a predictive class of modelsin type ii seesaw, light neutrinos couple to the su(2) l triplet Δ,...

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




✤ 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.




✤ 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



nB

s

≈ 0.9 10−10

In the early Universethe heavy particles may

decay out-of-equilibrium into leptons

Fukugita & Yanagida


WMAP



nB

s

≈ 0.9 10−10

In the early Universethe heavy particles may

decay out-of-equilibrium into leptons

Fukugita & Yanagida


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)



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.



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


⊃ fij Li Lj ∆

+ fij Lci Lc

j ∆

+ fij Li Lcj S


A lepton asymmetry is produced by the couplings fij only


⊃ fij Li Lj ∆

+ fij Lci Lc

j ∆

+ fij Li Lcj S


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



⊃ fij Li Lj ∆

+ fij Lci Lc

j ∆

+ fij Li Lcj S


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 !


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



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



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




(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



MSSMTeV scale SUSY spectrum

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


(1554, 15

54)

2454

(510

1 , 516

1 )

(510

2 , 516

2 )

(510

3 , 516

3 )

RGEs







Flavour and CP violating rare processes

MSSMTeV scale SUSY spectrum

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


(1554, 15

54)

2454

(510

1 , 516

1 )

(510

2 , 516

2 )

(510

3 , 516

3 )

RGEs





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)

a predictive class of modelsin type ii seesaw, light neutrinos couple to the su(2) l triplet Δ,...

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