Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://acat02.sinp.msu.ru/presentations/abdullin/acat2002.pdf Äàòà èçìåíåíèÿ: Mon Jul 15 00:06:53 2002 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 20:21:48 2012 Êîäèðîâêà:

GENETIC ALGORITM FOR SUSY TRIGGER OPTIMIZATION

S. Abdullin
University of Maryland ITEP (Moscow)

S.Abdullin, UMD

Genetic Algorithm for SUSY Trigger Optimization in CMS

ACAT'2002, June 24-28, 2002

1


OUTLINE
SUSY signal : with/without R-parity violation Trigger calculation basics What to optimize ? L1 and L2 triggers - how to optimize ? The genetics algorithm used L1 results L2 results Summary
S.Abdullin, UMD Genetic Algorithm for SUSY Trigger Optimization in CMS ACAT'2002, June 24-28, 2002

2


SUSY : mSUGRA MODEL

Multijet + (leptons) + E

miss T

events

Both with/without R-parity violation ... The simplest and most challenging case of R-parity violation is considered :
M
SUSY

~ 350-400 GeV (Tevatron II reach) ("preferred" )



0 1

3 quarks

tan = 10

one might expect 6 additional jets ?

µ > 0 - does not play a big role,
though positive one is favoured by g-2 "indirect" constraint - anomaluos magnetic momentum of muon
S.Abdullin, UMD Genetic Algorithm for SUSY Trigger Optimization in CMS

ACAT'2002, June 24-28, 2002

3


WHERE THE TEVATRON II REACH ENDS ...
H.Baer et al., hep-ph/9802441; Phys.Rev.D58:075008, 1998
m1/2 (GeV)
600 550 500 450 400 350 300 250 200 150 100 0 100
¦ ¨

TH exluded
~ m( ) ~ 1 = m( 0 1)
¤

A 0 = 0 , tan = 10 , µ > 0
h(118)
~
¢

uL (1000)
g(1000)
~

m( g
m(

5
§

h(110)

S. Abdullin 18/04/2002

4

Require Ldt < 10 pb (low luminosity LHC run)
S.Abdullin, UMD Genetic Algorithm for SUSY Trigger Optimization in CMS

-1



¸

¥

¤

¡

0 1

) = 70 GeV

m( h ) = 110 GeV m( u L ) = 410 GeV

) = 466 GeV




4
h(115)

~ 181 pb

tau-enriched, quite enough sleptons

20,190
0 1

uL (500)

~

m(

t

1)

= 281-296 GeV !
g(500)
~

m( g
m(

) = 66 GeV

m( h ) = 110 GeV m( u L ) = 415 GeV nothing special

) = 447 GeV




5

~ 213 pb

6

150,180
0 1

200

300

400

500

600

m0 ( GeV)

m( g
m(

) = 45 GeV

m( h ) = 106 GeV

) = 349 GeV


6

~ 500 pb

q

g

m( u L ) = 406 GeV + X, g





3 body,

300,130

more jets, less MET
4

ACAT'2002, June 24-28, 2002


THE SAME 3 PROBING POINTS, BUT WITH R-PARITY
The same 3 "Tevatron reach" points underwent a "sugrery" with the help of ISAJET 7.51 ISAWIG 1.104 HERWIG 6.301 to eventually acquire R-parity broken : Points
4R 5R 6R

MET shrinks (no 0 ) but not completely 1 copious b-jet production (lightest stop and sbottom) + 0 - 2 () for tan > 5 increasing couplings : 1 W's from both top and sparticle decays Additional jets are expected to be rather soft ... m( 0 ) = 45-70 GeV 1
S.Abdullin, UMD Genetic Algorithm for SUSY Trigger Optimization in CMS ACAT'2002, June 24-28, 2002

+X

5


MISSING ET @ L2 TRIGGER
Arbitrary units
225 200 175 150 125 100 75 50 25 0 0 200 400
miss T Mean 171.9

250 200 150 100 50 0

Mean

158.6

300 250 200 150 100 50

Mean

99.59

4

5

6

600

0

200

400
miss T

600

0

0

200

400

E

(GeV)
74.55

E
600 500 400 300
Mean

(GeV)
59.12

E
700 600 500 400 300 200 100
Mean

miss T

(GeV)
46.45

Arbitrary units

500 400 300 200

Mean

4R

5R

6R

200 100 0 100 0 200 400
miss T

600

0

0

200

400
miss T

600

0

0

200

400

E
S.Abdullin, UMD

(GeV)

E

(GeV)

