from exact asymptotic safety to physics beyond the Standard Model - - PowerPoint PPT Presentation

Daniel F Litim

from exact asymptotic safety to physics beyond the Standard Model

Heidelberg, 9 Mar 2017

DF Litim 1102.4624 DF Litim, F Sannino, 1406.2337 AD Bond, DF Litim, 1608.00519 AD Bond, G Hiller, K Kowalska, DF Litim, 1702.01727

standard model

local QFT for fundamental interactions strong nuclear force weak force electromagnetic force

• pen challenges

what comes beyond the SM? how does gravity fit in?

asymptotic safety

some or all couplings achieve interacting UV fixed point

Wilson ’71 Weinberg ’79

if so, new directions for BSM physics &, possibly, quantum gravity 4D gauge-Yukawa theory with exact asymptotic safety

Litim, Sannino, 1406.2337

idea: proof of existence:

Bond, Litim @ERG2016

• 1. theorems for asymptotic safety
• 2. weakly interacting UV completions
• f the Standard Model
• 3. constraints from data (colliders)

AD Bond, G Hiller, K Kowalska, DF Litim, 1702.01727 Bond, Litim 1608.00519

today:

asymptotic safety

• 1. theorems for asymptotic safety
• 2. weakly interacting UV completions
• f the Standard Model
• 3. constraints from data (colliders)

AD Bond, G Hiller, K Kowalska, DF Litim, 1702.01727 Bond, Litim 1608.00519

today:

asymptotic safety

conditions for asymptotic safety

*) provided certain auxiliary conditions hold true *) *)

results

Bond, Litim 1608.00519

t = ln µ/Λ

α∗ ⌧ 1

basics of asymptotic safety

∂tαg = −B α2

g + C α3 g − D α2 g αy

∂tαy = E α2

y − F αg αy

gauge Yukawa theory loop coefficients in any QFT D, E, F > 0 asymptotic freedom B > 0 C < 0 or C > 0 Banks-Zaks IR FP in the latter case: theory α∗

g = B

C 0 < α∗ = B/C ⌧ 1

t = ln µ/Λ

α∗ ⌧ 1

basics of asymptotic safety

∂tαg = −B α2

g + C α3 g − D α2 g αy

∂tαy = E α2

y − F αg αy

loop coefficients in any QFT D, E, F > 0 infrared freedom B < 0 gauge theory for C < 0 we must have CS

2 < 1

11CG

2

0 < α∗ = B/C ⌧ 1

asymptotic safety E8 E7 E6 F4 G2 SOHNL SpHNL SUHNL

5 10 15 20 0.0 0.2 0.4 0.6 0.8 1.0

3 8 1 2 1 11 2 3 7 12 13 18 19 24

1 N Χ

χ = min C2(R) C2(adj)

result:

asymptotic safety E8 E7 E6 F4 G2 SOHNL SpHNL SUHNL

5 10 15 20 0.0 0.2 0.4 0.6 0.8 1.0

3 8 1 2 1 11 2 3 7 12 13 18 19 24

1 N Χ

χ = min C2(R) C2(adj)

implication:

B ≤ 0 ⇒ C > 0

no go theorem

result:

t = ln µ/Λ

α∗ ⌧ 1

basics of asymptotic safety

∂tαg = −B α2

g + C α3 g − D α2 g αy

∂tαy = E α2

y − F αg αy

loop coefficients in any QFT D, E, F > 0 infrared freedom B < 0 B < 0 ⇒ C > 0

Bond, Litim 1608.00519

gauge theory 0 < α∗ = B/C ⌧ 1

t = ln µ/Λ

α∗ ⌧ 1

basics of asymptotic safety

∂tαg = −B α2

g + C α3 g − D α2 g αy

∂tαy = E α2

y − F αg αy

loop coefficients in any QFT D, E, F > 0 infrared freedom B < 0 B < 0 ⇒ C > 0 more gauge: useless scalar quartics: useless Yukawas: unique viable option

