CHARGE RADII AND HIGHER ELECTROMAGNETIC MOMENTS WITH LATTICE QCD IN - PowerPoint PPT Presentation

T H E 3 4 T H I N T E R N AT I O N A L S Y M P O S I U M O N L AT T I C E G AU G E T H E O R I E S U N I V E R S I T Y O F S O U T H A M P TO N , J U LY 2 4 - 3 0 , 2 0 1 6 CHARGE RADII AND HIGHER ELECTROMAGNETIC MOMENTS WITH LATTICE QCD IN NONUNIFORM BACKGROUND FIELDS Z O H R E H DAVO U D I M I T ZD and W. Detmold, Phys. Rev. D 92, 074506 (2015), ZD and W. Detmold, Phys. Rev. D 93, 014509 (2016).

E L E C T R O M A G N E T I C E F F E C T S I N S T R O N G LY I N T E R A C T I N G S Y S T E M S 1 ) D Y N A M I C A L P H O T O N S d ~ d ~ A A G A U S S ’ S L A W + P E R I O D I C I T Y ? Lucini, et, al., JHEP02(2016)076. Hayakawa and Uno, Prog. Theor. Phys. 120, 413 (2008) Endres, et, al., to appear in PRL, arXiv: ZD, M. J. Savage, Phys. Rev. D 90, 054503 (2014) 1507.08916 [hep-lat]. Borsanyi, et al., Science 347:1452-1455 (2015).

E L E C T R O M A G N E T I C E F F E C T S I N S T R O N G LY I N T E R A C T I N G S Y S T E M S 2 ) C L A S S I C A L E L E C T R O M A G N E T I S M d ~ d ~ A A B A C K G R O U N D F I E L D S + P E R I O D I C I T Y G. ’t Hooft, Nuclear Physics B 153, 141 (1979). J. Smit and J. C. Vink, Nucl.Phys. B286, 485 (1987). M. Al-Hashimi and U.-J. Wiese, Annals Phys. 324, 343 (2009).

S O M E R E C E N T S TAT E - O F - T H E - A R T A P P L I C AT I O N S F R O M L AT T I C E Q C D np → d γ Images by W. Detmold Beane, at al. [NPLQCD collaboration], Phys. Rev. Lett. 115, 132001 (2015).

S O M E R E C E N T S TAT E - O F - T H E - A R T A P P L I C AT I O N S F R O M L AT T I C E Q C D np → d γ A N E F F E C T I V E F I E L D T H E O RY R E S U LT Beane and Savage, Nucl.Phys. A694, 511 (2001). .2 � N E E D S L AT T I C E Q C D I N P U T L di ackgr .1 / 51 π L 1 .0 � Beane, at al. [NPLQCD collaboration], Phys. Rev. Lett. 115, 132001 (2015).

S O M E R E C E N T S TAT E - O F - T H E - A R T A P P L I C AT I O N S F R O M L AT T I C E Q C D np → d γ S E T U P A B A C K G R O U N D M A G N E T I C F I E L D Detmold and Savage, Nucl.Phys. A743, 170 (2004). Beane, at al. [NPLQCD collaboration], Phys. Rev. Lett. 115, 132001 (2015).

M O R E P H Y S I C S W I T H B A C K G R O U N D F I E L D S ? 1 ) E M C H A R G E R A D I U S =================================================== 2 ) E L E C T R I C Q U A D R U P O L E M O M E N T A. 4 ) A X I A L B A C K G R O U N D F I E L D S 3 ) F O R M FA C T O R S n p p p e + ν e Detmold, Phys.Rev. D71, 054506 (2005)

I M P L E M E N TAT I O N O F U ( 1 ) B A C K G R O U N D G A U G E F I E L D S O N A P E R I O D I C H Y P E R C U B I C L AT T I C E ZD and W. Detmold, Phys. Rev. D 92, 074506 (2015)

P E R I O D I C I M P L E M E N TAT I O N O F N O N U N I F O R M B A C K G R O U N D F I E L D S ✓ ◆ − E 0 h x 3 i L ) 2 , 0 A µ = 2 ( x 3 − E = E 0 x 3 ˆ x 3 → L ( T, L ) U = e ie ˆ R Q A µ ( z ) dz µ ( T, 0) (0 , 0) x 3 1 t

P E R I O D I C I M P L E M E N TAT I O N O F N O N U N I F O R M B A C K G R O U N D F I E L D S ✓ ◆ − E 0 h x 3 i L ) 2 , 0 A µ = 2 ( x 3 − E = E 0 x 3 ˆ x 3 → L ( T, L ) U = e ie ˆ R Q A µ ( z ) dz µ ( T, 0) (0 , 0) x 3 1 e − ie ˆ t QE 0 a t / 2

