Z -portal right-handed neutrino dark ma4er in the minimal U(1)x extended Standard Model

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, Japan) Ref: NO & S. Okada, PRD 93, 075003 (2016) [arxiv:1601.07526 [hep-ph]] NO & S.

1 Z -portal right-handed neutrino dark ma4er in the minimal U(1)x extended Standard Model Nobuchika Okada University of Alabama In collaborapon with Satomi Okada (Yamagata Univ., Japan) Ref: NO & S. Okada, PRD 93, (2016) [arxiv: [hep-ph]] NO & S. Okada, arxiv: 1611: 02672, under review in PRD. Miami Fort Lauderdale, Dec. 15 th, 2016

2 Problems in Standard Model The Standard Model (SM) is the best theory in describing the nature of elementary parpcle physics, which is in excellent agreement with almost of all current experimental results (including LHC Run-2 results) as of TODAY However, New Physics beyond SM is strongly suggested by both experimental & theorepcal points of view

3 14.9: The regions of squared-mass splitting and mixing angle favo What is missing in the Standard Model? 1. Neutrino masses and flavor mixings 10 0 KARMEN2 NOMAD MiniBooNE Bugey NOMAD CDHSW CHORUS NOMAD CHORUS LSND 90/99% PDG m 2 21 =(7.53 ± 0.18) 10 5 ev 2 m 2 32 =(2.44 ± 0.06) 10 3 ev 2 sin 2 (2θ 12 )=0.846 ± sin 2 (2θ 23 )= sin 2 (2θ 13 )=(9.3 ± 0.8) 10 2 m 2 [ev 2 ] OPERA Cl 95% Ga 95% ICARUS Daya Bay 95% ν e ν X ν µ ν τ ν e ν τ CHOOZ all solar 95% SNO 95% SuperK MINOS T2K K2K KamLAND 95% Super-K 95% Neutrinos are massless in the Standard Model ν e ν µ All limits are at 90%CL unless otherwise noted tan 2 θ 10 2

4 2. Cosmological Dark Ma4er Problem Existence of Dark Ma3er has been established! Energy budget of the Universe is precisely determined by recent CMB anisotropy observapons (WMAP & Planck) Dark Ma4er parpcle: non-baryonic electric charge neutral (quasi) stable No suitable DM candidates in the SM

5 The Standard Model + Right-Handed Neutrinos (RHNs) Ø To incorporate neutrino masses in the Standard Model (at the renormalizable level), we need right-handed neutrinos Ø Right-handed neutrinos are singlet, and only for generapng neutrino mass Minimal gauged B-L extension of the Standard Model would be more compelling? Ø B-L is the unique anomaly free global symmetry in the SM Ø Gauging the global B-L symmetry looks natural Ø Anomaly free requirement à 3 right-handed neutrinos

6 Minimal Gauged B-L Extension of the SM Mohapatra & Marshak; We4erich; others The model is based on ParPcle Contents New fermions: New scalar: SU(3) c SU(2) L U(1) Y U(1) B L ql i /6 +1/3 u i R /3 +1/3 d i R 3 1 1/3 +1/3 l i L 1 2 1/2 1 NR i e i R H 1 2 1/2 0 Φ

7 New Yukawa terms in Lagrangian L Yukawa i,j Y ij D li L HNj R 1 2 k YNΦN k R k CN R k +h.c. B-L symmetry breaking via B-L gauge boson (Z boson) mass m Z =2g BL v BL Heavy Majorana neutrino mass m k N = Y N k v BL 2 Mass scale is controlled by B-L Sym. Br. scale B-L sym breaking also generates RHN mass

neutrinos and Majorana masses L Yukawa Y D l L HN R 1 2 Y N Φ N C

8 Seesaw Mechanism Minkowski; Yanagida; Gell-Mann, Ramond & Slansky; Mohapatra & Senjanovic; others We introduce right-handed neutrinos and Majorana masses L Yukawa Y D l L HN R 1 2 Y N Φ N C R N R +h.c., IntegraPng out the heavy Majorana neutrino SM singlet fermion

9 What is the Majorana mass scale? m ν m ev Broad range of Majorana mass, depending on Dirac mass scale Example: Minimal TeV is well-mopvated from the LHC phys. We focus on TeV-scale minimal B-L model

10 DM candidate is spll missing in TeV-scale minimal B-L model There have been many proposal for introducpon of DM parpcles Concise model: no extension of the parpcle content Instead, introduce a parity J=1,2 SU(3) c SU(2) L U(1) Y U(1) B L Z 2 NO & Seto, PRD 82 (2010) N j R N R Φ Ø Assigning odd parity for one RHN Ø The others are all even Enhancement of symmetry: L Y 3j D N c 3l j H L Anisimov & Di Bari, PRD 80 (2009) Y 3j D 0

