Lepton number violation in tau lepton decays

0.27 MB·English

by  Gabriel Lopez Castro

NuclearPhysicsB
Proceedings
Supplement
NuclearPhysicsBProceedingsSupplement00(2013)1–5
Lepton number violation in tau lepton decays
G.Lo´pezCastroa,N.Quinteroa
aDepartamentodeF´ısica,CinvestavdelIPN,ApartadoPostal14-740,07000Me´xico,D.F.Me´xico
3
1
0 Abstract
2
Recentstudiesofnovelfour-bodyleptonnumberviolatingdecaysofτleptonsandneutralBmesonsaresummarized
n
andupdated. ThesedecaysareassumedtobeenhancedbytheexchangeofresonantMajorananeutrinos. Itisshown
a
J that the τ− → π+l−l−ντ decay channels, with l = e or µ, can provide stronger constraints on the mixing vs. mass
0 parameterspaceofresonantMajorananeutrinosthananalogousthree-bodydecaysofchargedBmesons.
1
Keywords:

] Leptonnumberviolation,Majorananeutrinos,heavyflavordecays,taulepton
h
p
-
p 1. Introduction Underthisscheme, thesensitivityofdifferentheavy
e flavorLNVdecays(Mdenotesavectororpseudoscalar
h Total lepton number L = Le + Lµ + Lτ is an ab- meson and l,l(cid:48) = e,µ,τ whenever they are allowed by
[
solutely conserved quantum number in the Standard kinematics)

2 Model (SM). Some extensions of the SM include in-
v teractionsthatcaninduceLnon-conservation[1]. Min- D+(s),B+,B+c → l+l(cid:48)+M−
7 imal extensions of the SM aiming to include massive D0,B0,B → l−l(cid:48)−M−M−
3 s 1 2
0 neutrinoscancontainMajoranamassterms,likeLM = τ− → l+M−M−
0 νRcMMνR+h.c.,whichprovidesanappealingmechanism τ− → ν l−l1(cid:48)−M2+
. thatviolatesleptonnumber bytwounits(∆L = 2)[2]. τ
2
A clear signal of Majorana mass terms are L-number is determined by comparing the mass scale of the ex-
1
2 violating processes that involve the production of two changedMajorananeutrinoswithtypicalenergiesofthe
1 equal-sign charged leptons, the most well known and decayprocess. Thus,wedistinguishthreecases[4]:
: widelystudiedexamplebeingneutrinolessdoublebeta
v • If neutrinos are very light compared to their four-
Xi decInaythinisncuocnlteriib[u3t]i.onweconsidertheexchangeofMa- momenta in the propagator (actually, m2ν << q2),
the decay rates become sensitive to the effective
r jorana neutrinos as a source of ∆L = 2 lepton number (cid:80)
a Majorana mass defined by (cid:104)m (cid:105) ≡ U U m,
violation (LNV) in decays of heavy flavors, and more ll(cid:48) i li l(cid:48)i i
whereU denotethemixingsoflight(active)neu-
specificallyinfour-bodydecaysoftheτlepton. These li
trinosdescribedbythePMNSmatrix;
Majorananeutrinosareassumedtobesterile,suchthat
theircouplingtotheweakchargedcurrentareverysup- • If neutrinos are heavy compared to the mass
pressed by tiny mixings with active neutrinos. Typical of the decaying state, the rate is sensitive to
(cid:80)
neutrino-exchangediagramscontributingtoLNVinde- V V /m ,whereV arethemixingsoflight
N lN l(cid:48)N N lN
caysoftheτleptonareshowninFigure1. (active)andheavy(sterile)neutrinosoftypeN(see
definitioninSection2).