P E R I O D I C I M P L E M E N TAT I O N O F N O N U N I F O R M B A C K G R O U N D F I E L D S ✓ ◆ − E 0 h x 3 i L ) 2 , 0 A µ = 2 ( x 3 − E = E 0 x 3 ˆ x 3 → L ( T, L ) U = e ie ˆ R Q A µ ( z ) dz µ ( T, 0) (0 , 0) x 3 1 e − ( L − a s ) 2 ie ˆ e − ie ˆ QE 0 a t / 2 t QE 0 a t / 2

P E R I O D I C I M P L E M E N TAT I O N O F N O N U N I F O R M B A C K G R O U N D F I E L D S ✓ ◆ − E 0 h x 3 i L ) 2 , 0 A µ = 2 ( x 3 − E = E 0 x 3 ˆ x 3 → L ( T, L ) 1 U = e ie ˆ R Q A µ ( z ) dz µ 1 ( T, 0) (0 , 0) x 3 1 e − ( L − a s ) 2 ie ˆ e − ie ˆ QE 0 a t / 2 t QE 0 a t / 2

P E R I O D I C I M P L E M E N TAT I O N O F N O N U N I F O R M B A C K G R O U N D F I E L D S ✓ ◆ − E 0 h x 3 i L ) 2 , 0 A µ = 2 ( x 3 − E = E 0 x 3 ˆ x 3 → L ( T, L ) 1 = e ie ˆ QE 0 a t a s / 2 1 ( T, 0) (0 , 0) x 3 1 e − ( L − a s ) 2 ie ˆ e − ie ˆ QE 0 a t / 2 t QE 0 a t / 2

P E R I O D I C I M P L E M E N TAT I O N O F N O N U N I F O R M B A C K G R O U N D F I E L D S ✓ ◆ − E 0 h x 3 i L ) 2 , 0 A µ = 2 ( x 3 − E = E 0 x 3 ˆ x 3 → L ( T, L ) 1 = e ie ˆ QE 0 a t a s / 2 1 ( T, 0) (0 , 0) x 3 1 e − ( L − a s ) 2 ie ˆ e − ie ˆ QE 0 a t / 2 t QE 0 a t / 2

P E R I O D I C I M P L E M E N TAT I O N O F N O N U N I F O R M B A C K G R O U N D F I E L D S ✓ ◆ − E 0 h x 3 i L ) 2 , 0 A µ = 2 ( x 3 − E = E 0 x 3 ˆ x 3 → L P E R I O D I C B C ( T, L ) 1 = e ie ˆ QE 0 a t a s / 2 1 ( T, 0) (0 , 0) x 3 1 e − ( L − a s ) 2 ie ˆ e − ie ˆ QE 0 a t / 2 t QE 0 a t / 2

P E R I O D I C I M P L E M E N TAT I O N O F N O N U N I F O R M B A C K G R O U N D F I E L D S ✓ ◆ − E 0 h x 3 i L ) 2 , 0 A µ = 2 ( x 3 − E = E 0 x 3 ˆ x 3 → L P E R I O D I C B C M O D I F I E D L I N K ( T, L ) × e − ie ˆ QE 0 L 2 t/ 2 1 = e ie ˆ QE 0 a t a s / 2 1 ( T, 0) (0 , 0) x 3 1 e − ( L − a s ) 2 ie ˆ e − ie ˆ QE 0 a t / 2 t QE 0 a t / 2

P E R I O D I C I M P L E M E N TAT I O N O F N O N U N I F O R M B A C K G R O U N D F I E L D S ✓ ◆ − E 0 h x 3 i L ) 2 , 0 A µ = 2 ( x 3 − E = E 0 x 3 ˆ x 3 → L P E R I O D I C B C M O D I F I E D L I N K ( T, L ) × e − ie ˆ QE 0 L 2 t/ 2 1 = e ie ˆ QE 0 a t a s / 2 1 ( T, 0) (0 , 0) x 3 1 e − ( L − a s ) 2 ie ˆ e − ie ˆ QE 0 a t / 2 t QE 0 a t / 2

P E R I O D I C I M P L E M E N TAT I O N O F N O N U N I F O R M B A C K G R O U N D F I E L D S ✓ ◆ − E 0 h x 3 i L ) 2 , 0 A µ = 2 ( x 3 − E = E 0 x 3 ˆ x 3 → L P E R I O D I C B C e ie ˆ QE 0 L 2 T/ 2 = 1 M O D I F I E D L I N K ( T, L ) × e − ie ˆ QE 0 L 2 t/ 2 1 = e ie ˆ QE 0 a t a s / 2 1 ( T, 0) (0 , 0) x 3 1 e − ( L − a s ) 2 ie ˆ e − ie ˆ QE 0 a t / 2 t QE 0 a t / 2

