Asymptotically safe extensions of the Standard Model and fmavor - PowerPoint PPT Presentation

Asymptotically safe extensions of the Standard Model and fmavor phenomenology Clara Hormigos-Feliu March �� st , ���� �� th Rencontres de Moriond, La Thuile In collaboration with G. Hiller, D. Litim and T. Steudtner

Asymptotic Safety: an alternative fate Couplings run into weakly interacting Fixed Point Condition d FP d ln FP Motivation Th: theory is UV complete, predictive at all scales Pheno: guides model-building, matching to SM gives BSM predictions at EW scale [Bond, Hiller, Kowalska, Litim (����)] SM: are AF, runs into Landau pole Asymptotic Safety - introduction [CMS (����)] Asymptotic Freedom: couplings vanish in the UV Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW ���� � / 6

Asymptotic Safety: an alternative fate Couplings run into weakly interacting Fixed Point Condition d FP d ln FP Motivation Th: theory is UV complete, predictive at all scales Pheno: guides model-building, matching to SM gives BSM predictions at EW scale [Bond, Hiller, Kowalska, Litim (����)] Asymptotic Safety - introduction [CMS (����)] Asymptotic Freedom: couplings vanish in the UV 0.010 SM Α 1 SM 0.008 Α 2 SM Α 3 0.006 Α SM � Μ � 0.004 0.002 0.1 10 5 10 11 10 17 10 23 10 29 10 35 Μ � TeV � SM: α 3 , α 2 are AF, α 1 runs into Landau pole Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW ���� � / 6

Asymptotic Safety - introduction Asymptotic Safety: an alternative fate ◮ Couplings run into weakly interacting Fixed Point Condition d α � � � β ( α ) FP = = 0 � � d ln µ [CMS (����)] � FP Asymptotic Freedom: couplings vanish in the UV Motivation 0.010 SM Α 1 SM 0.008 Α 2 Th: theory is UV complete, predictive at SM Α 3 all scales 0.006 Α SM � Μ � Pheno: guides model-building, 0.004 matching to SM gives BSM predictions 0.002 at EW scale 0.1 10 5 10 11 10 17 10 23 10 29 10 35 [Bond, Hiller, Kowalska, Litim (����)] Μ � TeV � SM: α 3 , α 2 are AF, α 1 runs into Landau pole Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW ���� � / 6

What works? Introduce large fmavor sector [Litim, Sannino (����)] Complex scalars: S Vector-like fermions: L R ( N F , SM-charged) ( N F , uncharged) Extending the BSM Yukawa sector Choose SU SU U Y reps. of to couple with SM ( L E H ) C L Case study A: , N F Y Y y tr L S y tr LH L S tr h c ES h c R R R L BSM BSM Other possibilities: ... AS models and the fmavor connection Modifying β -functions ◮ Gauge: β g = α 2 ◮ Yukawa: β y = α y ( E α y − F α g ) g ( − B + C α g − D α y ) Yukawa couplings essential Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW ���� � / 6

Extending the BSM Yukawa sector Choose SU SU U Y reps. of to couple with SM ( L E H ) C L Case study A: , N F Y y tr L S LH tr ES h c R R L BSM Other possibilities: ... AS models and the fmavor connection Modifying β -functions ◮ Gauge: β g = α 2 ◮ Yukawa: β y = α y ( E α y − F α g ) g ( − B + C α g − D α y ) Yukawa couplings essential What works? Introduce large fmavor sector [Litim, Sannino (����)] ◮ Vector-like fermions: ψ L , R ◮ Complex scalars: S ( N F , SM-charged) ( N 2 F , uncharged) −L Y BSM = y tr ψ L S ψ R + h . c . Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW ���� � / 6

AS models and the fmavor connection Modifying β -functions ◮ Gauge: β g = α 2 ◮ Yukawa: β y = α y ( E α y − F α g ) g ( − B + C α g − D α y ) Yukawa couplings essential What works? Introduce large fmavor sector [Litim, Sannino (����)] ◮ Vector-like fermions: ψ L , R ◮ Complex scalars: S ( N F , SM-charged) ( N 2 F , uncharged) Extending the BSM Yukawa sector Choose SU (3) C × SU (2) L × U (1) Y reps. of ψ to couple with SM ( L , E , H ) Case study A: ψ (1 , 1 , − 1) , N F = 3 −L Y −L Y BSM = y tr ψ L S ψ R + κ LH ψ R + tr κ ′ ES † ψ L + h . c . BSM = y tr ψ L S ψ R + h . c . Other possibilities: ψ (1 , 3 , − 1) , ψ (1 , 2 , 3/2) ... Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW ���� � / 6

Matching: connecting SM and BSM running Prediction of BSM Yukawas at low energies: Fixed Points and Matching Fixed Points exist for these models α FP α FP α FP α FP α FP FP y 1 2 κ ′ κ A 1 1 . 06 0 0 . 886 1 . 59 0 � β ( α ) FP = 0 � A 2 1 . 10 0 . 569 1 . 20 1 . 66 0 . . . . . . . . . . . . . . . . . . Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW ���� � / 6

