a predictive class of modelsin type ii seesaw, light neutrinos couple to the su(2) l triplet Δ,...
TRANSCRIPT
MF, P.Hosteins, S.Lavignac and A.Romanino, NPB 806 (2009) 84
L.Calibbi, MF, S.Lavignac and A.Romanino, JHEP 0912 (2009) 057
Galileo Galilei InstituteIndirect searches for new physics at the time of LHC
Arcetri, March 10, 2010
Michele Frigerio (IFAE, UAB, Barcelona)
GUT & leptogenesisa predictive class of models
GUT motivations (theory)
GUT motivations (theory)• Supersymmetric Grand Unification (SUSY GUTs) may account for
✤ the hierarchy problem, if the supersymmetry is realized close to the electroweak scale
✤ the relative values of the Standard Model (SM) gauge couplings
✤ the charge quantization, since the gauge group is simple
✤ the gauge quantum numbers of the SM fermions
✤ the mass relations between quarks and leptons
✤ the chiral anomaly cancellation
GUT motivations (theory)• Supersymmetric Grand Unification (SUSY GUTs) may account for
✤ the hierarchy problem, if the supersymmetry is realized close to the electroweak scale
✤ the relative values of the Standard Model (SM) gauge couplings
✤ the charge quantization, since the gauge group is simple
✤ the gauge quantum numbers of the SM fermions
✤ the mass relations between quarks and leptons
✤ the chiral anomaly cancellation
• SUSY Grand Unification should then be realized at some level. We adopt here the traditional picture, with low energy SUSY, four spacetime dimensions and gravity effects negligible below MPlanck
GUT motivations (exp)
GUT motivations (exp)• Supersymmetric Grand Unification (SUSY GUTs) may account for
✤ non-zero neutrino masses
✤ the matter-antimatter asymmetry
✤ the dark matter
GUT motivations (exp)• Supersymmetric Grand Unification (SUSY GUTs) may account for
✤ non-zero neutrino masses
✤ the matter-antimatter asymmetry
✤ the dark matter
• A GUT is expected to correlate the SM flavour parameters. However a realistic model tends to require several sets of Yukawa couplings, which are not all observable at low energies, so that predictions are dimmed.
GUT motivations (exp)• Supersymmetric Grand Unification (SUSY GUTs) may account for
✤ non-zero neutrino masses
✤ the matter-antimatter asymmetry
✤ the dark matter
• A GUT is expected to correlate the SM flavour parameters. However a realistic model tends to require several sets of Yukawa couplings, which are not all observable at low energies, so that predictions are dimmed.
• In the near future we will confront with
✤ precision neutrino flavour parameters
✤ enhanced sensitivity to flavour and CP violating rare processes
✤ direct tests of the low energy supersymmetry spectrum
GUT motivations (exp)• Supersymmetric Grand Unification (SUSY GUTs) may account for
✤ non-zero neutrino masses
✤ the matter-antimatter asymmetry
✤ the dark matter
• A GUT is expected to correlate the SM flavour parameters. However a realistic model tends to require several sets of Yukawa couplings, which are not all observable at low energies, so that predictions are dimmed.
