way that possible scattering pairs are considered in order of increasing rapidity separation, this introduces a bias towards pairs with small y separation.

parm HadronScatter:maxProbDS (default = 0.5; minimum = 0.0; maximum = 1.0)
The maximum probability P^max_DS for the scattering of two hadrons that are not part of the same string.

mode HadronScatter:neighbourNear (default = 2; minimum = 1; maximum = 10)
If scattering of hadrons within the same string is allowed this parameter gives the closest neighbour that is allowed. The value 1 corresponds to the direct neighbour. The probability associated with this potential scattering partner is minProbSS.

mode HadronScatter:neighbourFar (default = 4; minimum = 2; maximum = 15)
If scattering of hadrons within the same string is allowed this parameter gives the neighbour starting from which the maximum probability maxProbSS is applied.

parm HadronScatter:minProbSS (default = 0.5; minimum = 0.0; maximum = 1.0)
The minimum probability P^min_SS for the scattering of two hadrons within the same string. (Relative to that for different strings, i.e. for the total probability the baseline maxProbDS factor also enters.)

parm HadronScatter:maxProbSS (default = 1.0; minimum = 0.0; maximum = 1.0)
The maximum probability P^max_SS for the scattering of two hadrons within the same string. (Relative to that for different strings, i.e. for the total probability the baseline maxProbDS factor also enters.)

The Old Model for Hadron Scattering

Warning: This is still at an experimental level, and should not be used unless you know what you are doing.

flag HadronScatter:afterDecay (default = off)
Perform hadron scattering before or after first round of decays, involving very short-lived particles like the rho. The default is to perform scattering directly after the string fragmentation, before any decays.

flag HadronScatter:allowDecayProd (default = off)
Allow two hadrons with same parent hadron to scatter.

flag HadronScatter:scatterRepeat (default = off)
Allow hadrons which have already scattered to scatter again. Even if switched on, the same pair can not scatter off each other twice.

Hadron selection

mode HadronScatter:hadronSelect (default = 0; minimum = 0; maximum = 0)
Probability that a hadron is soft enough to scatter. (A high-pT hadron presumably being part of a jet, and thus produced away from the high-particle-density region at small transverse dimensions.)
option 0 : P = N exp(-pT^2 / 2 / sigma^2) / ( (1 - k) exp(-pT^2 / 2 / sigma^2) + k pT0^p / (pT0^2 + pT^2)^(p/2), with sigma = 2 StringPT:sigma and pT0 the same as that used in MultipartonInteractions.

parm HadronScatter:N (default = 1.0; minimum = 0.01; maximum = 1.0)
N parameter as above.

parm HadronScatter:k (default = 1.0; minimum = 0.01; maximum = 1.0)
k parameter as above.

parm HadronScatter:p (default = 6; minimum = 2; maximum = 30)
p parameter as above.

Scattering probability

mode HadronScatter:scatterProb (default = 0; minimum = 0; maximum = 2)
Probability for a pair of hadrons to scatter.
option 0 : All hadrons scatter with probability j max(0, 1 - dR^2 / rMax^2). Angular distribution is picked flat in cos(theta).
option 1 : As option 0, above, but only pi-pi, pi-K and pi-p scatterings are considered.
option 2 : Only pi-pi, pi-K and pi-p scatterings are considered, with probability given by (1 - exp(-j sigEl)) max(0, 1 - dR^2 / rMax^2). The elastic cross sections and angular distributions are taken from the partial-wave distributions.

parm HadronScatter:j (default = 0.5; minimum = 0.0; maximum = 10.0)
j parameter as above.

parm HadronScatter:rMax (default = 1.0; minimum = 0.1; maximum = 2.0)
rMax parameter as above.

flag HadronScatter:tile (default = off)
Use tiling in (eta, phi) to reduce number of pairwise tests.