PTSelection

## pT Selection

The `StringPT` class handles the choice of fragmentation transverse momentum pT. At each string breaking the quark and antiquark of the produced pair, or the diquark and antidiquark, are supposed to receive opposite and compensating pT kicks. How they are distributed depends on the following flag:

In more detail, the quarks receive pT kicks according to a Gaussian distribution in p_x and p_y separately. Call sigma_q the width of the p_x and p_y distributions separately, i.e.
d(Prob) = exp( -(p_x^2 + p_y^2) / 2 sigma_q^2).
Then the total squared width is
<pT^2> = <p_x^2> + <p_y^2> = 2 sigma_q^2 = sigma^2.
It is this latter number that is stored in

`parm` StringPT:sigma (`default = 0.335`; `minimum = 0.0`; `maximum = 1.0`)
the width sigma in the fragmentation process.

Since a normal hadron receives pT contributions for two string breakings, it has a
<p_x^2>_had = <p_y^2>_had = sigma^2,
and thus <pT^2>_had = 2 sigma^2.

Some studies on isolated particles at LEP has indicated the need for a slightly enhanced rate in the high-pT tail of the above distribution. This would have to be reviewed in the context of a complete retune of parton showers and hadronization, but for the moment we stay with the current recipe, to boost the above pT by a factor enhancedWidth for a small fraction enhancedFraction of the breakups, where

`parm` StringPT:enhancedFraction (`default = 0.01`; `minimum = 0.0`; `maximum = 1.`)
enhancedFraction,the fraction of string breaks with enhanced width.

`parm` StringPT:enhancedWidth (`default = 2.0`; `minimum = 1.0`; `maximum = 10.0`)
enhancedWidth,the enhancement of the width in this fraction.

In the context of some toy studies [Fis16] the following three options have also been introduced, but are not part of any recommended framework.

`parm` StringPT:widthPreStrange (`default = 1.0`; `minimum = 1.0`; `maximum = 10.0`)
Prefactor multiplying the Gaussian width for strange quarks.

`parm` StringPT:widthPreQQ0 (`default = 1.0`; `minimum = 1.0`; `maximum = 10.0`)
Prefactor multiplying the Gaussian width for spin-0 diquarks. In case of diquarks with one or two strange quarks the prefactor is calculated by multiplying widthPreQQ0 once or twice respectively with widthPreStrange.

`parm` StringPT:widthPreQQ1 (`default = 1.0`; `minimum = 1.0`; `maximum = 10.0`)
Prefactor multiplying the Gaussian width for spin-1 diquarks. In case of diquarks with one or two strange quarks the prefactor is calculated by multiplying widthPreQQ1 once or twice respectively with widthPreStrange.