### Selection on generator level particle list
+ [Primary particle selection convention](https://cds.cern.ch/record/2270008/files/cds.pdf):
> A primary, charged particle is a charged particle with a mean proper lifetime τ larger than 1 cm/c, which is either a) produced directly in the interaction, or b) from decays of particles with τ smaller than 1 cm/c, restricted to decay chains leading to the interaction.

+ How to apply $c\tau < 1 \rm cm$:
+ For Belle, Sherpa:
+ $c\tau$ is obtained by boosting the decaying mother hadron (h) to its rest frame: $c\tau = L/(\beta\gamma)_{h}$, and further apply a cut: $c\tau < 1 \rm cm$
+ For Herwig: top-down approach: `MaxLifeTime 10*mm`, asking them not to decay (https://herwig.hepforge.org/tutorials/faq/decay.html?#how-do-i-make-a-group-of-particles-stable)

+ Comparing the distribution
> 1. Here I useTgenNtrkBinning, since we want to see the effect of generator difference only.
> 2. It has only tiny effect to apply $c\tau < 1 \rm cm$ selection or not in comparing among different generators.
> 3. for Belle: comparing **production vertex cut** v.s. **w/ $c\tau$ seleciton]**
> 4. for Herwig/Sherpa: comparing **w/o $c\tau$ seleciton (and no production vertex cut)** v.s. **w/ $c\tau$ seleciton]**
> 5. **[newest candidate] production vertex cut: $V_r < 1 cm$**
> + [reco level]
> + previously: (all chgd trks) - ($e^{\pm}$ from $\gamma_c$)
> + $\gamma_c$ candidate: (1) $M_{\gamma_{c}} < 0.25 \rm GeV$ (2) z_dist <= 10 cm
> + now: (all chgd trks) - ($e^{\pm}$ from $\gamma_c$) - (daus from LLP $K_S^0, \Lambda^0, \bar{\Lambda^0}$)
> + $\gamma_c$ candidate: (1) $M_{\gamma_{c}} < 0.25 \rm GeV$ (2) z_dist <= 10 cm
> + $K_S^0$ candidate:
> (1) V0.kind()==1 (being identified as $K_S^0$)
> (2) with goodKs()==1
> (3) $0.48 \rm GeV \le M_{K_S^{0}} \le 0.516 \rm GeV$
> + $\Lambda^0, \bar{\Lambda^0}$ candidate:
> (1) V0.kind()==2 or 3 (being identified as $\Lambda$)
> (2) with goodLambda()==1
> (3) $1.111 \rm GeV \le M_{\Lambda} \le 1.121 \rm GeV$
> + [gen level]
> + previously: (trk in evtgen) + (trk (decay prodcts) in gsim: $K_S^0, K_L^0, \Lambda^0, \Sigma, \Xi, \Omega$)
> + now: (trk in evtgen) + (trk (decay prodcts) in gsim: $K_S^0, \Lambda^0, \Sigma, \Xi, \Omega$) - (daus from LLP $K_S^0, \Lambda^0, \bar{\Lambda^0}$)
> + (remove Klong since it has extremely long lifetime)
>
>
|| w/o $c\tau$ seleciton | w/o $c\tau$ seleciton (Y(dphi)) | w/ $c\tau$ seleciton | w/ $c\tau$ seleciton (Y(dphi)) | w/ & w/o ctau comparison | Vr<1cm | Vr<1cm (Y(dphi)) |
|---|---|---|---|---|---|---|---|
| Belle (reco) |  | | - | |
| Belle (gen) | (w/ production vertex sel: Vr, Vz: (5, 8))  |  | | |  |  |  |
| Herwig | | |  ||  |
| Sherpa | | | |  |  |
<!-- | Herwig (officialTune) | | |  | | -->
<!-- | Sherpa (officialTune) | |  | | | -->
<!-- | Sherpa (woISR) | | | |  | -->

### [Supplement] Some tuning (trial) of generators
> + Documenting the generator trials. (w.r.t Belle gen w/ production vertex cut)
> + It seems the original one is the best.
> + Original
> + Official: from Herwig/Sherpa manual or source
> (Herwig Official has swithced off ISR)
> + A trial on Herwig:MHatMin: 10.50.
+ Herwig:
| | beam | thrust |
| --- | --- | --- |
| official tune || |
| trial on MHatMin: 10.50 |  ||

> Remarks:
> + The result of MHatMin:10.50 is roughly equal to offical tune (where ISR is taken away), I think we can stay with the original tune. (MHatMin ~ √s/4), which better match to the Belle MC tuning.
> + To see the effect of the above tuning on the energy transfered to the virtual photon: (I print out first 50 events for below three tunes)
> + [originalTune](https://www.dropbox.com/s/z9nd48tc0ao862m/originalTune.txt?dl=0)
> + [officialTune](https://www.dropbox.com/s/0l8zdyhvym77178/officialTune.txt?dl=0)
> + [MHatMin_10.50](https://www.dropbox.com/s/rssy6czjctux9qf/MHatMin_10.50.txt?dl=0)

+ Sherpa:
| beam | thrust |
| --- | --- |
| | |

### Primary Particle Selection For All Sample
#### Belle
> Though in reco level we have limit and can only cut on Vr, (we want convince that) after efficinecy correction, it should be able to match back to the generator primary particle set ($c_{\tau}$ definition).
+ **Nominal**: (gen) $c_{\tau} < 1 cm$, (reco) $V_{r} < 1 cm$
+ **Systematics**: (gen) $V_{r} < 1 cm$, (reco) $V_{r} < 1 cm$

(To do)
1. (Check if the **nominal** definition is ok) See the gen/reco ratio.
2. Systematics: (on data) c.f. use the eff corrector from **nominal**, **systematics**

#### Generators
> First check the retention of QED events after HadronBJ skim.
1. Use $c_{\tau}$ definition to select parimary particles
2. Use reweighted-multiplicity to bin, and c.f. Belle gen/reco (corr)/data (corr)