Bond, Litim 1608.00519

gauge theory can other couplings help? 0 < α∗ = B/C ⌧ 1

t = ln µ/Λ

α∗ ⌧ 1

basics of asymptotic safety

∂tαg = −B α2

g + C α3 g − D α2 g αy

∂tαy = E α2

y − F αg αy

gauge Yukawa theory loop coefficients in any QFT D, E, F > 0

t = ln µ/Λ

α∗ ⌧ 1

basics of asymptotic safety

∂tαg = −B α2

g + C α3 g − D α2 g αy

∂tαy = E α2

y − F αg αy

gauge Yukawa theory Yukawa nullcline α∗

y = F

E α∗

g

t = ln µ/Λ

α∗ ⌧ 1

basics of asymptotic safety

∂tαg = −B α2

g + C α3 g − D α2 g αy

∂tαy = E α2

y − F αg αy

gauge Yukawa theory α∗

y = F

E α∗

g

βg| = (−B + C0 αg) α2

g

C → C0 = C − D F E shifted two-loop interacting UV fixed point iff D F − C E > 0 Yukawa nullcline

t = ln µ/Λ

α∗ ⌧ 1

basics of asymptotic safety

∂tαg = −B α2

g + C α3 g − D α2 g αy

∂tαy = E α2

y − F αg αy

gauge Yukawa theory α∗

y = F

E α∗

g

βg| = (−B + C0 αg) α2

g

(α⇤

g , α⇤ y) =

✓ B C0 , B C0 F E ◆ gauge-Yukawa UV or IR fixed point Yukawa nullcline

t = ln µ/Λ

α∗ ⌧ 1

basics of asymptotic safety

∂tαg = −B α2

g + C α3 g − D α2 g αy

∂tαy = E α2

y − F αg αy

gauge Yukawa theory summary of fixed points (α∗

g, α∗ y) = (0, 0)

(α∗

g, α∗ y) =

✓B C , 0 ◆ (α⇤

g , α⇤ y) =

✓ B C0 , B C0 F E ◆ Gaussian Banks-Zaks gauge-Yukawa IR UV or IR UV or IR

conditions for asymptotic safety

*) provided certain auxiliary conditions hold true *) *)

results

Bond, Litim 1608.00519

• Y4

G BZ

• Y4

G

• Y4

GY G

• Y4

GY G BZ

B > 0 > C 0 > B, C0 B, C, C0 > 0 B, C > 0 > C0

• 1. theorems for asymptotic safety
• 2. weakly interacting UV completions
• f the Standard Model
• 3. constraints from data (colliders)

AD Bond, G Hiller, K Kowalska, DF Litim, 1702.01727 Bond, Litim 1608.00519

asymptotic safety

AD Bond, G Hiller, K Kowalska, DF Litim, 1702.01727

asymptotic safety beyond the SM

L = LSM + LBSM, kin. + LBSM, pot. + LBSM, Yukawa BSM Lagrangean ψi(R3, R2, Y ) Sij flavors of BSM fermions BSM singlet scalars NF LBSM, Yukawa = −y Tr(ψL S ψR + ψR S† ψL) U(NF ) × U(NF ) global flavor symmetry

Bond, Hiller, Kowalska, Litim, 1702.01727

UV fixed points

BSM fixed points

FP4 FP3 FP2 weak becomes strong strong becomes weak strong remains strong weak remains weak weak becomes the new strong α∗

2

α∗

3

→ 3 2 α∗

3 > 0

α∗

2 = 0

α∗

2 > 0

α∗

3 = 0

δα2(Λ), δα3(Λ) δα2(Λ), δα3(Λ) δα3(Λ) UV critical surface UV critical surface UV critical surface

BSM fixed points

1 3 6 8 10 15 200 400 600 800

R3 NF

R2 = 3 R2 = 4 R2 = 5 6 8 10 15 15' 21 100 200 300

R3 NF

R2 = 1 R2 = 2 R2 = 3 3 6 8 10 15 15' 100 200

R3 NF

R2 = 1 R2 = 2 R2 = 3

FP4 FP3 FP2

α∗

2, α∗ 3 > 0

α∗

2 > 0

α∗

3 = 0

α∗

3 > 0

α∗

2 = 0

FP3 FP2 FP4

1 3 6 8 10 1 2 3 4 5 1 3 6 8 10 1 2 3 4 5

R3 R2

NF

summary of fixed points

benchmark models

benchmark models

Α3 Α2 Α y

matching

scale

cross - over scale

R3 = 1, R2 = 4, NF = 12 1000 104 105 106 10-4 0.001 0.01 0.1 1 m HGeVL

FP2

(1,4,12)

(R3, R2, NF ) =

model A

low scale

cross-over

“ w e a k b e c

• m

e s s t r

• n

g , s t r

• n

g b e c

• m

e s w e a k ”

benchmark models

model B

FP3

Α3 Α y Α2

matching

scale

cross - over scale

R3 = 10, R2 = 1, NF = 30 1000 2000 5000 1 ¥ 104 2 ¥ 104 10-4 0.001 0.01 0.1 1 m HGeVL

