from exact asymptotic safety to physics beyond the Standard Model

Transcription

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

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 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,

4 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,

5 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,

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

7 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

8 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

9 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

10 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

11 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

12 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

13 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

14 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

15 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

16 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

17 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

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

19 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

20 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,

21 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

22 UV fixed points

23 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 ( )

24 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

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

26 benchmark models

27 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

28 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

29 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

30 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

31 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

32 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

33 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

34 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)

35 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

36 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,

37 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

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

39 SU(2) BSM running a Model E ModelC Model A

40 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

41 dijet cross section ATLAS dijet bounds on BR A no interference max. interference Model B Model D A = % 0.1 M S =1.5 TeV M

42 mass exclusion limits 100 scan over masses R hadron searches Model B (10,1,30) BSM running M no interference di-jet limits max. interference LHC M

43 conclusions theorems for fixed points and asymptotic safety systematics 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

44 extra material

45 U(1)Y BSM a 3 * ı D C Û C Ìı B B U(1) Y Landau pole arising below M Pl ÒE Û A D a 2 * C ı

46 phase diagrams phase diagrams of simple gauge theories parameters B,C C 0 matter content Yukawa structure

47 phase diagrams asymptotic freedom Y4 G (B >0 >C,C 0 )

48 phase diagrams asymptotic freedom & BZ Y4 G G BZ (B,C > 0 >C 0 )

49 phase diagrams asymptotic freedom, BZ & GY Y4 GY G BZ (B,C,C 0 > 0)

50 phase diagrams asymptotic safety & GY GY Y4 G G (C >0 >B,C 0 )

51 extensions I interacting UV FPs with exact asymptotic safety exist for simple gauge theories Litim, Sannino, but: do interacting UV FPs with exact asymptotic safety exist for semi-simple gauge theories? Yes! ERG 2016 this meeting space of UV FP solutions is non-empty

52 extensions II what is the impact of couplings with non-vanishing canonical mass dimension? results: fixed point persists effective potential remains stable

53 extensions II Lagrangean Litim, Sannino, further scalar invariants gauge Nc colours Yukawa Nf flavours Higgs Nf times Nf ( 2 ) Buyukbese, Lattice2016 (in prep.)

54 extensions II results: exact eigenvalue spectrum n = D n + O( ) n

55 more weak sector contributions to muon anomalous magnetic moment together with a exp leads to constraint µ (2 3) 10 9 d(r 3 ) S(R 2 ) N F TeV M obeyed by all benchmark models. contributions to the rho parameter arise if fermion multiplets encounter mass splitting M M due to SU(2) breaking N F d(r 3 ) S(R 2 ) M 2. (40 GeV) 2 sub-percent splitting for TeV or higher BSM masses

56 R-hadron searches assume pair-production of BSM fermions 2M < p s at least the lightest has a long life ( > hadron ) and forms colorless QCD bound states with SM matter pp! via t-channel gluon fusion N F C 3 with C 3 =[C 2 (R 3 )] 2 d(r 3 ) d(r 2 ) lower limits M min from ATLAS and CMS gluino searches model B, C, D, E: 2.3, >2.4, 2.2, 2.0 TeV

57 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

58 decays into electroweak gauge bosons further signatures if d(r 2 ) 6= 1 general scalar resonance decaying into WW,ZZ,Z, growth with dim(r2) G VV êg gg R 3 = 3 WW ZZ Zg gg low Ms M S. M G VV êg gg R 3 = 10 WW gg ZZ Zg dhr 2 L dhr 2 L

59 decays into electroweak gauge bosons reduced decay widths VV = 1 F VV gg, with F = 4 3 C 2 (R 2 ) C 2 (R 3 ) 2 for small hypercharge coupling WW = , ZZ , Z , modification of widths for high Ms FP 4 WW, ZZ Z? FP 2 WW, ZZ, Z, FP 3 WW, ZZ, Z,