• In the near future we will confront with
✤ precision neutrino flavour parameters
✤ enhanced sensitivity to flavour and CP violating rare processes
✤ direct tests of the low energy supersymmetry spectrum
the only dimension-5 operator that can be added
to the Standard Model
Neutrino mass & GUT scale1
MLD=5 =
fij
MLiLjHH
(mν)ijνiνj =fij〈H0〉2
Mνiνj
the only dimension-5 operator that can be added
to the Standard Model
Neutrino mass & GUT scale1
MLD=5 =
fij
MLiLjHH
(mν)ijνiνj =fij〈H0〉2
Mνiνj
Seesaw mechanism: exchange of superheavy (<1015 GeV) particles induces tiny Majorana
neutrino masses
x
type IItype I
xf
Lepton flavour structureIn type I seesaw, light neutrinos couple
through yij to gauge singlets N’s, which have heavy Majorana masses Mij : there are
two sets of flavour parameters MN
Nx
Lepton flavour structureIn type I seesaw, light neutrinos couple
through yij to gauge singlets N’s, which have heavy Majorana masses Mij : there are
two sets of flavour parameters MN
Nx
In type II seesaw, light neutrinos couple to the SU(2)L triplet Δ, with couplings fij
mij =
µv2
M2∆
fij
The unique set of flavour parameters is the low energy one, that is, the light neutrino mass matrix mij
xf
3 necessary conditions to generate the matter-antimatter asymmetry:(i) violation of B-L symmetry: MN
(ii) violation of CP symmetry: y(iii) epoch out of thermal equilibrium
nB
s
≈ 0.9 10−10
Baryogenesis via leptogenesisSakharov
WMAP
3 necessary conditions to generate the matter-antimatter asymmetry:(i) violation of B-L symmetry: MN
(ii) violation of CP symmetry: y(iii) epoch out of thermal equilibrium
nB
s
≈ 0.9 10−10
In the early Universethe heavy particles may
decay out-of-equilibrium into leptons
Fukugita & Yanagida
Baryogenesis via leptogenesisSakharov
WMAP
3 necessary conditions to generate the matter-antimatter asymmetry:(i) violation of B-L symmetry: MN
(ii) violation of CP symmetry: y(iii) epoch out of thermal equilibrium
nB
s
≈ 0.9 10−10
In the early Universethe heavy particles may
decay out-of-equilibrium into leptons
Fukugita & Yanagida
Baryogenesis via leptogenesisSakharov
WMAP
Asymmetry suppressed by (i) large number of d.o.f. (ii) a loop factor (iii) dilution effects
nB
s≈ 10
−3εLη
obs
≈ 10−10
Is leptogenesis testable? Flavour
εL =3
8π
M1
M2
Im[(y†y)12(y†y)12]
(y†y)11
mij = −
∑
a
yia
v2
Ma
yTaj
εL ≡ [ Γ(N→LH) − Γ(N→L*H*) ] / Γtot
Is leptogenesis testable? Flavour
εL =3
8π
M1
M2
Im[(y†y)12(y†y)12]
(y†y)11
✏ the couplings yia are not directly accessible at low energy✏ N1 and N2 (at least) with different couplings are needed✏ the outcome depends on several high energy flavour parameters (minimal GUT models partially constrain yia and are more predictive)
mij = −
∑
a
yia
v2
Ma
yTaj
εL ≡ [ Γ(N→LH) − Γ(N→L*H*) ] / Γtot
Outline• Type I SO(10) unification vs type II SO(10) unification: a class
of models with no unknown flavour parameters at GUT scale
✤ some model building ...
• Baryogenesis via leptogenesis in type II SO(10)
✤ the CP asymmetry, the efficiency factor, the constraints on light neutrino parameters
• mSUGRA flavour & CP violating effects in type II SO(10)
✤ the prediction for BR(μ → eγ) waiting for the MEG experiment results
Neutrino masses in SO(10)In usual SO(10) one entire family sits in a spinor representation:
16 = (1 + 5 + 10)SU(5) = N c + (L, dc) + (Q, uc, ec)
Neutrino Yukawa couplings lead to type I seesaw:
Neutrino masses in SO(10)In usual SO(10) one entire family sits in a spinor representation:
16 = (1 + 5 + 10)SU(5) = N c + (L, dc) + (Q, uc, ec)
Neutrino Yukawa couplings lead to type I seesaw:
The fundamental representation also contains L and dc states:
10 = (5 + 5)SU(5) = (Lc, d) + (L, dc)
These L states have no Yukawas to Nc, but:
Light & heavy matter fieldsIf both 16 and 10 matter fields exist, the light lepton doublet L
is in general a linear combination of L16 and L10.
16 = (1 + 5 + 10)SU(5) = N c + (L, dc) + (Q, uc, ec)
10 = (5 + 5)SU(5) = (Lc, d) + (L, dc)
Light & heavy matter fieldsIf both 16 and 10 matter fields exist, the light lepton doublet L
is in general a linear combination of L16 and L10.
