GUT & leptogenesis a predictive class of models Michele - - PowerPoint PPT Presentation

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 Institute

Indirect searches for new physics at the time of LHC

Arcetri, March 10, 2010

Michele Frigerio (IFAE, UAB, Barcelona)

GUT & leptogenesis

a 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

• perator that can be added

to the Standard Model

Neutrino mass & GUT scale

1 M LD=5 = fij M LiLjHH

(mν)ijνiνj = fijH02 M νiνj

the only dimension-5

• perator that can be added

to the Standard Model

Neutrino mass & GUT scale

1 M LD=5 = fij M LiLjHH

(mν)ijνiνj = fijH02 M νiνj

Seesaw mechanism: exchange of superheavy (<1015 GeV) particles induces tiny Majorana neutrino masses

x type II type I x

f

Lepton flavour structure

In 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

M N Nx

Lepton flavour structure

In 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

M N Nx

In type II seesaw, light neutrinos couple to the SU(2)L triplet Δ, with couplings fij

mij = µv2 M 2

∆

fij

The unique set of flavour parameters is the low energy one, that is, the light neutrino mass matrix mij

x

f

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 leptogenesis

Sakharov 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 Universe the heavy particles may decay out-of-equilibrium into leptons

Fukugita & Yanagida

Baryogenesis via leptogenesis

Sakharov 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 Universe the heavy particles may decay out-of-equilibrium into leptons

Fukugita & Yanagida

Baryogenesis via leptogenesis

Sakharov WMAP Asymmetry suppressed by (i) large number of d.o.f. (ii) a loop factor (iii) dilution effects

nB s ≈ 10−3Lη

• bs

≈ 10−10

Is leptogenesis testable? Flavour

L = 3 8π M1 M2 Im[(y†y)12(y†y)12] (y†y)11 mij = −

• a

yia v2 Ma yT

aj

εL ≡ [ Γ(N→LH) − Γ(N→L*H*) ] / Γtot

Is leptogenesis testable? Flavour

L = 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 yT

aj

εL ≡ [ Γ(N→LH) − Γ(N→L*H*) ] / Γtot

Outline

• Type I SO(10) unification vs type II SO(10) unification: a class
• f 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 fields

If 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 fields

If 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 fields

If 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 masses

In 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 I SO(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 , 5 16 1 )

(510

2 , 5 16 2 )

(510

3 , 5 16 3 )

5

10 3

5

10 2

5

10 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) leptogenesis

WSO(10) ⊃ fij 10i 10j 54 ⊃ fij Li Lj ∆ + fij Lc

i Lc j ∆

+ fij Li Lc

j S

MF , P.Hosteins, S.Lavignac, A.Romanino, NPB 806 (2009) 84

Type II SO(10) leptogenesis

WSO(10) ⊃ fij 10i 10j 54 ⊃ fij Li Lj ∆ + fij Lc

i Lc j ∆

+ fij Li Lc

j 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) leptogenesis

WSO(10) ⊃ fij 10i 10j 54 ⊃ fij Li Lj ∆ + fij Lc

i Lc j ∆

+ fij Li Lc

j 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

L ≈ Tr(f ∗f) 10π M∆ MS Im[m11(m∗mm∗)11] (3

i=1 m2 i )2

A lepton asymmetry is produced by the couplings fij only

Type II SO(10) leptogenesis

WSO(10) ⊃ fij 10i 10j 54 ⊃ fij Li Lj ∆ + fij Lc

i Lc j ∆

+ fij Li Lc

j 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

L ≈ Tr(f ∗f) 10π M∆ MS Im[m11(m∗mm∗)11] (3

i=1 m2 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 , 5 16 1 )

(510

2 , 5 16 2 )

(510

3 , 5 16 3 )

5

10 3

5

10 2

5

10 1

Hu, Hd f11 fij σu,d

1016 GeV 1012 102 10-3

seesaw states

The decay channels

GUT MSSM

(1554, 15

54)

2454 (510

1 , 5 16 1 )

(510

2 , 5 16 2 )

(510

3 , 5 16 3 )

5

10 3

5

10 2

5

10 1

Hu, Hd f11 fij σu,d

1016 GeV 1012 102 10-3

seesaw states

Efficiency of leptogenesis

(L)max ≈ 0.1

• ∆m2

12

∆m2

23

s2

13

• max

≈ 10−3

nB s = 7.6 × 10−3 L η

• bs

= 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

• λ2

L + λ2 Lc + λ2 H

• Ka ≡ Γ(∆ → aa)

H(M∆)

?

< 1

(L)max ≈ 0.1

• ∆m2

12

∆m2

23

s2

13

• max

≈ 10−3

nB s = 7.6 × 10−3 L η

• bs

= 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

• λ2

L + λ2 Lc + λ2 H

• 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 (L)max ≈ 0.1

• ∆m2

12

∆m2

23

s2

13

• max

≈ 10−3

nB s = 7.6 × 10−3 L η

• bs

= 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

• λ2

L + λ2 Lc + λ2 H

• 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 (L)max ≈ 0.1

• ∆m2

12

∆m2

23

s2

13

• max

≈ 10−3

nB s = 7.6 × 10−3 L η

• bs

= 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

M1012GeV M1013GeV Ε 107 Ε 108 Ε 1010 KL 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 ΛH

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 parameters

The 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 Baryon asymmetry above 1011GeV Neutrinoless 2β decay of heavy nuclei