P E R I O D I C I M P L E M E N TAT I O N O F N O N U N I F O R M B A C K G R O U N D F I E L D S ✓ ◆ − E 0 h x 3 i L ) 2 , 0 A µ = 2 ( x 3 − E = E 0 x 3 ˆ x 3 → L P E R I O D I C B C e ie ˆ QE 0 L 2 T/ 2 = 1 M O D I F I E D L I N K ( T, L ) × e − ie ˆ QE 0 L 2 t/ 2 1 4 π n E 0 = e ˆ QL 2 T Q U A N T I Z AT I O N C O N D I T I O N F O R T H E S L O P E O F T H E F I E L D = e ie ˆ QE 0 a t a s / 2 1 ( T, 0) (0 , 0) x 3 1 e − ( L − a s ) 2 ie ˆ e − ie ˆ QE 0 a t / 2 t QE 0 a t / 2

P E R I O D I C I M P L E M E N TAT I O N O F N O N U N I F O R M B A C K G R O U N D F I E L D S E = E 0 x 3 ˆ x 3 N E U T R A L P I O N C O R R E L AT I O N F U N C T I O N C ( x 3 , τ ) ⌘ log C ( x 3 , τ + 1) , No modified links - Quantized No modified links - Nonquantized x (src) = 9 - 2.0 3 BOUNDARY - 2.1 - 2.2 - 2.3 - 2.4 11 3 5 6 7 8 9 10 0 1 2 4 x 3 − x (src) 3

P E R I O D I C I M P L E M E N TAT I O N O F N O N U N I F O R M B A C K G R O U N D F I E L D S E = E 0 x 3 ˆ x 3 N E U T R A L P I O N C O R R E L AT I O N F U N C T I O N C ( x 3 , τ ) ⌘ log C ( x 3 , τ + 1) , Modified links - Quantized Modified links - Nonquantized x (src) = 9 - 2.0 3 BOUNDARY - 2.1 - 2.2 - 2.3 - 2.4 2 4 6 8 10 12 11 3 5 6 7 8 9 10 0 1 2 4 x 3 − x (src) 3

P E R I O D I C I M P L E M E N TAT I O N O F N O N U N I F O R M B A C K G R O U N D F I E L D S M O D I F I E D L I N K S Y ( x ) × e ie ˆ e ie ˆ Q [ A ν ( x µ =0 ,x ν ) � e A ν ( x µ = L µ ,x ν ) ] f µ, ν ( x ν ) ⇥ δ xµ,Lµ − aµ U ( QCD ) ( x ) → U ( QCD ) QA µ ( x ) a µ × µ µ ν 6 = µ i W I T H L I N K F U N C T I O N S S AT I S F Y I N G h i h i A ν ( x µ = 0 , x ν + a ν ) − e A ν ( x µ = 0 , x ν ) − e A ν ( x µ = L µ , x ν + a ν ) f µ, ν ( x ν + a ν ) = A ν ( x µ = L µ , x ν ) ( f µ, ν ( x ν ) + a ν ) h . W. Detmold, Phys.Rev. D71, 054506 (2005) Q U A N T I Z AT I O N C O N D I T I O N S 2 3 " L ν � a ν # L µ � a µ Y Y e � ie ˆ e ie ˆ Q [ A µ ( x µ ,x ν =0) � e A µ ( x µ ,x ν = L ν ) ] a µ Q [ A ν ( x µ =0 ,x ν ) � e A ν ( x µ = L µ ,x ν ) ] a ν 4 5 = 1 . x µ =0 x ν =0 C H A R G E R A D I U S - Q U A D R U P O L E M O M E N T L I N E A R LY VA RY I N G F I E L D S O S C I L L AT O RY F I E L D S F O R M FA C T O R S VA R I O U S S PA C E / T I M E D E P E N D E N C E S P I N P O L A R I Z A B I L I T I E S O F N U C L E O N S

P E R I O D I C I M P L E M E N TAT I O N O F N O N U N I F O R M B A C K G R O U N D F I E L D S ✓ ia ◆ O S C I L L AT O RY F I E L D S → E = ae iq 3 x 3 ˆ e iq 3 x 3 , 0 , 0 , 0 A µ = ( A 0 , − A ) = x 3 q 3 P E R I O D I C B C e − e ˆ q 3 (1 − e iq 3 L ) T = 1 Qa M O D I F I E D L I N K ( T, L ) 1 × e − e ˆ q 3 (1 − e iq 3 L ) t Qa q 3 = 2 π n L Q U A N T I Z AT I O N C O N D I T I O N F O R T H E F R E Q U E N C Y O F T H E F I E L D As in: Bali and Endrodi, PhysRevD.92.054506 O R 1 Q U A N T I Z AT I O N C O N D I T I O N F O R T H E A M P L I T U D E O F T H E F I E L D ( T, 0) (0 , 0) a (Im) = π q 3 n 0 , a 1 e ˆ QT e − e ˆ q 3 e iq 3 a t e − e ˆ Qa Qa ( L − as ) e iq 3 a t x 3 q 3 sin( q 3 L ) , a (Re) = − 1 − cos( q 3 L ) a (Im) t