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The cost of gauge coupling unification in the SU(5) at 3 loops Luminita Mihaila KIT TTP Karlsruhe in collaboration with Luca Di Luzio Rencontres de Moriond EW 2013 Luminita Mihaila The cost of gauge coupling unification in SU(5) at 3

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SLIDE 1

The cost of gauge coupling unification in the SU(5) at 3 loops

Luminita Mihaila KIT – TTP Karlsruhe

in collaboration with

Luca Di Luzio

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.1

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Outline

Motivation Georgi-Glashow SU(5) model A minimal extension: SU(5)+ 24F Unification at 3-loop accuracy Results

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.2

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Motivation

The SM is amazingly successful, but it has many open questions Why are there so many free parameters ? What is the origin of the mass spectrum? Why is charge quantized? Are the fundamental forces unified? What is the origin of the neutrino masses and mixing? What is the dark matter? Why is there matter-antimatter asymmetry?

. . .

Possible answers in physics Beyond the Standard Model (BSM)

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.3

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Motivation

The SM is amazingly successful, but it has many open questions Why are there so many free parameters ? What is the origin of the mass spectrum? Why is charge quantized? Are the fundamental forces unified? What is the origin of the neutrino masses and mixing? What is the dark matter? Why is there matter-antimatter asymmetry?

. . .

Possible answers in physics Beyond the Standard Model (BSM) Here a GUT prototype: a minimal extension of the SU(5) model

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.3

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SLIDE 5

Georgi-Glashow Model

Particle content of minimal SU(5) and SM embedding [Georgi and Glashow ’74] Gauge sector: 24V = B(1, 1, 0)⊕W(1, 3, 0)⊕G(8, 1, 0)⊕X(3, 2, − 5

6)⊕X(3, 2, + 5 6)

SM fermions: 5F = (3, 1, + 1

3)

  • dc

⊕ (1, 2, − 1

2)

  • ℓ

and 10F = (3, 1, − 2

3)

  • uc

⊕ (3, 2, + 1

6)

  • q

⊕ (1, 1, +1)

  • ec

Scalar sector: 5H = (3, 1, − 1

3)H

  • T

⊕ (1, 2, + 1

2)H

  • h

and 24H = (1, 1, 0)H

  • SH

⊕ (1, 3, 0)H

  • TH

⊕ (8, 1, 0)H

  • OH

⊕ (3, 2, − 5

6)H

  • XH

⊕ (3, 2, + 5

6)H

  • XH

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.4

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Georgi-Glashow Model

Particle content of minimal SU(5) and SM embedding [Georgi and Glashow ’74] 24V , 5F , 10F , 5H , 24H

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.4

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Georgi-Glashow Model

Particle content of minimal SU(5) and SM embedding [Georgi and Glashow ’74] 24V , 5F , 10F , 5H , 24H SU(5) breaking: SU(5)

24H

− → SU(3)C ⊗ SU(2)L ⊗ U(1)Y

5H

− → SU(3)C ⊗ U(1)Q

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.4

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SLIDE 8

Georgi-Glashow Model

Particle content of minimal SU(5) and SM embedding [Georgi and Glashow ’74] 24V , 5F , 10F , 5H , 24H SU(5) breaking: SU(5)

24H

− → SU(3)C ⊗ SU(2)L ⊗ U(1)Y

5H

− → SU(3)C ⊗ U(1)Q Proton become unstable: τ th

p ∼ 1 α2

G

M 4

X

m5

p

⇒ MX ≥ 1015.5GeV τ exp

p

≥ 1033 yr

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.4

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SLIDE 9

Minimal SU(5) model is ruled out

Gauge couplings do not unify

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.5

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Minimal SU(5) model is ruled out

Gauge couplings do not unify SM input parameters:

αMS

1 (MZ) = 0.0169225 ± 0.0000039 ,

αMS

2 (MZ) = 0.0033735 ± 0.000020 ,

αMS

3 (MZ) = 0.1173 ± 0.00069 ,

αMS

t (MZ) = 0.07514 .

