from exact asymptotic safety to physics beyond the Standard Model - PowerPoint PPT Presentation

from exact asymptotic safety to physics beyond the Standard Model Daniel F Litim Heidelberg, 9 Mar 2017 DF Litim 1102.4624 DF Litim, F Sannino, 1406.2337 AD Bond, DF Litim, 1608.00519 AD Bond, G Hiller, K Kowalska, DF Litim, 1702.01727

standard model local QFT for fundamental interactions strong nuclear force weak force electromagnetic force open challenges what comes beyond the SM? how does gravity fit in?

asymptotic safety idea: some or all couplings achieve Wilson ’71 interacting UV fixed point Weinberg ’79 if so, new directions for BSM physics &, possibly, quantum gravity proof of existence: 4D gauge-Yukawa theory with Litim, Sannino, 1406.2337 exact asymptotic safety Bond, Litim @ERG2016

asymptotic safety today: 1. theorems for asymptotic safety Bond, Litim 1608.00519 2. weakly interacting UV completions of the Standard Model 3. constraints from data (colliders) AD Bond, G Hiller, K Kowalska, DF Litim, 1702.01727

asymptotic safety today: 1. theorems for asymptotic safety Bond, Litim 1608.00519 2. weakly interacting UV completions of the Standard Model 3. constraints from data (colliders) AD Bond, G Hiller, K Kowalska, DF Litim, 1702.01727

conditions for asymptotic safety results Bond, Litim 1608.00519 *) *) *) provided certain auxiliary conditions hold true

basics of asymptotic safety gauge Yukawa theory theory ∂ t α g = − B α 2 g + C α 3 g − D α 2 g α y t = ln µ/ Λ ∂ t α y = E α 2 0 < α ∗ = B/C ⌧ 1 y − F α g α y α ∗ ⌧ 1 in any QFT loop coefficients D, E, F > 0 asymptotic freedom B > 0 C < 0 or C > 0 g = B in the latter case: α ∗ Banks-Zaks IR FP C

basics of asymptotic safety gauge theory ∂ t α g = − B α 2 g + C α 3 g − D α 2 g α y t = ln µ/ Λ ∂ t α y = E α 2 0 < α ∗ = B/C ⌧ 1 y − F α g α y α ∗ ⌧ 1 in any QFT loop coefficients D, E, F > 0 infrared freedom B < 0 2 < 1 C S 11 C G for C < 0 we must have 2

result: 1.0 1 E 8 χ = min C 2 ( R ) C 2 (adj) E 7 19 0.8 24 E 6 13 18 F 4 2 3 SO H N L 0.6 7 12 Χ G 2 SU H N L 1 2 Sp H N L 0.4 3 8 0.2 1 11 asymptotic safety 0.0 5 10 15 20 N

result: 1.0 1 E 8 χ = min C 2 ( R ) C 2 (adj) E 7 19 0.8 24 E 6 13 18 F 4 2 3 SO H N L 0.6 7 12 Χ G 2 SU H N L 1 2 Sp H N L 0.4 3 8 implication: 0.2 B ≤ 0 C > 0 ⇒ 1 11 asymptotic safety no go theorem 0.0 5 10 15 20 N

basics of asymptotic safety gauge theory ∂ t α g = − B α 2 g + C α 3 g − D α 2 g α y t = ln µ/ Λ ∂ t α y = E α 2 0 < α ∗ = B/C ⌧ 1 y − F α g α y α ∗ ⌧ 1 in any QFT loop coefficients D, E, F > 0 infrared freedom B < 0 ⇒ C > 0 B < 0 Bond, Litim 1608.00519

basics of asymptotic safety gauge theory ∂ t α g = − B α 2 g + C α 3 g − D α 2 g α y t = ln µ/ Λ ∂ t α y = E α 2 0 < α ∗ = B/C ⌧ 1 y − F α g α y α ∗ ⌧ 1 in any QFT loop coefficients D, E, F > 0 infrared freedom B < 0 ⇒ C > 0 B < 0 Bond, Litim 1608.00519 can other couplings help? more gauge: useless scalar quartics: useless Yukawas: unique viable option

basics of asymptotic safety gauge Yukawa theory ∂ t α g = − B α 2 g + C α 3 g − D α 2 g α y t = ln µ/ Λ ∂ t α y = E α 2 y − F α g α y α ∗ ⌧ 1 in any QFT loop coefficients D, E, F > 0

