Dark Vector Boson from E /SU(2)N Extension of the ...research.ipmu.jp/seminar/sysimg/seminar/658.pdfKhalil/Lee/Ma(2009,2010): Simpler nonsupersymmetric versions exist with nc as a

Dark Vector Boson from E6/SU(2)NExtension of the Standard Model

Ernest MaPhysics and Astronomy Department

University of CaliforniaRiverside, CA 92521, USA

Dark Vector Boson from E6/SU(2)N Extension of the Standard Model back to start 1

Contents

• Dark Matter Varieties

• E6/SU(3)3 Extensions of the Standard Model

• Dark SU(2)N Model

• X1 Vector Boson as Dark Matter

• LHC Phenomenology

• Conclusion


Dark Matter Varieties

There used to be just one candidate dark-matter theory,

i.e. R−parity conserving supersymmetry (MSSM), but in

recent years, many more have been proposed.

Dark matter must be neutral (so that it is dark) and

stable (so that it is still here).

In the MSSM, the candidates are the lightest sneutrino

(scalar boson) or the lightest neutralino (spin-one-half

fermion).


The former is ruled out by direct-detection experiments,

because it interacts with quarks through the Z boson,

with a cross section many orders of magnitude larger

than is allowed by observation. The latter is OK, because

a neutralino mass eigenstate is Majorana which does not

contribute to the elastic scattering through Z exchange.

Ma(2006): Neutrino mass may also be due to dark

matter (scotogenic). Add to the Standard Model (SM) a

second scalar doublet (η+, η0) and 3 neutral singlet

Majorana fermions N1,2,3 which are odd under an exactly

conserved Z2, with all SM particles even.


ν νN

η0 η0×

Figure 1: One-loop mν

from Z2 dark matter.


Hence νNφ0 is forbidden and νNη0 is allowed, but

〈η0〉 = 0. Thus N is not the Dirac mass partner of ν.

Nevertheless, neutrino mass is generated in one loop, i.e.

scotogenic, being caused by darkness. Here, η0R is a

dark-matter candidate, studied two months later by

Barbieri/Hall/Rychkov(2006). They call η the inert Higgs

doublet. I call it the dark scalar doublet.

Since η is a scalar doublet just like the supersymmetric

(sneutrino, slepton) doublet, why is it not also ruled out?

The reason is that the quartic interaction (η†Φ)2 is

allowed by Z2 but not by supersymmetry.


This term splits η0R and η0

I , which serves two purposes.

(1) It allows the one-loop scotogenic diagram to be

nonzero and finite.

(2) Since Z couples to η0Rη

0I only, the direct-search

experiments using elastic nuclear recoil are rendered

ineffective for a mass gap of only 1 MeV.

Ma/Sarkar(2007): E6/U(1)N realization of scotogenic

neutrino mass in two loops.

Cao/Ma/Wudka/Yuan(2007): Multipartite dark matter

may exist, then the least abundant has the largest cross

section and may be discovered first at the LHC.


E6/SU(3)3 Extensions ofthe Standard Model

Shortly after the first string revolution (1984-6), the

superstring-inspired supersymmetric E6 model was

studied intensively. The fundamental 27 representation of

E6 is decomposed under its maximum subgroup

SU(3)C × SU(3)L × SU(3)R as d u h

d u h

d u h

+

N Ec ν

E N c e

νc ec nc

+

dc dc dc

uc uc uc

hc hc hc

.


The decomposition of SU(3)L→ SU(2)L × U(1)YLis

completely fixed because of the SM. However, there are

3 choices for SU(3)R → SU(2)′ × U(1)′.(1) The conventional choice of SU(2)R × U(1)YR

means

that (νc, ec) and (uc, dc) are SU(2)R doublets.

(2) Ma(1987): Alternative Left-Right Model, i.e. d u h

d u h

d u h

+

ν Ec N

e N c E

nc ec νc

+

hc hc hc

uc uc uc

dc dc dc

.

Here (nc, ec) and (uc, hc) are SU(2)R doublets.


