Flavor hierarchies from dynamical scales Giuliano Panico Barcelona CERN - CKC Workshop, Jeju sland 3/6/2017 based on GP and A. Pomarol arxiv:1603.06609
The SM and BSM flavor puzzle The SM has a peculiar flavor structure: where does it come from?... so far several ideas, but no compelling scenario Moreover strong theoretical considerations (naturalness problem) suggest the necessity of new physics related to the EW scale big effects are typically epected in flavor physics and CP violation (sensitive to energy scales much higher than TeV)... but basically no deviations seen eperimentally! How can we eplain this?
The SM and BSM flavor puzzle Cheap solutions: Very high BSM scale 10 3 TeV give up on naturalness BSM flavor structure similar to SM: flavor symmetries CP invariance
The SM and BSM flavor puzzle Cheap solutions: Very high BSM scale 10 3 TeV give up on naturalness BSM flavor structure similar to SM: flavor symmetries CP invariance This seems a step back from SM! in the SM global symmetries are accidental! [symmetries] are not fundamental at all, but they are just accidents, approimate consequences of deeper principles. S. Weinberg, referring to isospin in Symmetry: A Key to Nature s Secrets
Looking for a dynamical flavor structure s it possible to obtain the flavour structure as an emergent feature? n this talk will try to address this question in the contet of composite Higgs scenarios
The basic picture
Dynamical flavor in composite Higgs The standard partial compositeness flavor picture: Yukawa s from linear miing to operators from the strong sector L lin " i fi O fi size of R miings related to the dimension of O fi " fi ( ir ) ir uv i i =dim[o fi ] 5/2 > 1 smaller miings give smaller Yukawa s Y f g " fi " fj strong sector coupling
The geometric perspective We can easily visualize the anarchic flavor structure in the 5D holographic picture b L, b R s L, s R d L, d R Higgs warped etra-dimension R small masses from small overlapping with the Higgs
Favor and CP-violation constraints Strong bounds from F =2 transitions f i fl O F =2 g2 2 ir " i " j " k " l fi µ f j fk µ f l ε i ε l " K bound from : ir & 10 TeV f j ε j ε k f k... and especially from CP-violation and lepton flavor violation O dipole g g v 16 2 2 ir bound from n EDM: " i " j fi µ f j gf µ ir & 10 TeV(g /3) γ bound from e EDM: ir & 100 TeV(g /3) f i fj bound from µ! e : ir & 100 TeV(g /3)
How to suppress EDM s Large EDM s come from linear partial-compositeness miings of light fermions γ L lin " i fi O fi f i fj Significant improvement if miing through bilinear operators! L bilin f i O H f j f i f j EDM s generated only at two loops
An eplicit implementation Portal interaction for light fermions decouples at high energy eg. if a constituent has a mass f L lin " i fi O fi [GP and A. Pomarol, 1603.06609] [see also related works: Vecchi 12; Matsedonskyi 15; Cacciapaglia et al. 15] Bilinear miing generated at scale f L bilin f i O H f j composite operator that projects onto the Higgs at : ir h0 O H Hi 6=0 larger decoupling scales correspond to smaller fermion masses
The hierarchy of scales Eplicit eample: The down-quark sector decoupling energy scale operators d O dr, O QL1 s O sr, O QL2 b O br, O QL3 ir
The geometric perspective anarchic b L, b R s L, s R d L, d R Higgs R bilinears b L, b R s L, s R d L, d R Higgs d s b R small masses from small overlapping with the Higgs
The emergent flavor structure
The emergent flavor structure down-quark sector partial compositeness miings decoupling energy scale operators L (3) lin = "(3) b L Q L3 O QL3 + " (3) b R b R O br d s O dr, O QL1 O sr, O QL2 below b L (3) bilin = 1 d (" (3) H 1 b L Q L3 )O H (" (3) b R b R ) b b ir O br, O QL3 Y down = g 0 @ below ir 0 0 0 0 0 0 0 0 " (3) b L " (3) b R 1 A ir b dh 1
The emergent flavor structure down-quark sector decoupling energy scale operators partial compositeness miings L (2) lin =("(2) b L Q L3 + " (2) s L Q L2 )O QL2 +(" (2) b R b R + " (2) s R s R )O sr d s O dr, O QL1 O sr, O QL2 below s L (2) bilin = 1 d (" (2) H 1 b L Q L3 + " (2) s L Q L2 )O H (" (2) b R b R + " (2) s R s R ) d b ir O br, O QL3 Y down = g 0 B @ below ir 0 0 0 0 " (2) s L " (2) s R " (2) s L " (2) b R 0 " (2) b L " (2) s R 1 C A ir s dh 1
The emergent flavor structure down-quark sector decoupling energy scale operators partial compositeness miings L (1) lin =("(1) b L Q L3 + s L Q L2 + d L Q L1 )O QL1 +( b R b R + s R s R + d R d R )O dr d O dr, O QL1 below d s O sr, O QL2 b ir O br, O QL3 Y down = g 0 B @ below ir d L d R d L s R d L b R s L d R b L d R 1 C A dh 1 ir d
