Electroweak scale seesaw and heavy Dirac neutrino signals at LHC

0.24 MB·

by  F. del Aguila

Ele
troweak s
ale seesaw and heavy Dira
neutrino signals at LHC
F. del Aguila, J. A. Aguilar(cid:21)Saavedra
Departamento de Físi
a Teóri
a y del Cosmos and CAFPE,
Universidad de Granada, E-18071 Granada, Spain
Abstra
t
Models of type I seesaw
an be implemented at the ele
troweak s
ale in a
9
natural way provided that the heavy neutrino singlets are quasi-Dira
parti
les.
0
0 In su
h
ase, their
ontribution to light neutrino masses has the suppression of
2
a small lepton number violating parameter, so that light neutrino masses
an

n
a arise naturally even if the seesaw s
ale is low and the heavy neutrino mixing is
J
large. We implement the same me
hanism with fermioni
triplets in type III
5
1 seesaw, deriving the intera
tions of the new quasi-Dira
neutrinos and heavy

harged leptons with the SM fermions. We then study the observability of heavy
]
h
Dira
neutrino singlets (seesaw I) and triplets (seesaw III) at LHC. Contrarily to
p
-
ommon wisdom, we (cid:28)nd that heavy Dira
neutrino singlets with a mass around
p 5σ 1
−
e 100 GeV are observable at the level with a luminosity of 13 fb . Indeed,
h ℓ ℓ ℓ
± ± ∓
[ in the (cid:28)nal state with three
harged leptons , not previously
onsidered,

3 Dira
neutrino signals
an be relatively large and ba
kgrounds are small. In1the
v −
triplet
ase, heavy neutrinos
an be dis
overed with a luminosity of 1.5 fb for
6
9 a mass of 300 GeV in the same
hannel.
0
2
.
9
0
1 Introdu
tion
8
0
:
v The well-known seesaw me
hanism provides a simple and natural way to give tiny
i
X
masses to the three neutrinos present in the Standard Model (SM). In its initial re-
r
a alisation (type I seesaw) [1(cid:21)4℄ the SM is enlarged with the addition of three heavy
N i = 1,2,3
i′R
right-handed neutrino singlets ( ). These (cid:28)elds have Yukawa intera
tions
L
′iL
with the SM left-handed lepton doublets as well as a Majorana mass term,
1
= Y L¯ N φ˜ M N¯ N + ,
LImass − ij ′iL j′R − 2 ij i′L j′R H.
. (1)
φ N N′c = (N )c φ˜= iτ φ τ
where is the SM Higgs doublet, i′L ≡ iR i′R and 2 ∗, with i the Pauli
matri
es. After ele
troweak symmetry breaking, these terms generate a mass matrix
for neutrino (cid:28)elds and, in parti
ular, an e(cid:27)e
tive light neutrino mass matrix
v2
M = YM 1YT ,
ν −
− 2 (2)
1
v = 246
where GeV is the va
uum expe
tation value of the SM Higgs. For Yukawa
Y
ij

ouplings of order one without any parti
ular symmetry, light neutrino masses
m 0.1
ν
∼ eV
an be obtained if the heavy neutrino masses (whi
h are approximately
M m 1014
N
equal to the eigenvalues of ) are of the order ∼ GeV,
lose to the uni(cid:28)
ation
s
ale. However, the drawba
k of this pi
ture is that these new eigenstates are too
heavy to be observable, and this (cid:16)minimal(cid:17) type I seesaw me
hanism
annot be dire
tly
tested. Many attempts have been made in the literature to lower the heavy s
ale while
su

