asymptotic safety beyond the Standard Model

Transcription

1 asymptotic safety beyond the Standard Model Daniel F Litim Frankfurt, 18 May 2017

2 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?

3 asymptotic freedom triumph of QFT

4 asymptotic freedom free UV fixed point e.g. QCD

5 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

6 infrared freedom e.g. QED

7 asymptotic safety interacting UV fixed point

8 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, Bond,

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

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

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

12 basics of asymptotic safety gauge theory Yukawa t g = B g 2 + C g 3 D g 2 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

13 basics of asymptotic safety gauge t g = B g 2 + C g 3 D g 2 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

14 result: 1.0 E 8 = min C 2(R) C 2 (adj) 1 c E 7 E 6 F 4 G 2 SOHNL SUHNL SpHNL asymptotic safety N 1 11

15 result: 1.0 E 8 = min C 2(R) C 2 (adj) 1 c E 7 E 6 F 4 G 2 SOHNL SUHNL SpHNL implication: B apple 0 ) C>0 no go theorem asymptotic safety N 1 11

16 basics of asymptotic safety gauge t g = B g 2 + C g 3 D g 2 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

17 basics of asymptotic safety gauge t g = B g 2 + C g 3 D g 2 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

18 basics of asymptotic safety gauge Yukawa t g = B 2 g + C 3 g D 2 g y t t y = E 2 y F g y 1 loop coefficients D, E, F > 0 in any QFT

19 basics of asymptotic safety gauge Yukawa t g = B 2 g + C 3 g D 2 g y t t y = E 2 y F g y 1 Yukawa nullcline y = F E g

20 basics of asymptotic safety gauge Yukawa t g = B 2 g + C 3 g D 2 g y t 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

21 basics of asymptotic safety gauge Yukawa t g = B 2 g + C 3 g D 2 g y t 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

22 basics of asymptotic safety gauge Yukawa t g = B 2 g + C 3 g D 2 g y t 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

23 basics of asymptotic safety gauge Yukawa t g = B 2 g + C 3 g D 2 g y t t y = E 2 y F g y 1 exact proofs of existence (Veneziano limit) SU(N) + scalars + fermions DF Litim, F Sannino, SU(N) x SU(M) + scalars + fermions AD Bond, DF (to appear)

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

25 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

26 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

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

28 asymptotic safety beyond the SM Bond, Hiller, Kowalska, Litim, 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

29 UV fixed points

30 BSM fixed points weak becomes strong FP 2 > =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 ( )

31 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 = ' 10 15' R 3 6 R 3 10 R N F N F N F

32 summary of fixed points R FP 2 FP 3 1 N F FP R 3

33 benchmark models

34 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 a low scale R 3 = 1, R 2 = 4, N F = m HGeVL

35 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 low scale R 3 = 10, R 2 = 1, N F = m HGeVL

36 benchmark models model B weak BZ (R 3,R 2,N F )= (10,1,30) FP 4 Hmodel BL a a y NO matching onto SM a mêm 0

37 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 low scale R 3 = 10, R 2 = 4, N F = m HGeVL a 2

38 benchmark models model C weak becomes matching scale the new strong a 2 FP 4 cross - over scale (R 3,R 2,N F )= (10,4,80) a y a R 3 = 10, R 2 = 4, N F = 80 high scale m HGeVL

39 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 matching scale high scale cross-over II a 3 cross-over I R 3 = 10, R 2 = 4, N F = m HGeVL

40 benchmark models model D weak stronger matching than scalestrong FP 4 cross - over scale (R 3,R 2,N F )= (3,4,290) a 2 a cross-over a y low scale R 3 = 3, R 2 = 4, N F = m HGeVL

41 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)

42 summary of SM matching: when it works N F 4 FP 4 R 2 3 m low scale high scale no match HweakL no match HstrongL R 3

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

44 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

45 SU(3) BSM running ATLAS & CMS: a M 1.5 TeV Model E Model C Model B

46 SU(2) BSM running a Model E D ModelC Model A

47 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

48 dijet cross section ATLAS dijet bounds on BR A (up-date post-moriond) no interference max. interference Model B Model D A = % 0.1 M S =1.5 TeV M

49 mass exclusion limits scan over masses R hadron searches *) Model B (10,1,30) (10,1,30) BSM (up-date post-moriond ) M no inter ference max. interference di-jet limits LHC *) fudged from 13 TeV ATLAS + CMS gluino analysis M

50 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