11 TeV-scale minimal B-L model with RHN DM Ø 3 right-handed neutrinos à RHNs for the minimal seesaw ü Neutrino oscillapon data with one massless eigenstate ü leptogenesis at TeV Enhancement of epsilon necessary à Resonant leptogensis Suppression of lepton asymmetry via Z interacpon à some more enhancement by Y_D Ø Z2-odd 1 RHN for thermal Dark Ma4er King, NPB 576 (2000) 85; Frampton, Glashow & Yanagida, PLB 548 (2002) 119 Iso, NO & Orikasa, PRD 83 (2011)

12 More general gauged U(1) extension of the SM at TeV à Non-ExoPc U(1) extension Appelquist, Dobrescu & Hopper, PRD 68 (2003) U(1)X direcpon is a linear combinapon of the SM hypercharge & the gauged B-L direcpons U(1) Y angle U(1) X U(1) B L Ø ParPcle contents = the B-L model Ø Anomaly Free Ø One new parameter corresponding to angle

13 TeV-scale minimal U(1)X model with RHN DM SU(3) c SU(2) L U(1) Y U(1) X Z 2 ql i 3 2 1/6 (1/6)x H +(1/3)x Φ + u i R 3 1 2/3 (2/3)x H +(1/3)x Φ + d i R 3 1 1/3 (1/3)x H +(1/3)x Φ + l i L 1 2 1/2 ( 1/2)x H x Φ + e i R x H x Φ + H 1 2 1/2 ( 1/2)x H + N j R x Φ + N R x Φ Φ x Φ + x Φ =1 Ø Without los of generality, we fix Ø The minimal B-L model is in the limit of x H 0 Ø The U(1)X is oriented to the SM U(1) hypercharge for x H

14 Phenomenology of TeV-scale minimal U(1)X model with RHN DM (1) Z -portal RHN DM RHN DM communicates with the SM parpcles through Z boson mediated processes (2) Z boson search at the LHC Run-2 Search for a narrow resonance with the di-lepton final state at ATLAS and CMS with LHC Run-2 (3) We will discuss a complementarity between DM physics and LHC physics

15 (1) Z -portal RHN dark ma4er Z B-L case: NO & S. Okada, PRD 93 (2016) Ø The RHN dark ma4er communicate with the SM parpcles through its U(1)X gauge interacpon Ø For Dark Ma4er physics, only 4 free parameters are involved U(1)X gauge coupling: Z boson mass: m Z SM Higgs U(1)X charge: RHN DM mass: m DM α X = g2 X 4π x H Note that the RHN DM has U(1)X charge -1

16 Cosmological constraint on Z portal DM Observed Relic Abundance: Ω DM h 2 = ± Planck 2015 (68% CL) Thermal DM relic abundance is determined by the Boltzmann eq: dn dt +3Hn = σv (n2 n 2 EQ ), H(T ) = 8π 3 ρ M 2 Pl = 4π 3 45 g n(t )=sy EQ = g DM m 3 DM 2π 2 x s = 2π2 45 g m 3 DM x 3 σv = T 2 M Pl K 2(x), where x = m DM T Thermally averaged annihilapon cross secpon

17 Boltzmann equapon in terms of yield 45 Y = n s dy dx = s σv xh(m DM ) ( Y 2 Y 2 EQ) Ω DM h 2 = m DMs 0 Y ( ) ρ c /h 2 Ω DM h 2 = ± Planck 2015 (68% CL) s σv 1pb leads to the right abundance

18 Relic abundance for various α X and x H for m Z =4TeV h Planck 2015 x H =0 (B-L model limit) α X = m DM GeV Ø xh=0 fixed Ø As gauge coupling is lower, DM abundance becomes lower Ø DM mass ~mz /2 is adjusted to find the solupon Ø Too small gauge coupling, no solupon Lower bound on α X for x H =0 and m Z =4TeV

19 Relic abundance for various α X and x H for m Z =4TeV h α X = or or or 0 x H = m DM GeV x H α X =0.027 α X =0.027 Ø fixed Ø As xh is going away from -0.8, DM abundance becomes higher Ø DM mass ~mz /2 is adjusted to find the solupon Ø SoluPons only for -1.6 < xh <0 Allowed range for and m Z =4TeV

20 The lower bounds on α X as a function of m Z for various values of x H x H = ΑX As x_h is going away from xh=-0.8, the lower bound on alpha_x is increasing m Z' TeV

21 (2) LHC Run-2 phenomenology Ø The ATLAS and CMS collaborapons have been searching for Z boson resonance with a dilepton final state at the LHC Run-2 q q pp à Z +X à ll +X Z 0 l + l Ø Upper bounds on the cross secpon for the sequenpal Z model have been obtained SequenPal Z : heavy Z boson with exactly the same coupling as the SM Z boson We interpret the ATLAS & the CMS bounds into the our Z boson 21