essfully generating light neutrino masses
ompatible with experimental data. One
possibility is to have very small Yukawa
ouplings. Indeed, in the SM only the top
quark has a Yukawa
oupling of order unity, while for the
harged leptons they range
2.9 10 6 10 2
− −
from × for the ele
tron to for the tau. But heavy neutrinos are still
unobservable in this
ase be
ause their mixing with the SM leptons,
Y v
lN
V ,
lN
≃ √2m (3)
N
is very small and they
annot be dire
tly produ
ed at an observable rate. For example,
m v m . 0.1 V . 10 6
N ν lN −
for heavy neutrino masses ∼ the requirement eV implies ,
V 2 10 12
lN −
giving a suppression fa
tor of | | ∼ for heavy neutrino produ
tion
ross se
-
tions. A moreinteresting possibilityis tokeep sizeableYukawa
ouplingsbut introdu
e
some symmetry whi
h suppresses the seesaw-type
ontribution in Eq. (2). In the ex-
amples known in the literature [5(cid:21)11℄, this symmetry is lepton number. In this way,
m µ/2
N
two nearly-degenerate heavy Majorana neutrinos with masses ± and opposite
CP parities form a quasi-Dira
neutrino, whose
ontribution to light neutrino masses
µ/m
N
has the further suppression of the small ratio (see [12℄ and referen
es there in).
Then, this quasi-Dira
neutrino
an have a relativelylargemixingwith the SM leptons,
only
onstrained by ele
troweak pre
ision observables [13℄.
The sameme
hanism
an be implementedwithfermioni
tripletsintype IIIseesaw.
Σ
i
In its usual realisation [14,15℄, type III seesaw introdu
es three fermion triplets
i = 1,2,3 N
i
( )withzerohyper
harge, ea
hofthem
onsistingofoneMajorananeutrino
E
i
andtwoWeylspinorswhi
h
anformaDira

hargedlepton . Fermiontriplets
ouple
totheSM leptondoublets throughYukawa
ouplingsandhave Majorana masstermsas
m Y2v2/(2m )
ν N
well. Similarly to type I seesaw, light neutrino masses are of order ∼
V Yv/(√2m )
N
and the mixing of the heavy states is ∼ (see next se
tion). If the
new parti
les are near the ele
troweak s
ale, light neutrino masses
an be kept within
Y
1
experimental limits either with very small or by requiring some symmetry. In
this Letter we work out in detail the se
ond possibility. In full analogy with type
V
1
Notethatasizeablemixing isnotne
essarytoobservethenewheavystates,be
ausethey
anbe
Y &10−6
produ
edinpairsbyunsuppressedgaugeintera
tionsandde
aywithinthedete
torfor [16℄.
2
I seesaw, if the heavy neutrinos are quasi-Dira
parti
les the light neutrino masses
µ/m
N
get a further suppression , so that Yukawa
ouplings of order unity are possible
m
N
with at the ele
troweak s
ale. In this (cid:16)Dira
(cid:17) variant of type III seesaw ea
h
+
N E E
1− 2
heavy quasi-Dira
neutrino is asso
iated with two
harged leptons and ,
the three of them with lepton number equal to one and nearly degenerate in mass,
mN ≃ mE1− ≃ mE2+. Leptonnumberis
onservedex
eptforthelightneutrinoMajorana
+
N E E
1− 2
masses. We obtain the intera
tions between the new states , , and the SM
leptons, (cid:28)ndingsubstantial di(cid:27)eren
es withthe Majorana
ase, whi
h a(cid:27)e
ttheirde
ay