E

miss T

(GeV)
6

Genetic Algorithm for SUSY Trigger Optimization in CMS

ACAT'2002, June 24-28, 2002


NUMBER OF JETS @ L2
Arbitrary units
600
Mean 4.556

600
Mean 4.823

600
Mean 5.318

500 400 300 200 100 0

4

500 400 300 200 100

5

500 400 300 200 100

6

E

jet T

> 30 GeV

012345678911111 01234

0

012345678911111 01234

0

012345678911111 01234

N
Mean

jet

N
600
Mean

jet

N
600
Mean

jet

Arbitrary units

600
5.944

6.031

5.799

500 400 300 200 100 0

4R

500 400 300 200 100

5R

500 400 300 200 100

6R

012345678911111 01234

0

012345678911111 01234

0

012345678911111 01234

N
S.Abdullin, UMD

jet

N

jet
ACAT'2002, June 24-28, 2002

N

jet
7

Genetic Algorithm for SUSY Trigger Optimization in CMS


L2 DISTRIBUTIONS : LEADING JETS
Arbitrary units
0.2 0.2 0.2

4
0.15 0.15

2d jet

5
0.15

6

0.1

0.1

1st jet

0.1

0.05

0.05

0.05

0

0

200

400

600
jet T

800

0

0

200

400

600
jet T

800

0

0

200

400

600
jet T

800

E

(GeV)
0.2

E

(GeV)
0.2

E

(GeV)
6R

Arbitrary units

0.2

4R
0.15 0.15

5R
0.15

~ no big difference
0.1 0.1 0.1

0.05

0.05

0.05

0

0

200

400

600
jet T

800

0

0

200

400

600
jet T

800

0

0

200

400

600
jet T

800

E
S.Abdullin, UMD

(GeV)

E

(GeV)

E

(GeV)
8

Genetic Algorithm for SUSY Trigger Optimization in CMS

ACAT'2002, June 24-28, 2002


TRIGGER CALCULATION BASICS ...
Trigger is a multi-level selection (L1, L2, L3, L4) of the data to be stored on the tape L1 - essentially hardwared (programmable) selection L2 - mostly software-based ... 32 MHz L1 pp bunch crossing rate 2 kHz 3 Hz L2 L3

}

jets + missing ET channels

Low luminosity is considerd (first year of the LHC operation) 2 *10
33

cm s

-2

-1

( 2 Hz*nb )

Background samples analysed (PYTHIA + CMSIM + ORCA + ...) (full detector simulation and reconstruction) :
6 QCD di-jets : 55 mb @ LHC ~ 10 ev (in 22 ^ bins) p T 5 Wj (W ) : 4.7 nb ( * Br for p T > 30 GeV) ~ 1.5 *10 ev 4 t t : 0.8 nb ~ 4.6 *10 ev
S.Abdullin, UMD Genetic Algorithm for SUSY Trigger Optimization in CMS ACAT'2002, June 24-28, 2002

9


WHAT WE ARE TRYING TO OPTIMIZE ?
L1 and L2 trigger cuts to get maximal signals efficiency need to cope with a variety of possibilities ... @ given maximal signal + background rate
5
200 180 160 140 120 100 80 60 40 20 0
© ©

Signal efficiency
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
© © © © © © © © © ©

6R
©

QCD rate (Hz)
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
© © © © © © © © ©

miss T

miss T

miss T

120 100


120 1.0 10


E

E

E

100


1.0 10

80


80 60 40 20

60 40 20 0 200


0

100


200


300

50


100 150 200 250


400


600

800

0


200


400

miss T

miss T

miss T

120 100


120 1.0 10


E

E

E

100


1.0 10
S. Abdullin 25/04/2002

80


80 60 40
"

60 40
"

S. Abdullin 24/04/2002

S. Abdullin 24/04/2002

20 0


20 100 200
T

0


50

100


150

50


100

150

300

0


T

S.Abdullin, UMD

Genetic Algorithm for SUSY Trigger Optimization in CMS

ACAT'2002, June 24-28, 2002





Jet 3 E

(GeV)





Jet 3 ET (GeV)


Jet 4 ET (GeV)

Jet 4 ET (GeV)

Jet 3 E

(GeV)

Jet 4 ET (GeV)



©



©



©



©

0


50

100

150

50

100

150

0

0

50

100

150

200



0.1



#

©

©

©

©

©

©

©

©

©

©

©

©

©

©

©

%









©

%









©

©

©

©

©

©

©

©

©

©







©

©









©

200 180 160 140 120 100 80 60 40 20 0
©

200 180 160 140 120 100 80 60 40 20 0 200 0

(GeV)

(GeV)

(GeV)



Jet 1 ET (GeV)


