SUPERWEAK FORCE Zoltn Trcsnyi Etvs University and MTA-DE Particle - PowerPoint PPT Presentation

SUPERWEAK FORCE Zoltán Trócsányi Eötvös University and MTA-DE Particle Physics Research Group Matter to the Deepest, Chorzów, 4 September 2019

OUTLINE 1. Status of particle physics 2. U(1) Z extension of SM 3. Constraints on the parameter space 2

Status of particle physics: energy frontier LEP, LHC: SM describes final states of particle collisions precisely SM is unstable No proven sign of new physics beyond SM at colliders* *There are some indications below discovery significance (such as lepton flavor non-universality in meson decays) 3

Status of particle physics: cosmic and intensity frontiers Universe at large scale described precisely by cosmological SM: Λ CDM ( Ω m =0.3), without astrophysical explanation Neutrino flavours oscillate requiring neutrino masses Existing baryon asymmetry cannot be explained by CP asymmetry in SM Inflation of the early, accelerated expansion of the present Universe 4

Extension of SM There are many extensions proposed, mostly with the aim of predicting some observable effect at the LHC — but those have not been observed so far, so why not try something else 5

Extension of SM There are many extensions proposed, mostly with the aim of predicting some observable effect at the LHC — but those have not been observed so far, so why not try something else SM is highly efficient — let us stick to efficiency the only exception of economical description is the relatively large number of Yukawa couplings 5

Extension of SM Neutrinos must play a key role with non-zero masses they must feel another force apart from the weak one, such as Yukawa coupling to a scalar, which requires the existence of right-handed neutrinos 6

Extension of SM Neutrinos must play a key role with non-zero masses they must feel another force apart from the weak one, such as Yukawa coupling to a scalar, which requires the existence of right-handed neutrinos Simplest extension of G SM =SU(3) c × SU(2) L × U(1) Y is to G=G SM × U(1) Z 6

Extension of SM Neutrinos must play a key role with non-zero masses they must feel another force apart from the weak one, such as Yukawa coupling to a scalar, which requires the existence of right-handed neutrinos Simplest extension of G SM =SU(3) c × SU(2) L × U(1) Y is to G=G SM × U(1) Z renormalizable gauge theory without any other symmetry Fix Z-charges by requirement of 6

Extension of SM Neutrinos must play a key role with non-zero masses they must feel another force apart from the weak one, such as Yukawa coupling to a scalar, which requires the existence of right-handed neutrinos Simplest extension of G SM =SU(3) c × SU(2) L × U(1) Y is to G=G SM × U(1) Z renormalizable gauge theory without any other symmetry Fix Z-charges by requirement of gauge and gravity anomaly cancellation and gauge invariant Yukawa terms for neutrino mass generation 6

Focus only on addition to the SM, find SM in this new book: 7

Fermions (with new highlighted) fermion fields: ✓ U f ◆ f f q, 2 = U f f q, 3 = D f q, 1 = R , D f R L ✓ ⌫ f ◆ f f l, 2 = ⌫ f f l, 3 = ` f l, 1 = R , ` f R where L L / R ⌘ ⌥ = 1 2 (1 ⌥ � 5 ) ⌘ P L / R , ( ν L can ν R can also be Majorana neutrinos, embedded into different Dirac spinors) covariant derivative (includes kinetic mixing): ≡ g 0 Z r j +( g 0 Z − g 0 Y ) y j z }| { j = @ µ + i g L T · W µ + i g Y y j B 0 µ + i( g 0 D µ Y y j ) Z 0 µ Z z j − g 0 8

Scalars Standard Φ complex SU(2) L doublet and new � complex singlet: L φ , χ = [ D ( φ ) µ φ ] ⇤ D ( φ ) µ φ + [ D ( χ ) µ χ ] ⇤ D ( χ ) µ χ − V ( φ , χ ) ( with scalar potential ◆ ✓ | φ | 2 | φ | 2 , | χ | 2 � ✓ λ φ λ ◆ χ | χ | 2 + V ( φ , χ ) = V 0 − µ 2 φ | φ | 2 − µ 2 � 2 λ | χ | 2 λ χ 2 9