basics of asymptotic safety gauge Yukawa theory ∂ t α g = − B α 2 g + C α 3 g − D α 2 g α y t = ln µ/ Λ ∂ t α y = E α 2 y − F α g α y α ∗ ⌧ 1 y = F Yukawa nullcline α ∗ E α ∗ g

basics of asymptotic safety gauge Yukawa theory ∂ t α g = − B α 2 g + C α 3 g − D α 2 g α y t = ln µ/ Λ ∂ t α y = E α 2 y − F α g α y α ∗ ⌧ 1 y = F Yukawa nullcline α ∗ E α ∗ g β g | = ( − B + C 0 α g ) α 2 g C → C 0 = C − D F shifted two-loop E interacting UV fixed point iff D F − C E > 0

basics of asymptotic safety gauge Yukawa theory ∂ t α g = − B α 2 g + C α 3 g − D α 2 g α y t = ln µ/ Λ ∂ t α y = E α 2 y − F α g α y α ∗ ⌧ 1 y = F Yukawa nullcline α ∗ E α ∗ g β g | = ( − B + C 0 α g ) α 2 g gauge-Yukawa fixed point ✓ B ◆ C 0 , B F ( α ⇤ g , α ⇤ y ) = UV or IR C 0 E

basics of asymptotic safety gauge Yukawa theory ∂ t α g = − B α 2 g + C α 3 g − D α 2 g α y t = ln µ/ Λ ∂ t α y = E α 2 y − F α g α y α ∗ ⌧ 1 summary of fixed points Gaussian UV or IR ( α ∗ g , α ∗ y ) = (0 , 0) ✓ B ◆ ( α ∗ y ) = C , 0 g , α ∗ Banks-Zaks IR ✓ B ◆ C 0 , B F ( α ⇤ g , α ⇤ y ) = UV or IR gauge-Yukawa C 0 E

conditions for asymptotic safety results Bond, Litim 1608.00519 *) *) *) provided certain auxiliary conditions hold true

B, C > 0 > C 0 B > 0 > C Y 4 Y 4 G G BZ � � B, C, C 0 > 0 0 > B, C 0 GY Y 4 Y 4 GY G BZ G � �

asymptotic safety 1. theorems for asymptotic safety Bond, Litim 1608.00519 2. weakly interacting UV completions of the Standard Model AD Bond, G Hiller, K Kowalska, DF Litim, 1702.01727 3. constraints from data (colliders) AD Bond, G Hiller, K Kowalska, DF Litim, 1702.01727

asymptotic safety beyond the SM Bond, Hiller, Kowalska, Litim, 1702.01727 ψ i ( R 3 , R 2 , Y ) flavors of BSM fermions N F BSM singlet scalars S ij U ( N F ) × U ( N F ) global flavor symmetry L BSM , Yukawa = − y Tr( ψ L S ψ R + ψ R S † ψ L ) BSM Lagrangean L = L SM + L BSM , kin . + L BSM , pot . + L BSM , Yukawa

UV fixed points

BSM fixed points weak becomes strong α ∗ 2 > 0 FP 2 strong becomes weak α ∗ 3 = 0 δα 2 ( Λ ) , δα 3 ( Λ ) UV critical surface α ∗ 3 > 0 strong remains strong FP 3 α ∗ 2 = 0 weak remains weak δα 2 ( Λ ) , δα 3 ( Λ ) UV critical surface α ∗ → 3 weak becomes the 2 FP 4 new strong α ∗ 2 3 δα 3 ( Λ ) UV critical surface

BSM fixed points FP 2 FP 3 FP 4 α ∗ 3 > 0 α ∗ 2 > 0 α ∗ 2 , α ∗ 3 > 0 α ∗ 2 = 0 α ∗ 3 = 0 R 2 = 1 R 2 = 2 R 2 = 3 R 2 = 3 R 2 = 4 R 2 = 5 R 2 = 1 R 2 = 2 R 2 = 3 15' 15 21 15' 15 10 8 15 10 R 3 R 3 R 3 10 6 8 3 8 6 1 6 3 0 200 400 600 800 0 100 200 300 0 100 200 N F N F N F

summary of fixed points 1 3 6 8 10 5 5 4 4 R 2 3 3 2 2 FP 2 N F 1 1 FP 3 FP 4 1 3 6 8 10 R 3

