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A K a l ma n f i l t e r f o r t h e C M S M u o n T r i g g e r f o r R u n I I I a n d H L - L H C M i c h a l i s B a c h t i s U n i v e r s i t y o f C a l i f o

  1. A K a l ma n f i l t e r f o r t h e C M S M u o n T r i g g e r f o r R u n I I I a n d H L - L H C M i c h a l i s B a c h t i s U n i v e r s i t y o f C a l i f o r n i a , L o s A n g e l e s R e s e a r c h T e c h n i q u e s S e m i n a r F N A L , O c t . 2 3 d 2018

  2. T h e C M S L 1 T r i g g e r S y s t e m ● R e c e i v e s d a t a f r o m C a l o r i me t e r a n d M u o n D e t e c t o r s a t a r a t e o f 4 0 M H z a n d o u t p u t s d a t a a t 1 0 0 k H z ● C r e a t e s p h y s i c s o b j e c t s i n H W ( e l e c t r o n / p h o t o n s , mu o n s , j e t s , M i s s i n g e n e r g y ) D e c i s i o n t a k e n o n l y a t t h e G l o b a l T r i g g e r 2

  3. I n t r o d u c t i o n ● M u o n T r i g g e r : Wo r k h o r s e o f t h e C M S P h y s i c s p r o g r a m 7 5 % o f C M S p u b l i c a t i o n s r e l y i n mu o n t r i g g e r s t o g e t t h e d a t a o n t a p e ● F o u r o u t o f t h e “ b i g f i v e ” f l a g s h i p H i g g s a n a l y s e s – ● M u o n T r i g g e r R e q u i r e me n t s f o r t h e H L - L H C u p g r a d e T r i g g e r mu o n s f r o m e l e c t r o w e a k p r o c e s s e s w i t h a n e f f i c i e n c y > 9 5 % ● E n a b l e d i s p l a c e d mu o n t r i g g e r s t o g a i n a c c e s s t o n e w p h y s i c s mo d e l s ● Barrel Region ● U C L A F o c u s : B a r r e l M u o n T r i g g e r T r a c k ● f i n d i n g f o r H L - L H C A l r e a d y i n v o l v e d i n c u r r e n t ● B a r r e l M u o n T r i g g e r w i t h t h e E u r o p e a n g r o u p s 3

  4. C u r r e n t B a r r e l M u o n T r a c k F i n d e r ● C o n s i s t s o f 1 2 p r o c e s s o r s f e a t u r i n g a V i r t e x 7 6 9 0 T F P G A ● E � φ a c h p r o c e s s o r r e c e i v e s d a t a f r o m 5 w h e e l s i n x 3 s e c t o r s i n L e f t a n d r i g h t s e c t o r s s h a r e d i n e a c h p r o c e s s o r t o a c c o u n t f o r b o u n d a r i e s ● ● E a c h p r o c e s s o r f o r w a r d s 3 mu o n s t o t h e G l o b a l M u o n T r i g g e r ( G M T ) G M T c l e a n s o v e r l a p b e t w e e n s e c t o r s a n d t r a c k f i n d e r s a n d f o r w a r d s d a t a t o t h e ● G l o b a l t r i g g e r w h e r e d e c i s i o n i s ma d e 4

  5. T r a c k i n g i n t h e C M S b a r r e l mu o n s y s t e m φ b φ φ φ b ● F o u r s t a t i o n s : e a c h h i t w i t h p o s i t i o n () a n d b e n d i n g a n g l e ( ) 2 2 b i t s p e r s t a t i o n ( ma x i mu m 8 8 b i t s p e r t r a c k ) ● ● C Δφ u r r e n t t r a c k f i n d e r a s s i g n s mo me n t u m u s i n g t h e b e t w e e n t w o s t a t i o n s + a s s u mi n g t h e t r a c k c o me s f r o m t h e c e n t e r o f t h e d e t e c t o r ● B e a ms p o t c o n s t r a i n t i mp r o v e s r e s o l u t i o n 5

  6. B e a ms p o t c o n s t r a i n t a n d d i s p l a c e d mu o n s vertex constrained track extension decay 0-1cm 1-10cm 10-30cm real track extension 30-100cm ● Wh i l e t h e b e a ms p o t c o n s t r a i n t i mp r o v e s r e s o l u t i o n f o r p r o mp t mu o n s , i t i s s u b - o p t i ma l f o r d i s p l a c e d p a r t i c l e s M o me n t u m mi s - me a s u r e me n t r e s u l t s i n t r i g g e r i n e f f i c i e n c y ● ● D � i s p l a c e d p a r t i c l e mo d e l s v e r y p o p u l a r l a t e l y N e e d d i s p l a c e d t r i g g e r s 6

