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 - introduction

[CMS ()]

Asymptotic Freedom: couplings vanish in the UV SM: are AF, runs into Landau pole Asymptotic Safety: an alternative fate Couplings run into weakly interacting Fixed Point

Condition

FP

d 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 ()] Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW / 6

Asymptotic Safety - introduction

[CMS ()]

Asymptotic Freedom: couplings vanish in the UV

Α1

SM

Α2

SM

Α3

SM

0.1 105 1011 1017 1023 1029 1035 0.002 0.004 0.006 0.008 0.010 Μ TeV ΑSMΜ

SM: α3, α2 are AF, α1 runs into Landau pole Asymptotic Safety: an alternative fate Couplings run into weakly interacting Fixed Point

Condition

FP

d 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 ()] Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW / 6

Asymptotic Safety - introduction

[CMS ()]

Asymptotic Freedom: couplings vanish in the UV

Α1

SM

Α2

SM

Α3

SM

0.1 105 1011 1017 1023 1029 1035 0.002 0.004 0.006 0.008 0.010 Μ TeV ΑSMΜ

SM: α3, α2 are AF, α1 runs into Landau pole Asymptotic Safety: an alternative fate

◮ Couplings run into weakly interacting

Fixed Point

Condition β(α)

• FP =

dα d ln µ

• FP

= 0 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 ()] Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW / 6

AS models and the fmavor connection

Modifying β-functions ◮ Gauge: βg = α2

g(−B + Cαg −Dαy ) Yukawa couplings essential

◮ Yukawa: βy = αy(Eαy − Fαg) What works?

Introduce large fmavor sector

[Litim, Sannino ()]

Vector-like fermions:

L R

(NF, SM-charged) Complex scalars: S (NF, uncharged)

Y BSM

y tr

LS R

h c

Extending the BSM Yukawa sector

Choose SU

C

SU

L

U

Y reps. of

to couple with SM (L E H) Case study A: , NF

Other possibilities: ...

Y BSM

y tr

LS R

LH

R

tr ES

L

h c

Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW / 6

AS models and the fmavor connection

Modifying β-functions ◮ Gauge: βg = α2

g(−B + Cαg −Dαy ) Yukawa couplings essential

◮ Yukawa: βy = αy(Eαy − Fαg) What works?

Introduce large fmavor sector

[Litim, Sannino ()]

◮ Vector-like fermions: ψL,R

(NF, SM-charged)

◮ Complex scalars: S

(N2

F, uncharged)

−LY

BSM = y tr ψLSψR + h.c.

Extending the BSM Yukawa sector

Choose SU

C

SU

L

U

Y reps. of

to couple with SM (L E H) Case study A: , NF

Other possibilities: ...

Y BSM

y tr

LS R

LH

R

tr ES

L

h c

Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW / 6

AS models and the fmavor connection

Modifying β-functions ◮ Gauge: βg = α2

g(−B + Cαg −Dαy ) Yukawa couplings essential

◮ Yukawa: βy = αy(Eαy − Fαg) What works?

Introduce large fmavor sector

[Litim, Sannino ()]

◮ Vector-like fermions: ψL,R

(NF, SM-charged)

◮ Complex scalars: S

(N2

F, uncharged)

−LY

BSM = y tr ψLSψR + h.c.

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), NF = 3

Other possibilities: ψ(1, 3, −1), ψ(1, 2, 3/2)...

−LY

BSM = y tr ψLSψR + κLHψR + tr κ′ES†ψL + h.c.

Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW / 6

Fixed Points and Matching

Fixed Points exist for these models

FP

αFP

1

αFP

2

αFP

κ

αFP

κ′

αFP

y

A1

1.06 0.886 1.59

A2 . . .

1.10

. . .

0.569

. . .

1.20

. . .

1.66

. . . . . .

β(α)

• FP = 0

Matching: connecting SM and BSM running Prediction of BSM Yukawas at low energies:

Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW / 6

Fixed Points and Matching

Fixed Points exist for these models

FP

αFP

1

αFP

2

αFP

κ

αFP

κ′

αFP

y

A1

1.06 0.886 1.59

A2 . . .

1.10

. . .

0.569

. . .

1.20

. . .

1.66

. . . . . .

