asymptotic safety beyond the Standard Model Daniel F Litim Frankfurt, 18 May 2017
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 freedom triumph of QFT
asymptotic freedom 0.02 0.00-0.02-0.04 free UV fixed point -0.06-0.08 e.g. QCD -0.10-0.12 0.00 0.05 0.10 0.15 0.20 0.25
conditions for asymptotic freedom complete asymptotic freedom couplings achieve non-interacting UV fixed point fields scalars scalars with fermions U(1) w/o scalars or fermions non-abelian gauge fields non-abelian fields with fermions non-abelian fields, fermions, scalars caf no no no yes yes *) yes *) *) provided certain auxiliary conditions hold true
infrared freedom 0.10 0.02 0.00 0.05-0.02-0.04 0.00-0.06-0.08-0.05 e.g. QED -0.10-0.10-0.12 0.00 0.05 0.10 0.15 0.20 0.25
asymptotic safety 0.10 0.02 0.00 0.05-0.02-0.04 0.00-0.06-0.08-0.05 interacting UV fixed point -0.10-0.10-0.12 0.00 0.05 0.10 0.15 0.20 0.25
asymptotic safety idea: some or all couplings achieve interacting UV fixed point Wilson 71 Weinberg 79 if so, new directions for BSM physics &, possibly, quantum gravity proof of existence: 4D gauge-yukawa theory with exact asymptotic safety Litim, Sannino, 1406.2337 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 theory Yukawa theory @ t g = B g 2 + C g 3 D g 2 y @ 0 t < y = = E B/C y 2 F 1 g y t =lnµ/ 1 loop coefficients D, E, F > 0 in any QFT B>0 asymptotic freedom C<0or C>0 in the latter case: g = B C Banks-Zaks IR FP
basics of asymptotic safety gauge theory @ t g = B g 2 + C g 3 D g 2 y @ 0 t < y = = E B/C y 2 F 1 g y t =lnµ/ 1 loop coefficients D, E, F > 0 in any QFT B<0 infrared freedom for C < 0 we must have C S 2 < 1 11 CG 2
result: 1.0 E 8 = min C 2(R) C 2 (adj) 1 c 0.8 0.6 0.4 E 7 E 6 F 4 G 2 SOHNL SUHNL SpHNL 19 24 13 18 2 3 7 12 1 2 3 8 0.2 0.0 asymptotic safety 5 10 15 20 N 1 11
result: 1.0 E 8 = min C 2(R) C 2 (adj) 1 c 0.8 0.6 0.4 E 7 E 6 F 4 G 2 SOHNL SUHNL SpHNL 19 24 13 18 2 3 7 12 1 2 3 8 implication: B apple 0 ) C>0 no go theorem 0.2 0.0 asymptotic safety 5 10 15 20 N 1 11
basics of asymptotic safety gauge theory @ t g = B g 2 + C g 3 D g 2 y @ 0 t < y = = E B/C y 2 F 1 g y t =lnµ/ 1 loop coefficients D, E, F > 0 in any QFT B<0 infrared freedom B<0 ) C>0 Bond, Litim 1608.00519
basics of asymptotic safety gauge theory @ t g = B g 2 + C g 3 D g 2 y @ 0 t < y = = E B/C y 2 F 1 g y t =lnµ/ 1 loop coefficients D, E, F > 0 in any QFT B<0 infrared freedom B<0 ) C>0 can other couplings help? more gauge: useless scalar quartics: useless Yukawas: unique viable option Bond, Litim 1608.00519
basics of asymptotic safety gauge Yukawa theory @ t g = B 2 g + C 3 g D 2 g y t =lnµ/ @ t y = E 2 y F g y 1 loop coefficients D, E, F > 0 in any QFT
basics of asymptotic safety gauge Yukawa theory @ t g = B 2 g + C 3 g D 2 g y t =lnµ/ @ t y = E 2 y F g y 1 Yukawa nullcline y = F E g
basics of asymptotic safety gauge Yukawa theory @ t g = B 2 g + C 3 g D 2 g y t =lnµ/ @ t y = E 2 y F g y 1 Yukawa nullcline y = F E g g =( B + C 0 g ) 2 g shifted two-loop C! C 0 = C D F E interacting UV fixed point iff DF CE>0