16 = (1 + 5 + 10)SU(5) = N c + (L, dc) + (Q, uc, ec)
10 = (5 + 5)SU(5) = (Lc, d) + (L, dc)
When SO(10) is broken to SU(5) by the VEV of a dim-16 Higgs,the states (L, dc)16 acquire a mass of order MGUT :
The light L and dc states belong to the 10 multiplets.YD generates also down quark & charged lepton masses.
Light & heavy matter fieldsIf both 16 and 10 matter fields exist, the light lepton doublet L
is in general a linear combination of L16 and L10.
16 = (1 + 5 + 10)SU(5) = N c + (L, dc) + (Q, uc, ec)
10 = (5 + 5)SU(5) = (Lc, d) + (L, dc)
When SO(10) is broken to SU(5) by the VEV of a dim-16 Higgs,the states (L, dc)16 acquire a mass of order MGUT :
Charged fermion massesIn other words, type II SO(10) is a different route to embed the flexible SU(5) unification into the more constrained SO(10) unification:
type ISO(10)
type II SO(10)
SU(5)
The up-type Higgs doublet resides in 10U, as usual.The down-type Higgs doublet resides in 16D, which is needed anyway.
The mass spectrum
GUT
MSSM
(510
1 , 516
1 )
(510
2 , 516
2 )
(510
3 , 516
3 )
510
3
510
2
510
1
1016
GeV
1012
102
10-3
{
{
Model-building issues
• SO(10) is broken to the SM in one step by an appropriate choice of WGUT, involving extra fields with mass MGUT
• Natural doublet-triplet splitting: the MSSM Higgs doublets (HU ⊂ 10U & HD ⊂ 16D) are kept light by the ‘missing VEV’ mechanism
• Dim-5 operators contribute to p-decay through TU - TD mixing: this needs to be tuned down to about 10-2 MGUT, similarly to minimal SU(5)
• Dim-6 operators contribute to p-decay through the (X,Y) gauge bosons as in SU(5): the present bound is MGUT > 5 1015 GeV
Type II SO(10) leptogenesisWSO(10) ⊃ fij 10i 10j 54
⊃ fij Li Lj ∆
+ fij Lci Lc
j ∆
+ fij Li Lcj S
MF, P.Hosteins, S.Lavignac, A.Romanino, NPB 806 (2009) 84
Type II SO(10) leptogenesisWSO(10) ⊃ fij 10i 10j 54
⊃ fij Li Lj ∆
+ fij Lci Lc
j ∆
+ fij Li Lcj S
MF, P.Hosteins, S.Lavignac, A.Romanino, NPB 806 (2009) 84
A lepton asymmetry is produced by the couplings fij only
Type II SO(10) leptogenesisWSO(10) ⊃ fij 10i 10j 54
⊃ fij Li Lj ∆
+ fij Lci Lc
j ∆
+ fij Li Lcj S
MF, P.Hosteins, S.Lavignac, A.Romanino, NPB 806 (2009) 84
The leptons Lc in the loop are heavy, with masses M1,2,3 ≈ ye,μ,τ MGUT. In the case M1 << MΔ < M2 one finds
εL ≈
Tr(f∗f)
10π
M∆
MS
Im[m11(m∗mm∗)11]
(∑3
i=1m2
i)2
A lepton asymmetry is produced by the couplings fij only
Type II SO(10) leptogenesisWSO(10) ⊃ fij 10i 10j 54
⊃ fij Li Lj ∆
+ fij Lci Lc
j ∆
+ fij Li Lcj S
MF, P.Hosteins, S.Lavignac, A.Romanino, NPB 806 (2009) 84
The leptons Lc in the loop are heavy, with masses M1,2,3 ≈ ye,μ,τ MGUT. In the case M1 << MΔ < M2 one finds
εL ≈
Tr(f∗f)
10π
M∆
MS
Im[m11(m∗mm∗)11]
(∑3
i=1m2
i)2
Baryogenesis from the same CP phases observable in the lepton sector !
