Leaving Plato s Cave: Beyond The Simplest Models of Dark Matter

Leaving Plato s Cave: Beyond The Simplest Models of Dark Matter Alexander Natale Korea Institute for Advanced Study Nucl. Phys. B914 201-219 (2017), arxiv:1608.06999. High1 2017 February 9th, 2017 1/30

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Effects of DM 2/30

Effects of DM UV Physics 2/30

Effects of DM Dark Sector? UV Physics 2/30

Plato s Cave We are in Plato s Cave Something exists, we can see DM s gravitational effects, but we have no idea what DM is made of, what interactions DM can have (modulo existing constraints), whether we can even detect DM directly or produce it at colliders, and if it has connections to other unsolved problems in physics. 3/30

Dark Matter and Neutrino Mass: Neutrino mass is also unexplained in minimal SM, is there a connection between two unsolved phenomenon? Plato s Fire: Discrete symmetries have been fruitful in other fields, but can they be connected to DM and what signatures do such symmetries yield? Binary Tetrahedral Scotogenics: Discrete symmetries can predict correct neutrino mixing pattern, but is there a way with a scotogenic model to generate non-trivial quark mixing, and what are the consequences of this? 4/30

Dark Matter and Neutrino Mass: Neutrino mass is also unexplained in minimal SM, is there a connection between two unsolved phenomenon? Plato s Fire: Discrete symmetries have been fruitful in other fields, but can they be connected to DM and what signatures do such symmetries yield? Binary Tetrahedral Scotogenics: Discrete symmetries can predict correct neutrino mixing pattern, but is there a way with a scotogenic model to generate non-trivial quark mixing, and what are the consequences of this? 4/30

DM and Neutrinos...? DM and m ν are compelling experimental motivations for BSM, could they be related in a simple model? Can a model of DM and m ν be that: Explains nature of DM Explains nature and origin of ν Maintain Relative simplicity 5/30

DM and Neutrinos: A Scotogenic Solution Add a scalar doublet, and k majorana fermion singlets (minimal is k=1), odd under a dark parity: φ 0 φ 0 η 0 η 0 ν N N ν Majorana neutrino masses generated at loop level (E. Ma 2006): M ν ij = k h ik h jk M Nk ( 16π 2 m 2 R /(m2 R M 2 N ) log(m 2 k R /m2 N ) m 2 k I /(m2 I M 2 N ) log(m 2 ) k I /m2 N ) k Known as scotogenic (scoto means darkness in Greek) or Ma model. 6/30

Scotogenic Models The minimal model has nice features: DM candidate (N or η 0 R,I ) Loop can explain why m ν m l ± without tiny Yukawas and with new physics at EW scale (ie realistic m ν when m N O(100) GeV) However: Has only one Higgs Minimal extension to SM Collider Signatures of DM and m ν RGE equations, DM, collider and precision are severely constraining (M. Lindner, A. Merle, M. Platscher, C.E. Yaguna 2016) Cannot explain structure of ν oscillation 7/30

Dark Matter and Neutrino Mass: Neutrino mass is also unexplained in minimal SM, is there a connection between two unsolved phenomenon? Plato s Fire: Discrete symmetries have been fruitful in other fields, but can they be connected to DM and what signatures do such symmetries yield? Binary Tetrahedral Scotogenics: Discrete symmetries can predict correct neutrino mixing pattern, but is there a way with a scotogenic model to generate non-trivial quark mixing, and what are the consequences of this? 8/30

Plato s Fire The tetrahedral group (A 4 ): C B A D Alternating group of 4 elements (symmetry of the Tetrahedron) Has distinct singlet representations (1 0,1 1,1 2 ) Has triplet representations: 3 3 = 1 0 1 1 1 2 3 3 Plato thought fire was one of five elements in the universe and was represented by the tetrahedron. Basic methodology: miss-match between l and ν achieved via different reps. of discrete group, large difference in m l while also generating non-trivial PMNS matrix. 9/30