• Finally, if heavy neutrinos are of the order of the
Emailaddresses:[email protected](G.Lo´pez
Castro),[email protected](N.Quintero) heavyflavormassscalesuchthattheycanbepro-
/NuclearPhysicsBProceedingsSupplement00(2013)1–5 2
M1− 10-4
PDG
L) 10-5 BLAHBCAbR
U Belle
(a) τ− l+ atio ( 10-6
r
g
νN M2− nchin 10-7
a
Br 10-8
τ− ντ l− l′− 10-9 pfieeDmmpfiDmpfieDfiKeeDmmfiKDmfiKeDpfieeDsmmpfiDsmpfieDsfiKeeDsmmfiKDsmfiKeDspfieeBmmpfiBmpfieBfiKeeBmmfiKBmfiKeBfiDeeBmmfiDBmfiDeBmmfiDBsppfitepfitKefiteKKppmfitpmfitKmfitKK
(b)
Figure2: Experimentalupperlimitsonbranchingratiosof3-
νN M+ bodydecaysofchargedheavymesonsandτlepton[9-15].
Figure1:Neutrino-exchangediagramsinducedbycrossingsof recentproposals[17,18]whichconsiderthefour-body
theW−W−→l−l(cid:48)−∆L=2kernelleadingtoLNVin(a)three- decays τ− → ν l−l(cid:48)−M+ and B0 → D−l+l(cid:48)+M−, where
τ
and(b)four-bodytaudecays.
Misapseudoscalarorvectormesonthatcanbeallowed
by kinematics (the analogous decay π+ → e+e+µ−ν
ducedontheirmass-shell(q2 = m2),theratesare was considered in [19]). We illustrate our studies with
largely enhanced due to the resonNant effect asso- results on di-muonic channels (results on di-electrons
ciated to their decay widths Γ , with their decay modescanbefoundin[17,18]). Searchesforthesede-
N
amplitudesproportionalto(cid:80) V V /Γ . Thisis caychannelshavenotbeenundertakenbyexperiments
N lN l(cid:48)N N
up to now. Here we emphasize that they can provide
theso-calledresonantenhancementmechanism[4]
competitive or even stronger bounds on the parameter
for LNV decays and can occur only for time-like
spaceofMajorananeutrinosascomparedtothree-body
neutrino momenta as in the case of mesons and τ
decaysofheavyflavors.
leptondecays.
Note that in the first two cases, the rates of heavy
2. Resonantthree-bodydecays
flavor decays turn out to be very suppressed, making
uninteresting their searches at flavor factories [5, 6].
Theadditionofright-handedsingletneutrinostothe
Leptonnumberviolationinthree-bodydecaysofτlep-
SM leads in a natural way to the appearance of Ma-
tons and charged (D, D , B, B ) mesons have been
s c jorana and Dirac mass terms [2], with Majorana mass
widelyinvestigatedpreviously,bothfromthetheoretical terms allowing ∆L = 2 lepton number violation. The
[4,5,6,7,8]andexperimental[9,10,11,12,13,14,15]
heavier (sterile) neutrinos get involved into charged
points of view. The current best experimental upper
weakinteractions,sinceafterdiagonalizationofthefull
boundsavailableonthesedecaychannelsareshownin
neutrino matrix, neutrinos of defined flavor becomes a
Figure2;inaddition,verystringentboundsoftheorder
mixtureoflightandheavymasseigentstates,namely,
of 10−9 have been obtained (see for example [13]) for
K+ → π−l+l(cid:48)+ decays,withl, l(cid:48) = e, µ. Themeasured (cid:88)3 (cid:88)n+4
upper limits allow to exclude a region in the |V |2 vs. νl = Uliνi+ VlNνN (1)
lN
m planeoftheparameterspace,byassumingthatasin- i=1 N=4
N
gleresonantneutrino(usuallydenotedbythesubindex ifnright-handedsingletsareconsidered. Here, U are
li
N or 4) dominates the decay amplitude. Such sterile essentiallytheentriesofthePMNSmatrix,andV are
lN
Majorana neutrinos, with masses in the range of 1∼10 thetinymixingsoftheactiveandsterileneutrinos. The
GeV,canappearintheframeworkofsomeminimalex- chargedcurrentinteractionLagrangianintheflavorba-
tensions of the SM; forinstance, it has been suggested sisbecomes:
thattheycanplayanimportantroletoexplainsimulta-
g
neouslytheoscillationsofneutrinos, thebaryonasym- Lcc = √ ν¯lγµ(1−γ5)l·Wµ−+h.c. (2)
2 2
metryoftheUniverseandthedarkmatterproblem[16].
