From Flavour to SUSY Flavour Models Vinzenz Maurer Universitt Basel - PowerPoint PPT Presentation

From Flavour to SUSY Flavour Models Vinzenz Maurer Universität Basel 11th July 2011 Valencia, FlaSy 2011 Based on Antusch, Calibbi, V.M. & Spinrath arXiv:1104.3040v1 Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 1 / 17

Outline 1 Motivation 2 Defining a SUSY Flavour Model 3 Testing a SUSY Flavour Model 4 Summary Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 2 / 17

Outline 1 Motivation 2 Defining a SUSY Flavour Model 3 Testing a SUSY Flavour Model 4 Summary Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 2 / 17

What we want to describe Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 3 / 17

Outline 1 Motivation 2 Defining a SUSY Flavour Model 3 Testing a SUSY Flavour Model 4 Summary Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 3 / 17

Class of Models: Matter Fields • Symmetries: SU ( 5 ) × G family • Matter fields: F ∼ (¯ 5 , 3 ) T 1 , 2 , 3 ∼ ( 10 , 1 ) N 1 , 2 ∼ ( 1 , 1 ) • SU ( 5 ) → SM F = ( d c , L ) T = ( Q , u c , e c ) Y d ∼ Y T e Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 4 / 17

Class of Models: GUT Symmetry Breaking • Adjoint of SU ( 5 ) : H 24 ∼ ( 24 , 1 ) • Broken into direction 1   3 1   3  1  H 24 ∝ Y =   3   − 1   2 − 1 2 ⇒ Different coupling to F -submultiplets Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 5 / 17

Class of Models: Family Symmetry Breaking • Flavon fields: φ i ∼ ( 1 , 3 ) • G family broken by VEVs in the directions [Antusch, King, Spinrath ’10]         0 1 0 0  , ˜ φ 1 ∼ 1  , φ 2 ∼ 1 φ 2 ∼ i  , φ 3 ∼ 0      − 1 1 w 1 • Yukawa matrices of the form   ↑ ↑ ↑ Y ∼ 1  H 24 � φ 2 � + � ˜ � φ 1 � φ 2 � � φ 3 � (1)  M M ↓ ↓ ↓ Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 6 / 17

Class of Models: Matrix Textures M N diagonal � 0 ⇒ m 1 = 0, ∼ TBM � y 1 − y 1 Y T ν = y 2 y 2 y 2 Y u diagonal  0 − ǫ 1  ǫ 1 Y d = ǫ 2 ǫ 2 + i ˜ ǫ 2 ǫ 2 + w ˜ ǫ 2   ⇒ y τ y b = 3 2 , θ CKM 0 0 ǫ 3 13   0 c 1 ǫ 1 − c 1 ǫ 1 Y T c 2 ǫ 2 + i ˜ c 2 ǫ 2 + w ˜ e = c 2 ǫ 2 c 2 ˜ ǫ 2 c 2 ˜ ǫ 2   0 0 c 3 ǫ 3 with c 1 = c 2 = c 3 = − 3 ˜ 2 , c 2 = 6 [Antusch, Spinrath ’09] Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 7 / 17

Kähler Potential and Canonical Normalisation • Kähler potential i T i + φ † M 2 F † F + φ † i φ i i φ i K = F † F + T † M 2 T † i T i • Using hierarchy ǫ 3 ∼ y b ≫ y d , s ∼ ǫ 1 , 2 , ˜ 2 : K FF † ≈ diag ( 1 , 1 , 1 + ζ 2 ) ˜ φ † 3 φ 3 with ζ 2 ∼ M 2 • Non-canonical kinetic terms ⇒ F → diag ( 1 , 1 , 1 − 1 2 ζ 2 ) F [Antusch, King, Malinsky ’07] [Antusch, Calibbi, V.M., Spinrath ’11] Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 8 / 17

Class of Models: Matrix Textures in Canonical Basis M N diagonal � 0 ⇒ m 1 = 0, ∼ TBM + ζ 2 � y 1 − y 1 k Y T ν = y 2 y 2 y 2 k Y u diagonal   0 ǫ 1 − ǫ 1 k Y d = ǫ 2 + i ˜ ( ǫ 2 + w ˜ ǫ 2 ) k ǫ 2 ǫ 2   ⇒ y τ y b = 3 2 , θ CKM − ζ 2 0 0 ǫ 3 k 13 Y T e = . . . with k = 1 − 1 2 ζ 2 [Antusch, Calibbi, V.M., Spinrath ’11] Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 9 / 17