(10,1,30)

(R3, R2, NF ) =

low scale

cross-over

“strong remains strong, weak remains weak”

benchmark models

model B

(10,1,30)

(R3, R2, NF ) =

FP4

Hmodel BL

Α3 Αy Α2

1 10 100 1000 104 0.001 0.005 0.010 0.050 0.100 0.500

ΜêΜ0

weak BZ

NO matching

• nto SM

benchmark models

(10,4,80)

(R3, R2, NF ) =

R3 = 10, R2 = 4, NF = 80

Α y Α3 Α2

matching

scale

cross - over scale

1000 2000 5000 1 ¥ 104 2 ¥ 104 10-5 10-4 0.001 0.01 0.1 1 m HGeVL

FP3

model C

low scale

cross-over

“strong remains strong weak remains weak”

benchmark models

(10,4,80)

(R3, R2, NF ) =

model C

R3 = 10, R2 = 4, NF = 80

Α y Α3 Α2

matching scale cross - over scale

5 ¥ 1010 1 ¥ 1011 2 ¥ 1011 5 ¥ 1011 1 ¥ 1012 0.001 0.002 0.005 0.010 0.020 0.050 0.100 0.200 m HGeVL

FP4 high scale

“weak” becomes the new “strong”

benchmark models

(10,4,80)

(R3, R2, NF ) =

model C

R3 = 10, R2 = 4, NF = 80

Α2 Α y Α3

matching

scale

cross - over scale

2 ¥ 1010 5 ¥ 1010 1 ¥ 1011 2 ¥ 1011 5 ¥ 1011 1 ¥ 1012 10-4 0.001 0.01 0.1 1 m HGeVL

c r

• s

s

• v

e r I

FP4 (model C)

c r

• s

s

• v

e r I I m a t c h i n g s c a l e

FP2

high scale

cross-over II

F P 4

“flyby” FP2

“ w e a k b e c

• m

e s s t r

• n

g & s t r

• n

g b e c

• m

e s w e a k ”

R3 = 3, R2 = 4, NF = 290

Α y Α3 Α2

matching

scale

cross - over scale

1000 10 000 5000 2000 3000 1500 7000 0.001 0.002 0.005 0.010 0.020 0.050 0.100 m HGeVL

benchmark models

(3,4,290)

(R3, R2, NF ) =

model D

cross-over

FP4 low scale

“weak stronger than strong”

summary of SM matching: when it works

FP3

FP2

genuinely, except in special circumstances (competition with other nearby FPs) genuinely, except in special circumstances (competition with other nearby FPs)

summary of SM matching: when it works

NF Μ

high scale no match HweakL low scale no match HstrongL

1 3 6 8 10 1 2 3 4 5 1 3 6 8 10 1 2 3 4 5

R3 R2

FP4

• 1. theorems for asymptotic safety
• 2. weakly interacting UV completions
• f the Standard Model
• 3. constraints from data (colliders)

AD Bond, G Hiller, K Kowalska, DF Litim, 1702.01727 Bond, Litim 1608.00519

asymptotic safety

phenomenology

assume low scale matching some BSM masses within TeV energy range assume R3 6= 1 for LHC R3 = 1 ( can be tested at future colliders) e+e− 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

Model E M

• d

e l C Model B

500 1000 1500 2000 2500 3000 0.006 0.007 0.008 0.009 0.010

Q @GeVD

Α3

Mψ ≥ 1.5 TeV

ATLAS & CMS:

SU(3) BSM running

Model A Model C Model E

500 1000 2000 5000 0.0020 0.0025 0.0030 0.0035 0.0040 0.0045 0.0050

Q @GeVD

Α2

SU(2) BSM running

di-boson spectra and resonances

assume resonant production of BSM scalars loop-mediated decay into

Sii ψi ψi G G g g

GG = gg, γγ, ZZ, Zγ, or WW interference effects Mψ . MS < 2Mψ “high Ms” MS . Mψ “low Ms” MS < √s MS < 2Mψ

dijet cross section

Model B Model D

2 5 10 20 50 100 200 0.1 10 1000 105

My @TeVD

sHppÆSÆggL @fbD

m a x . i n t e r f e r e n c e no interference

ATLAS dijet bounds on

σ × BR × A

MS = 1.5 TeV

A = 50 − 100%

Model B

1 2 5 10 20 50 1 2 5 10 20 50 100

MΨ @TeVD MS @TeVD

LHC

• max. interference

no interference

R hadron searches

BSM running

di-jet limits

(10,1,30)