Scalars Standard Φ complex SU(2) L doublet and new � complex singlet: L φ , χ = [ D ( φ ) µ φ ] ⇤ D ( φ ) µ φ + [ D ( χ ) µ χ ] ⇤ D ( χ ) µ χ − V ( φ , χ ) ( with scalar potential ◆ ✓ | φ | 2 | φ | 2 , | χ | 2 � ✓ λ φ λ ◆ χ | χ | 2 + V ( φ , χ ) = V 0 − µ 2 φ | φ | 2 − µ 2 � 2 λ | χ | 2 λ χ 2 After SSB, G → SU(3) c × U(1) QED : ✓ ◆ � = 1 0 � ( x ) = 1 2 e i T · ξ ( x ) /v & e i ⌘ ( x ) /w � � w + s 0 ( x ) p p v + h 0 ( x ) 2 9

Anomaly free charge assignment is added for later convenience. (a) (b) (c) field SU (3) c SU (2) L y j z j z j r j = z j /z φ − y j 1 1 U L , D L 3 2 Z 1 0 6 6 2 7 1 U R 3 1 Z 2 3 6 2 − 1 − 5 − 1 D R 3 1 2 Z 1 − Z 2 3 6 2 − 1 − 1 ⌫ L , ` L 1 2 − 3 Z 1 0 . 2 2 1 1 1 1 0 Z 2 − 4 Z 1 ⌫ R 2 2 − 3 − 1 1 1 − 1 − 2 Z 1 − Z 2 ` R 2 2 1 1 1 2 z φ 1 � 2 2 1 1 0 z χ − 1 − 1 � 10 (a) anomaly free charges (b) from neutrino-scalar interactions (c) from re-parametrization of couplings

Fermion-scalar interactions Standard Yukawa terms: � ¯ � ¯  ✓ � (+) ◆ ✓ � (0) ⇤ ◆ ✓ � (+) ◆ � U, ¯ U, ¯ ⌫ ` , ¯ � � � � L Y = � D R + c U U R + c ` ¯ c D D D ` ` R � (0) � � (+) ⇤ � (0) L L L + h . c . lead to fermion masses after SSB: ◆ ⇥ ¯ ✓ 1 + h ( x ) U L M U U R + ¯ D L M D D R + ¯ ⇤ L Y = − + h . c . ` L M ` ` R v 11

Fermion-scalar interactions Standard Yukawa terms: � ¯ � ¯  ✓ � (+) ◆ ✓ � (0) ⇤ ◆ ✓ � (+) ◆ � U, ¯ U, ¯ ⌫ ` , ¯ � � � � L Y = � D R + c U U R + c ` ¯ c D D D ` ` R � (0) � � (+) ⇤ � (0) L L L + h . c . lead to fermion masses after SSB: ◆ ⇥ ¯ ✓ 1 + h ( x ) U L M U U R + ¯ D L M D D R + ¯ ⇤ L Y = − + h . c . ` L M ` ` R v Neutrino Yukawa terms ( ): lation z χ = − 2 z ν R ✓ φ ν j, R + 1 ◆ ( c ν ) ij ¯ L i, L · ˜ X L ν 2( c R ) ij ν c Y = − + h . c . i, R ν j, R χ 11 i,j (Dirac mass terms)

Fermion-scalar interactions Standard Yukawa terms: � ¯ � ¯  ✓ � (+) ◆ ✓ � (0) ⇤ ◆ ✓ � (+) ◆ � U, ¯ U, ¯ ⌫ ` , ¯ � � � � L Y = � D R + c U U R + c ` ¯ c D D D ` ` R � (0) � � (+) ⇤ � (0) L L L + h . c . lead to fermion masses after SSB: ◆ ⇥ ¯ ✓ 1 + h ( x ) U L M U U R + ¯ D L M D D R + ¯ ⇤ L Y = − + h . c . ` L M ` ` R v Neutrino Yukawa terms ( ): lation z χ = − 2 z ν R ✓ φ ν j, R + 1 ◆ ( c ν ) ij ¯ L i, L · ˜ X L ν 2( c R ) ij ν c Y = − + h . c . i, R ν j, R χ 11 i,j (Majorana mass terms)