hannels and the possible signals at
olliders. It must be remarked that the seesaw
me
hanism with heavy quasi-Dira
neutrinos is naturally realised in models with new
physi
s at the ele
troweak s
ale, like in little Higgs models with simple groups [17℄ or
in models with extra dimensions and matter in the bulk implying in(cid:28)nite Kaluza-Klein
towers of Dira
fermions (see for example Refs. [18,19℄).
After des
ribing in detail this variant of type III seesaw, we study the observability
of heavy Dira
neutrino singlets and triplets at the Large Hadron Collider (LHC).
We follow the pro
edure previously used in Ref. [20℄, and systemati
ally study all the
observable multi-lepton signals (up to six leptons) in
luding all signal
ontributions
from the various produ
tion pro
esses and de
ay
hannels. By
omparing with the
(cid:16)minimal(cid:17) seesaw IandIIIs
enarioswithheavy Majorananeutrinosstudied inRef.[20℄
weshowthatthedis
riminationbetweenthetwopossibilitiesisveryeasy, providedthat
a positive signal is observed. In parti
ular we also (cid:28)nd that, in
ontrast with
ommon
wisdom, heavy Dira
neutrino singlets
ould be observed at LHC in the trilepton (cid:28)nal
ℓ ℓ ℓ m = 100
± ± ∓ N
state . Forexample,a heavy neutrinowith GeV
ouplingtothemuon
V2 = 0.0032 5σ 1
µN −
with
an be seen with signi(cid:28)
an
e with only 13 fb of luminosity.
1
−
For a 300 GeV Dira
fermion triplet the dis
overy is possible with only 1.5 fb .
2 Heavy Dira
neutrinos in type III seesaw
Here we will follow the notation in Ref. [20℄ and quote some results obtained there
Σ i = 1,...,n
i
without proof. Fermion triplets , (we leave their number arbitrary)
are
omposed of three Weyl spinors of zero hyper
harge, and we
hoose them to be
right-handed under Lorentz transformations. They
ouple to the SM lepton doublets
L = (ν l )T
′iL i′L i′L
(we use primes for weak intera
tion eigenstates when ne
essary to
distinguish them from mass eigenstates) and have a Majorana mass term,
1
= Y L¯ (Σ~ ~τ)φ˜ M Σ~c Σ~ + ,
LImIIass − ij ′iL j · − 2 ij i · j H.
. (4)
3
Σ~ = (Σ1, Σ2, Σ3)
j j j j
where are the triplets written in Cartesian
omponents. Noti
e that
Σ1 Σ2 Σ3 Σ M
j j j j
all the members , , of the triplet have the same mass, and the matrix
Σ
j
(whi
h is symmetri
)
an be assumed diagonal in full generality. For ea
h triplet ,
the
harge eigenstates are related to the Cartesian
omponents by
1 1
+ 1 2 0 3 1 2
Σ = (Σ iΣ ), Σ = Σ , Σ = (Σ +iΣ ),
j √2 j − j j j −j √2 j j (5)
and from them we
an build one
harged Dira
and one neutral Majorana fermion,
E = Σ +Σ+c, N = Σ0 +Σ0c.
j′ −j j j′ j j
(6)
Σ
j
With our
hoi
e of right-handed
hirality for , we have
E = Σ+c, E = Σ , N = Σ0c, N = Σ0.
j′L j j′R −j j′L j j′R j
(7)
After spontaneous symmetry breaking, the terms in Eq. (4) yield the neutrino and

harged lepton mass matri
es
1 0 v Y ν
= ν¯ N¯ √2 R′ +H.c.,
Lν,mass −2 L′ L′ √v2YT M ! NR′ !
(cid:0) (cid:1)
v Yl vY l
= ¯l E¯ √2 R′ +H.c.,
Ll,mass − L′ L′ 0 M ! ER′ ! (8)
(cid:0) (cid:1)
ν ν′c N N′c
where we have de(cid:28)ned i′R ≡ iL, i′L ≡ iR. Note that we have not spe
i(cid:28)ed the num-
Y 3 n M n n
ber oftriplets, so isa matrixofdimension × and is × . The masseigenstates
are obtained from the diagonalisation of these mass matri
es. Their intera
tions with
l = e,µ,τ
the SM leptons (with ) are given by [20℄
= g E¯ γµN W +N¯ γµE W+
LW − i i µ− i i µ
g
(cid:0)V ¯lγµP N W +V N¯(cid:1)γµP l W+
− √2 lNi L i µ− l∗Ni i L µ
g V(cid:0) E¯ γµP ν W +V ν¯γµP E W+(cid:1),
− lNi i R l µ− l∗Ni l R i µ
= gc(cid:0) E¯ γµE Z (cid:1)
Z W i i µ
L
g
+ V ν¯γµP N +V N¯ γµP ν Z
2c lNi l L i lN∗i i L l µ
W
g
+ (cid:0) V ¯lγµP E +V E¯ γµP l(cid:1)Z ,
√2c lNi L i lN∗i i L µ
W
(cid:0) (cid:1)
= eE¯ γµE A ,
γ i i µ
L
gm
= Ni V ν¯P N +V N¯ P ν H
LH 2M lNi l R i l∗Ni i L l
W
gm
+ Ei(cid:0) V ¯lP E +V E¯ P l (cid:1)H ,
√2M lNi R i l∗Ni i L (9)
W
(cid:0) (cid:1)
4
where the mixing is Y v
V lNi .
lNi ≃ −√2m (10)
Ni
E N
i i
In the general Majorana
ase, the mass eigenstates are , . This stillholds when
two Majorana neutrinos form a Dira
fermion, but in this
ase the two degenerate Ma-
jorana states interfere, and further rede(cid:28)nitions are
onvenient to simplifythe analysis.
N N
1 2
Then, let us assume that we have two Majorana neutrinos and degenerate in
mass and with opposite CP parities (the small mass di(cid:27)eren
e in the quasi-Dira