Jet 2 ET (GeV)
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 100 90 80 70 60 50 40 30 20 10 0

Jet 1 E

T

(GeV)
100 90 80 70 60 50 40 30 20 10 0 200 0

Jet 2 ET (GeV)
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 160 140

Jet 1 E

T

(GeV)
160 140

Jet 2 ET (GeV)
0.1 10 10 10 10 10 10 1 10 10 10
6 5 4 3 2



©





©



©



©

0

100


200

300

50


100 150 200 250

0

0

600



0.1



©

©

©

©

©

%



$





"





©

%



$





"







200 180 160 140 120 100 80 60 40 20 0 400 0
© ©

100 90 80 70 60 50 40 30 20 10 0

100 90 80 70 60 50 40 30 20 10 0 400 0

(GeV)

(GeV)

(GeV)

160 140

160 140 0.1

10 10 10 10 10 10 10 1 10 10 10

!

7 6 5 4 3 2

-1 -2 -3

-1 -2 -3

10


L1 AND L2 CUTS
notations

L1 :

Jet1 || Jet2 || Jet3 || Jet4 (L1A) (L1A) || (Jet1 && MET) (L1B) (L1B) || MET (L1C) (Jet1 (L2A) (L2A) (L2C)

JetN : E T > cutN MET : missing E T > cut

jetN

L2 :

&& MET) || (Jet2 && MET) || (Jet3 && MET) || (Jet4 && MET) (L2A) && (Jet1,Jet2) (L2B) || Jet1 || Jet2 || Jet3 || Jet4 (L2C) || ( (Jet1,Jet2) &&(L2C)) (L2D)

L1 and L2 jets and MET differ since calculated out of different quantities raw @ L1 finer @ L2

S.Abdullin, UMD

Genetic Algorithm for SUSY Trigger Optimization in CMS

ACAT'2002, June 24-28, 2002

11


TRIGGER PARAMETER COMBINATIONS
N param. L1A L1B L1C 4 6 7 N combin. 1.6 * 10 6.0 * 10 1.3 * 10 ~1012 ~1013 ~1017 ~1035
S.Abdullin, UMD

Time (s) Total time 0.5 -"-"~ 1 day ~ 1 year ~ 20 years

5 5 6

L2A L2B L2C L2D

9 10 13 27

0.1 -"-"-"-

~ 1000 years ~ 10000 years ~ 107 years ~ 1026 years

Range of 20 (integer) bins is assumed Pentium III, 650 MHz
10 Age of the Universe ~ 1.5 * 10 years
ACAT'2002, June 24-28, 2002

Genetic Algorithm for SUSY Trigger Optimization in CMS

12


ALGORITHM (I)
"Society of individuals" with a fixed-size population ~ 100-1000 Each individual is characterized by its own unique combination of parameters ("genes") P - cuts listed earlier. Hierarchy is established according to evaluation function F(P) B1
S
& &

P F(P)

= S eff (P) -

W R max - R(P) B

R(P) < R max R(P) > R max _

(1)
F B
1

Fmax R
max

R(P)

P F(P)

= S eff (P) - R(P)
2

(2)

P S

eff (P) - weighted sum of all signal efficiencies W - tunable wieght which controls the closeness of the current rate R(P) to the maximal rate R max
Genetic Algorithm for SUSY Trigger Optimization in CMS ACAT'2002, June 24-28, 2002

F

B

2

S.Abdullin, UMD

13


ALGORITHM (II)
creation breeding - random - random crossover of genes ("uniform") between two parents, offspring is added, parents retained; - probability to participate ~ place in the hierarchy. - randomly chosen individuals undergo a random change of a random gene by one bit ("up/down"); - mutation probability is significant (10-100 %); - initial individual retained, the result of mutation added.

"Behaviour" functions defined :

mutation

selection

- after breeding and mutation, clones are removed (replaced with newly created individuals); - desc. ordering according to the evaluation function; - removal of redundant individuals; - "Top 10" separate list update (if any); cataclysmic - complete random renewal of the population (not "Top 10"), update except the best individual; - applied in case of stagnation (50-100 gener.) a few times
Genetic Algorithm for SUSY Trigger Optimization in CMS ACAT'2002, June 24-28, 2002

