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A monte carlo generation method with importance sampling for high energy collisions of hadrons
C-48 COMPUTER PHYSICS COMMUNICATIONS 1 (1970) 425-436. NORTH-HOLLAND PUBLISHING COMPANY
A IMPORTANCE
MONTE
CARLO
SAMPLING
GENERATION
FOR
HIGH
METHOD
ENERGY
COLLISIONS
WITH OF
HADRONS
W. KITTEL and L. VAN HOVE CERN, European Organisation f o r Nuclear R e s e a r c h , Geneva, Switzerland and
W. WOJCIK * CEN, Centre d'Etudes NuclOaires, Saclay, France
Received 18 July 1970
PROGRAM
SUMMARY
Title o f program (32 c h a r a c t e r s m a x i m u m ) : GENIS Catalogue number: AAUA Computer f o r which the program is designed and others upon which it is operable Computer: CDC 6600; all types with FORTRAN IV c o m p i l e r . Installation: CERN, Geneva, Switzerland Operating s y s t e m or monitor under which the program is executed: CERN v e r s i o n of CDC SCOPE 2.0 P r o g r a m m i n g languages used: FORTRAN IV High speed s t o r e required: 877 words. No. of bits in a word: 60 Is the program overlaid? No No. of magnetic tapes required:
None
What other peripharals are u s e d ? Card Reader; Line P r i n t e r No. of cards in combined program and test deck: 400 Keywords d e s c r i p t i v e o f problem and method o f solution: Nuclear, High Energy, Hadron, P h a s e Space. Collision, ELementary P a r t i c l e , Monte Carlo Integration, I m p o r t a n c e Sampling. R e s t r i c t e d , T r a n s v e r s e Momenta.
Nature o f physical problem
R e s t r i c t i o n s on the complexity of the problem
In the t h e o r e t i c a l a n a l y s i s of hadron collisions at high e n e r g i e s the n u m e r i c a l evaluation of i n t e g r a l s o v e r compLete p h a s e s p a c e is wasteful of c o m p u t e r time b e c a u s e e x p e r i m e n t shows that onLy a s m a l l r e gion of the i n t e g r a t i o n domain is r e l e v a n t for m o s t p h y s i c a l p u r p o s e s . T h i s region is c h a r a c t e r i s e d by s m a l l values of the t r a n s v e r s e m o m e n t a of the p a r ticles produced in the collision.
The p r o g r a m is d e s i g n e d for a n u m b e r n of outgoing p a r t i c l e s of up to 18. T h i s limit can be i n c r e a s e d e a s i l y by the u s e r if r e q u i r e d .
Method o f solution We u s e a Monte Carlo integration method with i m portance s a m p l i n g , taking as integration v a r i a b l e s the m o m e n t a of the outgoing particLes in the c e n t r e - o f m a s s s y s t e m and d i s t i n g u i s h i n g between their longitudinal and t r a n s v e r s e components. The f o r m e r i n c r e a s e with energy, the Latter grow only at low e n e r g i e s and r e m a i n essentiaLLy c o n s t a n t at high e n e r g i e s [1].
Typical running time The n u m b e r s in table 1 apply for the CDC 6600 c o m p u t e r at CERN. T h e f i r s t column gives the n u m b e r of outgoing p a r t i c l e s , the second the a p p r o x i m a t e c o m puting t i m e p e r g e n e r a t e d point for points fuLfilling the k i n e m a t i c c o n s t r a i n t (eq. (14) of long write-up). Except at low e n e r g y , p r a c t i c a l l y all g e n e r a t e d points s a t i s f y the c o n s t r a i n t . The r e s t of the table shows the p e r c e n t a g e of g e n e r a t e d points which violate it for two v a l u e s of the e n e r g y , the l a t t e r being e x p r e s s e d in t e r m s of the l a b o r a t o r y m o m e n t u m PLAB of the incident b e a m p a r t i c l e .
* O n leave from the Institute of Experimental Physics, University of Warsaw, Warsaw, Poland.
C-49 426
W. K I T T E L et at. Table 1
n 3 6 10 18
Time/point in m s e c
Pl.ABin
2 5 9 21
0.3 1.0 2.3 6.0
Unusual features of the program
p.erc.
PLABin GEV/c
pert.
25% 15% 7~o 2%
3.0 8.0 17.5 8.0
1% 1% 1% 1%
~6~/c
GENIS is a s u b p r o g r a m to be u s e d with a n y m a i n p r o g r a m f e e d i n g it with the i n f o r m a t i o n on the i n c o m i n g l a b o r a t o r y m o m e n t u m and total e n e r g y in the c e n t r e of m a s s a s welt a s the m a s s e s of i n c o m i n g a n d o u t g o i n g p a r t i c l e s . It is in p a r t i c u l a r s u i t e d to be u s e d with F O W L [2].