  7. A K a l ma n F i l t e r f o r B M T F P r o p a g a t e P r o p a g a t e U p d a t e U p d a t e U p d a t e I n i t i a l i z e U p d a t e P r o p a g a t e P r o p a g a t e V e r t e x C o n s t r a i n e d V e r t e x U n c o n s t r a i n e d M e a s u r e me n t M e a s u r e me n t χ 2 S e q u e n t i a l a l g o r i t h m: ( ma t h e ma t i c a l l y e q u i v a l e n t t o a f i t ) ● P r o p a g a t e t r a c k i n w a r d s f r o m s t a t i o n t o s t a t i o n a n d ma t c h w i t h a s t u b ● U p d a t e t r a c k p a r a me t e r s a n d c o n t i n u e ● � A f t e r r e a c h i n g s t a t i o n 1 s a v e me a s u r e me n t w i t h o u t v e r t e x c o n s t r a i n t ● � P r o p a g a t e t o v e r t e x a n d u p d a t e v e r t e x c o n s t r a i n e d me a s u r e me n t ● � M C h a l l e n g e f o r a n F P G A i mp l e me n t a t i o n a t r i x a l g e b r a ● 7

  8. T r a c k p r o p a g a t i o n f r o m s t a t i o n t o s t a t i o n φ φ b ● T r a c k p a r a me t e r s i n t h e mu o n s y s t e m: x = (, , k = q / p ) n T U n c e r t a i n t i e s o n p a r a me t e r s e x p r e s s e d b y a 3 x 3 c o v a r i a n c e ma t r i x P ● ● A s s u mi n g a p e r f e c t h e l i x ( P = 0 . 3 B R ) a n d a p p r o x i ma t i n g w i t h a p a r a b o l a T ( o f c o n s t a n t 1 / ( 2 R ) ) a n d c o n v e r t i n g t o t h e t r a c k p a r a me t e r s p a c e , w e g e t a l i n e a r p r o p a g a t i o n r e l a t i o n : Propagation Matrix F Propagation of uncertainties Multiple scattering ● C o n s t a n t s a , b , c d e p e n d o n B - f i e l d a n d d i me n s i o n s a n d a r e d i f f e r e n t f r o m s t a t i o n t o s t a t i o n ● E n e r g y l o s s n e g l e c t e d f o r s t a t i o n - t o - s t a t i o n p r o p a g a t i o n a n d a d d e d i n c l u s i v e l y a t t h e e n d 8

  9. P e r f o r mi n g l i n e a r a l g e b r a i n F P G A s ● U s e o f “ t r a d i t i o n a l ” l o g i c ( L U T s a n d F F s ) r e q u i r e s ma n y mu l t i p l i c a t i o n s t h a t a r e e x p e n s i v e i n F P G A r e s o u r c e s ● M o d e r n F P G A s i n c l u d e D S P c o r e s u n u s e d i n t h e c u r r e n t t r i g g e r s y s t e m P r e s e n c e o f D S P i n mo d e r n F P G A s mo t i v a t e d b y f i l t e r i n g a p p l i c a t i o n s , ma c h i n e ● l e a r n i n g , a n d mi l i t a r y s t u f f ● T h e o p e r a t i o n x + y * z c a n b e ma p p e d t o a D S P c o r e r e d u c i n g s u b s t a n t i a l l y t h e r e s o u r c e s K a l ma n f i l t e r ma t r i x a l g e b r a ma p p e d t o D S P s ● 9

  10. A d d i n g h i t s t o t h e t r a c k φ φ b ● E a c h d e t e c t o r s t u b i s a me a s u r e me n t z = (, ) n ● A r e s i d u a l i s f o r me d : Propagated track Associated Stub Matrix H ● T h e c o v . ma t r i x i s t r a n s f o r me d t o me a s u r e me n t s p a c e a n d p o s i t i o n r e s o l u t i o n i s a c c o u n t e d f o r Transformation of P Chamber Hit resolution ● F i n a l l y a w e i g h t ( K a l ma n G a i n ) i s e s t i ma t e d a n d t h e s t a t e i s u p d a t e d Kalman Gain matrix inversion... 1 0

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