The cost of gauge coupling unification in the SU(5) at 3 loops - PowerPoint PPT Presentation

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

Outline Motivation Georgi-Glashow SU(5) model A minimal extension: SU(5)+ 24 F 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

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

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

Georgi-Glashow Model Particle content of minimal SU(5) and SM embedding [Georgi and Glashow ’74] Gauge sector: 24 V = B (1 , 1 , 0) ⊕ W (1 , 3 , 0) ⊕ G (8 , 1 , 0) ⊕ X (3 , 2 , − 5 6 ) ⊕ X (3 , 2 , + 5 6 ) SM fermions: 5 F = (3 , 1 , + 1 ⊕ (1 , 2 , − 1 3 ) 2 ) and � �� � � �� � d c ℓ 10 F = (3 , 1 , − 2 ⊕ (3 , 2 , + 1 3 ) 6 ) ⊕ (1 , 1 , +1) � �� � � �� � � �� � e c u c q Scalar sector: 5 H = (3 , 1 , − 1 ⊕ (1 , 2 , + 1 3 ) H 2 ) H and � �� � � �� � T h ⊕ (3 , 2 , − 5 ⊕ (3 , 2 , + 5 24 H = (1 , 1 , 0) H ⊕ (1 , 3 , 0) H ⊕ (8 , 1 , 0) H 6 ) H 6 ) H � �� � � �� � � �� � � �� � � �� � S H T H O H X H X H Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.4

Georgi-Glashow Model Particle content of minimal SU(5) and SM embedding [Georgi and Glashow ’74] 24 V , 5 F , 10 F , 5 H , 24 H Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.4

Georgi-Glashow Model Particle content of minimal SU(5) and SM embedding [Georgi and Glashow ’74] 24 V , 5 F , 10 F , 5 H , 24 H SU(5) breaking: � 24 H � � 5 H � SU(5) − → SU(3) C ⊗ SU(2) L ⊗ U(1) Y − → 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

Georgi-Glashow Model Particle content of minimal SU(5) and SM embedding [Georgi and Glashow ’74] 24 V , 5 F , 10 F , 5 H , 24 H SU(5) breaking: � 24 H � � 5 H � SU(5) − → SU(3) C ⊗ SU(2) L ⊗ U(1) Y − → SU(3) C ⊗ U(1) Q Proton become unstable: M 4 1 τ th p ∼ X α 2 m 5 p G ⇒ M X ≥ 10 15 . 5 GeV ≥ 10 33 yr τ exp p Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.4

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

Minimal SU(5) model is ruled out Gauge couplings do not unify 3-loop running: [L.M., J. Salomon, M. Steinhauser ’12] 0.05 SM input parameters: 0.045 0.04 α MS 1 ( M Z ) = 0 . 0169225 ± 0 . 0000039 , α 1 , α 2 , α 3 0.035 α MS 2 ( M Z ) = 0 . 0033735 ± 0 . 000020 , 0.03 α MS 3 ( M Z ) = 0 . 1173 ± 0 . 00069 , 0.025 α MS t ( M Z ) = 0 . 07514 . [PDG 2012] 0.02 0.015 0.01 2 4 6 8 10 12 14 16 log 10 ( µ /GeV) Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.5

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

Minimal SU(5) model is ruled out Gauge couplings do not unify Neutrinos are massless L Y = Y d 5 F 10 F 5 ∗ + Y u 10 F 10 F 5 H + h.c. + . . . . H � �� � � �� � M U M D = M L Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.5

Minimal SU(5) model is ruled out Gauge couplings do not unify Neutrinos are massless � � L Y = Y d 5 F 10 F 5 ∗ + h.c. + 1 + Y u 10 F 10 F 5 H Y ν 5 F 5 F 5 H 5 H + . . . H Λ � �� � � �� � M U M D = M L m ν ∼ Y ν v 2 for Λ ≈ 10 17 GeV: m ν ≈ 10 − 4 eV ⇒ Λ ⇒ much too light! Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.5