22 dσ fb GeV Sample: B-L model case (x_h=0) dσ = Final state dilepton invariant dmmass ll a,b dmμμ distribupon for mz =2.5 TeV dσ = 1 dx 2M ( ) ll M f dm ll xe 2 a (x, Q 2 2 of-mass energy of the LHC Run-2. In our numerical )f ll b analysis,,q 2 we a,b CM xecm 2 M ll 2 E CM parton distribution functions with) the 2 factorization scale Q = m α BL = g2 BL 4π =0.008 By integrating the differential cross section over a range of M CTEQ6L for PDF CMS analysis, respectively, we obtain the cross section to be com M ΜΜ GeV 1 M 2 ll E 2 CM dx 2M ( ) ll M f xecm 2 a (x, Q 2 2 )f ll b,q 2 ˆσ(q q xecm 2 where f a is the parton distribution function for a parton a, an the colliding partons is given by X ˆσ = 4πα2 BL 81 ˆσ(q q Z BL l+ l ) M 2 ll (M 2 ll m2 Z ) 2 + m 2 Z Γ 2 Z. obtained by the ATLAS and the CMS collaborations. In the analysis by the ATLAS and the CMS collaborations,

23 Σ B pb ATLAS & CMS bounds on sequenpal Z model and the consistency of 25 our analysis with their analysis m Z'SSM TeV ATLAS Results Integrate the differenpal Xsec for mz' TeV gx Solid: our calculabon (k=1.28) Dashed: ATLAS analysis data 2015 data Σ pp Z' X ll X Σ pp Z X ll X data CMS Results Solid: our calculabon (k=1.6) Dashed: CMS analysis x H data FIG. 5. The lower bound on1.5m Z /g X as a function of x H.Weha m Z'SSM TeV at 95% confidence level. Integrate the differenpal Xsec for 128 GeV Mcross ll section 6000 GeV in the range of 0.95 M ll /m Z FIG. 4. Left panel: the cross SSM In t section ratio as a fun

24 Bounds from ATLAS and CMS at LHC Run-2 (Example: x_h=0 case) Σ B pb ATLAS Σ pp Z' X ll X Σ pp Z X ll X CMS m Z' TeV m Z' TeV α X =10 5, , 10 4, , 10 3, , 10 2, α X =10 4.5, 10 4, , 10 3, , 10 2, Upper bound on α X as a funcpon of m Z for a fixed x H

25 Other constraints LEP 2 bound on effecpve 4 Fermi interacpons from Z e + l e + l e l + l + e B-L limit General xh 35 m Z g BL 6.9 TeV Carena et al., PRD 70 (2004) Heeck, PLB 739 (2014) 256 mz' TeV gx x H

26 Other constraints (cont d) PerturbaPvity of the U(1)X coupling up to the Planck scale α X < 2π [ b X ln M Pl m Z ] 1-loop with b X =(72+64x H +41x 2 H )/6

27 LHC bounds (ATLAS & CMS combined) 0.1 PertubaPbity bounds for xh=-1, 0, +1 from top to bo4om 0.01 ΑX xh = m Z' TeV

28 (3) Complementarity between Cosmological & LHC bounds xh=0 (B-L limit) PerturbaPvity LEP bound ΑX Relic abundance m Z' TeV

29 0.050 xh= xh= ΑX ΑX m Z' TeV m Z' TeV xh= xh= ΑX ΑX m Z' TeV m Z' TeV

30 For Z boson mass =4 TeV ΑX Relic abundance x H

31 Summary Ø We have considered the minimal U(1)_X extension of the Standard Model with right-handed neutrino dark ma4er Minimal seesaw with 2 RHNs for the neutrino oscillapon data 1 RHN serves as DM Ø The RHN DM communicates with the SM parpcles through the Z -boson exchange (Z -portal DM) Phenomenology is controlled by U(1)X gauge coupling: Z boson mass: m Z SM Higgs U(1)X charge: RHN DM mass: m DM α X = g2 X 4π x H

32 Summary (cont d) Ø We have considered a variety of phenomenological constraints The observed DM relic abundance LHC Run-2 constraints from Z resonance search LEP 2 bounds PerturbaPvity of the U(1)x gauge coupling and idenpfied an allowed parameter region. These constraints are complementary with each other to narrow the model parameter space

33 !ank y" for y"r a$ention!

Neutrino Masses and Dark Matter in Gauge Theories for Baryon and Lepton Numbers

Neutrino Masses and Dark Matter in Gauge Theories for Baryon and Lepton Numbers DPG Frühjahrstagung 014 in Mainz Based on Phys. Rev. Lett. 110, 31801 (013), Phys. Rev. D 88, 051701(R) (013), arxiv:1309.3970