Table Of ContentIPM Conference on Lepton and Hadron Physics, Tehran, Iran, May 15-20, 2006 1
Low scale leptogenesis with an SU(2) singlet scalar
L
M.Frigerio
ServicedePhysiqueThe´orique,CEA/Saclay,F-91191Gif-sur-YvetteCedex,FRANCE
We consider thermal leptogenesis as the origin of the matter-antimatter asymmetry of the Universe. Some
phenomenologicallyunpleasantfeaturesoftheusualleptogenesis scenarioarereviewed. Weproposeaminimal
alternative,whichmakesuseofachargedscalarδ+,singletunderSU(2)L. Suchparticleiscontainedinnatural
extensionsoftheStandardModel. Theleptonasymmetryisgeneratedbythedecaysofaright-handedneutrino
intoδ+ andaright-handedcharged leptonanditturnsouttobesufficientlylargeforscales aslowas ∼TeV.
Thephenomenological signatures atcollidersarediscussed.
SACLAY-T06/125
7
0
0 1. LEPTOGENESIS: MOTIVATIONS AND estimate gives
2 SOME DRAWBACKS
n ǫL YN2iM1 . (2)
a ∼Xi6=1 Mi
J Averywellmotivatedexplanationfornon-zerotiny
2 neutrinomassisleptonnumberviolation(LNV)atan A very similar combination of parameters determines
2 energyscaleM muchlargerthantheelectroweaksym- lightneutrino masses throughthe seesawmechanism:
metrybreakingscalev. ThisleadstoaMajorana-type
2 neutrino mass mν v2/M. The most popular way mν YN2i v . (3)
v to introduce LNV ∼is to add to the Standard Model v ∼Xi Mi
1
021 (lsaSterMgrie)leMsnteaeurjoitlrreiannroiasghdmte-achsaasyensidne(dtsheee(sReaaHwr)lymnUeecunhtivariennriossems,)Na.ti,aTtwheeimtshe- 1(S30in)6cvaenmdν1t/0hv8e∼Greeq1Vu0i−r[31e2m].,etnThtehiǫcsLomm∼epaa1nr0sis−ot6nhaiomtfpleelqpiests.o(g2Me)n1aens>∼ids
1 peratureoftheorderoftheirmass. Ifthedecaysoccur ∼
maybesuccessfulonlyifittakesplaceatsuper-heavy
6 (partially)out-of-equilibriumandviolateCP,adiffer-
0 ent number of leptons and antileptons is produced. scales. Qualitatively the same lower bound on the
/ leptogenesis scale persists [4] in models including the
h Such lepton asymmetry is efficiently converted into a
p baryon asymmetry by SM (B + L)-violating effects contribution to mν from SU(2)L triplet scalars (type
- (sphalerons), which are in thermal equilibrium down II seesawmechanism). Evenafine-tuned cancellation
p to temperatures T v. This mechanism to explain between the type I and II seesawcontributions to mν
he the matter-antimatt∼er asymmetry of the Universe is doesnothelp,sincetherelationǫL ∝mν =mIν+mIνI
still holds [5].
: known as baryogenesis via leptogenesis [1].
v Theneedforasuper-heavyscaleisphenomenologi-
i Let us give a semi-quantitative description of lep-
X cally unpleasant, since it is not directly accessible ex-
togenesis. In general, the interactions of the lightest
perimentally. Moreover, in most (unified) extensions
ar RHneutrinoN1eraseanyasymmetrycreatedatscales of the SM, the neutrino Yukawa couplings YN are re-
largerthanitsmass. TheleptonasymmetryfromN1- lated to those of charged fermions, therefore one ex-
decays is defined by
pects YN to have a hierarchical structure. This im-
plies a further suppression of ǫL, which may prevent
Γ(N1 LH) Γ(N1 L¯H¯) successfulleptogenesisevenatsuper-heavyscales. Fi-
ǫL = Γ(N1 →LH)−+Γ(N1 →L¯H¯) , (1) nally, a reheating temperature TRH larger than M1
→ →
is needed in order for thermal leptogenesis to occur.