Inthispaperwepresentasummaryandupdateofour whereν isgivenabove.
l
/NuclearPhysicsBProceedingsSupplement00(2013)1–5 3
[4]andincorporaterecentlyupdatedmeasurementsob-
2|N 1 tained by B-factory experiments [9] and LHCb [10].
Vm10-1
| Note that despite the large improvement recently ob-
10-2 tained by LHCb [10, 14], B(B+ → π−µ+µ+) ≤ 1.3 ×
10-3
10−8,theconstraintsonthe|V |2mixingarenotlargely
10-4 µN
improved owing to the Cabibbo suppresion factor de-
10-5 KBfifi ppmmmm scribedinthepreviousparagraph.
10-6 DDfisfi p pmmmm
10-7 Btfifi nDmmmmpp
t
10-8 3. Four-bodyB0decays
10-9
2· 10-1 3· 10-1 1 2 3 4 5 InordertoavoidthesuppressionduetoCKMfactors
m [GeV]
N in the B+ decay vertex, we have proposed to consider
thefour-bodydecaysofneutralmesons, namely B0 →
Figure3:Constrainsonmixingvs. massofMajorananeutrino D−M−l+l(cid:48)+ withl, l(cid:48) = e, µorτand M apseudoscalar
parameterspacefromdi-muonicthree-bodydecaysofcharged
mesons. Constraints from four-body B0 → D−π−µ+µ+ and orvectormeson[17].Thedecayamplitudeforthisfour-
τ− → ν µ−µ−π+ byassumingupperboundsof10−7 and10−8 bodydecayisgivenby:
τ
ontheirbranchingratios,respectively,arealsoshownforcom-
MB0 ∼G2V V m F(q2)VCKMf FB→D(t), (4)
parison. 4 F lN l(cid:48)N N cb M +
whereFB→D(t)isthevectorformfactorforthe B→ D
+
Under the assumption that only one Majorana neu- transitionandt=(pB−pD)2isthesquareofthemomen-
trino N is resonant in three-body τ− → l(cid:48)+M−M− and tumtransfer(thecontributionofthescalarformfactoris
1 2
M− → l−l(cid:48)−M+ decays, the generic form of the de- negligibleinthiscase). Inthisupdatedcontributionwe
1 2
cay amplitudes is (properly antisymmetrization under usetheB→ DvectorformfactorobtainedfromLattice
exchange of identical leptons in the final state must be QCD [21], in order to avoid the model dependence of
understood) thevectorformfactorusedin[17].
In the neutrino narrow width approximation, the
M3τ,M1− ∼G2FVlNVl(cid:48)NmNF(q2)VMCK1MVMCK2MfM1fM2 ,(3) genericexpressionforthebranchingratiosofthree-and
where VCKM is the Cabibbo-Kobayashi-Maskawa four-bodydecayscanbewrittenas:
Mi
m(fCMiKineiMtds)bdmyecatahtryeixncoeeunletsrmtianenont.tprfToohpreatghraeetsocorhnaFarng(ceqed2)fma∼cets(ooqrn2i−sMdmie2atenr+d- Bll(cid:48) ∼ |VlNΓVNl(cid:48)N|2G(mN), (5)
im Γ )−1 where q is the momenta of the exchanNged whereΓ =(cid:80) f(m )|V |2istheneutrinodecaywidth;
N N N l l N lN
neutrino. The neutrino decay width Γ ≤ 10−3 eV for thesumextendsovertheleptonflavorsthatareallowed
N
the mass scales of interest in τ lepton and in other me bykinematicsforagivenneutrinomassm ,and f(m )
N l N
sondecays(m ≤5GeV)[4]. dependsondecayconstantsandmassesoffinalstatesin
N
FromEq. (3)wenotethatthebiggeristheCKMma- neutrinodecaychannels[4]. ThefunctionG(m )con-
N
trixelement,thestrongeristheconstraintthatcanbeset tainstheproductoffundamentalconstants,hadronicpa-
ontheneutrinomixingsfromthemeasuredupperlimits rametersaswellastheintegratedfour-bodyphasespace
onLNVbranchingfractions. Sincetheratesof B±, D± ofthespecificchannels[17].
