Table Of ContentSingle neutral heavy lepton production at electron-muon colliders.
F.M.L. Almeida Jr.∗,Y. A. Coutinho†,
J. A. Martins Sim˜oes‡, M.A.B. do Vale§
Instituto de F´ısica
Universidade Federal do Rio de Janeiro, RJ, Brazil
NewheavyMajorana andDiracneutrinosproductionatfutureelectron-muoncollidersareinves-
tigated. Theproductionofasingleheavyneutrinoisshowntobemorerelevantthanpairproduction
when comparing cross sections and neutrino mass ranges. The process e±µ∓ −→νℓ±W∓ is stud-
ied including on-shell and off-shell heavy neutrino effects. Distributions are calculated including
hadronization effects and experimental cuts that suppress background, in order to have a clear
signal for heavy neutralleptons.
1
0
0
PACS: 12.60.-i, 13.85.-t, 14.60.-z
2
n There is an increasing experimental evidence for neu- In many models the mixing of neutral and heavy neu-
a
trino oscillations and non zero neutrino masses [1]. The trino states implies [4,5] that in the light-to-heavy neu-
J
smallnessofneutrinomassesisgenerallyunderstoodasa trino vertex we have a single power of the mixing an-
5
consequenceofsomesee-sawmechanism. Thisbringsthe gle, contrary to the double mixing angle power in the
question of the possibility of new heavy neutrino states. heavy-to-heavy neutrino vertex. Another factor that fa-
2
v So far none of these new states was experimentally ob- vors single heavy lepton production is a smaller phase
1 served[1,2]withmassesuptoMN 100GeV.Forhigher space suppression. We are then lead to study the chan-
3 masses there are many suggestions≃of experimental pos- nel e±µ∓ νℓ±W∓. We have calculated the stan-
2 sibilities in the next highenergyhadron-hadroncolliders dardmode−lb→ackgroundcontributionforthisprocessand
8
[3], in electron-positron linear accelerators [4–6], in neu- shown that, with appropriated cuts, it can be reduced
0
trinoless double-beta decay [7]. The properties of these well bellow the signal. In order to have a more realis-
0
newheavystatesareacentralpointinmanyofthetheo- tic estimate for the signal and background distributions
0
/ reticalmodelsproposedasextentionsofthepresentstan- we have hadronized the final W. We discuss throughout
h
dard model of elementary particle physics. Besides the this paper both the Majorana and Dirac heavy neutrino
p
masses and mixing angle values, an important point is contributions.
-
p the Majorana or Dirac nature of new heavy states. This Most extended models predict new fermions and new
e is directly connected with lepton number conservation gauge vector bosons. Since we presently have no signal
h
and to the general symmetries of any extended model. for new interactions, we will make the hypothesis that
:
v thenewheavyneutrinostatesbehaveasSU (2) U (1)
Thesuggestionofanewtypeofelectron-muoncolliders L ⊗ Y
i basicrepresentations. Wecanresumethenewparticlein-
X [8]seemstobeaninterestingproposaltoverifytheprop-
teractionsintheneutralandchargedcurrentlagrangians:
r ertiesofnewheavyleptons. Muonbeamsarewellknown
a to have a reducedsynchrotronradiationloss andthe ab- g
sence ofanZ-mediateds channelmakescleanerthe high Lnc =−4c sinθmixZµψNγµ(1−γ5)ψν +h.c.. (1)
W
energy properties of charged current interactions. An-
and
other interesting point is the fact that eµ colliders will
g
test directly the propertiesof twoleptonic families. This cc = sinθmixWµψNγµ(1 γ5)ψe+h.c. (2)
option was considered recently by Cveti˘c and Kim [9], L −2√2 −
who studied the production of a pair of heavy Majorana
and similar terms for the other leptonic families. In the
leptons in the reaction ℓ−ℓ′+ NN W±ℓ∓W±ℓ∓
−→ −→ i j Majorana case, each completely neutral heavy lepton is
for N on and off shell.
coupled to all charged leptons and we are considering
Inthispaperwecallattentiontoamorefeasiblechan- only the lower mass state. For the Dirac case, in princi-
nel for detecting neutral heavy leptons in eµ colliders. ple we have three different heavy neutrinos, one for each
∗E-mail: [email protected]
†E-mail: [email protected]
‡E-mail: [email protected]
§E-mail: [email protected]
1
family. In this last case we have considered their masses pairMajoranaproductionforneutrinomassesabove√s.
to be all equal. In Fig. 3 we have the total cross sections for the signal
Throughout this paper we will suppose that mixing (Dirac and Majorana) and standard model background
angles for heavy-to-light neutrinos and new heavy neu- for the specific final states e−µ+ invisibleµ+W−,
−→
trino masses are independent parameters [10]. The light where invisible means the sum of all undetected possi-
neutrinos couplings to the neutral Z are givenby g = blefinalneutrinoandanti-neutrinostates. Thestandard
V,A
gSM sin2θ /2. Taking the experimental values for model background is clearly above the signal and the
V,A − mix
g and the standard model predictions we obtain a central problem for a possible experimental detection of
V,A
smallupper boundfor θ . A recentestimate [11]gives heavy neutral leptons is to study the distributions that
mix
sin2θ <0.0052with95%C.L.Thislimitvalueisused could separate signal from background.