whereLandH aretheSMleptonandHiggsdoublets. If one invokes supersymmetry above the scale v, in
The asymmetry arises from the interference between particular to stabilize the large hierarchy M/v, then
tree leveland one loop Feynman diagramsfor the de- TRH > 108 GeV leads in general to overproduction
cays of N1, which are shown in Fig.1. Cosmological ofgra∼vitinos,inseveretensionwithcosmologicaldata
data determine the baryon number density over en- (see [6] and references therein).
tropy ratio, nB/s 10−10. In the case of thermal The lower bound on the leptogenesis scale can be
leptogenesis one fin≈ds nB/s 10−3ηǫL, where the circumvented by some strong tuning of parameters:
≈ −
washoutfactorη is atmostoforderone(see e.g. [2]). if the two lightest RH neutrinos are quasi-degenerate
As a consequence, a sufficient baryon asymmetry can in mass, eq.(2) does not hold and the asymmetry ǫL
only be produced for ǫL > 10−6 10−7. Indicating may be resonantly enhanced. As a consequence, the
with YNi the typical size∼of Ni Y−ukawa couplings to leptogenesis scale M1 M2 can be as small as
∼ ≈ ∼
leptondoubletsandcallingMithemassofNi,arough TeV(seee.g. [7]). InthiscasetheYN couplingsshould
IPM-LHP06-19May
2 IPM Conference on Lepton and Hadron Physics, Tehran, Iran, May 15-20, 2006
Figure 1: TheFeynmandiagrams for N1 decaysin theusualleptogenesis scenario. Only oneheavier RHneutrinoN2 is
displayed, butin general one sumsover thesame one-loop diagrams for each RH neutrinoheavier than N1.
be also tuned, since the contributions YN2i/Mi to In SO(10) models, which contain the left-right
∼ •
mν need to cancel each other. In this talk we do not symmetric group, the two possibilities corre-
consider the resonant scenario, rather we develop a spond to δ+ 120H or δ+ 126H, respectively.
∈ ∈
minimal alternative.
The coupling (5) is forbidden by the gaugesymmetry
in the case δ+ ∆R (δ+ 126H).
∈ ∈
2. LEPTON YUKAWA COUPLINGS IN Let us consider the minimal left-right symmetric
STANDARD MODEL EXTENSIONS model. TheRHtriplet∆R couplestoRHleptondou-
blets R=(N lR)T as
The non-zero neutrino masses and leptogenesis re- T
Y∆R Ciτ2∆RR+h.c. . (6)
quiretoaddseveralingredientstotheSM:newsterile −
leptons, a super-heavy scale for their mass, Yukawa
The vacuum expectation value vR of the ∆R neutral
couplingsbetweenthemandSMleptondoublets. One
component breaks SU(2)R and gives mass to the RH
may wonder if a complete theory, which naturally
neutrinos. At the same time, the interaction (6) con-
accommodates these ingredients, does contain other
tainsthesecondtermineq.(4),sothatY∆ andYR are
sources of lepton asymmetry. If this were the case,
identified. TheRHneutrinomassmatrixMR =vRY∆
some of the constraints discussed in the previous sec- andthe couplingmatrixYR =√2Y∆ arediagonalized
tion could be evaded.
at the same time, therefore there is no flavor mixing
Letusbeginbyaskingwhatscalarmultipletscouple
intheRHsector: thei-thRHneutrinoNi decaysonly
a RH neutrino N to the SM leptons L and lR. In full into δ+lRi and no lepton asymmetry is generated. To
generality, the two Yukawa interactions read
achieveleptogenesis,onehasto resorttoless minimal
YNHN¯L YRδ+NTClR+h.c. , (4) models,e.g.,(i)tointroduceasecondSU(2)R triplet;
− − (ii) to admit a source of RH neutrino masses other
where H = (H+ H0)T has the quantum numbers than vR; (iii) to add a δ+ which is singlet under both
of the SM Higgs, while δ+ is a SU(2)L singlet with SU(2)L and SU(2)R.