εL mee(eV)

Region of weak washout mν1(eV) mν1(eV) sinθ13 sinθ13

Constraints on ν parameters

Unfortunately weak washout requires |mee| < 10-2 eV εL

Weak washout |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, A0

Flavour universal SUSY breaking mediation

Soft SUSY breaking parameters

GUT

m0, m1/2, A0

Flavour universal SUSY breaking mediation

Soft SUSY breaking parameters

(1554, 15

54)

2454 (510

1 , 5 16 1 )

(510

2 , 5 16 2 )

(510

3 , 5 16 3 )

RGEs

Flavour and CP violating thresholds determined by Yukawa couplings related to seesaw & leptogenesis

Borzumati & Masiero, 1986; Rossi, 2002

GUT

m0, m1/2, A0

Flavour universal SUSY breaking mediation

MSSM

TeV scale SUSY spectrum

mL,e,Q,d,u , M1,2,3, ae,d,u

Soft SUSY breaking parameters

(1554, 15

54)

2454 (510

1 , 5 16 1 )

(510

2 , 5 16 2 )

(510

3 , 5 16 3 )

RGEs

Flavour and CP violating thresholds determined by Yukawa couplings related to seesaw & leptogenesis

Borzumati & Masiero, 1986; Rossi, 2002

GUT

m0, m1/2, A0

Flavour universal SUSY breaking mediation Flavour and CP violating rare processes

MSSM

TeV scale SUSY spectrum

mL,e,Q,d,u , M1,2,3, ae,d,u

Soft SUSY breaking parameters

(1554, 15

54)

2454 (510

1 , 5 16 1 )

(510

2 , 5 16 2 )

(510

3 , 5 16 3 )

RGEs

Flavour and CP violating thresholds determined by Yukawa couplings related to seesaw & leptogenesis

Borzumati & Masiero, 1986; Rossi, 2002

Sfermion masses

Taking mSUGRA boundary conditions at MGUT:

type II seesaw à la SU(5)

3 heavy matter families from SO(10) breaking

MSSM like effects ( ˜ m2

L)ij ≈ ( ˜

m2

dc)ji ≈ 3m2 0 + A2

16π2

• a=1,2,3

f ∗

ia

• 6 log

M∆ MGUT + 24 5 log MS + Ma MGUT

• faj

( ˜ m2

ec)ij ≈ 3m2 0 + A2

16π2

• a=1,2,3

4|αd|2y∗

ia log

Ma MGUT yaj

Sfermion masses

Taking 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 ( ˜ m2

L)ij ≈ ( ˜

m2

dc)ji ≈ 3m2 0 + A2

16π2

• a=1,2,3

f ∗

ia

• 6 log

M∆ MGUT + 24 5 log MS + Ma MGUT

• faj

( ˜ m2

ec)ij ≈ 3m2 0 + A2

16π2

• a=1,2,3

4|αd|2y∗

ia log

Ma MGUT yaj

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 parameters as before, scanning over m0 and m1/2

Now Now

μ to e conversion on Titanium could be probed down to 10-16 (Mu2e)

• r 10-18 (PRISM)

MΔ (GeV)

BR(μ→eγ)

εL

mSUGRA parameters fixed to tan β = 10 m0 = 700 GeV m1/2 = 700 GeV

λH λH

the slope of the contours (λH / MΔ) is fixed by the size

• f neutrino masses

no leptogenesis

MΔ (GeV)

BR(μ→eγ)

εL

mSUGRA parameters fixed to tan β = 10 m0 = 700 GeV m1/2 = 700 GeV

λH λH

the slope of the contours (λH / MΔ) is fixed by the size

• f neutrino masses

no leptogenesis

Leptogenesis dynamics is constrained by LFV bounds: no strong washout Requiring leptogenesis determines the

• verall size of LFV

100 200 300 400 500 600 700 800 900 1000 1100 1200 mi (GeV) h0 A0, H0 H± ˜ τ1 ˜ τ2 ˜ lL ˜ lR ˜ χ0

1

˜ χ0

2, ˜

χ±

1

˜ χ0

3

˜ χ0

4, ˜

χ±

2

˜ g ˜ t1 ˜ t2 ˜ b1 ˜ b2 ˜ uL, ˜ dL ˜ uR, ˜ dR

mSUGRA parameters fixed to tan β = 10 m0 = 700 GeV m1/2 = 700 GeV A0 = 0 μ > 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 2 yij16i16j10 + hij16i10j16 + 1 2 fij10i10j54

up quarks: mu = y vu no neutrino Dirac mass!

y QucHu

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

• L16Lc116

H + ecL10Hd

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 5 16 M + M10 5 10 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 SM

To 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 =   ηV1 M10 gVB−L  

MT =   αVB−L ηV1 −αVB−L M10 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 3

B−L

• 1

MGUT

Hu = H10

u

Hd = cH10

d + sH16 d

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 )

• ∆

B−L = 2 · Γ(∆ → L∗L∗) − Γ(∆∗ → LL)

Γtot(∆∗) + Γtot(∆) ∆

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 part

• f the loop integral

Mk + Ml → 0 F ≈ MR

M∆ log

• 1 + M 2

∆

M 2

R

• Fmax ≈ 0.8 for

MR M∆ ≈ 0.5

Mk + Ml → M∆ F → 0 Mk + 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 problem

In 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

• verproduction 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 ≈ 10−3Lη

• bs

≈ 10−10

L = 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)