Adding Support for (anti) Hyper-Tritons in STARSIM

Abstract: Until we develop a new Monte Carlo application based on Virtual Monte Carlo technology, starsim and geant 3 remain as our only simulation framework.  Geant 3 is a robust simulation platform, but has some limitations which measurements at STAR need to take account of.  In this blog entry I seek to outline the changes necessary to STAR's geant installation which are required to simulate hyper-tritons, and some of the limitations of the simulations based on geant 3.

1.0 Limitations of GEANT 3

Geant defines 8 seperate classes of particles.  These particles are enumerated in gstar_part.g:
   Integer kGtGAMA / 1 /! A photon                 Subroutine GtGAMA
   Integer kGtELEC / 2 /! An electron or positron  Subroutine GtELEC
   Integer kGtNEUT / 3 /! A neutral hadron         Subroutine GtNEUT
   Integer kGtHADR / 4 /! A charged hadron         Subroutine GtHADR
   Integer kGtMUON / 5 /! A muon                   Subroutine GtMUON
   Integer kGtNINO / 6 /! A geantino               Subroutine GtNINO
   Integer kGtHION / 8 /! A heavy ion              Subroutine GtHION
   Integer kGtCKOV / 7 /! A cherenkov photon       Subroutine GtCKOV
Each particle class is transported through the detector setup using the subroutine specified above.  At present, none of these particle transport codes is appropriate for the simulation of unstable nuclei, anti-nuclei or hyper-nuclei.  Heavy ions are subject to energy-loss corrections which depend on their energy.  This is simulated properly only in the GtHION routine.  However, GtHION makes two assumptions which are problematic for simulations of hyper-nuclei and anti-nuclei:
1) It assumes that all ions are stable
2) It assumes that all ions have positive charge
These limitations (and others) are noted in the geant manual entry for GtHION:
GTHION transports heavy ions (A,Z > 1, particle type 8). For the moment the only discrete processes
activated are δ-ray and Cˇherenkov photon generation.
It should be noted that there is a third limitation imposed by Geant:
3) Hadronic interactions of heavy ions with material in the detector is switched off.
In fact, STARSIM imposes this limitation in its implementation of GupHAD (asps/simulation/atmain/guphad.age). 
4) Only particles with ID < 48 are permitted to undergo hadronic interactions. 
This limits the list of heavy ions which undergo hadronic interactions to the deuteron, triton and alpha.  3He will have no interaction with detector material beyond energy loss and delta-ray production.  Likewise, the anti-nuclei defined in gstar_part.g will not undergo hadronic interactions, nor will hyper-nuclei.  (And neither will all of the particles with altered decay modes used in embedding...)  I presume this protection is in place because of limitations in the underlying hadronic response packages (gheisha, fluka, fluka+micap, gcalor).    It is not clear from reading either the geant manual or the source code whether these packages support nuclei heavier than the alpha (or 3He), or anti-nuclei.  They certainly will not have support for hyper-nuclei.

2.0 Proposed Implementation

In order to overcome some of these limitations, I propose the following modifications to STAR's installation of geant 3.
1) In order to allow GtHION to transport anti-nuclei, make the change CHARGE --> abs(CHARGE) when calculating the effective charge of the nucleus for energy loss.  Energy loss should (probably) not depend on the sign of the charge.  So I believe this will result in a correct description of energy loss for anti-nuclei.
2) A new particle class kGtHYPER will be defined, and a new tracking subroutine GtHYPER created.  GtHYPER will be based on the GtHION subroutine, with decays in flight enabled.
3) The GtHYPER subroutine should support a user-supplied hadronic interaction routine in order to study possible systematic uncertainties.
Limitations of this implementation:
1) The hadronic interaction of hypertritons in the beam pipe, HFT (once present), etc... will not be simulated.  We have no model for this,... but we can provide a user hook to enable studies for developing such a model. 
2) Geant will treat nuclei and anti-nuclei differetnly.  So the decay modes of the hyper-triton need to be simulated with care. 
3ΛH --> 3He + pi-  ==> 3He not subject to hadronic interactions
3ΛH --> d + p + pi-  ==> d and p ARE subject to hadronic interactions.  (But not anti-d in the decay of anti-3ΛH)
So there are some important asymmetries between matter and anti-matter which are built into starsim which must be kept in mind. 
--> Are they large enough given current and expected yields? <--

3.0 On the Decays of Hyper-Tritons

The decay mode 3ΛH --> 3He + pi- is straightforward to simulate.  The 3He and pi- only need to conserve E,p.  The decay mode of 3ΛH --> d + p + pi- is less straightforward.  Here, the dynamics of the decay come into play.  
Figure 6 from reference [1] indicates that the pi- daughter will take a significant amount of the available energy of the decay in the CMS frame, while the proton and deuteron will be rather slow.

--> Is it adequate to allow the hypertriton to decay into its full phase space, or do we need to implement a model for its decay? <--

4.0 References