basics of asymptotic safety gauge Yukawa theory @ t g = B 2 g + C 3 g D 2 g y t =lnµ/ @ t y = E 2 y F g y 1 Yukawa nullcline y = F E g g =( B + C 0 g ) 2 g gauge-yukawa fixed point ( g, y)= B C 0, B F C 0 E UV or IR
basics of asymptotic safety gauge Yukawa theory @ t g = B 2 g + C 3 g D 2 g y t =lnµ/ @ t y = E 2 y F g y 1 summary of fixed points ( g, y)=(0, 0) B Gaussian UV or IR ( g, y)= ( g, y)= C, 0 B C 0, B F C 0 E Banks-Zaks gauge-yukawa IR UV or IR
basics of asymptotic safety gauge Yukawa theory @ t g = B 2 g + C 3 g D 2 g y t =lnµ/ @ t y = E 2 y F g y 1 exact proofs of existence (Veneziano limit) SU(N) + scalars + fermions DF Litim, F Sannino, 1406.2337 SU(N) x SU(M) + scalars + fermions AD Bond, DF Litim, @ERG2016 (to appear)
conditions for asymptotic safety results Bond, Litim 1608.00519 *) *) *) provided certain auxiliary conditions hold true
B>0 >C B,C > 0 >C 0 Y4 Y4 G G BZ 0 >B,C 0 B,C,C 0 > 0 GY Y4 Y4 GY G G BZ
B>0 >C B,C > 0 >C 0 not available Y4 Y4 N=1 SUSY G G BZ 0 >B,C 0 B,C,C 0 > 0 not available GY Y4 Y4 GY G G BZ
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 AD Bond, G Hiller, K Kowalska, DF Litim, 1702.01727
asymptotic safety beyond the SM Bond, Hiller, Kowalska, Litim, 1702.01727 N F flavors of BSM fermions BSM singlet scalars i(r 3,R 2,Y) S ij global flavor symmetry U(N F ) U(N F ) L BSM, Yukawa = y Tr( L S R + R S L) BSM Lagrangean L = L SM + L BSM, kin. + L BSM, pot. + L BSM, Yukawa
UV fixed points
BSM fixed points weak becomes strong FP 2 > 0 2 3 =0 strong becomes weak UV critical surface 2 ( ), 3 ( ) FP 3 3 > 0 strong remains strong 2 =0 weak remains weak UV critical surface 2 ( ), 3 ( ) FP 4 2 3! 3 2 UV critical surface weak becomes the new strong 3 ( )
BSM fixed points FP 2 2 > 0 3 =0 R 2 = 3 R 2 = 4 R 2 = 5 FP 3 3 > 0 2 =0 R 2 = 1 R 2 = 2 R 2 = 3 FP 4 2, 3 > 0 R 2 = 1 R 2 = 2 R 2 = 3 15 21 15' 10 15' 15 8 15 10 R 3 6 R 3 10 R 3 8 3 8 6 1 6 3 0 200 400 600 800 N F 0 100 200 300 N F 0 100 200 N F
summary of fixed points 1 3 6 8 10 5 5 4 4 R 2 3 3 2 2 1 FP 2 FP 3 1 N F FP 4 1 3 6 8 10 R 3
benchmark models
benchmark models model A 1 weak becomes strong, strong becomes weak matching scale cross - over scale FP 2 (R 3,R 2,N F )= (1,4,12) 0.1 a y cross-over a 2 0.01 a 3 0.001 10-4 low scale R 3 = 1, R 2 = 4, N F = 12 1000 10 4 10 5 10 6 m HGeVL
benchmark models 1 strong remains strong, weak remains weak model B FP matching cross - over scale 3 scale (R 3,R 2,N F )= (10,1,30) 0.1 a y cross-over 0.01 a 3 a 2 0.001 low scale R 3 = 10, R 2 = 1, N F = 30 10-4 1000 2000 5000 1 10 4 2 10 4 m HGeVL
benchmark models model B 0.500 weak BZ (R 3,R 2,N F )= (10,1,30) 0.100 0.050 FP 4 Hmodel BL a 2 0.010 0.005 a y NO matching onto SM 0.001 a 3 1 10 100 1000 10 4 mêm 0
benchmark models model C 1 strong matching remains strong scale weak remains weak FP 3 cross - over scale (R 3,R 2,N F )= (10,4,80) 0.1 a 3 a y 0.01 cross-over 0.001 10-4 low scale R 3 = 10, R 2 = 4, N F = 80 10-5 1000 2000 5000 1 10 4 2 10 4 m HGeVL a 2