Khalil/Lee/Ma(2009,2010): Simpler nonsupersymmetric

versions exist with nc as a dark-matter fermion (scotino).

(3) London/Rosner(1986): SU(2)′ = SU(2)N , i.e. d u h

d u h

d u h

+

N ν Ec

E e N c

νc nc ec

+

dc dc dc

hc hc hc

uc uc uc

.

Here (νc, nc) and (hc, dc) are SU(2)N doublets.

Diaz-Cruz/Ma(2010): The analog of the W±R gauge

boson in (2) is now neutral and could be a vector-boson

dark-matter candidate.


Dark SU(2)N Model

Fermion content with S = L− T3N :

uc ∼ 0, (hc, dc) ∼ −12, h ∼ 1, ec ∼ −1, (νc, nc) ∼ −1

2,(

u

d

)∼ 0,

(N ν

E e

)∼ 1

2,

(Ec

N c

)∼ 0.

All fields are left-handed, with SU(2)L doublets vertical

[T3L = ±1/2 for upper (lower) components] and

SU(2)N doublets horizontal [T3N = ±1/2 for right (left)

components].


Higgs sector:(φ0

1 φ02

φ−1 φ−2

)∼ 1

2,

(η+

η0

)∼ 0, (χ0

1, χ02) ∼ −1

2.

Allowed Yukawa couplings are

(dφ01 − uφ−1 )dc − (dφ0

2 − uφ−2 )hc, (uη0 − dη+)uc,(hcχ0

2 − dcχ01)h, (Nφ−2 − νφ−1 − Eφ0

2 + eφ01)e

c,

(Eη+ −Nη0)nc − (eη+ − νη0)νc, (EEc −NN c)χ02 –

(eEc − νN c)χ01, (Ecφ−1 −N cφ0

1)nc − (Ecφ−2 −N cφ0

2)νc.

Thus md,me come from 〈φ01〉 = v1; mu,mν from

〈η0〉 = v3; mh,mE,mN from 〈χ02〉 = u2.


This structure conserves L and guarantees the absence of

tree-level flavor-changing neutral currents. SU(2)N is

completely broken by u2 so that m2X = (1/2)g2

Nu22 for

each X1,2,3 gauge boson. Whereas X3 = Z ′ has L = 0,

(X1 ∓ iX2)/√

2 are the neutral analogs of W±R with

L = ±1 and can be dark matter. Consider now the

addition of a Higgs triplet (ξ03, ξ

04, ξ

05) ∼ 1, with 〈ξ0

3〉 = u3

and 〈ξ05〉 = u5. Then L is broken by u5 to (−1)L and

neutrinos obtain seesaw Majorana masses. There is also a

large Majorana mass term for nc from u3 so that there is

no more massless particle in the (N,N c, nc) sector.


X1 Vector Boson as Dark Matter

Gauge boson masses:

m2W =

12g2

2(v21 + v2

3), m2X1,2

=12g2N [u2

2 + 2(u3 ∓ u5)2],

m2Z,Z′ =

12

((g2

1 + g22)(v

21 + v2

3) −gN√g2

1 + g22v

21

−gN√g2

1 + g22v

21 g2

N [u22 + v2

1 + 4(u23 + u2

5)]

).

Let X1 be the lightest particle of odd R = (−1)3B+L+2j,

then it can be a viable dark-matter candidate.


Note that there is no X1X1Z′ interaction; only X1X2Z

′

is allowed. However, X1X1 annihilation to

dd̄, νν̄, e−e+, φ1φ†1 is possible through h,N,E, φ2

exchange respectively. The nonrelativistic cross section ×relative velocity is (g4

Nm2X/72π) ×∑

h

3(m2

h +m2X)2 +

∑E

2(m2

E +m2X)2

+2

(m2φ2

+m2X)2 +

1m2X(m2

φ2+m2

X)+

38m4

X

.

where the sum over h,E is for 3 generations.


The factor of 3 for h is the number of colors, the factor

of 2 for E, φ2 is to account for them being doublets.