Fixed Points and Matching Fixed Points exist for these models α FP α FP α FP α FP α FP FP y 1 2 κ ′ κ A 1 1 . 06 0 0 . 886 1 . 59 0 � β ( α ) FP = 0 � A 2 1 . 10 0 . 569 1 . 20 1 . 66 0 . . . . . . . . . . . . . . . . . . Matching: connecting SM and BSM running M F � 1 TeV 1 1 Α 1 0.1 0.1 Α 2 Α � Μ � Α � Μ � Α y 0.01 0.01 Α Κ 0.001 0.001 Α Κ ' A 1 A 2 10 � 4 10 � 4 10 � 20 10 � 16 10 � 12 10 � 8 10 7 10 12 10 17 10 22 10 � 4 0.001 100 1 Μ � TeV � Μ � M FP Prediction of BSM Yukawas at low energies: α κ , α κ ′ ∼ 3 · 10 − 3 Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW ���� � / 6

LFV decays h Induced by new Yukawas e ij L i H Rj Constraints EW precision parameters M 2 W , Y ∝ α 2 , 1 W ∆ B 2 , 1 10 M 2 F change in �-loop coeffjcient 2.00 A 1.00 B D 0.50 W,Y x 10 3 LHC 8 TeV � LEP 0.20 0.10 LHC 13 TeV 0.05 0.02 0.01 0.1 0.2 0.5 1.0 2.0 5.0 M F � TeV � Bounds from [Farina et. al. (����)] Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW ���� � / 6

Constraints EW precision parameters LFV decays M 2 W , Y ∝ α 2 , 1 h W ∆ B 2 , 1 Induced by new Yukawas 10 M 2 F ψ µ e κ ij L i H ψ Rj change in �-loop coeffjcient κ κ γ 2.00 A Μ� e Γ 100 1.00 B Τ�ΜΓ D 0.50 1 W,Y x 10 3 LHC 8 TeV � LEP 0.20 Α Κ ij 0.10 LHC 13 TeV 0.01 0.05 10 � 4 Μ� e Γ � MEG � II � 0.02 0.01 0.1 0.2 0.5 1.0 2.0 5.0 1 2 5 10 20 50 100 M F � TeV � M F � TeV � Bounds from [Farina et. al. (����)] Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW ���� � / 6

Use predictions from matching: Explaining a possible Summary SM can be made asymptotically safe by coupling SM-BSM in the Yukawa sector Matching sets NP scale, predicts BSM couplings at low energy BSM sector can be produced at colliders and probed by EW precision tests, LFV decays a can be explained Contributions to ( g − 2) µ ( g − 2) µ anomaly: ∆ a µ = 268(63)(43) · 10 − 11 [PDG (���8)] γ Contribution through ψ 2 ψ 2 ◮ Two Yukawas: κ LH ψ + tr κ ′ ES † ψ L κ κ ′ s 22 h ◮ Scalar mixing: δ HH † tr [ SS † ] δ µ µ m µ a NP µ ∝ δ m h κκ ′ M S M F 16 π 2 Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW ���� 6 / 6

Summary SM can be made asymptotically safe by coupling SM-BSM in the Yukawa sector Matching sets NP scale, predicts BSM couplings at low energy BSM sector can be produced at colliders and probed by EW precision tests, LFV decays a can be explained Contributions to ( g − 2) µ ( g − 2) µ anomaly: ∆ a µ = 268(63)(43) · 10 − 11 [PDG (���8)] γ Contribution through ψ 2 ψ 2 ◮ Two Yukawas: κ LH ψ + tr κ ′ ES † ψ L κ κ ′ s 22 h ◮ Scalar mixing: δ HH † tr [ SS † ] δ µ µ Use predictions from matching: α κ , α κ ′ ∼ 3 · 10 − 3 m µ a NP µ ∝ δ m h κκ ′ M S M F 16 π 2 Explaining ∆ a µ possible Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW ���� 6 / 6

Contributions to ( g − 2) µ ( g − 2) µ anomaly: ∆ a µ = 268(63)(43) · 10 − 11 [PDG (���8)] γ Contribution through ψ 2 ψ 2 ◮ Two Yukawas: κ LH ψ + tr κ ′ ES † ψ L κ κ ′ s 22 h ◮ Scalar mixing: δ HH † tr [ SS † ] δ µ µ Use predictions from matching: α κ , α κ ′ ∼ 3 · 10 − 3 m µ a NP µ ∝ δ m h κκ ′ M S M F 16 π 2 Explaining ∆ a µ possible Summary SM can be made asymptotically safe by coupling SM-BSM in the Yukawa sector Matching sets NP scale, predicts BSM couplings at low energy BSM sector can be produced at colliders and probed by EW precision tests, LFV decays ∆ a µ can be explained Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW ���� 6 / 6

Extra slides Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW ���� � / �

BSM sector production ψ Q − 1 f ψ ψ − d f h γ, Z W f u ψ − Q ψ f ℓ + (c) (a) (b) ψ − ℓ − ℓ − ψ − h , S h ψ + ℓ + ℓ + ℓ + (d) (e) f S † ℓ − S † h ψ S / h ℓ + S / h f (f) (g) Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW ���� � / �