Class of Models: Matrix Textures in Canonical Basis M N diagonal � 0 ⇒ m 1 = 0, ∼ TBM + ζ 2 � y 1 − y 1 k Y T ν = y 2 y 2 y 2 k Y u diagonal   0 ǫ 1 − ǫ 1 k Y d = ǫ 2 + i ˜ ( ǫ 2 + w ˜ ǫ 2 ) k ǫ 2 ǫ 2   ⇒ y τ y b = 3 2 , θ CKM − ζ 2 0 0 ǫ 3 k 13 Y T e = . . . with k = 1 − 1 2 ζ 2 [Antusch, Calibbi, V.M., Spinrath ’11] Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 9 / 17

Class of Models: Matrix Textures in Canonical Basis M N diagonal � 0 ⇒ m 1 = 0, ∼ TBM + ζ 2 � y 1 − y 1 k Y T ν = y 2 y 2 y 2 k Y u diagonal   0 ǫ 1 − ǫ 1 k Y d = ǫ 2 + i ˜ ( ǫ 2 + w ˜ ǫ 2 ) k ǫ 2 ǫ 2   ⇒ y τ y b = 3 2 , θ CKM − ζ 2 0 0 ǫ 3 k 13 Y T e = . . . with k = 1 − 1 2 ζ 2 [Antusch, Calibbi, V.M., Spinrath ’11] Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 9 / 17

✘✘✘✘ ✘ SUSY Mediation and Soft Terms SUSY breaking mediated by supergravity • Typically SUSY breaking by all fields with VEVs F φ = O ( 1 ) m 3 / 2 � φ � • SUGRA & sequestering results in m 2 = m 2 3 / 2 ˜ n ∂ m ˜ ˜ K − F ¯ n F m ∂ ¯ K A = A 0 Y + F m ∂ m Y with n , m running over flavons Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 10 / 17

✘✘✘✘ ✘ SUSY Mediation and Soft Terms SUSY breaking mediated by supergravity • Typically SUSY breaking by all fields with VEVs F φ = O ( 1 ) m 3 / 2 � φ � • SUGRA & sequestering results in m 2 = m 2 3 / 2 ˜ n ∂ m ˜ ˜ K − F ¯ n F m ∂ ¯ K A = A 0 Y + F m ∂ m Y with n , m running over flavons Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 10 / 17

Class of Models: Soft Terms Small Deviations from CMSSM • Soft masses m 2 F = m 2 x 2 3 ζ 2 ) 0 diag ( 1 , 1 , 1 − ˆ ˜ • Trilinear couplings − x 1 ǫ 1 ( 1 − 1 2 ζ 2 )   0 x 1 ǫ 1 ǫ 2 ) ( 1 − 1 2 ζ 2 ) x 2 ǫ 2 + i ˜ ( x 2 ǫ 2 + ˜ A d = A 0 x 2 ǫ 2 x 2 ˜ ǫ 2 x 2 w ˜   x 3 ǫ 3 ( 1 − 1 2 ζ 2 ) 0 0 ∝ Y d ⇒ not diagonal in SCKM basis ✚ ✚ • Almost CMSSM spectrum • Flavour and CP violation effects dominated by A terms Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 11 / 17

Class of Models: Soft Terms Small Deviations from CMSSM • Soft masses m 2 F = m 2 x 2 3 ζ 2 ) 0 diag ( 1 , 1 , 1 − ˆ ˜ • Trilinear couplings − x 1 ǫ 1 ( 1 − 1 2 ζ 2 )   0 x 1 ǫ 1 ǫ 2 ) ( 1 − 1 2 ζ 2 ) x 2 ǫ 2 + i ˜ ( x 2 ǫ 2 + ˜ A d = A 0 x 2 ǫ 2 x 2 ˜ ǫ 2 x 2 w ˜   x 3 ǫ 3 ( 1 − 1 2 ζ 2 ) 0 0 ∝ Y d ⇒ not diagonal in SCKM basis ✚ ✚ • Almost CMSSM spectrum • Flavour and CP violation effects dominated by A terms Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 11 / 17