[PDG 2012] 3-loop running: [L.M., J. Salomon, M. Steinhauser ’12]

log10(µ/GeV) α1, α2, α3

0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 2 4 6 8 10 12 14 16

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.5

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SLIDE 11

Minimal SU(5) model is ruled out

Gauge couplings do not unify Neutrinos are massless

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.5

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Minimal SU(5) model is ruled out

Gauge couplings do not unify Neutrinos are massless LY = Yd5F10F5∗

H

  • MD=ML

+ Yu10F10F5H

  • MU

+h.c. + . . . .

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.5

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SLIDE 13

Minimal SU(5) model is ruled out

Gauge couplings do not unify Neutrinos are massless LY = Yd5F10F5∗

H

  • MD=ML

+ Yu10F10F5H

  • MU

+h.c. + 1

Λ

  • Yν5F5F5H5H + . . .
  • mν ∼ Yν v2

Λ

⇒ for Λ ≈ 1017GeV: mν ≈ 10−4eV ⇒ much too light!

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.5

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SLIDE 14

SU(5)+ 24F

Add an adjoint fermionic multiplet: 24F

[Bajc, Senjanovic ’06], [Bajc,Nemevsek, Senjanovic ’07]

24F = (1, 1, 0)F

  • SF

⊕ (1, 3, 0)F

  • TF

⊕ (8, 1, 0)F

  • OF

⊕ (3, 2, − 5

6)F

  • XF

⊕ (3, 2, + 5

6)F

  • XF

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.6

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SLIDE 15

SU(5)+ 24F

Add an adjoint fermionic multiplet: 24F

[Bajc, Senjanovic ’06], [Bajc,Nemevsek, Senjanovic ’07]

24F = (1, 1, 0)F

  • SF

⊕ (1, 3, 0)F

  • TF

⊕ (8, 1, 0)F

  • OF

⊕ (3, 2, − 5

6)F

  • XF

⊕ (3, 2, + 5

6)F

  • XF

Gauge coupling can unify (see below)

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.6

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SLIDE 16

SU(5)+ 24F

Add an adjoint fermionic multiplet: 24F

[Bajc, Senjanovic ’06], [Bajc,Nemevsek, Senjanovic ’07]

24F = (1, 1, 0)F

  • SF

⊕ (1, 3, 0)F

  • TF

⊕ (8, 1, 0)F

  • OF

⊕ (3, 2, − 5

6)F

  • XF

⊕ (3, 2, + 5

6)F

  • XF

Gauge coupling can unify (see below) Neutrinos get masses

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.6

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SLIDE 17

SU(5)+ 24F

Add an adjoint fermionic multiplet: 24F

[Bajc, Senjanovic ’06], [Bajc,Nemevsek, Senjanovic ’07]

24F = (1, 1, 0)F

  • SF

⊕ (1, 3, 0)F

  • TF

⊕ (8, 1, 0)F

  • OF

⊕ (3, 2, − 5

6)F

  • XF

⊕ (3, 2, + 5

6)F

  • XF

Gauge coupling can unify (see below) Neutrinos get masses New Yukawa interactions:

δLY = yν5F24F5H ⇒

after EW breaking:

mν

ij = − v2 2

  • yi

T yj T

mTF + yi

Syj S

mSF

  • 2 neutrinos are massive

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.6

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Unification Pattern

Renormalization Group Equations

µ2 d dµ2 αi π = βi({αj}) = − αi π 2

  • b(i)

+

  • j

αj π b(ij)

1

+ . . .

  • ¯

q q g ¯ q q g ¯ q q g ∼ gs ∼ gs

3

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.7

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SLIDE 19

Unification Pattern

Renormalization Group Equations

µ2 d dµ2 αi π = βi({αj}) = − αi π 2

  • b(i)

+

  • j

αj π b(ij)

1

+ . . .

  • QCD

O( 251 MeV 178 MeV

MS

(5)

  • s

Z

0.1215 0.1153

0.1 0.2 0.3 0.4 0.5

s (Q)

1 10 100

Q [GeV]

Heavy Quarkonia Hadron Collisions e

+e

  • Annihilation

Deep Inelastic Scattering

NLO NNLO

Theory Data

Lattice

213 MeV 0.1184

s 4

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.7

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SLIDE 20

Unification Pattern

Renormalization Group Equations

µ2 d dµ2 αi π = βi({αj}) = − αi π 2

  • b(i)

+

  • j

αj π b(ij)

1

+ . . .

