Accidental Composite Dark Matter

Transcription

1 Accidental Composite Dark Matter Michele Redi Based on: arxiv in collaboration with O. Antipin, A. Strumia, E. Vigiani SAIFR-ICTP, Sao Paulo - November 24, 2015

2 Motivation In the SM, all observed global symmetries arise as accidental symmetries of the renormalizable Lagrangian. This explains why the proton is stable. It also explains flavour. We need at least one more stable particle for Dark Matter New gauge theory + gap DM is an accidentally stable techni -baryon

3 Vector-like confinement: Kilic, Okui, Sundrum 09 Q i G µ ij New confining gauge theory with fermions vectorial under SM

4 Vector-like confinement: Kilic, Okui, Sundrum 09 g SM + H Q i y G µ ij New confining gauge theory with fermions vectorial under SM SM including Higgs couples to the strong sector with renormalizable couplings:

5 Technicolor G SM 2 G/H H f = v Composite Higgs G SM 2 H f>v

6 Higgs is a pseudo-goldstone boson. Electro-weak scale determined by vacuum alignment. DEVIATION SM = 1 TUNING Electro-weak preserving dynamics: g SM + H G SM 2 H Higgs is elementary. y

7 Very weak bounds: - Automatic MFV - Precision tests ok - LHC: m > 1 2TeV Interesting phenomenology: - Plausible at LHC13 - Automatic dark matter candidates - Simple UV models - Relaxion

8 Models SU(N) gauge theory with NF flavors. Techni-quarks are vectorial with respect to SM. Fermions P SM SU(n) TC L Pi r i n n R i r i X i d[r i ]=N F Goldstone bosons: h i j i 4 f 3 ij SU(N F ) SU(N F ) SU(N F ) Adj SU(NF ) = KX i=1 r i KX i=1 r i 1 Vacuum does not break electro-weak symmetry.

9 Accidental symmetries: Techni-Baryon number U(1) TB i! e i i Species number U(1) Fi i! e i i i KX i i =0 G-parity! e i J 2 c Broken by hypercharge.

10 Automatic dark matter candidates: Baryons B = i 1i 1...i n Q { 1 i 1 Q 2 i 2...Q n} i n m B Nm Lightest multiplet has minimum spin among reps. n =3 n =4 DM candidate: Q TB = T 3 + Y TB =0 Y TB =0 J=0,1,2,...

11 Pions Bai, Hill 10 Pions can be stable due to G-parity or species number:! S C W a µ J a! W a µ J a S = e i J 2 A a t a! A a ( t a ) J! ( 1) J J Triplet is stable. Behaves as minimal dark matter. Strumia, Cirelli 05 m J=1 2.5TeV SI =0.12 ± cm 2

12 Baryon number can be broken by dimension 6 operators 8 M 4 M 5 DM sec M MPl TeV M DM 5 Species symmetry and G-parity can be broken by Yukawa couplings or dim 5 operators 1 M QQHH, 1 M Q µ QB µ Within EFT baryons more likely cosmologically stable.

13 Flavor multiplets are split by quark masses and gauge interactions: quark masses m 2 mm m B m gauge interactions Charged pions acquire positive mass. m 2 = 3g2 i (4 ) 2 C 2( )m 2 After electro-weak symmetry breaking multiplets further split. Neutral component is the lightest. For triplets: m + m 0 = 166 MeV

14 m TCb 0 m TCb m2 TC m TCb TC { m = 2 Q 2 m W sin 2 W MeV m TC 0

15 We take branches of unified representations R =(N,SM) ( N, SM) R =(N, SM) ( N,SM) - SU(N) asymptotically free - No Landau poles below the Planck scale. - Lightest techni-baryon with Q=Y=0 - No unwanted stable particles

16 Two classes of models: Golden These models fulfil all requirements with renormalizable lagrangian Ex: N =3 Q=V DM=VVV Silver Higher dimensional operators needed Ex: N =3 Q=L+E DM=LLE

17 Renormalizable models:

18 Unification Incomplete SU(5) reps modify SM running Giudice, Rattazzi, Strumia, 12 1 i (M Z ) = 1 + bsm i GUT 2 log M GUT + b i M Z 2 log M X + TC b 2 log M GUT M X ln M X TC = 68 b b 32, ln M GUT M X = 35.3 b b 32 b b 32