β(α)

• FP = 0

Matching: connecting SM and BSM running

0.001 100 107 1012 1017 1022 104 0.001 0.01 0.1 1 Μ TeV ΑΜ

MF 1 TeV

A1

1020 1016 1012 108 104 1 104 0.001 0.01 0.1 1 Μ MFP ΑΜ

A2

Α1 Α2 Αy ΑΚ ΑΚ'

Prediction of BSM Yukawas at low energies: ακ, ακ′ ∼ 3 · 10−3

Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW / 6

Constraints

EW precision parameters

W, Y ∝ α2,1

10

M2

W

M2

F

∆B2,1

change in -loop coeffjcient

A B D

0.1 0.2 0.5 1.0 2.0 5.0 0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 MF TeV W,Y x 103

LHC 8 TeVLEP LHC 13 TeV

Bounds from [Farina et. al. ()]

LFV decays

Induced by new Yukawas

ij LiH Rj

e h Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW / 6

Constraints

EW precision parameters

W, Y ∝ α2,1

10

M2

W

M2

F

∆B2,1

change in -loop coeffjcient

A B D

0.1 0.2 0.5 1.0 2.0 5.0 0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 MF TeV W,Y x 103

LHC 8 TeVLEP LHC 13 TeV

Bounds from [Farina et. al. ()]

LFV decays

Induced by new Yukawas

κ ij LiHψRj

µ

e

ψ

h

κ κ γ ΜeΓ ΤΜΓ

1 2 5 10 20 50 100 104 0.01 1 100 MF TeV ΑΚij

ΜeΓ MEGII Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW / 6

Contributions to (g − 2)µ

(g − 2)µ anomaly: ∆aµ = 268(63)(43) · 10−11

[PDG (8)]

Contribution through

◮ Two Yukawas: κ LHψ + tr κ′ES†ψL ◮ Scalar mixing: δ HH†tr[SS†]

µ µ γ ψ2 ψ2

h s22

κ κ′ δ

aNP

µ ∝ δ mh

MS mµ MF

κκ′ 16π2

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

Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW 6 / 6

Contributions to (g − 2)µ

(g − 2)µ anomaly: ∆aµ = 268(63)(43) · 10−11

[PDG (8)]

Contribution through

◮ Two Yukawas: κ LHψ + tr κ′ES†ψL ◮ Scalar mixing: δ HH†tr[SS†]

µ µ γ ψ2 ψ2

h s22

κ κ′ δ

aNP

µ ∝ δ mh

MS mµ MF

κκ′ 16π2

Use predictions from matching: ακ, ακ′ ∼ 3 · 10−3 Explaining ∆aµ 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

Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW 6 / 6

Contributions to (g − 2)µ

(g − 2)µ anomaly: ∆aµ = 268(63)(43) · 10−11

[PDG (8)]

Contribution through

◮ Two Yukawas: κ LHψ + tr κ′ES†ψL ◮ Scalar mixing: δ HH†tr[SS†]

µ µ γ ψ2 ψ2

h s22

κ κ′ δ

aNP

µ ∝ δ mh

MS mµ MF

κκ′ 16π2

Use predictions from matching: ακ, ακ′ ∼ 3 · 10−3 Explaining ∆aµ 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

∆aµ 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

f f

ψ ψ γ, Z

(a)

u d

ψ−Q ψQ−1

W

(b)

f f

ℓ+ ψ−

h

(c)

ℓ− ψ− ψ+ ℓ+

h, S

(d)

ℓ− ψ− ℓ+ ℓ+

h

(e)

ℓ−

S† S/h

ℓ+ ψ

(f)

f f S/h S† h

(g)

Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW /

Running with scalar sector

Previous analysis: 210 approximation, β-functions computed at

◮ Gauge: -loop ◮ Yukawa: -loop ◮ Scalar: -loop (decoupled)

Example at 222, case A, with scalar potential V(H, S) = − µ2H†H − µ2

s tr[S†S] − µdet

• detS + detS†

+ λ(H†H)2 + u tr

• S†SS†S
• + v
• tr
• S†S

2 + δ H†H tr

• S†S
• 1

2 5 10 20 50 100 105 104 0.001 0.01 0.1 Μ TeV ΑΜ Α1 Α2 Αy ΑΚ ΑΚ' ΑΛ Α∆ Αu Αv 1 1017 1034 1051 1068 1085 105 104 0.001 0.01 0.1 1 Μ TeV ΑΜ Α1 Α2 Αy ΑΚ ΑΚ' ΑΛ Α∆ Αu Αv

Clara Hormigos-Feliu Asymptotic safety and fmavor Moriond EW /