mix
throughout this paper for all curves and distributions. Angulardistributionscanbeveryhelpfulinseparating
The decay modes for these leptons, in the Majorana signal from background as well as Majorana from Dirac
case [3] must include both signatures N ℓ∓W± and heavy neutrinos. In Fig. 4 we show the angular distri-
−→
N ν (ν¯ )Z, with ℓ = e,µ,τ. For the Dirac case, we bution (cosθ ) for the final muon (relative to the initial
ℓ ℓ µ
hav−e→thesimpledecaysN µ−W+ andN ν Z. electron). The standard model distribution is peaked at
µ µ µ
−→ −→
Forthe specific channelconsideredinthis paperwe have cosθ 1. For lower heavy neutrino masses we have
µ
≃ −
an undetected final neutrino state. In the heavy Dirac differentDiracandMajoranadistributionshapesbut for
neutrino production we have lepton number conserva- higher masses this difference almost disappears. In Fig.
tion, and only reactions like e−µ+ ν µ+W− are 5we showthe distributionofthe anglebetweenthe final
e
−→
allowed. But for the Majorana case, as we have lepton muon with respect to the direction of the heavy lepton
numberviolation,wemustsumoverallthefinalneutrino in its center of mass (cosθ∗). This distribution shows
µ
and antineutrino states in e−µ+ µ+W−ν (ν¯ ). that we can eliminate most of the standard model con-
i j
From equations 1 and 2 we ca−n→readily calculate the tribution with a cut like cosθ∗ <0.5 and that this cut is
µ
decay widths for the neutral leptons and find almost independent of the heavy neutrino mass.
In order to enhance the relationsignal to background,
g2sin2θmixMN we can apply some heavy neutrino mass dependent cuts,
Γ(N ν Z)= f(y )
→ i 128πc2 Z based on kinematical relations only. Let us consider the
W
g2sin2θ M case where at √s center of mass energy particles A and
Γ(N ℓ±W∓)= mix Nf(yW) (3) B are produced and then the particle B decays into par-
→ 64π
ticles C and D. Let us suppose further that the particles
where f(y)=y 3/y+2/y2 and y =(M /M )2. A and C are massless. After doing a simple calculation
N Z,W
−
we obtain that the energy of the particle C, E , should
C
In Fig. 1 we show the structure of the Feynman be in the range:
diagrams that contribute for the signal. We have in-
cluded in our results all the off-shell and on-shell contri- 1√s(MB2 −MD2) <E < 1(MB2 −MD2) (4)
butions. The calculations for both the standard model 2 M2 C 2 √s
B
background and signal were done using the high energy
The shaded area in Fig. 6 shows the allowed region
program CompHep [12]. We call attention to the fact
for the muon energy E when √s = 2000 GeV and fi-
thattheNwidthisverynarrowforlowerheavyneutrino µ
nal state ν, µ+, W−. For M =200 GeV, 800 GeV and
masses and increase for higher masses. Propagator ef- N
1600GeV,wehave8.38GeV<E <838.62GeV,158.38
fects must then be handled with care. Another possible µ
background contribution comes from e−µ+ e−µ+Z GeV<Eµ <989.91GeVand638.38GeV<Eµ <997.47
−→ GeV, respectively.
where the final electron goes along the initial electron
Another interesting heavy neutrino mass dependent
direction andescapes fromthe detection. This contribu-
variable is the angle between the final particles C and
tion is almost eliminated by requiring a good resolution
D, originated from the particle B decay in the center of
in the hadronization, with an invariant hadronic mass
mass of the incident particles. After doing a Lorentz
peaked around M .
W
transformation, we obtain that cosθ should be in the
The cross sections for single and pair heavy neutrino CD
region:
production (on-shell) are displayed in Fig. 2 for √s =
2000GeV.Inallourresultswehavedonegeneraldetector
γ2pE∗2+M2 E∗
aculltsanEglleepstoanr>e d5eGfineeVdarnedla−tiv0e.9t9o5t<hecoisnθitii<al0e.l9e9ct5r,ownh.eIrne −1<cosθCD < √1+γvvpγCv2(EC∗2+DM−D2)C+EC∗2 (5)
theMajoranacasewehavesummedoverallthepossibili-
where
tiesofundetectedfinalneutrinostates. Thisfigureshows
clearly the dominance of single heavy neutrino produc- (s M2)
tion over pair production. We also show the possibility γv = − B (6)
2√sM
of Majorananeutrino contribution to e−µ+ W−W+ B
−→
accordingto Fig. 1b. This channeldominates single and and
2
E∗ = (MB2 −MD2) (7) increases. Our analysis of single heavy neutrino pro-
C 2M duction via the process e−µ+ invisibleµ+W− can
B
be generalized for any process−→of the type e±µ∓
The shaded area on Fig. 7 shows the allowed kine- invisible ℓ±hadrons. For values of the center of m−a→ss
maticalregionasafunctionoftheheavyneutralparticle
energies other than √s = 2000 GeV, we have similar
mass for our case where √s = 2000 GeV and A, B, C
conclusions: heavy neutrino masses can be investigated
and D are the standard neutrino, heavy neutral parti-
up to √s; angular and kinematical cuts can help in es-
cle, muon and gauge boson W, respectively. For M =
N tablishingdistributionsthatcandifferentiatesignalfrom
200 GeV, 800 GeV and 1600 GeV, we have for cosθ
Wµ backgroundand the strong correlationbetween the vari-
the following upper limits: 0.914, 0.0588 and 0.9003,
− ables E/ and Mµ+hadrons gives a very clear signature for
respectively. Dynamical bounds will further limit this
the signal.