S.Abdullin, UMD

14


ALGORITHM (III)
"Hybrid" algorithm (written from scratch) not binary coding of a problem, rather finite alphabet some ideas (parents retained) from GENITOR cataclysmic update from CHC algorithm some improvization : probability to enter crossover ~ to hierarchy Some parameters were varied to get the best evolution size of population (crucial for CPU time comsumption) mutation probability (-"-) stagnation period (in number of generations) CPU time estimates : a few CPU hours (~ 10 generations) with 100 individuals at 10 % mutation rate, with 5 cataclysmic updates, maximum 50 % probability to participate in crossover, 21 genes with total grid size of 1025 combinations ...
S.Abdullin, UMD Genetic Algorithm for SUSY Trigger Optimization in CMS ACAT'2002, June 24-28, 2002

3

15


L1 RESULTS
Jets and missing E
T

cuts (GeV) for optimal signal effficiency @ L1

J1 Cuts (GeV) signal efficiency (%) Point Point Point 4 5 6 150 79 (79) 81 (81) 66 (66) 88 (88) 87 (87) 71 (71)

J3 55 87 (60) 88 (65) 80 (68) 94 (89) 95 (90) 88 (84)

J1 + MET 70 + 60 93 (83) 92 (83) 84 (62) 94 (54) 95 (44) 88 (32)

L1B trigger

Point 4R Point 5R Point 6R

Algorithm found other cuts insignificant (pushing them to quite high values)

Background rate (kHz)

QCD tt W j (l )

0.78 (0.78)

1.63 (1.06)

2.05 (0.54)

}

irrelevant !

S.Abdullin, UMD

Genetic Algorithm for SUSY Trigger Optimization in CMS

ACAT'2002, June 24-28, 2002

16


L2 RESULTS
L1B + L2D trigger
(J1,J2) < 160
MET
signal efficiency w.r.t. L1 (%)
o

J3 & MET J4 & MET 80 + 110 61 (33) 56 (34) 32 (24) 18 (17) 10 (10) 6 (5) 100 + 40 62 (9) 59 (10) 38 (12) 28 (16) 23 (16) 13 (10)

MET 110 76 (65) 72 (60) 48 (35) 31 (15) 25 (9) 14 (4)

J2 & MET J4 & MET 90 + 100 78 (51) 74 (52) 51 (31) 33 (16) 25 (9) 15 (5) 60 + 80 79 (19) 76 (23) 54 (21) 36 (16) 28 (12) 17 (7)

L2 rate (Hz)

Cuts (GeV) Point Point Point 4 5 6

170 50 (50) 43 (43) 17 (17) 6 (6) 3 (3) 2 (2)

0.26 0.30 0.46 0.12 0.11 0.15

Point 4R Point 5R Point 6R

Background rate (Hz)

QCD tt W j (l )

0.29 (0.29) 0.73 (0.51) 1.79 (1.12)

2.0 (0.44) 2.14 (0.41) 2.37 (0.50) 0.12 0.17

+


Genetic Algorithm for SUSY Trigger Optimization in CMS

2.67

S.Abdullin, UMD

ACAT'2002, June 24-28, 2002

17


SUMMARY
LHC "starting" low-mass scale (low luminosity reach) mSUGRA points w/wo R-parity violation are considered

L1 and L2 trigger cuts optimized for given bandwidths with hybrid genetic algorithm

Various cuts tested (including global variables) Sum ET seems to be ineffective @ L1 Similar Meff cut -"@ L2

Obtained combination of cuts is a compromise to cope with a variety of possible SUSY scenarios ...

S.Abdullin, UMD

Genetic Algorithm for SUSY Trigger Optimization in CMS

ACAT'2002, June 24-28, 2002

18


APPENDIX
Rate / bin (arbitrary units)
0.4 3 jets (ET > 30 GeV)
1

200
'

0.2

100

0

1
)

2

3

0

1
)

2

(Jet1,Jet2)
4
4 (

(Jet1,Jet2)

Rate / bin (arbitrary units)

0.8
'

0.6
'

3 2 1
2 '

0.4
'

0.2
'

Rate / bin (arbitrary units)

2
7

60 40 20
' 4

1
3

0

1

2

3

0

1

2

(Jet1,Jet2)
Genetic Algorithm for SUSY Trigger Optimization in CMS

(Jet1,Jet2)
ACAT'2002, June 24-28, 2002

S.Abdullin, UMD

(

'

(

'

0

0

3

S. Abdullin 23/04/2002

9

8

tt : no cuts
6

-

80

mSUGRA : point 5

)

(Jet1,Jet2)
)

2

2

0

1

2

3

0

1

2

(Jet1,Jet2)

(

3

'

(

3

'

0

0

5

QCD : E
1

miss T

> 100 GeV

Wj : W ¡ l

(

'

(

0

'

0

0

1

QCD : no cuts
'

0

'

0

300

QCD : E

miss T

'

'

'

(

> 50 GeV
jet

3

3

A1