A lepton asymmetry is produced by the couplings fij only
The decay channels
GUT
MSSM
(1554, 15
54)
2454
(510
1 , 516
1 )
(510
2 , 516
2 )
(510
3 , 516
3 )
510
3
510
2
510
1
Hu, Hd
f11
fij σu,d
1016
GeV
1012
102
10-3
seesawstates
The decay channels
GUT
MSSM
(1554, 15
54)
2454
(510
1 , 516
1 )
(510
2 , 516
2 )
(510
3 , 516
3 )
510
3
510
2
510
1
Hu, Hd
f11
fij σu,d
1016
GeV
1012
102
10-3
seesawstates
Efficiency of leptogenesis(εL)max ≈ 0.1
√
∆m212
∆m223
s2
13
∣
∣
∣
∣
∣
max
≈ 10−3nB
s= 7.6 × 10
−3εL η
obs= 0.9 × 10
−10
Efficiency of leptogenesis
The efficiency parameter η is determined by the Boltzmann equations for the decays of Δ in the three channels LL, LcLc and HH
Γtot(∆) =M∆
32π
[
λ2L + λ
2Lc + λ
2H
]
Ka ≡
Γ(∆ → aa)
H(M∆)
?
< 1
(εL)max ≈ 0.1
√
∆m212
∆m223
s2
13
∣
∣
∣
∣
∣
max
≈ 10−3nB
s= 7.6 × 10
−3εL η
obs= 0.9 × 10
−10
Efficiency of leptogenesis
The efficiency parameter η is determined by the Boltzmann equations for the decays of Δ in the three channels LL, LcLc and HH
Γtot(∆) =M∆
32π
[
λ2L + λ
2Lc + λ
2H
]
Ka ≡
Γ(∆ → aa)
H(M∆)
?
< 1
Large (order one) efficiency η is obtained when Γtot is larger than Hubble, but one decay channel is out-of-equilibrium
Hambye, Raidal, Strumia
(εL)max ≈ 0.1
√
∆m212
∆m223
s2
13
∣
∣
∣
∣
∣
max
≈ 10−3nB
s= 7.6 × 10
−3εL η
obs= 0.9 × 10
−10
Efficiency of leptogenesis
The efficiency parameter η is determined by the Boltzmann equations for the decays of Δ in the three channels LL, LcLc and HH
Γtot(∆) =M∆
32π
[
λ2L + λ
2Lc + λ
2H
]
Ka ≡
Γ(∆ → aa)
H(M∆)
?
< 1
Large (order one) efficiency η is obtained when Γtot is larger than Hubble, but one decay channel is out-of-equilibrium
Hambye, Raidal, Strumia
(εL)max ≈ 0.1
√
∆m212
∆m223
s2
13
∣
∣
∣
∣
∣
max
≈ 10−3nB
s= 7.6 × 10
−3εL η
obs= 0.9 × 10
−10
• The neutrino mass scale fixes KL KH = 220 (Σi mi2) / Δm223 >> 1
• A good efficiency requires KLc = |mee|2 / (Σi mi2) KL << 1
M!"1012GeV
M!"1013GeV
Ε " 10$7Ε " 10$8Ε " 10$10KL%1
KH % 1
KL1
c & 1
0.00 0.05 0.10 0.15 0.20 0.25 0.30
0.00
0.05
0.10
0.15
0.20
0.25
0.30
ΛL
Λ H
λL
λH
w e a k w a s h o u t
strong washout
Define Yp = (np - np*)/s for each species p. At the end of baryogenesis epoch we find YLc =YL - YH≠ 0.Later Lc’s decay and asymmetry in light leptons is left.
Constraints on ν parametersThe washout may be weak & the CP asymmetry sufficiently large
for MΔ > 1011GeV and specific ν parameters. If one takes MΔ = 1012 GeV, successful leptogenesis requires: (i) suppression of 0ν2β decays (ii) normal ν mass hierarchy (iii) sin θ13 close to the upper bound ≈ 0.2
Baryonasymmetry
above 1011GeV
Neutrinoless2β decay of heavy nuclei
εL mee(eV)
Regi
on o
f wea
k w
asho
ut
mν1(eV)mν1(eV)
sinθ13 sinθ13
Constraints on ν parameters
Unfortunately weak washout requires |mee| < 10-2 eV
εL
Weak w
ashout|mee|2
Successful leptogenesis implies also non-zero Majorana-type CP violating phases, ρ and σ. They are the same phases entering 0ν2β decay.