Clashing Symmetries Original proposal (E. Ma, G. Rajasekaran 2001): Suppose: Φ Φ i 3,(ν, l + ) L 3, and l k,r 1 0, 1 1, 1 2 then m ν 0 and θ 13 = 0, θ 23 = π/4, sin(θ 12 ) = 1 3 However... θ 13 0 and isn t really small either. In original Plato s Fire model A 4 Z 3, but θ 13 requires A 4 Z 2 for neutrinos and A 4 Z 3 for leptons. Clashing symmetries between charged leptons and neutrinos. 10/30

Plato s Fire Utilizing flavor symmetries scotogenic models can accommodate co-bimaximal mixing (θ 13 0, sin(θ 23 ) = 1/ 2, δ CP = ±π/2): Φ φ 0 N N φ 0 E 0 N E 0 E 0 ν s ν l L x y l R 11/30

Clashing Symmetries There is a problem with this mechanism: In order to properly produce ν oscillation with A 4 where TBM is slightly perturbed and θ 13 0 there must be a clashing symmetry: Z 3 Z 2. φ 0 N N φ 0 E 0 E 0 ν s ν Where the s 1 s 2 terms in the ν loop break A 4 Z 3 Z 2 12/30

Softly Broken These terms allow x 1 x 2 s 1 s 2 : s 1 s 2 x 1 x 2 Requires Z 3 breaking counter-terms! Thus, the residual symmetry scheme of Z 3 is badly broken. Generically an issue in models without A 4 but with the same loop. 13/30

Salvaging Cobimaximal Ma Models However there is a solution to the soft-breaking problem (E. Ma 2016): Allow charged lepton loop to carry U(1) D, and the ν loop to have dark Z 2 (exactly conserved), make N dirac, and add F Majorana fermion: Φ F 0 E 0 E 0 Φ Φ η + χ + ν L s ν L l L N R N L l R s 1 s 2 terms break A 4 to Z 2, N L N R terms break A 4 to Z 3. No more arbitrary corrections to Lepton mixing matrix! 14/30

Cobimaximal Particle Content Extra particle content and symmetries are required: Particles SU(3) C SU(2) L U(1) Y U(1) D dark Z 2 A 4 Z 2 SM Particles: (ν, l) L 1 2-1/2 0 + 3 + l R 1 1-1 0 + 3 - Φ 1 2 1/2 0 + 1 + Fermions: N L,R 1 1 0 1 + 3 + E L,R 1 2 1/2 0-1 + FL 0 1 1 0 0-1 + Scalars: η 1 2 1/2-1 + 1 + χ + 1 1 1-1 + 1 - s 1 1 0 0-3 + As a bonus this model can easily accommodate multi-component DM! 15/30

Dark Matter and Neutrino Mass: Neutrino mass is also unexplained in minimal SM, is there a connection between two unsolved phenomenon? Plato s Fire: Discrete symmetries have been fruitful in other fields, but can they be connected to DM and what signatures do such symmetries yield? Binary Tetrahedral Scotogenics: Discrete symmetries can predict correct neutrino mixing pattern, but is there a way with a scotogenic model to generate non-trivial quark mixing, and what are the consequences of this? 16/30

Binary Tetrahedral Model An alternative to A 4 is the binary tetrahedral group of T. T has the same multiplication rules as A 4 however, it also has doublet representations: 2 2 i 2 j = 1 i+j mod 3 3, 2 i 3 = Used to predict the Cabibbo Angle (P.H. Frampton 2009) Note: Any model of m ν that uses A 4 could really use T since singlets and triplets are the same. i=0 2 i 17/30

Cabibbo Angle from T Q L = To produce Cabibbo angle (P.H. Frampton 2009): ( ) (c, s) 2 (u, d) 0, C R = (c R, u R ) 2 2, S R = (s R, d R ) 2 1, Φ Φ i 3 2 Yields tan(2θ c ) = 3 (not quite the correct angle but close) Binary Tetrahedral Scotogenics: In a scotogenic model the idea would be to keep Φ 1, can co-bimaximal ν oscillation be implemented in scotogenic model with non-trivial quark-mixing? 18/30

