Kamila Kowalska. TU Dortmund. based on and work in progress with A.Bond, G.Hiller and D.Litim EPS-HEP Venice, 08 July 2017

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1 Towards an asymptotically safe completion of the Standard Model Kamila Kowalska TU Dortmund based on and work in progress with A.Bond, G.Hiller and D.Litim EPS-HEP 2017 Venice, 08 July 2017 Kamila Kowalska (TU Dortmund) Asymptotically Safe Standard Model / 14

2 Overview 1 Basics of asymptotic safety 2 Asymptotically safe extensions of the SM 3 Summary Kamila Kowalska (TU Dortmund) Asymptotically Safe Standard Model / 14

3 Basics of asymptotic safety The set of RGEs for gauge (SU(N c )) and Yukawa couplings: (where α g = g2 (4π) 2, αy = β g = dα g d ln µ = α2 g ( B + Cα g Dα y ) β y = dα y d ln µ = α y (Eα y F α g ) y2 (4π) 2 ) B > 0 (asymptotic freedom) or B < 0 (asymptotic safety) C > 0 if B < 0 in any QFT (proof in Bond, Litim, arxiv: ) D, E, F > 0 for any quantum field theory C = C DF E β i (α i ) = 0 Kamila Kowalska (TU Dortmund) Asymptotically Safe Standard Model / 14

4 Basics of asymptotic safety Different types of fixed points possible: B > 0, C > β g B > 0, C' > G IR BZ IR GY UV GY B > 0, C < 0 B < 0, C' < α g Kamila Kowalska (TU Dortmund) Asymptotically Safe Standard Model / 14

5 Asymptotically safe extensions of the SM The setting: (following Litim, Sannino, JHEP 1412 (2014) 178, arxiv: ) N F flavors of VL BSM fermions ψ i SU(3) C SU(2) L U(1) Y ψ i (R 3, R 2, Y ) N F N F scalar singlets S ij L y( ψ Li S ij ψ Rj + ψ Ri S ij ψ Lj) In this talk: we neglect the effects from the scalar potential (three loop effect) and SM Yukawas Kamila Kowalska (TU Dortmund) Asymptotically Safe Standard Model / 14

6 Asymptotically safe extensions of the SM Case 1: R 3 0, R 2 0, Y = 0 Renormalization group equations where we define β 3 dα 3 d ln µ = ( B 3 + C 3 α 3 + G 3 α 2 D 3 α y ) α 2 3, β 2 dα 2 d ln µ = ( B 2 + C 2 α 2 + G 2 α 3 D 2 α y ) α 2 2, β y dα y d ln µ = (E α y F 2 α 2 F 3 α 3 ) α y. α 2 = g 2 2 (4π) 2, α 3 = g 2 3 (4π) 2, α y = y 2 (4π) 2 Kamila Kowalska (TU Dortmund) Asymptotically Safe Standard Model / 14

7 UV fixed points Possible types of fixed points: case gauge couplings BSM Yuk type info FP 1 α3 = 0 α 2 = 0 α y = 0 G G non-interacting FP 2 α3 = 0 α 2 > 0 α y > 0 G GY partially interacting FP 3 α3 > 0 α 2 = 0 α y > 0 GY G partially interacting FP 4 α3 > 0 α 2 > 0 α y > 0 GY GY fully interacting The existence of a UV fixed point depends on transformation properties under SU(3) C SU(2) L and N F. Kamila Kowalska (TU Dortmund) Asymptotically Safe Standard Model / 14

8 UV fixed points An example: FP 3 (α 3 > 0, α 2 = 0) R 2 = 1 R 2 = 2 R 2 = 3 R 3 N AF N AS N AF N AS N AF N AS AF is lost if B 3 < 0 physicality condition D 3 F 3 EC 3 > 0 N F α 3 O(1 10) Kamila Kowalska (TU Dortmund) Asymptotically Safe Standard Model / 14

9 Matching onto the SM UV fixed point should be connected through a RG trajectory with the SM partially interacting UV fixed point: one relevant, one irrelevant, one marginal eigendirection 2D critical surface given by α y (α AS ). fully interacting UV fixed point: 1 relevant, 2 irrelevant eigendirection 1D critical surface with α y (α 3 ) and α 2 (α 3 ) Kamila Kowalska (TU Dortmund) Asymptotically Safe Standard Model / 14

10 Matching onto the SM Matching at any scale: partially interacting fixed points 1 FP 2 model A (R 3, R 2, N F ) = (1, 4, 12) matching scale cross over scale 1 FP 3 model C (R 3, R 2, N F ) = (10, 4, 80) matching scale cross over scale 0.1 Α y Α Α 3 Α y 0.01 Α R 3 = 1, R 2 = 4, N F GeV 10 4 R 3 = 10, R 2 = 4, N F Μ GeV Α 2 Kamila Kowalska (TU Dortmund) Asymptotically Safe Standard Model / 14

11 Matching onto the SM High scale matching: fully interacting fixed point FP 4 model C (R 3, R 2, N F ) = (10, 4, 80) matching scale cross over scale Α 2 matching scale is fixed Α y enhanced predictivity with respect to the SM Α 3 α 2 = F (α 3 ) R 3 = 10, R 2 = 4, N F Kamila Kowalska (TU Dortmund) Asymptotically Safe Standard Model / 14

12 Matching onto the SM No matching (all models with R 2 = 1): trajectory attracted to BZ IR FP FP 4 model B (R 3, R 2, N F ) = (10, 1, 30) FP 4 Hmodel BL a 2 weak BZ a y a mêm 0 Kamila Kowalska (TU Dortmund) Asymptotically Safe Standard Model / 14

13 Non-zero hypercharge Case 2: we add Y 0 There is always a lower bound on the hypercharge, above which α 1 becomes asymptotically free. It is also possible to make α 1 asymptotically safe Model A Α y Model Z 1, 1, 1, N F 20 Α Α 3 Α Α 3 Α y Α Α Μ GeV Μ GeV Kamila Kowalska (TU Dortmund) Asymptotically Safe Standard Model / 14

14 Summary Yukawa couplings offer the ONLY dynamical mechanism to obtain interacting fixed points in gauge theories. To make the SM asymptotically safe new fermions in reps. higher then fundamental are required. Matching with the SM possible for certain types of FP and matter content. There are experimental signatures to test at the colliders (running of the couplings, precision observables, R-hadrons, diboson searches). Perturbativity should be closer analyzed. Kamila Kowalska (TU Dortmund) Asymptotically Safe Standard Model / 14