GUT m0, m1/2, A0Flavour universal
SUSY breaking mediation
Soft SUSY breaking parameters
GUT m0, m1/2, A0Flavour universal
SUSY breaking mediation
Soft SUSY breaking parameters
(1554, 15
54)
2454
(510
1 , 516
1 )
(510
2 , 516
2 )
(510
3 , 516
3 )
RGEs
Flavour and CP violating thresholds
determined by Yukawa couplings related to
seesaw & leptogenesis
Borzumati & Masiero, 1986; Rossi, 2002
GUT m0, m1/2, A0Flavour universal
SUSY breaking mediation
MSSMTeV scale SUSY spectrum
mL,e,Q,d,u , M1,2,3, ae,d,u
Soft SUSY breaking parameters
(1554, 15
54)
2454
(510
1 , 516
1 )
(510
2 , 516
2 )
(510
3 , 516
3 )
RGEs
Flavour and CP violating thresholds
determined by Yukawa couplings related to
seesaw & leptogenesis
Borzumati & Masiero, 1986; Rossi, 2002
GUT m0, m1/2, A0Flavour universal
SUSY breaking mediation
Flavour and CP violating rare processes
MSSMTeV scale SUSY spectrum
mL,e,Q,d,u , M1,2,3, ae,d,u
Soft SUSY breaking parameters
(1554, 15
54)
2454
(510
1 , 516
1 )
(510
2 , 516
2 )
(510
3 , 516
3 )
RGEs
Flavour and CP violating thresholds
determined by Yukawa couplings related to
seesaw & leptogenesis
Borzumati & Masiero, 1986; Rossi, 2002
Sfermion massesTaking mSUGRA boundary conditions at MGUT:
type II seesaw à la SU(5)3 heavy matter families from
SO(10) breaking
MSSM like effects
(m2L)ij ≈ (m2
dc)ji ≈3m2
0 + A20
16π2
∑
a=1,2,3
f∗
ia
[
6 logM∆
MGUT+
24
5log
MS + Ma
MGUT
]
faj
(m2
ec)ij ≈3m2
0 + A20
16π2
∑
a=1,2,3
4|αd|2y∗
ia logMa
MGUTyaj
Sfermion massesTaking mSUGRA boundary conditions at MGUT:
After RGE evolution, flavour violations are “minimal” both for quarks and leptons (CP violation depends also on 5 high energy phases)
type II seesaw à la SU(5)3 heavy matter families from
SO(10) breaking
MSSM like effects
(m2L)ij ≈ (m2
dc)ji ≈3m2
0 + A20
16π2
∑
a=1,2,3
f∗
ia
[
6 logM∆
MGUT+
24
5log
MS + Ma
MGUT
]
faj
(m2
ec)ij ≈3m2
0 + A20
16π2
∑
a=1,2,3
4|αd|2y∗
ia logMa
MGUTyaj
Lepton flavour & CP violations
Choosing (i) a heavy mass spectrum compatible with unification, (ii) the parameters leading to leptogenesis, (iii) approximatively
equal superpartner masses, we roughly estimate:
The MEG experiment is taking data: from 10-11 (already last summer) to 2 10-13 (three years data taking)
Strong correlations with τ → μγ, eγ (A.Rossi)
Masina, Savoy, ’03; Paradisi, ’05; Ciuchini et al. , ’07; ...
Lepton flavour & CP violations
Choosing (i) a heavy mass spectrum compatible with unification, (ii) the parameters leading to leptogenesis, (iii) approximatively
equal superpartner masses, we roughly estimate:
The MEG experiment is taking data: from 10-11 (already last summer) to 2 10-13 (three years data taking)
Strong correlations with τ → μγ, eγ (A.Rossi)
The present bound is 7 10-28 e cm, prospects to reach 10-30 : out of reach
Masina, Savoy, ’03; Paradisi, ’05; Ciuchini et al. , ’07; ...