Class of Models: Soft Terms Small Deviations from CMSSM • Soft masses m 2 F = m 2 x 2 3 ζ 2 ) 0 diag ( 1 , 1 , 1 − ˆ ˜ • Trilinear couplings − x 1 ǫ 1 ( 1 − 1 2 ζ 2 )   0 x 1 ǫ 1 ǫ 2 ) ( 1 − 1 2 ζ 2 ) x 2 ǫ 2 + i ˜ ( x 2 ǫ 2 + ˜ A d = A 0 x 2 ǫ 2 x 2 ˜ ǫ 2 x 2 w ˜   x 3 ǫ 3 ( 1 − 1 2 ζ 2 ) 0 0 ∝ Y d ⇒ not diagonal in SCKM basis ✚ ✚ • Almost CMSSM spectrum • Flavour and CP violation effects dominated by A terms Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 11 / 17

Class of Models: Soft Terms Small Deviations from CMSSM • Soft masses m 2 F = m 2 x 2 3 ζ 2 ) 0 diag ( 1 , 1 , 1 − ˆ ˜ • Trilinear couplings − x 1 ǫ 1 ( 1 − 1 2 ζ 2 )   0 x 1 ǫ 1 ǫ 2 ) ( 1 − 1 2 ζ 2 ) x 2 ǫ 2 + i ˜ ( x 2 ǫ 2 + ˜ A d = A 0 x 2 ǫ 2 x 2 ˜ ǫ 2 x 2 w ˜   x 3 ǫ 3 ( 1 − 1 2 ζ 2 ) 0 0 ∝ Y d ⇒ not diagonal in SCKM basis ✚ ✚ • Almost CMSSM spectrum • Flavour and CP violation effects dominated by A terms Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 11 / 17

Outline 1 Motivation 2 Defining a SUSY Flavour Model 3 Testing a SUSY Flavour Model 4 Summary Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 11 / 17

SUSY Threshold Corrections and Parameterisation Simple formulae for tan β enhanced corrections to Y d and Y e H u y SM e ,µ,τ ≈ ( 1 + ǫ l tan β ) y MSSM cos β e ,µ,τ ˜ H u y SM d , s ≈ ( 1 + ǫ q tan β ) y MSSM cos β ˜ d , s W ˜ H d y SM ≈ ( 1 + ( ǫ q + ǫ A ) tan β ) y MSSM cos β e c L ˜ L b b H u 1 + ǫ q tan β θ SM 1 + ( ǫ q + ǫ A ) tan β θ MSSM ≈ i 3 i 3 ˜ Q d c ˜ Q ˜ d c G H u θ SM 12 ≈ θ MSSM 12 δ SM CKM ≈ δ MSSM CKM u c ˜ ˜ Q Q H u ˜ ˜ d c H d [Antusch, Calibbi, V.M., Spinrath ’11] Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 12 / 17

SUSY Threshold Corrections and Parameterisation Simple formulae for tan β enhanced corrections to Y d and Y e H u y SM e ,µ,τ ≈ ( 1 + ǫ l tan β ) y MSSM cos β e ,µ,τ ˜ H u y SM d , s ≈ ( 1 + ǫ q tan β ) y MSSM cos β ˜ d , s W ˜ H d y SM ≈ ( 1 + ( ǫ q + ǫ A ) tan β ) y MSSM cos β e c L ˜ L b b H u 1 + ǫ q tan β θ SM 1 + ( ǫ q + ǫ A ) tan β θ MSSM ≈ i 3 i 3 ˜ Q d c ˜ Q ˜ d c G H u θ SM 12 ≈ θ MSSM 12 δ SM CKM ≈ δ MSSM CKM u c ˜ ˜ Q Q H u ˜ ˜ d c H d [Antusch, Calibbi, V.M., Spinrath ’11] Vinzenz Maurer (Uni Basel) From Flavour to SUSY Flavour Models FlaSy 11th July ’11 12 / 17