benchmark models model C 0.200 0.100 weak becomes matching scale the new strong a 2 FP 4 cross - over scale (R 3,R 2,N F )= (10,4,80) 0.050 0.020 a y 0.010 0.005 a 3 0.002 0.001 R 3 = 10, R 2 = 4, N F = 80 high scale 5 10 10 1 10 11 2 10 11 5 10 11 1 10 12 m HGeVL
benchmark models model C 1 weak becomes strong & strong becomes weak FP 2 matching scale (model C) cross-over II cross - over scale a 2 FP 2 (R 3,R 2,N F )= (10,4,80) 0.1 FP 4 a y 0.01 FP4 flyby 0.001 matching scale high scale cross-over II a 3 cross-over I R 3 = 10, R 2 = 4, N F = 80 10-4 2 10 10 5 10 10 1 10 11 2 10 11 5 10 11 1 10 12 m HGeVL
benchmark models model D 0.100 0.050 weak stronger matching than scalestrong FP 4 cross - over scale (R 3,R 2,N F )= (3,4,290) 0.020 a 2 a 3 0.010 cross-over 0.005 a y 0.002 0.001 low scale R 3 = 3, R 2 = 4, N F = 290 1000 1500 2000 3000 5000 7000 10000 m HGeVL
summary of SM matching: when it works FP 2 genuinely, except in special circumstances (competition with other nearby FPs) FP 3 genuinely, except in special circumstances (competition with other nearby FPs)
summary of SM matching: when it works 1 3 6 8 10 5 5 4 N F 4 FP 4 R 2 3 m 3 2 1 low scale high scale no match HweakL no match HstrongL 2 1 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
phenomenology assume low scale matching some BSM masses within TeV energy range assume R 3 6= 1 for LHC ( R 3 = 1 can be tested at future e + e colliders) flavor symmetry: stable BSM fermions broken flavor symmetry: lightest BSM fermion stable constraints from running couplings the weak sector long-lived QCD bound states di-boson searches
SU(3) BSM running 0.010 ATLAS & CMS: 1702.01727 a3 0.009 0.008 M 1.5 TeV Model E Model C Model B 0.007 0.006 500 1000 1500 2000 2500 3000 Q @GeVD
SU(2) BSM running 0.0050 1702.01727 0.0045 a2 0.0040 0.0035 0.0030 Model E D ModelC Model A 0.0025 0.0020 500 1000 2000 5000 Q @GeVD
di-boson spectra and resonances assume resonant production of BSM scalars low Ms M S < p s M S. M M S < 2M high Ms M. M S < 2M loop-mediated decay into GG = gg,,zz,z, or WW g G ψ i S ii ψ i g G interference effects
dijet cross section ATLAS dijet bounds on BR A 1702.01727 (up-date post-moriond) shppæsæggl @fbd 10 5 1000 10 no interference max. interference Model B Model D A = 50 100% 0.1 M S =1.5 TeV 2 5 10 20 50 100 200 M y @TeVD
mass exclusion limits 100 50 scan over masses R hadron searches *) Model B (10,1,30) (10,1,30) BSM 1702.01727 (up-date post-moriond ) M S @TeVD 20 10 5 2 no inter ference max. interference di-jet limits LHC 1 1 2 5 10 20 50 100 200 *) fudged from 13 TeV ATLAS + CMS gluino analysis M y @TeVD
conclusions theorems for fixed points and asymptotic safety new directions beyond asymptotic freedom weakly interacting UV completions of the SM UV FPs can be partially or fully interacting matching to SM explained, works in many cases window of opportunities for BSM new physics can be probed at LHC constraints from colliders