19 Example: Q + D DM = QQ D 60 1êa êa 30 1êa 2 GUT êa 3 M GUT GeV 10 3HQ+DL 3HU+L+EL Energy in GeV TC = 100 TeV M X GeV

20 Relic abundance of TB: H Thermal abundance determined by annihilation into technipions

21 If charged TB dark matter interacts as usual WIMPS 3 SI = cm 2

22 Even if TB is SM singlet can have dipole interactions e 2m B µ (g M + ig E 5 ) F µ. Magnetic g M = O(1) Electric Need CP violation: TC 32 2 G µ G µ g E e TC min[m Q ] M DM

23 10-42 DM cross section s SI in cm LUX % CL bound techni-pion DM HMDM tripletl * techni-baryon DM for g = 1 or g E = n background Dark Matter mass in GeV Dipole interactions: d de R e 2 Z 2 16 m 2 B E R g 2 M + g2 E v 2 g 2 M g 2 E < mb 5TeV 3

24 N = N F =3 Pions and lightest baryons are adjoint of SU(3). Rescale QCD: m m B 1.3 f 7 m g m 2 2 J(J + 1)m 2 b 2 2b m 1 B D =0.6 F =0.4 Technibaryon thermal abundance: QCD p p 100 GeV 2 DM c DM 2 MB 200 TeV

25 Q=L+E m N 4m (b 1 m L + b 2 m E ) m 4m (b 2 m L + b 1 m E ) m 4m (b 1 + b 2 )m L m 4 3 m (b 1 + b 2 )(m L +2m E ) Triplet is never lightest. Singlet can be DM: Dipole interactions: m L m E 1 4 m B B µ (g M + ig E 5 )BeF µ g M O(1) g B 1 E 0.15 m2 f 2 log m2 B m 2 TC.

26 SO(N) models With NF fundamental flavors: h0 q a i q b i 0i 4 f 3 ab SU(N F ) SO(N F ) Fermions are in a real TC representation: - No difference between baryons and anti-baryons. Two baryons can annihilate into N pions i 1i 2...i N j 1j 2...j N =( i1 j 1 i 2 j 2... i N j N ± permutations) - Majorana masses are possible for real SM reps. NN VV GG

27 After electro-weak symmetry breaking neutral baryons with hyper charge mix with Majorana ones. Mass eigenstates are real. Similar to neutralinos. SO(N) baryons are Majorana fermions or real scalars: production Cannot be produced through an asymmetry. Thermal abundance: detection m DM 100 TeV There are no vector couplings with Z and no dipole interactions. This avoids spin independent bounds.

28 Renormalizable models:

29 Q=L+N Lightest baryons are likely a quintuplet of SO(5): Higgsino" + bino /2 2 1/ m 10 y L v y R v 2 1/2 yl v 0 m 2 1/2 2 1/2 B v m 2 1/ C A Higgsino DM m 21/2 <m 10 m M y2 v 2 m yv m m m 21/2 m 10 m> m B

30 - spin-dependent x-sec g 2 µ 5 g A Z µ cos W 2 g A < 1.2 M DM TeV g A y2 v 2 ( m) inelastic dark matter g 2Y cos W + M µ M Z µ m M > 100 KeV y> m 100 TeV - spin-independent x-sec SI = g2 DM m4 N f 2 N 2 v 2 M 4 h g DM < p M DM /75TeV g DM y

31 OTHER PHENO (O. Antipin, MR, arxiv: )

32 COLLIDER SIGNATURES Kilic, Okui, Sundrum 09 Framework predicts Goldstone bosons and vector bosons with SM charges: h0 µ T a b i = ab m f µ h0 µ 5 T a b i = i ab fp µ Heavy vectors mix with SM gauge bosons q q + g 2 SM g m g f Differently from composite Higgs fermions are elementary.