BR(μ→eγ)
parameters leading to successful leptogenesis at 1012 GeV, tan β = 10
too light chargino
no mSUGRA boundary conditions
MEG future bound
L.Calibbi, MF, S.Lavignac, A.Romanino, JHEP 0912 (2009) 057
no radiative EWSB
too light Higgs
MEGA present bound
Mslepton (GeV)
same parametersas before,
scanning over m0 and m1/2 Now
Now
μ to e conversion on Titanium could
be probed down to 10-16 (Mu2e) or 10-18 (PRISM)
MΔ (GeV)
BR(μ→eγ)
εL
mSUGRA parameters fixed
to tan β = 10m0 = 700 GeVm1/2 = 700 GeV
λH
λH
the slope of the contours (λH / MΔ) is fixed by the size of neutrino masses
no leptogenesis
MΔ (GeV)
BR(μ→eγ)
εL
mSUGRA parameters fixed
to tan β = 10m0 = 700 GeVm1/2 = 700 GeV
λH
λH
the slope of the contours (λH / MΔ) is fixed by the size of neutrino masses
no leptogenesis
Leptogenesis dynamics is
constrained by LFV bounds: no strong
washout
Requiring leptogenesis
determines the overall size of LFV
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
mi (
GeV
)
h0
A0, H0 H±
τ1
τ2lLlR
χ01
χ02, χ±
1
χ03
χ04, χ±
2
g
t1
t2 b1
b2
uL, dL
uR, dR
mSUGRA parametersfixed to tan β = 10m0 = 700 GeVm1/2 = 700 GeVA0 = 0μ > 0
large unified gauge coupling
makes all sfermions
heavier than all neutralinos and
charginos; never stau LSP
Quark flavour & CP violations
The presently allowed range is (1.8 -4.3) 10-4. RR and RL contributions can be enhanced by the factor (fij / 0.05)4 .
Other constraints from CP violating observables as εK or EDMn.They are sensitive to both low and high energy CP phases.
Correlated analysis of the hadronic observables gives weaker constraints.
Most noticeable difference with the MSSM is δRRd ≠ 0 at leading log.
BR(b → sγ)|g ∼(
100 GeV
MS
)4[
(3.9 · 10−6)LL + (1.9 · 10−7)RR
]
+(
100 GeV
MS
)2[
(5.4 · 10−7)LR + (1.2 · 10−8)RL
]
SM may account only for 80-90% of this measured value (Buras, Guadagnoli)
but hadronic uncertainties large
exp
no radiative EWSB
Text
μ→eγ
arbitrary choice of a CP violating phase
Conclusions✴ Several upcoming experiments will provide new severe &
complementary tests of SUSY GUTs
✴ In type II SO(10) models, the low energy fermion masses & mixing angles are the only flavour parameters of the full theory
✴ Baryogenesis via leptogenesis & neutrino masses are determined by the same Yukawa coupling matrix, and significantly constrain the parameters of this scenario
✴ A specific pattern is predicted for SUSY flavour violating effects, the strongest constraint coming from the present & near future bounds on BR(μ → eγ)
BACKUP SLIDES
The model: Yukawa sector
WY =1
2yij16i16j10 + hij16i10j16 +
1
2fij10i10j54
up quarks: mu = y vu
no neutrino Dirac mass!