  • New particles w.r.t. SM that can contribute to the gauge coupling running (1-loop)

SU(5) State ∆b0 5H T ( 1

6 , 0, 1 15 )

24H TH (0, 1

3 , 0)

24H OH ( 1

2 , 0, 0)

24F TF (0, 4

3 , 0)

24F OF (2, 0, 0) 24F XF ( 4

3 , 2, 10 3 )

2 4 6 8 10 12 14 16 10 20 30 40 50 60 Αi1 log10ΜGeV

proton decay

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.7

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SLIDE 21

Unification Pattern

Renormalization Group Equations

µ2 d dµ2 αi π = βi({αj}) = − αi π 2

  • b(i)

+

  • j

αj π b(ij)

1

+ . . .

  • New particles w.r.t. SM that can contribute to the gauge coupling running (1-loop)

SU(5) State ∆b0 5H T ( 1

6 , 0, 1 15 )

24H TH (0, 1

3 , 0)

24H OH ( 1

2 , 0, 0)

24F TF (0, 4

3 , 0)

24F OF (2, 0, 0) 24F XF ( 4

3 , 2, 10 3 )

2 4 6 8 10 12 14 16 10 20 30 40 50 60 Αi1 log10ΜGeV

proton decay triplets

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.7

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SLIDE 22

Unification Pattern

Renormalization Group Equations

µ2 d dµ2 αi π = βi({αj}) = − αi π 2

  • b(i)

+

  • j

αj π b(ij)

1

+ . . .

  • New particles w.r.t. SM that can contribute to the gauge coupling running (1-loop)

SU(5) State ∆b0 5H T ( 1

6 , 0, 1 15 )

24H TH (0, 1

3 , 0)

24H OH ( 1

2 , 0, 0)

24F TF (0, 4

3 , 0)

24F OF (2, 0, 0) 24F XF ( 4

3 , 2, 10 3 )

proton decay triplets

  • ctets

2 4 6 8 10 12 14 16 10 20 30 40 50 60 Αi1 log10ΜGeV

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.7

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SLIDE 23

Mass Spectrum of SU(5) + 24F

Unification requires: MT ≈ 1 TeV, MO ≈ 108 GeV Unification constraints max. value of m3 ≡ (M 4

TF MTH)1/5

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.8

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SLIDE 24

Mass Spectrum of SU(5) + 24F

Unification requires: MT ≈ 1 TeV, MO ≈ 108 GeV Unification constraints max. value of m3 ≡ (M 4

TF MTH)1/5

1-loop running analysis

15.5 15.6 15.7 15.8 15.9 16.0 16.1 l 2.0 2.5 3.0 3.5

log10(mmax

3

/GeV) log10(MG/GeV)

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.8

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SLIDE 25

Mass Spectrum of SU(5) + 24F

Unification requires: MT ≈ 1 TeV, MO ≈ 108 GeV Unification constraints max. value of m3 ≡ (M 4

TF MTH)1/5

2-loop running analysis

15.5 15.6 15.7 15.8 15.9 16.0 16.1 l 2.0 2.5 3.0 3.5

log10(mmax

3

/GeV) log10(MG/GeV)

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.8

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SLIDE 26

Mass Spectrum of SU(5) + 24F

Unification requires: MT ≈ 1 TeV, MO ≈ 108 GeV Unification constraints max. value of m3 ≡ (M 4

TF MTH)1/5

Interplay between LHC and HK to check the model

15.5 15.6 15.7 15.8 15.9 16.0 16.1 l 2.0 2.5 3.0 3.5

LHC - 14 TeV Hyper-Kamiokande - 2025

log10(mmax

3

/GeV) log10(MG/GeV)

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.8

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SLIDE 27

Mass Spectrum of SU(5) + 24F

Unification requires: MT ≈ 1 TeV, MO ≈ 108 GeV Unification constraints max. value of m3 ≡ (M 4

TF MTH)1/5

Theory side: 3-loop analysis is required !