ase
is
ru
ial in order to generate light neutrino masses but irrelevant for heavy lepton
Y = iY
intera
tions). Moreover, their Yukawa
ouplings satisfy lN2 lN1, so that
V = iV .
lN2 lN1 (11)
The
al
ulation of quantities su
h as
ross se
tions for heavy neutrino produ
tion with
N
1
subsequent de
ay
an be done in terms of two interfering Majorana neutrinos and
N
2
(ea
h with two degrees of freedom). Alternatively, it
an be done in terms of a
Dira
neutrino with
omponents
1 1
N (N +iN ), N (N +iN ),
L 1L 2L R 1R 2R
≡ √2 ≡ √2 (12)
whi
h has four degrees of freedom. The
harged se
tor
an also be des
ribed in terms
+
E E E E
1 2 1− 2
of the two interfering degenerate states , or in terms of two fermions ,
(the latter is positively
harged), whi
h are de(cid:28)ned as
1 1
E (E +iE ), E (E +iE ),
1−L ≡ √2 1L 2L 1−R ≡ √2 1R 2R
1 1
E+ (Ec +iEc ), E+ (Ec +iEc ).
2L ≡ √2 1R 2R 2R ≡ √2 1L 2L (13)
N
These states have diagonal
ouplings to the Dira
neutrino and do not interfere in
the pro
esses analysed in this paper, so the des
ription turns out to be mu
h simpler.
+
N E E
1− 2
The intera
tions of the Dira
mass eigenstate fermions , and are obtained
i = 1,2
from Eqs. (9) for using Eqs. (11)-(13),
= g E¯ γµN N¯γµE+ W g N¯γµE E¯+γµN W+
LW − 1− − 2 µ− − 1− − 2 µ
g
(cid:0)V ¯lγµP N W +(cid:1)V N¯γµP(cid:0) l W+ (cid:1)
− √2 lN L µ− l∗N L µ
+g V(cid:0) ν¯γµP E+ W +V E¯+γµP ν W(cid:1)+ ,
lN l L 2 µ− lN∗ 2 L l µ
= gc(cid:0) E¯ γµE E¯+γµE+ Z (cid:1)
Z W 1− 1− 2 2 µ
L −
g
+ (cid:0)V ν¯γµP N +V N¯(cid:1)γµP ν Z
2c lN l L lN∗ L l µ
W
g
+ (cid:0) V ¯lγµP E +V E¯ γµP(cid:1)l Z ,
√2c lN L 1− l∗N 1− L µ
W
(cid:0) (cid:1)
5
= e E¯ γµE E¯+γµE+ A ,
γ 1− 1− 2 2 µ
L −
gm
= (cid:0) N V ν¯P N +V (cid:1)N¯P ν H
LH 2M lN l R lN∗ L l
W
gm
+ E1(cid:0) V ¯lP E +V E¯ P(cid:1)l H,
√2M lN R 1− lN∗ 1− L (14)
W
(cid:0) (cid:1)
with mN = mE1− = mE2+ and VlN = √2VlN1. The Feynman rules for these intera
tions
are
olle
ted in the Appendix. The main di(cid:27)eren
es with the Majorana
ase are:
+
E E
2 1−
(i) the gauge
ouplings with two heavy fermions have opposite sign for and ;
+
E E
2 1−
(ii) light neutrinos only
ouple to , while light
harged leptons only
ouple to .
On the other hand, the heavy Dira
neutrino
ouples to light
harged and neutral
leptons in the same way as a heavy Majorana neutrino, ex
ept that in the latter
ase
N = Nc ν = νc
the neutral
ouplings
an be rewritten using , . These equations also
+
L = 1 N E E
1− 2
show
learly that, if lepton number is assigned to , and , then it is

onserved ex
ept for light neutrino masses. When the two Majorana states are not
m µ/2 N
N
degenerate but have masses ± and is quasi-Dira
, lepton number violating
µ/m
N
(LNV) e(cid:27)e
ts are of order .
There are several implementations of this me
hanism in the heavy lepton mass
matri
es (see for example Refs. [5(cid:21)11℄). A parti
ularly simple model
an be built by
assigningleptonnumbertotheheavytripletsandrequiringapproximateleptonnumber
Σ Σ
1 2