charge+1. Intheusualleptogenesisscenarioonlythe
coupling YN is considered. However, if δ+ is lighter
than RH neutrinos, the coupling YR allows for the
3. RIGHT-HANDED SECTOR
alternative decaychannel N δ+lR, which may pro-
→ LEPTOGENESIS
vide a new source of lepton asymmetry [8]. Notice
that only SU(2)L singlet particles are involved in the
decay. In general, the charged singlet δ+ may couple In this section we compute the lepton asymmetry
also to SM left-handed leptons as generated in the decays of the lightest RH neutrino
−YLδ+LTCiτ2L+h.c. , (5) tMhrδo<ugMh1t,hwehYeRrecMouδpislinthge, mNa1ss→ofδδ++l.RIin. tWheeopaspsousmitee
where the matrix YL is antisymmetric. case a lepton asymmetry would be produced in δ+
SeveralsimpleextensionsoftheSMcontainthesin- decays,butitwouldbewashedoutbyNi interactions
glet δ+: as well as by gauge scattering (more details in [8]).
In SU(5) models, δ+ is part of the Higgs multi- The decay of N1 occurs through the same tree and
• oneloopFeynmandiagramsastheusualleptogenesis,
plet 10H. by replacing Li with lRi as well as H with δ+, as
In left-right symmetric models, based on the shown in Fig.2. While H has zero lepton number,
• gaugegroupSU(2)L SU(2)R U(1)B−L,there the lepton number of δ+ has to be determined by its
are two possibilities:×either δ+× (1,1,2) or δ+ dominant decay channel. The interaction YL given in
can be identified with the singl∼y charged com- eq.(5) leads to the two-body decay δ+ l+ν¯, so that
ponent of an SU(2)R triplet ∆R (1,3,2). L(δ+) = 2. If YL is forbidden, than→δ+ may only
∼ −
IPM-LHP06-19May
IPM Conference on Lepton and Hadron Physics, Tehran, Iran, May 15-20, 2006 3
Figure 2: The Feynman diagrams for N1 decays in the right-handedsector leptogenesis scenario.
decay into three bodies through a virtual N. The ful leptogenesis is the following:
dominant channel turns out to be δ+ l+l−H+ [8],
sothatL(δ+) 0. Inbothcases,anet→leptonnumber M1 2TeV , M2 6TeV , Mδ 750GeV ,
is produced in≈the decay N1 →δ+lRi and therefore a ≃ YR2 ≃4·10≃−3 , YR1 ≃10≃−7 .
lepton asymmetry may be generated. We call this (10)
scenario RH sector leptogenesis. Infact, leptogenesiscanbe successfulforMδ assmall
OfcourseN1 decaysalsothroughtheusualYukawa asallowedbydirectsearchesatcollider(∼100GeV).
coupling YN. For simplicity, in the following we will The lightest RH neutrino mass M1 needs to be few
not display this additional contribution to the lepton timeslargerthanvtoallowforleptontobaryonasym-
asymmetry. In fact, it is negligible as long as M1 metry conversionby sphalerons. The mass M2 has to
108 GeV, as demonstrated in section 1. ≪ be heavier than 4 TeV to suppress the washout in-
∼
We consider for definiteness only one RH neutrino duced by N2 mediated ∆L = 2 scatterings (for this
estimate we did not consider the additional resonant
heavier than N1 (the results can be immediately gen-
enhancement of the asymmetry which may occur if
eralizedtoanarbitrarynumberofRHneutrinos). The
computation of the lepton asymmetry then gives M1 M2).