Charge assignment from gauge invariant neutrino interactions is added for later convenience. (a) (b) (c) field SU (3) c SU (2) L y j z j z j r j = z j /z φ − y j 1 1 U L , D L 3 2 Z 1 0 6 6 2 7 1 U R 3 1 Z 2 3 6 2 − 1 − 5 − 1 D R 3 1 2 Z 1 − Z 2 3 6 2 − 1 − 1 ⌫ L , ` L 1 2 − 3 Z 1 0 . 2 2 1 1 1 1 0 Z 2 − 4 Z 1 ⌫ R 2 2 − 3 − 1 1 1 − 1 − 2 Z 1 − Z 2 ` R 2 2 1 1 1 2 z φ 1 � 2 2 1 1 0 z χ − 1 − 1 � 12 (a) anomaly free charges (b) from neutrino-scalar interactions (c) from re-parametrization of couplings

Charge assignment from re-parametrization of couplings is added for later convenience. (a) (b) (c) field SU (3) c SU (2) L y j z j z j r j = z j /z φ − y j 1 1 U L , D L 3 2 Z 1 0 6 6 2 7 1 U R 3 1 Z 2 3 6 2 − 1 − 5 − 1 D R 3 1 2 Z 1 − Z 2 3 6 2 − 1 − 1 ⌫ L , ` L 1 2 − 3 Z 1 0 . 2 2 1 1 1 1 0 Z 2 − 4 Z 1 ⌫ R 2 2 − 3 − 1 1 1 − 1 − 2 Z 1 − Z 2 ` R 2 2 1 1 1 2 z φ 1 � 2 2 1 1 0 z χ − 1 − 1 � 13 (a) anomaly free charges (b) from neutrino-scalar interactions (c) from re-parametrization of couplings

After SSB neutrino mass terms appear ✓ ν c " # Y = − 1 ◆ X L ν � � ν L , ν c L i M ( h, s ) ij + h . c . R ν R 2 j i,j where ! � 1 + h � 0 m D v M ( h, s ) ij = � 1 + h � � 1 + s � m D M M v w ij 6x6 symmetric matrix ( m D complex, M M real) 14

After SSB neutrino mass terms appear ✓ ν c " # Y = − 1 ◆ X L ν � � ν L , ν c L i M ( h, s ) ij + h . c . R ν R 2 j i,j where ! � 1 + h � 0 m D v M ( h, s ) ij = � 1 + h � � 1 + s � m D M M v w ij 6x6 symmetric matrix ( m D complex, M M real) in diagonal: Majorana mass terms (so ν L massless!) 14

After SSB neutrino mass terms appear ✓ ν c " # Y = − 1 ◆ X L ν � � ν L , ν c L i M ( h, s ) ij + h . c . R ν R 2 j i,j where ! � 1 + h � 0 m D v M ( h, s ) ij = � 1 + h � � 1 + s � m D M M v w ij 6x6 symmetric matrix ( m D complex, M M real) in diagonal: Majorana mass terms (so ν L massless!) but ν L and ν R have the same q-numbers, can mix, leading to type-I see-saw 14

Effective light neutrino masses If m i << M j , can integrate out the heavy neutrinos ◆ 2 ⇣ ✓ dim � 5 = � 1 1 + h ⌘ X 0 c i, L ν 0 m M ,i i, L + h . c . L ν ν 2 v i m M ,i = m 2 where are Majorana masses i M i 15

Effective light neutrino masses If m i << M j , can integrate out the heavy neutrinos ◆ 2 ⇣ ✓ dim � 5 = � 1 1 + h ⌘ X 0 c i, L ν 0 m M ,i i, L + h . c . L ν ν 2 v i m M ,i = m 2 where are Majorana masses i M i if m i ~ O(100keV) and M j ~ O(100GeV), then m M,i ~ O(0.1eV) 15