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.8

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SLIDE 28

Effective Field Theory Approach

M M M M M

T Z O G X

SM SM+T SM+T+O SU(5) ...

Matching Matching R u n n i n g Running R u n n i n g S M SM+T S M + T + O T O

αi (M ) αi (M )

G Z

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.9

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SLIDE 29

Effective Field Theory Approach

3-loop running analysis for the gauge couplings requires: 3-loop gauge beta functions of SM

[L.M., Salomon, Steinhauser ’12], [Bednyakov, Pikelner, Velizhanin’12]

2-loop matching coefficients for T and O (here) 3-loop gauge beta functions of SM+T , SM+T+O, ... (here) 2-loop matching coefficients for super heavy particles ≈ MG (missing)

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.9

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3-loop gauge β functions

Calculation of Zgi to 3 loops:

Zgi = ZV

  • k

Zk,WF

= Z1,gici ¯

ci

Z2,ci

Z3,gi

= Z1,gigigi (

Z3,gi)3 = · · ·

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.10

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SLIDE 31

3-loop gauge β functions

Calculation of Zgi to 3 loops:

Zgi = ZV

  • k

Zk,WF

= Z1,gici ¯

ci

Z2,ci

Z3,gi

= Z1,gigigi (

Z3,gi)3 = · · ·

O(105) Feynman diagrams

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.10

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SLIDE 32

3-loop gauge β functions

Calculation of Zgi to 3 loops:

Zgi = ZV

  • k

Zk,WF

= Z1,gici ¯

ci

Z2,ci

Z3,gi

= Z1,gigigi (

Z3,gi)3 = · · ·

O(105) Feynman diagrams

MS scheme

1 non zero external momentum & all masses set to zero

⇒ MINCER [Larin, Tkachov, Vermaseren’91]

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.10

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SLIDE 33

2-loop matching coefficients

Effective Field Theory: Lfull(α(full)

i

, . . .) → Leff(α(eff)

i

, . . .) at energy µ

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.11

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SLIDE 34

2-loop matching coefficients

Effective Field Theory: Lfull(α(full)

i

, . . .) → Leff(α(eff)

i

, . . .) at energy µ “Matching” : low energy physics must be unchanged !!

α(eff)

i

= ζi α(full)

i

. . . ζi = ζi(αi, Mheavy, µ)

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.11

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SLIDE 35

2-loop matching coefficients

Effective Field Theory: Lfull(α(full)

i

, . . .) → Leff(α(eff)

i

, . . .) at energy µ “Matching” : low energy physics must be unchanged !!

α(eff)

i

= ζi α(full)

i

. . . ζi = ζi(αi, Mheavy, µ)

An example: matching of SM+T to SM+T+O

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.11

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SLIDE 36

3-loop results

Input: SM low-energy gauge couplings αi(MZ) , i = 1, 2, 3 Assumptions: MTF = MTH, MOF = MOH ≈ 107.5GeV

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.12

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SLIDE 37

3-loop results

Input: SM low-energy gauge couplings αi(MZ) , i = 1, 2, 3 Assumptions: MTF = MTH, MOF = MOH ≈ 107.5GeV 1- and 2-loop correlation 15.5 15.6 15.7 15.8 15.9 16.0 16.1 2.0 2.5 3.0 3.5 4.0 log10MGGeV log10m3

maxGeV

mTF mTH

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.12

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SLIDE 38

3-loop results

Input: SM low-energy gauge couplings αi(MZ) , i = 1, 2, 3 Assumptions: MTF = MTH, MOF = MOH ≈ 107.5GeV 3-loop correlation 15.5 15.6 15.7 15.8 15.9 16.0 16.1 2.0 2.5 3.0 3.5 4.0 log10MGGeV log10m3

maxGeV

mTF mTH

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.12

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SLIDE 39

Conclusions

Minimal extension of SU(5) Unification possible at O(1016 GeV) Light electroweak triplets at O(1 TeV) Interplay between LHC and Hyper-Kamiokande to constraint the parameter space Theory: precise (3-loop) running analysis required

Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.13