mass exclusion limits

scan over masses

conclusions

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 theorems for fixed points and asymptotic safety systematics

extra material

U(1)Y BSM

· Û Û ı ı ı Ì Ì Ò

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

a2

*

a3

*

C C C A D E

B

U ( 1 )Y L a n d a u p

• l

e a r i s i n g b e l

• w

MPl

B

D

phase diagrams

phase diagrams of simple gauge theories parameters B, C C0 matter content Yukawa structure

phase diagrams

• Y4

G (B > 0 > C, C0) asymptotic freedom

phase diagrams

• Y4

G

• Y4

G BZ (B, C > 0 > C0) asymptotic freedom & BZ

phase diagrams

• Y4

G

• Y4

GY G BZ (B, C, C0 > 0) asymptotic freedom, BZ & GY

phase diagrams

• Y4

G

• Y4

GY G (C > 0 > B, C0) asymptotic safety & GY

extensions I

but: do interacting UV FPs with exact asymptotic safety exist for semi-simple gauge theories? Yes! space of UV FP solutions is non-empty interacting UV FPs with exact asymptotic safety exist for simple gauge theories

Litim, Sannino, 1406.2337 Bond @ ERG 2016 and @ this meeting

extensions II

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

Lagrangean gauge Yukawa Higgs Nc colours Nf flavours Nf times Nf

extensions II

further scalar invariants

Litim, Sannino, 1406.2337

2

( )

Buyukbese, Litim @ Lattice2016 (in prep.)

extensions II

results: exact eigenvalue spectrum n

✓n = Dn + O(✏)

more weak sector

d(R3) S(R2) NF ✓TeV Mψ ◆2 . 104 contributions to muon anomalous magnetic moment together with leads to constraint ∆aexp

µ

∼ (2 − 3) · 10−9

• beyed by all benchmark models.

contributions to the rho parameter arise if fermion multiplets encounter mass splitting due to SU(2) breaking δM ⌧ Mψ NF d(R3) S(R2) δM 2 . (40 GeV)2 sub-percent splitting for TeV or higher BSM masses

R-hadron searches

assume pair-production of BSM fermions 2Mψ < √s at least the lightest has a long life ( ) and forms colorless QCD bound states with SM matter > τhadron σψ ¯

ψ ∼ NF C3

with C3 = [C2(R3)]2 d(R3) d(R2) via t-channel gluon fusion pp → ψ ¯ ψ

from ATLAS and CMS gluino searches

M min

ψ

lower limits

model B, C, D, E: 2.3, >2.4, 2.2, 2.0 TeV

di-boson spectra and resonances

assume resonant production of BSM scalars loop-mediated decay into

Sii ψi ψi G G g g

GG = gg, γγ, ZZ, Zγ, or WW interference effects Mψ . MS < 2Mψ “high Ms” MS . Mψ “low Ms” MS < √s MS < 2Mψ

R3 = 3 WW ZZ Zg gg

Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê 1 2 3 4 5 6 7 8 10-4 10-3 10-2 0.1 1 10

dHR2L GVVêGgg

Ê Ê Ê Ê Ê Ê Ê

WW ZZ Zg gg

Ê Ê Ê Ê Ê Ê Ê

R3 = 10

Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê Ê 1 2 3 4 5 6 7 8 10-4 0.001 0.01 0.1 1 10

dHR2L GVVêGgg

decays into electroweak gauge bosons

further signatures if d(R2) 6= 1 general scalar resonance decaying into WW, ZZ, Zγ, γγ MS . Mψ “low Ms” growth with dim(R2)

¯ ΓW W = α2

2

α2

3

, ¯ ΓZZ ≈ 1 2 α2

2

α2

3

, ¯ ΓZγ ≈ α1 α3 α2 α3 , ¯ Γγγ ≈ 1 2 α2

1

α2

3

¯ ΓV V = 1 F ΓV V Γgg , with F = ✓4 3 C2(R2) C2(R3) ◆2 “reduced” decay widths for small hypercharge coupling modification of widths for “high Ms” FP3 FP2 ¯ ΓW W , ¯ ΓZZ, ¯ ΓZγ, ¯ Γγγ ¯ ΓW W , ¯ ΓZZ, ¯ ΓZγ, ¯ Γγγ FP4 ¯ ΓW W , ¯ ΓZZ ¯ Γγγ ¯ ΓZγ

decays into electroweak gauge bosons ?