**From:** Alfredo Ferrari (*alfredo.ferrari@cern.ch*)

**Date:** Thu Jun 19 2003 - 17:38:07 CEST

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Hi Graham

I include below the explanation from the manual together with some extra

comment to clarify the LAM-BIAS behaviour with GDECAY:

WHAT(1) < 0.0 : the mean DECAY LENGTH (in cm) of the particle in the

LABORATORY frame is set = |WHAT(1)| if smaller than

the physical decay length (otherwise it is left

unchanged). At the decay point sampled according to

the biased probability, Russian Roulette (i.e.

random choice) decides whether the particle actually

will survive or not after creation of the decay

products. The latter are created in any case and

their weight adjusted taking into account the ratio

between biased and physical survival probability.

* > 0.0 : the mean DECAY LENGTH (in cm) of the particle in the
*

LABORATORY frame is set = WHAT(1) if smaller than

the physical decay length (otherwise it is left

unchanged). At the decay point sampled according to

the biased probability, the particle always survives

with a reduced weight. Its daughters are given the

same weight.

Comments:

last line (Its daughters are given the same weight) should be substituted

by "Its daughters are given the same weight as for what(1) > 0.0"

The decay point is really selected according to the biased distribution

but this is correct since both parent and daughter weights are set

properly. In particular, consider a muon with 100 km decay length and

a biased one of 100 m. It will "decay" on average after 100 m, the

daughters having weight 1/1000 and the parent having weight 1 - 1/1000

(what(1) < 0) or having weight 1 999 out of 1000 decays, while dying

(zero weight) in 1 out of 1000 decays. Next after (on average) an extra

100 m it will decay again with the same algorithm (now starting from the

current parent weight, ie 999/1000 in the waht(1) < 0 case). As you can

easily check, both the muon flux and the daughter one are perfectly

ok and in particular the former is attenuating according to exp(-x/100 km)

as expected. If you want, this is a sort of stratified sampling, for

dX = |what(1)| << physical lamda, every dX you produce decay

products with dX/lamda x original weight, and you remove dX/lamda x

original weight muons, which is exactly what the differential equation for

the decay is dictating. With this algorithm you do not need to force

to have more than one decay per step, simply you choose the biased decay

length as short as it is comfortable for your problem and that's all.

We applied it to a variety of problems, ranging from nToF, to WANF and

later CNGS and to atmospheric muons, always with great success (and no

bias in the results). Let me know if the explaination is understandable,

and if it can fit your needs!

Ciao

Alfredo

On Thu, 19 Jun 2003, Graham Roger Stevenson wrote:

*>
*

*> Greetings
*

*>
*

*> 2 questions linked with MUON production
*

*>
*

*> 1. In the GDECAY option of LAM-BIAS for WHAT(1)>0.0 the manual says:
*

*> "At the decay point sampled according to the biased probability..."
*

*> Surely the point of decay should be sampled according to the UNBIASED
*

*> decay length. Take the example of a 100 GeV pion step between
*

*> interactions of 100cm where the decay length is about 55 km. The decay
*

*> points are part of a uniform distribution over the 100 cm. If you force
*

*> the day length to be 1 cm and sample the decay points from the biased
*

*> probability then you will force the decay point to be in the first few cm
*

*> of the step. Generally this will be unimportant given the usual
*

*> dimensions of 10-100m in a muon problem, but please could you check what
*

*> is in fact written in the code (and not in the manual!)
*

*>
*

*> 2. Coupled with this, I would like to create more than one muon per parent
*

*> step. Now I can pick up the "death" of the pion or kaon from the STACK
*

*> common at the time of a call to USRSCS in GEODEN, but where can I find
*

*> it's "birth coordinates". There is an index NEVENT in STACK which is the index
*

*> of the event which created the particle but which common block contains
*

*> the details (position etc) of the event itself?
*

*>
*

*> Many thanks
*

*> Graham
*

*>
*

*>
*

-- +----------------------------------------------------------------------------+ | Alfredo Ferrari || Tel.: +41.22.767.6119 | | CERN-AB || Fax.: +41.22.767.7555 | | 1211 Geneva 23 || e-mail: Alfredo.Ferrari@cern.ch | | Switzerland || Alfredo.Ferrari@mi.infn.it | +----------------------------------------------------------------------------+

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