References [1] L. Van Hove, Nucl. P h y s . B9 0-969) 331. [2] F. J a m e s , F O W L , CERN P r o g r a m L i b r a r y (1970) W505.
A IMPORTANCE
MONTE
CARLO
SAMPLING
GENERATION
FOR
HIGH
METHOD
ENERGY
COLLISIONS
WITH OF
HADRONS
W. KITTEL and L. VAN HOVE CERN, European Organisation f o r Nuclear R e s e a r c h , Geneva, Switzerland and
W. WOJCIK * CEN, Centre d'Etudes NuclOaires, Saclay, France
Received 18 July 1970
PROGRAM
SUMMARY
Title o f program (32 c h a r a c t e r s m a x i m u m ) : GENIS Catalogue number: AAUA Computer f o r which the program is designed and others upon which it is operable Computer: CDC 6600; all types with FORTRAN IV c o m p i l e r . Installation: CERN, Geneva, Switzerland Operating s y s t e m or monitor under which the program is executed: CERN v e r s i o n of CDC SCOPE 2.0 P r o g r a m m i n g languages used: FORTRAN IV High speed s t o r e required: 877 words. No. of bits in a word: 60 Is the program overlaid? No No. of magnetic tapes required:
None
What other peripharals are u s e d ? Card Reader; Line P r i n t e r No. of cards in combined program and test deck: 400 Keywords d e s c r i p t i v e o f problem and method o f solution: Nuclear, High Energy, Hadron, P h a s e Space. Collision, ELementary P a r t i c l e , Monte Carlo Integration, I m p o r t a n c e Sampling. R e s t r i c t e d , T r a n s v e r s e Momenta.
Nature o f physical problem
R e s t r i c t i o n s on the complexity of the problem
In the t h e o r e t i c a l a n a l y s i s of hadron collisions at high e n e r g i e s the n u m e r i c a l evaluation of i n t e g r a l s o v e r compLete p h a s e s p a c e is wasteful of c o m p u t e r time b e c a u s e e x p e r i m e n t shows that onLy a s m a l l r e gion of the i n t e g r a t i o n domain is r e l e v a n t for m o s t p h y s i c a l p u r p o s e s . T h i s region is c h a r a c t e r i s e d by s m a l l values of the t r a n s v e r s e m o m e n t a of the p a r ticles produced in the collision.
The p r o g r a m is d e s i g n e d for a n u m b e r n of outgoing p a r t i c l e s of up to 18. T h i s limit can be i n c r e a s e d e a s i l y by the u s e r if r e q u i r e d .
Method o f solution We u s e a Monte Carlo integration method with i m portance s a m p l i n g , taking as integration v a r i a b l e s the m o m e n t a of the outgoing particLes in the c e n t r e - o f m a s s s y s t e m and d i s t i n g u i s h i n g between their longitudinal and t r a n s v e r s e components. The f o r m e r i n c r e a s e with energy, the Latter grow only at low e n e r g i e s and r e m a i n essentiaLLy c o n s t a n t at high e n e r g i e s [1].
Typical running time The n u m b e r s in table 1 apply for the CDC 6600 c o m p u t e r at CERN. T h e f i r s t column gives the n u m b e r of outgoing p a r t i c l e s , the second the a p p r o x i m a t e c o m puting t i m e p e r g e n e r a t e d point for points fuLfilling the k i n e m a t i c c o n s t r a i n t (eq. (14) of long write-up). Except at low e n e r g y , p r a c t i c a l l y all g e n e r a t e d points s a t i s f y the c o n s t r a i n t . The r e s t of the table shows the p e r c e n t a g e of g e n e r a t e d points which violate it for two v a l u e s of the e n e r g y , the l a t t e r being e x p r e s s e d in t e r m s of the l a b o r a t o r y m o m e n t u m PLAB of the incident b e a m p a r t i c l e .
* O n leave from the Institute of Experimental Physics, University of Warsaw, Warsaw, Poland.
C-49 426
W. K I T T E L et at. Table 1
n 3 6 10 18
Time/point in m s e c
Pl.ABin
2 5 9 21
0.3 1.0 2.3 6.0
Unusual features of the program
p.erc.
PLABin GEV/c
pert.
25% 15% 7~o 2%
3.0 8.0 17.5 8.0
1% 1% 1% 1%
~6~/c
GENIS is a s u b p r o g r a m to be u s e d with a n y m a i n p r o g r a m f e e d i n g it with the i n f o r m a t i o n on the i n c o m i n g l a b o r a t o r y m o m e n t u m and total e n e r g y in the c e n t r e of m a s s a s welt a s the m a s s e s of i n c o m i n g a n d o u t g o i n g p a r t i c l e s . It is in p a r t i c u l a r s u i t e d to be u s e d with F O W L [2].
References [1] L. Van Hove, Nucl. P h y s . B9 0-969) 331. [2] F. J a m e s , F O W L , CERN P r o g r a m L i b r a r y (1970) W505.