area. Another important kinematical constraint comes
from the fact that on-shell heavy neutrino contributions
are dominant. Then the missing energy of the final neu-
trino has a sharp distribution given by
E =(s M2)/2√s (8)
ν − N
Themostdefinite separationbetweensignalandback-
groundisgivenbythecorrelationbetweenthefinalmiss-
ing energy and the invariant visible mass of the system
Acknowledgments: This work was partially supported
muon + hadrons. For the signal the missing neutrino
by the following Brazilian agencies: CNPq, FUJB,
energyisstronglypeakedbyEq. 9andthe invariantvis-
FAPERJ and FINEP.
ible muon + hadrons mass is also peaked around M .
N
In order to have a more realistic estimate for the experi-
mentalpossibilities ofdetectionofheavyneutrinoeffects
we have hadronized the final W, for the signal and the
background, using the program Pythia [13]. The results
are shown in Figs. 8, 9, 10 for heavy Majorana neu-
trino masses of 200, 800 and 1600 GeV respectively. In [1] D.E. Groom et al, Eur. Phys.Jour. C15 (2000) 1.
Fig. 8a we show the arbitrary number of events plot in [2] K. Zuber, Phys.Rep. 305 (1998) 295.
the plane E/ and muon + hadrons invariant mass. For
[3] F.M.L. Almeida Jr., Y.A. Coutinho, J.A. Martins
MN = 200 GeV we include only the general detector Sim˜oes, P.P. Queiroz Filho and C.M.Porto, Phys. Lett.
cuts, E/ > 5 GeV; Eµ > 5 GeV; cosθµ < 0.995; — B400(1997)331;A.FerrarietalPhys.Rev.D62(2000)
| |
cosθhadron < 0.995, and require an hadronic invariant 013001-1.
|
mass limited to MW 2 GeV. In this heavy neutrino [4] F.M.L. Almeida Jr., J.H. Lopes, J.A. Martins Sim˜oes
±
mass region the background is clearly mixed with the and C.M. Porto Phys. Rev. D44 (1991) 2836 ; F.M.L.
signal. If we start doing more restrictive cuts we can re- Almeida Jr., J.H. Lopes, J.A. Martins Sim˜oes, P. P.
duce the background contribution. In Fig. 8b we have QueirozFilhoandA.J.RamalhoPhys.Rev.D51(1994)
done the cut E/ < 1050 GeV, according to Eq. 9, and 5990.
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[7] W. Rodejohann and K. Zuberhep-ph/0005270.
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[8] S.Y.Choi,C.S.Kim,Y.J.KwonandS.H.Lee,Phys.Rev.
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3
Figure Captions
1. General Feynman graphs for heavy Majorana and
Diracneutrinocontributiontoe−µ+ νµ+W−.
−→
2. Single and pair production of on-shell heavy Dirac
and Majorana neutrinos at √s = 2000 GeV for
e−µ+ colliders (sin2θ =0.0052).
mix
3. Signaland background(standardmodel)contribu-
tions to e−µ+ invisibleµ+W− at √s = 2000
−→
GeV.
4. Finalmuonangulardistributionrelativeto theini-
tial electron cosθ , for the standard model back-
µ
ground and for Dirac and Majorana heavy neutri-
nos, at √s= 2000 GeV.
5. Final muon angular distribution relative to the di-
rection of the heavy lepton in its center of mass
cosθ∗, for the standard model background and for
µ
DiracandMajoranaheavyneutrinos,at√s=2000
GeV.
6. Kinematical limits for the muon energy E versus
µ
heavy neutrino mass M at √s= 2000 GeV.
N
7. Angulardistributionfortheanglebetweenthefinal
muon and W, cosθ at √s= 2000 GeV.
Wµ
8. Invariantvisible mass Mµ+hadrons andmissing en-
ergy E/ for background and signal for M = 200
N
GeV (in arbitrary units). Fig. 8a was done with
the general cuts, Fig. 8b was done with the ad-
ditional mass independent cuts as discussed in the
text and Fig. 8c with the more restrictive cuts.
9. Same as Fig. 8, for M = 800 GeV at √s = 2000
N
GeV.
10. Same asFig. 8,for M =1600GeVat√s= 2000
N
GeV.
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