Scotogenic T Model Same particle content as previous A 4 model (with q under U(1) D q/2), and the A 4 assignments stay the same (AN 2016), but: Particles U(1) Y U(1) D dark Z 2 T Z 2 SM Particles: ( ) (c, s)l Q L = 1/6 0 + 2 (u, d) 0 + L C R = (c R, u R ) 2/3 1 + 2 2 + S R = (s R, d R ) -1/3-1 + 2 1 + Fermions: U L,R 2/3 1/2-2 0 + D L,R -1/3-1/2-2 2 + T L 2/3-1/2 + 1 0 - T R 2/3 3/2 + 1 0 - B L -1/3 1/2 + 1 0 - B R -1/3-3/2 + 1 0 - Scalars: ρ 1/2 1/2-3 + σ 0 0-1/2-1 2 + ζ1 0 0 1 + 3 + ζ2 0 0 2 + 1 0 + Note: T and B are added to cancel anomalies and t and b receive masses at tree level from SM Higgs. 19/30

Lepton & Quark Mixing Lepton mixing is same as A 4 model, new particles in T model yield one-loop Quark Mass: ζ 1 ρ 0 Φ σ Q L V R V L q R V are the vector-like quarks U,D, ζ 1 gets a VEV (gives Z a mass). V L V R softly breaks T Z 4 20/30

Quark Mixing ζ 1 Φ ρ 0 σ Generates first two generations of quark Q L V R V L q R masses: M q = f qlf qr sin(θ ρ σ ) cos(θ ρ σ ) 32π 2 I Q, I Q are 2 2 matrices that depends on T assignment & loop functions: F [X ij ] = m Vj X ij log(x ij )/(X ij 1), X ij = m 2 ρ σ,j/m Vi 21/30

Quark Mixing 16 θ 14 12 10 8 θ c ±30% θ c ±20% θ c ±10% θ c ±5σ 0.5 0.6 0.7 0.8 0.9 1.0 δ m13 Yields a more realistic θ C compared to A 4 model as long as T is broken by VLQ masses (ie δ, m 13 0). 22/30

Breaking U(1) D Z 2 Both ζ 1 and ζ 2 are able to receive VEVs: v 1,2 v Φ allows Φ to be SM-like ) m 2 h 2v2 (λ H 3λ2 H1 2(λ 13 +λ 13 ) 2 v 2 2 λ2 H2 λ 2 v2 2 3 2 µ v 1 2 12 v2 v 2 m T (B) 0 and on order of v 2 (TeV) Generates non-zero mass for Z : m 2 Z g 2 ζ (3v2 1 + 4v2 2 ) Reminder: Φ is a T singlet in the scotogenic models. 23/30

Some Important Constraints 24/30

Dark Sector In addition to DM-SM there are noteworthy DM-DM interactions: Scalar-Fermion Interactions f NE (cos(θ y )y 0 1 sin(θ y )y 0 2)N 1,2,3 E 0 R Scalar Interactions λ D ρ ηsζ 1 Allows mediation between Z 2 stabilized and U(1) stabilized sectors 25/30

Dark Sector Scalar interactions (ρs ζ 1 η and ρ sη) add additional complications Suppose ρ isn t DM, but has relatively long life-time, then DM s history can be much more complicated as ζ 1 and η decay to DM+SM. If m ρ, m s, and m η are close then three stable species of DM is possible if ρ NE cannot happen Assume: we can choose the masses and the coupling constants to ignore this term. Focus on the case of a simple multi-component DM scenario with the lightest N and s as DM with various mediators. 26/30

Dark Sector 400 300 ms [GeV] 200 100 Relic Denisty LUX (2016) Overlap 0 50 100 150 200 m N [GeV] 27/30

Collider Signatures The vector-like quarks T and B have interesting signatures: b R e t R e T L B L N 1 N 1 N 1 N 1 T L B L b R e + t R e + Similar to SUSY/VLQ searches but only decay through these channels No dijet + MET, no W decays, etc. 28/30

Summary Possible to generate non-trivial CKM and realistic PMNS in a Scotogenic model using T Extension to quark sector allows new DM-SM interactions (uses VLQ instead of colored-scalars) and adds interesting Z interactions Yields viable two-component DM model New particles, many interesting signatures at colliders are possible 29/30