Let σvrel > 0.86 pb be the benchmark for the correct

dark-matter relic abundance and assuming

g2N = g2

2 = e2/ sin2 θW ' 0.4 with all exotic particle

masses equal, the upper bound mX < 1.28 TeV is

obtained.

The fundamental interaction of X1 with nuclei is only

through the d quark, but there are induced effective

interactions. [Hisano/Ishiwata/Nagata/Yamanaka(2010)]


The coherent spin-independent elastic cross section is

σ0 =1π

(mN

mX

)2 ∣∣∣∣Zfp + (A− Z)fnA

∣∣∣∣2 ,where fp and fn are form factors, and (Z,A) are the

atomic and mass numbers of the target nucleus,

say 73Ge with Z = 32 and A− Z = 41.

Using the recent CDMS(2010) result that

σ0 < 2.2× 10−7 pb (mX/1 TeV)0.86 in the range

0.3 < mX < 1.0 TeV, a lower bound on mh (the one

that couples to d) as a function of mX is obtained.


RelicAbundance

Direct DetectionRed : mÆ = 120Blue : mÆ = 200

(in GeV)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.0

0.2

0.4

0.6

0.8

1.0

m X

∆

Allowed region in δ = mh/m

X− 1 versus m

X(in TeV)

from relic abundance and from CDMS direct search.


LHC Phenomenology

Since mX ∼ 1 TeV or less, Z ′ is expected to be

observable at the LHC, with B(Z ′ → µ−µ+) = 1/16.

It is in fact the linear combination√

5/8Zχ +√

3/8Zψfrom E6 models. Distinguishing this Z ′ from others

[Godfrey/Martin(2008)] is possible from

Γ(Z ′ → tt̄)/Γ(Z ′ → µ−µ+) = 0, and

Γ(Z ′ → bb̄)/Γ(Z ′ → µ−µ+) = 3.

Since Z − Z ′ mixing is limited to a few × 10−4, which is

of order v21/u

22, v1 may be around 10 GeV. This means

that the φ1 Yukawa coupling to b quarks is large,


making φ01 observable at the LHC

[Balazs/Diaz-Cruz/He/Tait/Yuan(1999)].

A favorable scenario for observing the structure of this

model is possible with the following spectrum:

mh > mX2 > mE,N > mX1.

[Bhattacharya/Diaz-Cruz/Ma/Wegman(2011)].

Consider the production d + gluon to h + X1. Now h

will decay into X1d and X2d, then X2 will decay into

E+l−, E−l+, N̄ν, Nν̄, and E+ → X1l+, E− → X1l

−,

N̄ → X1ν̄, N → X1ν.


This means that about 1/4 of the time, pp→ hX1 will

end up with one quark jet + missing energy + l+i l−j .

We choose mX1 = 700 GeV, mE,N = 735 GeV,

mX2 = 770 GeV, mh = 980 GeV, and the basic cuts

pT > 20 GeV and |η| < 2.5 for each lepton and pT > 50GeV for the quark jet. The background is then

suppressed by choosing a large missing energy cut. At

the LHC with Ecm = 14 TeV, we find a signal cross

section of 1.6 fb with essentially no background if a cut

on missing Et > 200 GeV is made.


0

0.05

0.1

0.15

0.2

0.25

0.3

0 200 400 600 800 1000

Num

ber

Of E

vent

s (N

orm

alis

ed)

Missing Energy (GeV)

DM modelttbar


Conclusion

Instead of a spin-zero scalar or a spin-one-half fermion or

combinations of the two, dark matter may be a spin-one

vector boson. The first such example from a unifiable

theory based on E6 has been proposed. This SU(2)Nextension of the Standard Model allows one of the 3

gauge bosons, say X1, to be the lightest particle with

odd R parity. From the requirement of relic abundance,

mX ∼ 1 TeV or less is predicted. It is verifiable at the

LHC.


Documents

Dark Vector Boson from E /SU(2)N Extension of the ...research.ipmu.jp/seminar/sysimg/seminar/658.pdfKhalil/Lee/Ma(2009,2010): Simpler nonsupersymmetric versions exist with nc as a