onservation. Let us assume that we have two triplets and , to whi
h we assign
1 1
lepton numbers equal to and − , respe
tively. Then, for one lepton generation the
(cid:28)elds are
l , l , E , E , ν , N , (L = 1) ; N , E , E (L = 1),
L′ R′ 1′R 2′L L′ 1′R 2′R 1′L 2′R − (15)
ν ν′c N N′c N N′c
whereas the
harge
onjugate (cid:28)elds R′ ≡ L, 2′L ≡ 2R, 1′L ≡ 1R have opposite
lepton number. If we impose lepton number
onservation, for one lepton generation
the neutrino mass term is [21℄
0 vY 0 ν
R′
1
= ν¯ N¯ N¯ vY 0 M N +H.c.
Lν,mass −2 L′ 1′L 2′L    1′R (16)
0 M 0 N
(cid:0) (cid:1)   2′R
   
2 2
The × submatrix in the heavy se
tor
orresponds to the mass term of a heavy Dira
N = N +N m = M
2′L 1′R N
neutrino with mass ,
M M
N¯ N +N¯ N = N′c N′c +N N = MN¯ N .
− 2 1′L 2′R 2′L 1′R − 2 1R 2L 2′L 1′R − 2′L 1′R (17)
(cid:16) (cid:17)
(cid:0) (cid:1)
6
This de(cid:28)nition is
onsistent with Eqs. (12). A tiny light neutrino Majorana mass
µv2Y2
m =
ν 2M2 (18)
µ M (3,3)

an be introdu
ed with a LNV entry ≪ in the position of this matrix,
in whi
h
ase the heavy neutrino is quasi-Dira
, being the masses of the two heavy
M µ/2
Majorana (cid:28)elds ± . For three lepton generations and six fermion triplets (in
order to yield three heavy Dira
neutrinos) the stru
ture of the neutrino mass matrix
Y M 3 3 YT
is the same but and are × matri
es, and they have to be replated by and
MT (2,1) (3,2)
in the and positions of the matrix in Eq. (16), respe
tively.
In the
harged se
tor the mass term is, for one lepton generation,
v Yl √2vY 0 l
√2 R′
Ll,mass = − ¯lL′ E¯1′L E¯2′L  0 0 M  E1′R +H.c. (19)
0 M 0 E
(cid:0) (cid:1)   2′R
   
2 2
By inspe
tion of the mass matrix one observes that the × submatrix in the heavy
E = E +E
1− 2′L 1′R
se
tor
orresponds to the diagonal mass term of two Dira
fermions ,
E2+ = E1′cL +E2′cR = 1 mE− = mE+ = M
, both with L and 1 2 . This is
onsistent with the
de(cid:28)nition of (cid:28)elds in Eqs. (13).
We(cid:28)nallypointoutthatfor
olliderphenomenology(wheretheenergys
aleismu
h
larger than light neutrino masses, whi
h
an then be negle
ted), Dira
and quasi-Dira
neutrinos are equivalent, thus in our simulations we assume that heavy neutrinos are
Dira
parti
les.
3 Heavy Dira
neutrino signals at LHC
The produ
tion pro
esses of heavy Dira
neutrino singlets and triplets are the same as
2
for their Majorana
ounterparts. Dira
neutrino singlets
an be produ
ed at hadron

olliders in the pro
ess
qq¯ W l N .
′ ∗ ±
→ → (20)
qq¯ Z νN
∗
They
an also be produ
ed in → → but the resulting signal has at most one