SU(5)+ 24 F Add an adjoint fermionic multiplet: 24 F [Bajc, Senjanovic ’06], [Bajc,Nemevsek, Senjanovic ’07] ⊕ (3 , 2 , − 5 ⊕ (3 , 2 , + 5 24 F = (1 , 1 , 0) F ⊕ (1 , 3 , 0) F ⊕ (8 , 1 , 0) F 6 ) F 6 ) F � �� � � �� � � �� � � �� � � �� � S F T F O F X F X F Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.6

SU(5)+ 24 F Add an adjoint fermionic multiplet: 24 F [Bajc, Senjanovic ’06], [Bajc,Nemevsek, Senjanovic ’07] ⊕ (3 , 2 , − 5 ⊕ (3 , 2 , + 5 24 F = (1 , 1 , 0) F ⊕ (1 , 3 , 0) F ⊕ (8 , 1 , 0) F 6 ) F 6 ) F � �� � � �� � � �� � � �� � � �� � S F T F O F X F X F 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

SU(5)+ 24 F Add an adjoint fermionic multiplet: 24 F [Bajc, Senjanovic ’06], [Bajc,Nemevsek, Senjanovic ’07] ⊕ (3 , 2 , − 5 ⊕ (3 , 2 , + 5 24 F = (1 , 1 , 0) F ⊕ (1 , 3 , 0) F ⊕ (8 , 1 , 0) F 6 ) F 6 ) F � �� � � �� � � �� � � �� � � �� � S F T F O F X F X F 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

SU(5)+ 24 F Add an adjoint fermionic multiplet: 24 F [Bajc, Senjanovic ’06], [Bajc,Nemevsek, Senjanovic ’07] ⊕ (3 , 2 , − 5 ⊕ (3 , 2 , + 5 24 F = (1 , 1 , 0) F ⊕ (1 , 3 , 0) F ⊕ (8 , 1 , 0) F 6 ) F 6 ) F � �� � � �� � � �� � � �� � � �� � S F T F O F X F X F Gauge coupling can unify ( see below ) Neutrinos get masses δ L Y = y ν 5 F 24 F 5 H ⇒ New Yukawa interactions: after EW breaking: � � T y j S y j y i y i ij = − v 2 m ν m TF + T S 2 m SF 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

Unification Pattern Renormalization Group Equations � � � α i � 2 µ 2 d α i α j � b ( i ) π b ( ij ) = β i ( { α j } ) = − + + . . . 0 1 dµ 2 π π j ¯ q ¯ ¯ q q g g q q g q 3 ∼ g s ∼ g s Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.7

Unification Pattern Renormalization Group Equations � � � α i � 2 µ 2 d α i α j � b ( i ) π b ( ij ) = β i ( { α j } ) = − + + . . . 0 1 dµ 2 π π j 0.5 Lattice Theory NLO NNLO � s (Q) Data Deep Inelastic Scattering + e - e Annihilation 0.4 Hadron Collisions Heavy Quarkonia (5) �������� s Z MS 251 MeV 0.1215 0.3 QCD 4 � 0.1184 213 MeV O(���� s 178 MeV 0.1153 0.2 0.1 1 10 100 Q [GeV] Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.7

Unification Pattern Renormalization Group Equations � � � α i � 2 µ 2 d α i α j � b ( i ) π b ( ij ) = β i ( { α j } ) = − + + . . . 0 1 dµ 2 π π j New particles w.r.t. SM that can contribute to the gauge coupling running ( 1-loop ) Α i � 1 proton decay SU (5) ∆ b 0 State 60 ( 1 1 5 H T 6 , 0 , 15 ) 50 ( 0 , 1 24 H T H 3 , 0 ) 40 ( 1 24 H O H 2 , 0 , 0 ) 30 ( 0 , 4 24 F T F 3 , 0 ) 20 24 F O F ( 2 , 0 , 0 ) 10 ( 4 3 , 2 , 10 24 F X F 3 ) 2 4 6 8 10 12 14 16 log 10 � Μ � GeV � Rencontres de Moriond EW 2013 Luminita Mihaila – The cost of gauge coupling unification in SU(5) at 3 loops – p.7