33 LHC8 Greco, Liu 14 (pp! + + X) g4 2 g 2 (pp! + X) g4 2 g 2 u d dū (pp! 0 + X) g4 2 g 2 ( uū + d d) Decay to hidden pions and back to SM gauge bosons through anomalies or qqbar Pions can also be collider stable or long lived. q q Br(! q q) / g4 2 g 4

34 Pions can also be produced through SM interactions s HfbL 8 TeV 13 TeV p p 3 p p p p 3 p p 3 -- p p 3 p p m p HGeVL Br H%L p ± 3 Æ W ± g p 0 3 Æ gg p 0 3 Æ ZZ p 0 3 Æ Zg -- p ± 3 Æ W ± Z m p HGeVL Only search from CDF! pp! W ±! ± 3 0 3! 3 + W ± m 3 > 230 GeV

35 New features arise with Yukawa couplings H Q i (y L ijp L + y R ijp R )Q j ym fh MIXING : y m f m 2 2 W BR(! W ) 2 W BR(! WW) 4 W - Pions with species number decay through Higgs: 21/2! H 10, 11! HH 10 - Small effects in precision tests, Higgs couplings etc ˆT v2 f 2 4 Ŝ m2 W m 2 2 h WW h SM WW 3 v2 f 2

36 M 2 m 2 = 0 m 2 2 m 2 2 m 2 2 Electro-weak VEV m m < 1 Elementary Higgs > 1 Composite Higgs Elementary Higgs generates vacuum misalignment of composite Higgs! H q L q R y SM Viable UV completion of composite Higgs. Not natural supersymmetry? relaxion?

37 EDM for SM particles generated with complex Yukawas: Q=L+V m L LL + m V 2 VV + y LH VL+ y RHV L +h.c. WEAK STRONG d e ecm Im[y L y R ] N 3 TeV m 4 m TeV 2 d e < % C.L.

38 CONCLUSIONS Stability of DM suggests the existence of accidental symmetries beyond the SM. DM can be naturally realised within Vector-like confinement models as techni-baryons. SU(N) models generate complex DM with sizeable electric and magnetic dipoles. SO(N) models give Majorana DM giving rise for example to inelastic DM. The models automatically realize MFV and predict very small deviations from SM, yet they could be discovered at colliders if the dynamical scale is around TeV. Interesting effects include: resonances production, electron EDMs, gravitational waves, unification

39 OBRIGADO!!!

40 Gravitational waves (GW) SU(N) confining theories with N F massless flavours give rise to a 1st order P.T. for 3 apple N F apple 4N and N>3 P.T. occurs at : T TC O(10 TeV) Peak frequency of the GW signal : f peak = Hz T 10 TeV 10H Amplitude of the GW signal : X h 2 GW 10 9 P. Schwaller 15

41 Electron EDM Q=L+N Anomalies: L M = m L LL c + m N NN c + yhln c +ỹh L c N + h.c. L EDM = + m ( a 3) 2 m Im(yỹ)g2 f 3 g 1 g 2 N 64 2 f a 3W a µ B µ N m 2 K 2 64 p 3 2 f H a H a 3 1 p H H 3 hg 2 2 W iµ W i µ + g 2 1 B µ B µ i Integrate out GBs: L EDM = m2 3 2 Le EDM e2 N Im(yỹ)(3m 2 2m 2 3 )m m 2 3 m 2 m 2 F Fh 0 h 0 c H K 2 2 F Fh 0 h 0 d e em ec H log 2 m 2 h

42 -angle X i m i Qi Q i + TC 32 2 G µ G µ Vacuum: V (U) = f 2 2 Tr[MU + M U ] a N ( i log det U )2 U = U 0 V U 0 = Diag[e 1,e 2,...,e i N F ] Dashen equations: µ 2 i sin i = a N ( X i) i =1,...,N F ( m 2 0 3a N µ 2 i 4 p N fm i X i a N )

43 Baryons action depends on Crewther et al. 79 Pich, de Rafael 91 L B B(i µ D µ m B )B b Tr B B + c f D µ B µ 5 B = v 0 M U = 2 CP violating interactions from mass terms. As for the neutron EDM is generated: L i a Nf b B B i d DM 2 B µ 5 BF µ c f d DM e 16 2 abc Nf 2 log m2 B m 2

44 Baryons in SO(N) models Start from the SU(NF) HB and decompose under SO(NF) Example: QCD eightfold way splits spin-1/2 HB similarly for the heavier spin-3/2 HB :

45 Heavier baryons s = 3 2 s =1 s =2 M B Nm 0 + m 1 + J(J + 1) N m 2 + O 1 N 2 Baryons with species number can also be stable Ex: (sss)! 0 (uss)+k (ūs) Forbidden by phase space in QCD.