harged lepton, and is swamped by the ba
kground. The
harged and neutral members
2
The transition between the Dira
and Majorana
ases
an be made smooth by varying
ontinu-
ously the
ouplings and masses in Eq. (8), as it happens, for instan
e, for gluinos and neutralinos in
supersymmetry [22℄.
7
of a Dira
triplet
an be produ
ed in
+
qq¯ Z /γ E E ,
→ ∗ ∗ → i i−
qq¯ W E N ,
′ → ∗ → i± (21)
+
E L = 1 E E
i± 1− 2
where refers here to the fermions and de(cid:28)ned in the previous se
tion.
The
ross se
tions of these pro
esses are shown in Fig. 1. The de
ays are di(cid:27)erent in
105 105
104 104 Ei±N
+ −
E E
b) 103 i i
2V| (plN103 σ (fb)102
σ / | 102 10
10 1
1 50 100 150 200 10-1100 200 300 400 500 600 700 800 900 1000
m m (GeV)
N Σ
Figure 1: Cross se
tions for heavy Dira
neutrino singlet (left) and fermion triplet
E
1−
produ
tion (right). In the latter
ase the produ
tion of both
harged leptons and
+
E2 is summed and the triplet masses are taken equal, mΣ ≡ mN = mEi±.
the Dira
and Majorana
ases, however. Heavy Dira
neutrinos de
ay in the
hannels
N W+l N Zν N Hν N W ℓ+
− l l −
→ , → and → , but not in the LNV mode → , whi
h
l N N
±
leadstolike-signdileptonsignalsin produ
tion when isaMajorana fermion(for
a
omplete study see Ref. [23℄). The intera
tions of a heavy Dira
neutrino singlet
an
be found in Ref. [27℄, and the relevant Feynman rules are
olle
ted in the Appendix.
N
The partial widths for de
ays, both in the singlet and triplet
ases, are
g2 m3 M2 M2 M4
Γ(N l W+) = V 2 N 1 W 1+ W 2 W ,
→ − 64π| lN| M2 − m2 m2 − m4
W (cid:18) N (cid:19)(cid:18) N N (cid:19)
g2 m3 M2 M2 M4
Γ(N ν Z) = V 2 N 1 Z 1+ Z 2 Z ,
→ l 128πc2 | lN| M2 − m2 m2 − m4
W Z (cid:18) N(cid:19)(cid:18) N N(cid:19)
g2 m3 M2 2
Γ(N ν H) = V 2 N 1 H .
→ l 128π| lN| M2 − m2 (22)
W (cid:18) N (cid:19)
+
E
2
For heavy
harged leptons the de
ays are di(cid:27)erent in the Dira

ase too. Sin
e
E+ ν W+
2 l
does not
ouple to
harged leptons, it always de
ays in the →
hannel. The
E E l Z/H
1− 1− −
opposite happens for , whi
h does not de
ay in this mode but in → .
8
The
orresponding partial widths are
g2 m3 M2 M2 M4
Γ(E+ ν W+) = V 2 E 1 W 1+ W 2 W ,
2 → l 32π| lN| M2 − m2 m2 − m4
W (cid:18) E (cid:19)(cid:18) E E (cid:19)
g2 m3 M2 M2 M4
Γ(E l Z) = V 2 E 1 Z 1+ Z 2 Z ,
1− → − 64πc2 | lN| M2 − m2 m2 − m4
W Z (cid:18) E(cid:19)(cid:18) E E(cid:19)
g2 m3 M2 2
Γ(E l H) = V 2 E 1 H .
1− → − 64π| lN| M2 − m2 (23)
W (cid:18) E (cid:19)
The simulation of the seesaw I and III signals with Majorana neutrinos and the
SM ba
kgrounds has been previously performed in Ref. [20℄. Here we generate the
signals
orresponding to Dira
neutrinos and
ompare with the former ones, taken
from that study. In our simulations, the heavy Dira
neutrino singlet signal in Eq. (20)
is
al
ulated with the Alpgen extension in Ref. [23℄. The triplet signals in Eqs. (21) are

al
ulated implementing the pro
esses for Dira
neutrinos in Eqs. (21) in the generator
2 6
Triada [20℄. The matrix elements for the → pro
esses are
al
ulated taking (cid:28)nite
width andspin e(cid:27)e
ts intoa

ount. Allthede
ay
hannelsoftheheavy leptons andthe
W/Z/H
subsequent boson de
ays are in
luded, whi
h is a
umbersome task involving
+ +
E E E E E N
1 1− 2 2− i±
144, 25 and 578 (cid:28)nal states for , and produ
tion, respe
tively.
tt¯nj nj n
SM ba
kgrounds in
lude (where stands for additional jets at partoni
level),
¯
W/Znj W/Zbbnj
singletop, , ,dibosonandtribosonprodu
tionplusjets,andotherless
important pro
esses. They are all generated with Alpgen [24℄. Signal and ba
kground
events are passed through the parton shower Monte Carlo Pythia [25℄ and a fast
simulationoftheATLASdete
tor[26℄. Furtherdetailsaboutthesignalandba
kground
generation
an be found in Ref. [20℄. As it has been done in that work, here we

