Controlled Flavour Changing Neutral Couplings in Two Higgs Doublet - PowerPoint PPT Presentation

Controlled Flavour Changing Neutral Couplings in Two Higgs Doublet Models Fernando Cornet-G´ omez IFIC, Universitat de Val` encia-CSIC BSM Journal Club Valencia, Sep 20, 2017 Fernando Cornet-G´ omez 1 / 20 Generalized BGL-2HDM

Collaboration: 1703.03796 Fernando Cornet-G´ omez 2 / 20 Generalized BGL-2HDM

Introduction and Motivation Higgs-fermions couplings SM-like or expanded complex scalar sector A natural scenario is Two Higgs Doublet Model (2HDM) ◮ Symmetries are needed to avoid or suppress FCNC. To avoid FCNC: postulate that quarks of a given charge receive contributions to their mass only from one Higgs doublet. A Z 2 symmetry (Glashow-Weinberg) leads to Natural Flavour Conservation (NFC) in the scalar sector. Minimal Flavour Violation (MFV) 2HDM ◮ Enforced by symmetries ⇒ FCNC controlled by V CKM ◮ BGL models (Branco, Grimus, Lavoura) that have FCNC in the up or in the down sector, but not in both. Here we will present a new family of models generalizing the BGL one and having FNCN both in the up and in the down scalar sectors. Fernando Cornet-G´ omez 3 / 20 Generalized BGL-2HDM

General 2HDM � � ∆ 1 � Φ 1 + ∆ 2 � L Y = − Q L (Γ 1 Φ 1 + Γ 2 Φ 2 ) d R − Q L Φ 2 u R + .h.c. √ With the vev’s given by � Φ i � T = e iθ i � � 0 υ i / 2 we define the Higgs � √ � � � basis by � H 1 � T = , � H 2 � T = , υ 2 = υ 2 1 + υ 2 0 υ/ 2 0 0 2 , c β = υ 1 /υ, s β = υ 2 /υ, t β = υ 2 /υ 1 � e − iθ 1 Φ 1 � � c β � � H 1 � s β = e − iθ 2 Φ 2 s β − c β H 2 then we have � � � � G + H + � υ + H 0 + iG 0 � √ � � √ H 1 = ; H 2 = R 0 + iA / 2 / 2 Fernando Cornet-G´ omez 4 / 20 Generalized BGL-2HDM

G ± and G 0 longitudinal degrees of freedom of W ± and Z 0 . H ± new charged Higgs bosons. A new CP odd scalar (we will have CP invariant Higgs potential). H 0 and R 0 CP even scalars. If they do not mix, H 0 the SM Higgs. √ � � 2 H + V N d γ R − N † L Y = − u ¯ u V γ L d + h.c. v − H 0 � � uM u u + ¯ ¯ dM d d − υ � � − R 0 u γ L ) u + ¯ d ( N d γ R + N † u ( N u γ R + N † ¯ d γ L ) d υ � � + iA u γ L ) u − ¯ d ( N d γ R − N † u ( N u γ R − N † ¯ d γ L ) d υ Fernando Cornet-G´ omez 5 / 20 Generalized BGL-2HDM

BGL A BGL model is enforced by the U (1) flavour symmetry (top type model) u R 3 → e i 2 α u R 3 Q L 3 → e iα Q L 3 Φ 2 → e iα Φ 2 ; ; In the quark mass basis it correspond to the model defined by the MFV expansion - ( P 3 ) ij = δ i 3 δ j 3 - � � � � N d = U d † t β + t − 1 L N 0 d U d V † P 3 V R = t β I − M d β � � � � N u = U u † t β + t − 1 L N 0 u U u R = t β I − P 3 M u β or to the model with the following Yukawa couplings     × × × 0 0 0     Γ 1 = × × × ; Γ 2 = 0 0 0 0 0 0 × × ×     × × 0 0 0 0     ∆ 1 = × × 0 ; ∆ 2 = 0 0 0 0 0 0 0 0 × Fernando Cornet-G´ omez 6 / 20 Generalized BGL-2HDM

Generalizing BGL models: gBGL The generalized BGL models (gBGL) are implemented through a Z 2 symmetry, where u R and d R are even and only one of the scalars doublets and one of the left-handed quark doublets are odd: Q L 3 → − Q L 3 , d R → d R , Φ 1 → Φ 1 u R → u R , Φ 2 → − Φ 2 Now the Yukawa textures are:     × × × 0 0 0     Γ 1 = × × × ; Γ 2 = 0 0 0 0 0 0 × × ×     × × × 0 0 0     ∆ 1 = × × × ; ∆ 2 = 0 0 0 0 0 0 × × × Fernando Cornet-G´ omez 7 / 20 Generalized BGL-2HDM

This time, in the quark sector, the model is fully defined , in the mass basis, by � � � � t β + t − 1 N d = t β I − | � n d � � � n d | M d β � � � n d | V † � t β + t − 1 N u = t β I − V | � n d � � � M u β or if we call | � n u � = V | � n d � we also have � � � � V † | � t β + t − 1 N d = t β I − n u � � � n u | V M d β � � � � t β + t − 1 N u = t β I − | � n u � � � n u | M u β the free parameters are two angles to define the unitary vector | � n u � or | � n d � and two phases of the three complex component Fernando Cornet-G´ omez 8 / 20 Generalized BGL-2HDM