mesondecayverticesareCabibbo-suppressedby|V |2 No upper limits have been reported so far for four-
ub
and |V |2 factors, respectively, the constraints that are body LNV decays of neutral B mesons. Upper limits
cd
derivedfromthemwillnotbeverystrong. Onanother for four-body LNV decays have been reported only in
hand,τleptondecays(takingl=τinEq. (3)above)al- thecaseof D0 → M−M−l+l(cid:48)+ decayswithl, l(cid:48) = e, µ
1 2
low to constrain only the product |V V | (l(cid:48) = e,µ) and M = π, K [20]; in all cases, the upper lim-
τN l(cid:48)N 1,2
from the measured upper limits of τ− → l(cid:48)+M−M− its obtained for the branching ratios are at the level of
1 2
branchingfractions. 10−5 ∼ 10−4 which loosely constrain the mixing an-
In Figure 3 we show the constraints in the |V |2 vs gles. Very recently, the LHCb collaboration has re-
µN
m regionthatcanbegottenfromthree-bodyLNVde- portedthefirstupperlimitonthechargedBdecaychan-
N
cays of charged D and B mesons by using the ex- nel, B(B− → D0π+µ−µ−) ≤ 1.5×10−6 atthe95%c. l.
(s)
perimental upper limits on di-muonic channels. These [10]. Theconstraintsinthe|V |2 vs. m planethatare
µN N
plotswereobtainedbyusingtheratescalculatedinRef. obtainedbyassuming B(B0 → D−µ+µ+π−) ≤ 10−7 are
/NuclearPhysicsBProceedingsSupplement00(2013)1–5 4
[22],wecomputethefollowingbranchingfraction(we
2|N 1 usesimilarvaluesofmixingsandmassesfortheheavy
Vm
|10-1 sterileneutrino)
10-2
B(τ− →ν µ−µ−π+)≤1.4×10−5. (7)
τ
10-3
10-4 tt fifi nn tmm mm pr Ourresultsturnsouttobeofsimilarsize. Themaindif-
t ference comes from the models we have used to com-
10-5 tt fifi nn ttmm mm KK* putetheheavyneutrinolifetime.
10-6 In summary, LNV decays of heavy flavors can pro-
0 200 400 600 800 1000 1200 1400 1600 1800
mN (MeV) vide important constraints on tiny mixing angles of
Majorana neutrinos with masses in the range m ≤
π
Figure4: Constraints on Majorana neutrino parameter space m ≤ m . This is possible if a single heavy neu-
N B
fromfour-bodydi-muonicchannelsofτleptondecays. trinoresonantlyenhancesthedecayamplitudes. Inthis
contribution we have shown that the four-body decays
B0 → D−π−µ+µ+ and τ− → ν µ−µ−π+ can provide
showninFigure3. Weobservethattheconstraintofthe τ
strongerconstrainsonthe|V |2mixinganglesthanthe
µN mixing angle that can be obtained from this decay µN
onesobtainedfromthree-bodydecaysofchargedheavy
channeliscompetitiveorevenbetterwhencomparedto
otherthree-bodyLNVdecaysofB+mesons,foramass mesons.
The authors are grateful to the organizing committee of
regionm ≤1.5GeV.
N
Tau2012 for the opportunity to present this work. They ac-
knowledgethefinancialsupportfromConacyt(Mexico)and
4. Four-bodyτleptondecays thecollaborationofD.Delepineattheearlystageofthiswork.
In order to look for better constraints on mixing of
resonant neutrinos, we consider the τ− → ν l−l(cid:48)−M+ References
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