lassify signals by lepton multipli
ity and
ompare the possible (cid:28)nal states to (cid:28)nd the
di(cid:27)eren
es between the Dira
and Majorana
ases.
It must be pointed out that, sin
e the Dira
and Majorana neutrino amplitudes are
N = Nc
di(cid:27)erent (although the intera
tions are formally the same, in the latter
ase ),
one expe
ts to (cid:28)nd di(cid:27)erent angular distributions, for example the forward-ba
kward
W A
asymmetry in the rest frame FB [27℄. Nevertheless, measuring this asymmetry is
M2 /m2
W N
very di(cid:30)
ult. Its value isproportionalto , and fora 300GeV Dira
neutrino it
A = 0.094
isalready very small, FB , and measuringitrequires highstatisti
s. Moreover,
its measurement requires either to distinguish between the two quarks produ
ed in the
W W
hadroni
de
ay, or, in leptoni
de
ays, to distinguish between the
harged lepton
W ℓν
produ
ed in → and the other leptons present in the event. For
harged heavy
E
i±
leptons the de
ay matrix elements are the same in the Dira
and Majorana
ases,
+
E
2
so that asymmetries are equal. This happens even in the
harged
urrent de
ay of ,
9
where the
hiralityof the
ouplinginvolved isdi(cid:27)erent inthe Dira
and Majorana
ases
but the
harge of the heavy lepton too, with the net result that the amplitudes are the
same. As we will (cid:28)nd, the dis
rimination between Dira
and Majorana neutrinos in
terms of
harged lepton multipli
ities is mu
h more interesting.
3.1 Neutrino singlets
ForDira
andMajorana neutrinosingletswe examine(cid:28)nalstates with(a)three leptons
ℓ ℓ ℓ X ℓ ℓ X ℓ = e,µ X
± ± ∓ ± ±
and (b) two like-sign leptons , where and denotes possible
additional jets. We take the same heavy neutrino parameters used in Ref. [20℄ for
m = 100 N
N
Majorana neutrinos, that is, GeV and two s
enarios:
oupling only to the
V2 = 0.0030 V2 = 0.0032
eN µN
ele
tron with (S1) or, alternatively, only to the muon with
(S2). We also use the same pre-sele
tion and sele
tion
riteria and re
onstru
tion
uts,
summarised below for
ompleteness. Further details, in parti
ular regarding the mass
re
onstru
tion,
an be found in Ref. [20℄.
ℓ ℓ ℓ 1
± ± ∓
(a) Three leptons . Pre-sele
tion: three leptons with total
harge ± , the two
p > 30
T
like-sign ones having transverse momentum GeV. Two event samples
2e
are
onsidered, one with two or more ele
trons ( ) and the other one with two
2µ
or more muons ( ). Sele
tion and re
onstru
tion: the opposite pairs
annot
M b
Z
have an invariant mass
loser to than 10 GeV; no jets
an be present; the
φℓℓ π/2
T
transverse angle between the like-sign pair must be larger than ; missing
p < 100 m < 125
energy 6 T GeV; re
onstru
ted mass of the heavy neutrino rNe
GeV.
ℓ ℓ p > 30
± ± T
(b) Two like-sign leptons . Pre-sele
tion: two like-sign leptons with
GeV. Two di(cid:27)erent event samples are
onsidered: with two ele
trons and with
p > 20
T
two muons. Sele
tion and re
onstru
tion: at least two jets with GeV,
b p < 30 φℓℓ < π/2 m < 180
with no -tagged jets; 6 T GeV; T ; rNe
GeV.
1
−
The number of events for30 fb withthese
riteriais
olle
tedinTable 1 forthe heavy
neutrino signalins
enarios S1 and S2, in
ase that the heavy neutrino has Majorana or
Dira

hara
ter. The SM ba
kground is also in
luded. It is very interesting to observe
that heavy Dira
neutrinos
ould be observed at LHC in the trilepton (cid:28)nal state.
This fa
t
ontradi
ts previous
ommon wisdom that heavy Dira
neutrino signals are
overwhelmed by the SM ba
kground (whi
h isa
tuallyhuge for the (cid:28)nal state with two
ℓ+ℓ m = 100
− N
opposite sign leptons ). For a Dira
neutrino with GeV the trilepton
signal is a
tually larger than for a Majorana neutrino. This is easily understood from
10