benchmark models

benchmark models model A “ w e a k b e c o m e s s t r o n g , FP 2 m at c h i ng c r o ss - ov e r s c a l e 1 s t r o n g b e c o m e s w e a k ” s c a l e ( 1 , 4 ,12) ( R 3 , R 2 , N F ) = Α 2 0.1 Α y cross-over 0.01 Α 3 0.001 low scale R 3 = 1 , R 2 = 4 , N F = 12 10 - 4 10 4 10 5 10 6 1000 m H GeV L

benchmark models 1 model B “strong remains strong, FP 3 c r o ss - ov e r s c a l e m at c h i ng weak remains weak” s c a l e 0.1 ( 10 , 1 ,30) ( R 3 , R 2 , N F ) = cross-over Α y Α 3 0.01 Α 2 0.001 low scale R 3 = 10 , R 2 = 1 , N F = 30 10 - 4 1 ¥ 10 4 2 ¥ 10 4 1000 2000 5000 m H GeV L

benchmark models model B weak BZ 0.500 FP 4 Α 2 H model B L 0.100 ( 10 , 1 ,30) ( R 3 , R 2 , N F ) = 0.050 NO Α y matching 0.010 onto SM 0.005 Α 3 0.001 1 10 100 1000 10 4 Μ ê Μ 0

benchmark models model C 1 “strong remains strong FP 3 m at c h i ng c r o ss - ov e r s c a l e weak remains weak” s c a l e 0.1 Α 3 Α y ( 10 , 4 ,80) ( R 3 , R 2 , N F ) = cross-over 0.01 0.001 low scale 10 - 4 R 3 = 10 , R 2 = 4 , N F = 80 Α 2 10 - 5 1 ¥ 10 4 2 ¥ 10 4 1000 2000 5000 m H GeV L

benchmark models model C 0.200 “weak” becomes FP 4 c r o ss - ov e r s c a l e m at c h i ng s c a l e the new “strong” 0.100 Α 2 0.050 ( 10 , 4 ,80) ( R 3 , R 2 , N F ) = Α y 0.020 0.010 0.005 Α 3 0.002 high scale 0.001 R 3 = 10 , R 2 = 4 , N F = 80 5 ¥ 10 10 1 ¥ 10 11 2 ¥ 10 11 5 ¥ 10 11 1 ¥ 10 12 m H GeV L

benchmark models model C 1 “ w e a k b e c o m e s s t r o n g c r o ss - ov e r s c a l e FP 2 m at c h i ng & s t r o n g b e c o m e s w e a k ” FP 2 s c a l e Α 2 (model C) cross-over II 0.1 ( 10 , 4 ,80) ( R 3 , R 2 , N F ) = FP 4 Α y F P 4 “flyby” 0.01 0.001 e l a I c high scale I I Α 3 s r r e e g v v n o o i h - - s s c s s t R 3 = 10 , R 2 = 4 , N F = 80 o o a m r r c c 10 - 4 2 ¥ 10 10 5 ¥ 10 10 1 ¥ 10 11 2 ¥ 10 11 5 ¥ 10 11 1 ¥ 10 12 m H GeV L

benchmark models model D 0.100 “weak stronger FP 4 c r o ss - ov e r s c a l e m at c h i ng than strong” 0.050 s c a l e Α 2 Α 3 ( 3,4 ,290) ( R 3 , R 2 , N F ) = 0.020 cross-over 0.010 0.005 Α y 0.002 low scale 0.001 R 3 = 3 , R 2 = 4 , N F = 290 1000 1500 2000 3000 5000 7000 10 000 m H GeV L

summary of SM matching: when it works genuinely, except in special circumstances FP 2 (competition with other nearby FPs) genuinely, except in special circumstances FP 3 (competition with other nearby FPs)

summary of SM matching: when it works 1 3 6 8 10 5 5 N F 4 4 Μ R 2 FP 4 3 3 2 2 low scale high scale 1 1 no match H weak L no match H strong L 1 3 6 8 10 R 3

asymptotic safety 1. theorems for asymptotic safety Bond, Litim 1608.00519 2. weakly interacting UV completions of the Standard Model 3. constraints from data (colliders) AD Bond, G Hiller, K Kowalska, DF Litim, 1702.01727