Fernando Cornet-G´ omez 9 / 20 Generalized BGL-2HDM

Intesity of FCNC I The Yukawa coupling to the 125 GeV Higgs 1 Y ( q ) = υ [ s βα M q + c βα N q ] � � � � t β + t − 1 N d = t β I − | � n d � � � n d | M d β in general generate FCNC � � � � M q Y ( q ) = t β + t − 1 ( s βα + c βα ) I − c βα | � n q � � � n q | β υ � � ◮ All FCNC effects are proportional to c βα t β + t − 1 β ◮ In an i → j transition it is proportional to m q i /υ ◮ In an i → j transition it is proportional to ( | � n q � � � n q | ) ji with maximal � √ � � √ � value 1 / 2 1 / 2 = 1 / 2 Fernando Cornet-G´ omez 10 / 20 Generalized BGL-2HDM

Intesity of FCNC II ◮ To be compared with the most intense case of BGL u model in the s → d transition ∼ V ∗ ud V us ∼ λ From meson mixing we have the following naive constraints D 0 − D 0 K 0 − K 0 B 0 − B 0 0 B 0 s − B � �� � s � � t β + t − 1 � c βα � ≤ 0.02 0.04 0.003 0.007 β and from rare top decays t → hq � � �� � � t β + t − 1 � c βα � ≤ 0 . 4 β There are many regions of the model parameter space where � � �� � � t β + t − 1 � c βα � can get its maximum value of order one. β Fernando Cornet-G´ omez 11 / 20 Generalized BGL-2HDM

Near Top model We will study the properties of gBGL that are close to the t BGL model in the sense that they give the same contribution to meson mixing   V ∗ td (1 + δ d ) ��� � � � t + δ �   V ∗ t = N ts (1 + δ s ) d V ∗ tb (1 + δ b ) The up models near the top give the same contribution to meson mixing than the top BGL model provided � λ 2 � � λ 3 � Re ( δ d,s,b ) ∼ Im ( δ s ) ≤ O , and Im ( δ d,b ) ≤ O 0 contribution is easily seen to be and the contribution to D 0 − D controlled from  � λ 5 �  O � ��� � � � D 0 � � δ b V cb λ 5 � 2 ≤ λ 18 t + δ �   ⇒ M 12 V t ∼ δ b V cb ∝ d 1 + δ b Fernando Cornet-G´ omez 12 / 20 Generalized BGL-2HDM

BAU I The contribution to the Baryon asymmetry of the Universe is proportional the a weak basis invariant with an imaginary piece. In the SM it appears for the first time at order 12th in Yukawa couplings and is given by the Jarlskog (see also Bernabeu, Branco, Gronau) Invariant: �� � 2 � � � � � � 2 � d M 0 † d M 0 † M 0 u M 0 † M 0 M 0 u M 0 † M 0 I 12 = Im Tr u u d d m 4 t m 2 c m 4 b m 2 ∼ s J where J ≡ Im ( V us V cb V ∗ ub V ∗ cs ) Fernando Cornet-G´ omez 13 / 20 Generalized BGL-2HDM

BAU II In the BGL models an imaginary part appears first at order 8th in Yukawa couplings and is given by � � t β + t − 1 m 4 b m 2 c m 2 I 8 ( t ) ∼ s J β � � t β + t − 1 m 4 t m 2 c m 2 I 8 ( b ) ∼ s J β � � t β + t − 1 m 4 t m 2 c m 2 I 8 ( d ) ∼ b J β Fernando Cornet-G´ omez 14 / 20 Generalized BGL-2HDM

BAU III In the gBGL models an imaginary part appears first at order 4th in Yukawa couplings and is given by � � t β + t − 1 m 2 t m 2 n d | ) 32 V tb V ∗ I 4 ( � n d ) ∼ b Im [( | � n d � � � ts ] β A summary of enhancements in the CP violating weak basis invariant factors of the BAU respect to the SM one is given bellow where we use cs ) ∼ 3 × 10 − 5 . The contribution to E ∼ 100 GeV and J ≡ Im ( V us V cb V ∗ ub V ∗ the BAU should be proportional to Im I n E n and we define the enhancement respect to the SM factor by � Im I n � � Im I 12 � η ( model ) = / E n E 12 Fernando Cornet-G´ omez 15 / 20 Generalized BGL-2HDM

BAU IV top bottom E 4 E 4 η ( t β + t − 1 β ) m 4 m 4 t b 10 5 η ∼ 1 near top near bottom 10 16 | V ts | Im ( δ b + δ ∗ 10 16 | V ts | Im ( δ ∗ η t − δ ∗ s ) c ) ( t β + t − 1 β ) 10 12 10 13 η � � | V ts | E 8 � � � Where 10 16 = m 2 t m 2 c m 2 b m 2 / s J . Note also that we have two BGL models d, s where � � t β + t − 1 E 4 β ∼ 10 10 η d,s ∼ m 2 b m 2 s Fernando Cornet-G´ omez 16 / 20 Generalized BGL-2HDM

Other Phenomenological Implications I The most relevant: the presence of FCNC at tree level, in the Higgs sector and at an important rate. As in BGL In gBGL models one has, in general, FCNC both in the up and in the down sectors simultaneously. Fernando Cornet-G´ omez 17 / 20 Generalized BGL-2HDM

Other Phenomenological Implications II With the trajectories in model space Fernando Cornet-G´ omez 18 / 20 Generalized BGL-2HDM

Other Phenomenological Implications III One can draw correlations of the down and the up sector Fernando Cornet-G´ omez 19 / 20 Generalized BGL-2HDM

Conclusions I Fernando Cornet-G´ omez 20 / 20 Generalized BGL-2HDM

Thanks! Fernando Cornet-G´ omez 21 / 20 Generalized BGL-2HDM