The emergent flavor structure The Yukawa matri has an onion structure Y down ' 0 B @ Y d R dsy d R dby d L dsy d Y s R sby s db L Y d sb L Y s Y b 1 C A where the Yukawa s are given by Y f g " (i) f Li " (i) f Ri ir f dh 1 ' m f /v smaller Yukawa s for larger decoupling scale miing angles suppressed by Yukawa s: ij Y i /Y j CKM mostly the rotation in the down-quark sector
Comparison with anarchic bilinears anarchic 0 B @ Y d R dsy d R dby d L dsy d Y s R sby s db L Y d sb L Y s Y b 1 C A 0 B @ Y d p Yd Y s p Yd Y b p Yd Y s Y s p Ys Y b p Yd Y b p Ys Y b Y b 1 C A The bilinear scenario predicts smaller off-diagonal elements particularly relevant for R rotations: suppressed w.r.t. anarchic
The geometric picture Leading contributions to the Yukawa s come from different branes b L, b R s L, s R d L, d R Higgs d s b R g 0 B @ d L d R d L s R d L b R s L d R b L d R 1 C A dh 1 ir d g 0 @ 0 0 0 0 0 0 0 0 " (3) b L " (3) b R 1 A ir b dh 1 g 0 B @ 0 0 0 0 " (2) s L " (2) s R " (2) s L " (2) b R 0 " (2) b L " (2) s R 1 C A dh 1 ir s
The hierarchy of scales decoupling energy scale operators u d O ur O dr, O QL1 s O sr c b O cr, O QL2 O br t ir O tr, O QL3
Scales of decoupling Λ [ ] - - d H 2 needed to pass FCNC
Scales of decoupling Λ [ ] b L, b R s L, s R d L, d R Higgs d - - s b R d H determines the profile of the Higgs d H 2 needed to pass FCNC
Flavor and CP-violating effects
R effects: F =2 transitions Top partial compositeness at ir gives rise to flavor effects F =2 operators u d O ur O dr, O QL1 Y t 2 2 ir (Q L3 µ Q L3 ) 2 rotation to physical basis V L V ckm s O sr corrections to " K, M Bd, M Bs c b O cr, O QL2 O br correlated: interesting prediction t ir O tr, O QL3 M Bd M Bs ' M B d M Bs SM close to eperimental bounds ir & 2 3TeV
R effects: F =1 transitions Top partial compositeness at ir gives rise to flavor effects F =1 operators u d s c b t ir O ur O dr, O QL1 O sr O cr, O QL2 O br O tr, O QL3 corrections to g Y t ir Q L3 µ Q L3 ih! D µ H rotation to physical basis V L V ckm K! µµ, " 0 /", B! X``,Z! bb correlated and close to eperimental bounds ir & 4 5TeV can be suppressed by left-right symmetry
Effects at higher scales Partial compositeness at s gives rise to additional contributions F =2 operators u d O ur O dr, O QL1 g2 2 s (Q L2 s R )(s R Q L2 ) rotation to physical basis V L V ckm s O sr corrections to " K c b t ir O cr, O QL2 O br O tr, O QL3 close to eperimental bounds for s 10 5 TeV bound on Higgs dimension d H 2
Effects at higher scales Partial compositeness at s gives rise to additional contributions F =2 operators - - u d s O ur O dr, O QL1 c b t ir O sr Λ [ ] g2 2 s (Q L2 s R )(s R Q L2 ) rotation to physical basis V L V ckm O cr, O QL2 O br O tr, O QL3 corrections to " K close to eperimental bounds for s 10 5 TeV bound on Higgs dimension d H 2
EDM s EDM s for u, d and e suppressed by u,d,e > 10 6 TeV large effects to neutron EDM from top compositeness g2 c t m t top EDM edm 16 2 2 neutron EDM d N ir γ t L h two-loop Barr-Zee effects electron EDM e h γ e n and e EDM s lead to the bound ir & TeV
Summary of the bounds Δ ϵ Λ ( ) μ + μ - μ γ huge improvement with respect to the anarchic case (especially in the lepton sector) several effects close to eperim. bounds for ir few TeV
Conclusions
Conclusions The flavour structure of the SM could be an emergent feature: Yukawa hierarchies linked to dynamically generated mass scales Successful implementation in composite Higgs scenarios modification of partial compositeness flavor from miing with the composite dynamics at different scales (at low energy equivalent to bilinear miings) compatibility with flavour bounds + several new physics effects around the corner
Backup
One scale for each family More economical construction by associating one scale to each generation decoupling energy scale operators u d e O QL1, O dr, O ur,... c s µ O QL2, O sr, O cr,... t b O QL3, O br, O tr,... Yukawa differences within each generation due to different miings Only main difference: µ! e close to ep. bounds
Neutrino masses Majorana masses realization: 1 2d H 1 L c O H O H L m ' g2 v 2 ir ir 2dH 1 for d H 2 dimension-7 operators: m 0.1 0.01 ev ) 0.8 1.5 10 8 GeV e Dirac masses realization: 1 d H 1 O H L R for d H 2 dimension-5 operators as in SM