≈
Let us restate the reason why the scale of RH sec-
ǫL = 81πYR22MM12 , YR22 ≡ Imi(|Y(RYRYR)†1)i21|22 , (7) tlreoepprtlloaegcpeetdnoegbseiynseǫssLcisencaarnYioR2b.2eMIm1n/uMcthh2eloapwnrdeerseYtnRht2anccaaisnnetbeheqe.(tu2as)kueainsl
P relativelylargew∼ithoutinducinganyneutrinomasses,
up to corrections of order (Mδ/M1)2 and (M1/M2)2. whichdependonlyonYN asineq.(3). Inotherwords,
The quantity YR2 is of the order of the Yukawa cou- barring resonant effects, TeV scale RH neutrinos re-
plings of N2 to lRi. The N1 decay width is given by quireverysmallYN couplingsandleptogenesisatlow
scale may occur only if another set of couplings (YR)
1
Γ1 = 16πYR21M1 , YR21 ≡ |(YR)1i|2 , (8) insaninttlreopdtuocgeedneisnistshceentahreioo,ryn.osCtaotnetsrqaruyasti-odetgheenerreasote-
Xi
inmassareneeded,norcancellationsbetweenYN cou-
where YR1 is of the order of the Yukawa couplings of plings. The price to pay is to introduce an extra de-
N1 to lRi. In order to suppress washout from N1 in- gree of freedom, the scalar δ+.
versedecays,onehastoimposetheout-ofequilibrium
condition Γ1 < H(T = M1), where H is the Hubble
constant. Req∼uiring also ǫL > 10−6, we find the con- 4. PHENOMENOLOGICAL SIGNATURES
straint ∼ AT TeV SCALE
YR1 <0.2 M1 M1 . (9) Leptogenesis relies on the assumption that heavy
YR2 ∼ ·rM2r109GeV RH neutrinos exist. In the usual scenario, they de-
cay into a lepton doublet and the SM Higgs dou-
Therefore, RH sector leptogenesis is successful even blet, yet to be discoveredat LHC. A sufficiently light
for M1 much smaller than 109 GeV, provided a hi- charged singlet scalar δ+, if any, would also be dis-
erarchy in the Yukawa coupling matrix YR is as- covered in colliders, by Drell-Yan pair production:
sumed. Inparticular,M1aslightasfewTeVsrequires qq¯ (e+e−) γ (Z) δ+δ− (for an estimate of the
YR1/YR2 10−4, which is comparable with observed cross-sectio→n see [8]).→If δ+ were observed, RH lepto-
∼
hierarchies in charged fermion Yukawa matrices. We genesis would become as plausible as the usual one,
checkedthat other sources of asymmetry washout (in since RH neutrinos will naturally decay into δ+lR.
particular∆L=2scatteringduetoN2 exchange)are If δ+ couples (antisymmetrically) to left-handed
also under control down to these low scales [8]. leptons as in eq.(5), it would mainly decay into an-
Anillustrativesetofparametersleadingtosuccess- tilepton and antineutrino. The decay into τ+ is the
IPM-LHP06-19May
4 IPM Conference on Lepton and Hadron Physics, Tehran, Iran, May 15-20, 2006
more interesting one, because it can be used to iden- same sizable coupling YR2 that generates the lepton
tifyattheLHCarelativelylightMSSMchargedHiggs asymmetry.
H+ [9]. The two particle decays can be distinguished
by analyzing the angular distribution of the outgoing
antilepton, since it is left-handed in the case of H+
and right-handed in the case of δ+. If the coupling Acknowledgments
in eq.(5) is absent, δ+ can decay only very slowly to
three bodies. Therefore, the δ+δ− pair will leave in
I would like to thank Yasaman Farzan for invita-
the detector a pair of long curved charged particle
tion and the Organizers for local financial support.
trackswhichcouldbe distinguishedfromamuonpair
The efforts of them all made this week in Tehran a
by the fact that they are less relativistic.
memorable experience. The results presented in this
The δ+ exchange may also mediate lepton number
talkwerederivedincollaborationwithThomasHam-
violating processes. In the case of µ eγ, the domi-
→ byeandErnestMa. Myworkispartiallysupportedby
nant contribution is found to come from the YL cou-
theRTNEuropeanProgramMRTN-CT-2004-503369.
plingsandcanbeaslargeasthepresentexperimental
limit if Mδ <1 TeV [8].
If also N∼2 is as light as few TeVs, it can be pro-
duced through the relatively large Yukawa coupling
YR2 > 10−3. Notice that such low scales RH neutri- References
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IPM-LHP06-19May