y Quc〈Hu〉
1
2fL10L10〈∆〉
54 is needed to make neutrinos massive (type II seesaw): mν = f vΔ
heavy lepton & d-quark masses: ME = MDT = h VGUT
light lepton & d-quark masses: me = mdT = h vd
h(
L16
Lc〈116
H 〉 + ecL
10〈Hd〉)
Type I versus type II SO(10)
The most general superpotential for dim-10 and dim-16 multiplets:
WY =1
2y16M16M10H + h16M10M16H +
1
2M1010M10M
The singlet VEV in 16H mixes the (L, dc) states in 16M and 10M :
The orthogonal combination defines the light (L,dc) states
WY ⊃ 510
M
(
〈116
H 〉 516
M + M10 510
M
)
In general Llight = cosθ L10 + sinθ L16 :
Type I SO(10) limit is θ = π/2 ; type II scenario is θ = 0 (it occurs for
M10 = 0; notice that DT splitting requires MH 10H 10H to be forbidden)
SO(10) breaking to the SMTo break SO(10), besides 16 one may use 45 and 54 Higgs multiplets, acquiring a GUT scale VEV
To align a 45 VEV along TB-L one needs a non-generic WGUT
In this way SO(10) is broken in one step (at M16) to the SM, with the correct VEV alignment required by DT-splitting
All (un)eaten fields in WGUT get mass at the GUT scale ∼ M16
DT-splitting and p-decay
Doublet-Triplet splitting by the missing VEV mechanism(Dimopoulos-Wilczek), but with the down Higgs partly in 16:
WDT = α10 45B−L 10′+ M 10
′10
′+ η 16 16 10 + g16 45B−L 16
MD =
0 0 ηV1
0 M10 0
0 0 gVB−L
MT =
0 αVB−L ηV1
−αVB−L M10 0
0 0 gVB−L
Due to the type II SO(10) structure, the D=5 p-decay can be mediated only through T10 - T16 mixing
ηV1M10
α2gV 3B−L
!1
MGUT
Hu = H10u
Hd = cH10d
+ sH16d
Full computation of εL
The loop contains 2 heavy sleptons with masses Ml and Mk , and a Higgsino from 54, either S ∼ (1,1,0)SM or T ∼ (1,3,0)SM
F (x, xk, xl) = Θ(1 − xk − xl) x log
[
1 + 2x2− x2
k− x2
l+
√
λ(1, x2
k, x2
l)
1 + 2x2− x2
k− x2
l−
√
λ(1, x2
k, x2
l)
]
ε∆B−L = 2 ·
Γ(∆ → L∗L∗) − Γ(∆∗→ LL)
Γtot(∆∗) + Γtot(∆)
ε∆B−L =1
16π
∑
R=S,T
cR
3∑
k,l=1
F
(
MR
M∆
,Mk
M∆
,Ml
M∆
)
Im[f∗
kl(ff∗f)kl]
Tr(f∗f) + . . .
F is the imaginary partof the loop integral
Mk + Ml → 0 F ≈MR
M∆log
(
1 +M
2
∆
M2
R
)
Fmax ≈ 0.8 for MR
M∆≈ 0.5
Mk + Ml → M∆ F → 0Mk + Ml > M∆ F = 0
Ways out :
➡ Non-supersymmetric scenario, with a real 54 Higgs
➡ Gravitino very heavy (m3/2 >> 100 TeV), e.g. significantly split SUSY
➡ Gravitino very light (m3/2 < 100 eV), e.g. some gauge-mediation models
➡ Non-thermal production of Δ’s even for TRH << MΔ
The gravitino problemIn our scenario, at least in the weak washout region, thermal leptogenesis requires MΔ ≥ 1011-12 GeV
In SUGRA, if m3/2 is close to the electroweak scale, the gravitino overproduction bound on the reheating temperature is TRH < 109-10 GeV (much stronger bounds from BBN, but more model-dependent)
• In SO(10) models with type I seesaw, further suppression of εL comes from small Yukawa couplings: y = yup
• Some tuning of parameters is needed to enhance the asymmetry:
- quasi-degeneracy of two decaying states N1 & N2
- interplay with type II seesaw
- N2 decays plus flavour effects
nB
s≈ 10
−3εLη
obs
≈ 10−10
εL =3
8π
M1
M2
Im[(M†uMu)12]2
v2(M†uMu)11
Flanz, Paschos, Sarkar, Weiss; Covi, Roulet, Vissani; Pilaftsis, Underwood; Akhmedov, MF, Smirnov
Joshipura, Paschos, Rodejohann; Hambye, Senjanovic;Hosteins, Lavignac, Savoy, Abada, Josse-Michaux
Di Bari; Vives; Riotto
εL ∼ [ Γ(N→LH) − Γ(N→L*H*) ]
Leptogenesis in type I SO(10)