Thank you! Thank you very much your attention! 30/30

Backup Slides Backup Slides 30/30

Plato s Fire Original proposal (E. Ma, G. Rajasekaran 2001): Suppose: Φ Φ i 3,(ν, l + ) L 3, and l k,r 1 0, 1 1, 1 2 then m ν 0 and: 1 1 1 m e 0 0 a b b M l = 1 3 1 ω 2 ω 0 m µ 0 M ν = b a b 1 ω ω 2 0 0 m τ b b a M ν is exactly diagonalized by: 2/3 1/ 3 0 1/ 6 1/ 3 1/ 2 1/ 6 1/ 3 1/ 2 30/30

Scotogenic Extensions Quark and Charged Lepton Masses φ 0 φ 0 ξ 1/3 ζ 1/3 η + χ + d L N R N L d R l L N R N L l R Alternative m ν φ 0 N N φ 0 E 0 E 0 ν s ν 30/30

Dark Sector Determining DM Constraints: Implement relevant terms in CalcHEP model files Scan over allowed mass range in MicrOmegas Let 0.1 Ωh 2 0.13 Take into account indirect detection cross section constraint 30/30

Lepton Mixing Φ F 0 E 0 E 0 Φ Φ η + χ + ν L s ν L l L N R N L l R The T model produces same M ν as the A 4 model, however 2.5 σ tension between NOνA and cobimaximal Possible to perturb cobimaximal mixing away from maximal θ 23 (E. Ma, AN, O. Poppov 2015) However, cobimaximal still broadly consistent with ν data. 30/30

Dark Sector Automatically two DM candidates: Z 2 stabilized (E 0 F 0 or s i ), U(1) stabilized (ρ η σ or N i ) Besides gauge interactions (Z ) there are many SM-DM terms: λ ψ ψ ψφ Φ, f ll [ ll N lr (cos(θ x )x 1 sin(θ x)x 2 ) + ν LN R x 0], f lr [ lr N ll (cos(θ x )x 2 + sin(θ x)x 1 ) + ν LN 1R x 0], f s s l (l L E + R + ν LE 0 R), Note: x i and y i are mass eigenstates from η χ and ρ σ mixing 30/30

Quark Mixing The CKM is from the miss-match of T assignments in up-like and down-like sector, and depends on vector-like quark mass: ( ) 2m11 + 2m M V = 13 + δ δ δ 2m 11 2m 13 + δ From the form of I q this CKM angle can be extracted: tan(2θ U ) = δ/(2m 13 ), tan(2θ D ) = δɛ/(2m 13 ), Thus: θ c δ/m 13 where m 13, δ 1, m 11 = 1 ɛ m 13, ɛ 1/2 30/30

Some Important Constraints 30/30

Flavor FCNCs from new particles are severely restricted: Z 4 residual symmetry, U(1) D, and terms that do not break T T only broken by s 1 s 2 and fermion masses, so scalar terms generically respect either full T or residual Z 2 from neutrino sector Example for K 0 K 0 mixing: c/λ 2 10 7 m 2 y ± TeV 4 30/30

Dark Sector The dark sector is rich even with bland choices of DM (N,s): N l N Z N qr Z x ± 1,2,x 0 N N l N Z N qr s l s Φ, y 0 1,2, y±, ζ 1, ζ 2 E L,R s l s Φ, y 0 1,2, y, ζ 1, ζ 2 30/30

Dark Sector: Mass Scheme To better explore DM in the model, let s pick a concrete set of masses: m E 0 = 455 GeV, m E ± = 450 GeV, m F 0 = 600 GeV, m x ± = 646 GeV, 1 m x ± = 654 GeV, m 2 x 0 = 650 GeV, m y ± = 247 GeV, m y 0 1 = 250 GeV, m y 0 2 = 252 GeV, with g ζ = 0.1 and m Z = 1200 GeV Thus m N < 245 GeV and m s < 450 GeV in order to simplify the DM scheme, where the main annihilations are ss e ± e, νν, and NN e ± e, νν, qq, where the quarks can be the first two generations only. 30/30