tev-scale leptogenesis scenarios · 12/11/2014 · sphaleron interactions. [s. yu. khlebnikov, m....

TeV-scale Leptogenesis Scenarios

P. S. BHUPAL DEV

Consortium for Fundamental Physics, The University of Manchester

XXI DAE-BRNS High Energy Physics Symposium 2014IIT Guwahati

December 11, 2014

Outline

Motivation

TeV-scale (Resonant) Leptogenesis

Flavor Effects

Phenomenology

Conclusion

Matter-Antimatter Asymmetry

η∆B ≡ nB − nB

nγ= (6.04± 0.08)× 10−10 [Planck (2014)]

Baryogenesis

Dynamical generation of baryon asymmetry.Sakharov conditions: [A. D. Sakharov, JETP Lett. 5, 24 (1967)]

B violation.C and CP violation.Out-of-equilibrium dynamics.

SM has all these ingredients.B violation through EW sphalerons. [G. ’t Hooft, Phys. Rev. Lett. 37, 8 (1976); F. R. Klinkhamer and N. S. Manton,

Phys. Rev. D 30, 2212 (1984); V. A. Kuzmin, V. A. Rubakov and M. E. Shaposhnikov, Phys. Lett. B 155, 36 (1985)]

Maximal C violation due to weak interactions. CP violation in the quark sector due tothe K-M phase.Departure from thermal equilibrium at the EWPT.

However, the observed CP violation is too small (by ∼ 10 orders of magnitude).

Also, no strong first-order phase transition, unless mH . 70 GeV. [K. Kajantie, M. Laine, K.

Rummukainen and M. E. Shaposhnikov, Phys. Rev. Lett. 77, 2887 (1996); F. Csikor, Z. Fodor and J. Heitger, Phys. Rev. Lett. 82, 21 (1999)]

Requires some New Physics:Must introduce new sources of CP violation.Must either provide a departure from equilibrium (in addition to EWPT) or modify theEWPT itself.

Leptogenesis

[M. Fukugita and T. Yanagida, Phys. Lett. B 174, 45 (1986)]

Introduce SM singlet heavy Majorana neutrinos.

New source of CP violation through Yukawa couplings.

Departure from equilibrium when Yukawa interaction rates are slower than H(t).

L violation due to the Majorana nature.

L asymmetry partially converted to B asymmetry through (B + L)-violatingsphaleron interactions. [S. Yu. Khlebnikov, M. E. Shaposhnikov, Nucl. Phys. B 308, 885 (1988)]

Singlet neutrinos naturally motivated from the seesaw mechanism.

Simplest paradigm to explain the observed neutrino oscillation data.

Neutrino Oscillations

Seesaw Mechanism

LH neutrinos exactly massless in the SM to all orders in perturbation theory,because

No RH counterpart (i.e. no Dirac mass term).νL part of SU(2)L doublet. So no Majorana mass term νT

L C−1νL.Accidental B− L symmetry, even after non-perturbative effects.

Simply adding RH neutrinos leads to tiny Yukawa couplings YN . 10−12.

A more natural way is to break B− L.

Within the SM, parametrized through dimension-5 operator λij(LTi Φ)(LT

j Φ)/Λ.[S. Weinberg, Phys. Rev. Lett. 43, 1566 (1979)]

Three tree-level realizations: Type-I, II, III seesaw mechanism.

! masses beyond the SM : tree level

Fermionic Singlet

Seesaw ( or type I)

2 x 2 = 1 + 3


Fermionic Triplet

Seesaw ( or type III)

2 x 2 = 1 + 3


2 x 2 = 1 + 3

Scalar Triplet

Seesaw ( or type II)

Fermion singlets:(type-I seesaw)

Scalar triplet:(type-II seesaw)

Fermion triplets:(type-III seesaw)

m = Y TN

1

MNYNv2 m = Y

µ

M2

v2 m = Y T

1

MYv

2

Minkowski; Gellman, Ramon, Slansky; Yanagida;Glashow; Mohapatra, Senjanovic

Magg, Wetterich; Lazarides, Shafi; Mohapatra, Senjanovic; Schechter, Valle

Foot, Lew, He, Joshi; Ma; Ma, Roy;T.H., Lin, Notari, Papucci, Strumia; Bajc, Nemevsek,

Senjanovic; Dorsner, Fileviez-Perez;....

The 3 seesaw models

L YLiLj

µHH + h.c.

L YNijNiLjH

mNi

2N c

i Ni + h.c. mi

2c

ii + h.c.

L YijiLjH

NRii (+

i ,0i ,

i )

YN Y

(++,+,0)

for example with requiresYN 1, m 0.1 eV

requires

MN 1015 GeV

with YN 106, m 0.1 eV MN TeV

µ


Fermionic Singlet

Seesaw ( or type I)

2 x 2 = 1 + 3


Fermionic Triplet


2 x 2 = 1 + 3


2 x 2 = 1 + 3

Scalar Triplet





m = Y TN

1

MNYNv2 m = Y

µ

M2

v2 m = Y T

1

MYv

2





The 3 seesaw models

L YLiLj

µHH + h.c.

L YNijNiLjH

mNi

2N c

i Ni + h.c. mi

2c

ii + h.c.

L YijiLjH

NRii (+

i ,0i ,

i )

YN Y

(++,+,0)


requires

MN 1015 GeV


µ


Fermionic Singlet

Seesaw ( or type I)

2 x 2 = 1 + 3


Fermionic Triplet


2 x 2 = 1 + 3


2 x 2 = 1 + 3

Scalar Triplet





m = Y TN

1

MNYNv2 m = Y

µ

M2

v2 m = Y T

1

MYv

2





The 3 seesaw models

L YLiLj

µHH + h.c.

L YNijNiLjH

mNi

2N c

i Ni + h.c. mi

2c

ii + h.c.

L YijiLjH

NRii (+

i ,0i ,

i )

YN Y

(++,+,0)


requires

MN 1015 GeV


µ

Type-I Seesaw

[Minkowski ’77; Mohapatra, Senjanovic ’79; Yanagida ’79; Gell-Mann, Ramond, Slansky ’79; Glashow ’79]

Seesaw messenger: SM singlet fermions (RH neutrinos).Have a Majorana mass term MNNT

R C−1NR, in addition to the Dirac mass MD = vYN .In the flavor basis νC

L ,NR, leads to the general structure

Mν =

(0 MD

MTD MN

)In the seesaw approximation ||ξ|| 1, where ξ ≡ MDM−1

N and ||ξ|| ≡√

Tr(ξ†ξ),Mlightν ' −MDM−1

N MTD is the light neutrino mass matrix.

ξ ≡ MDM−1N is the heavy-light neutrino mixing.

Complex YN elements can give a non-zero CP asymmetry.Leptogenesis is a cosmological consequence of the seesaw mechanism.

=⇒

Leptogenesis for Pedestrians

[W. Buchmuller, P. Di Bari and M. Plumacher, Annals Phys. 315, 305 (2005)]

Consider a hierarchical heavy neutrino spectrum (mN1 mN2 < mN3 ).

Final baryon asymmetry due to N1 decay is given by

η∆B = d · ε1 · κf

d ' 0.96× 10−2 is the dilution factor (in converting /L to /B).ε1 ≡

∑l εl1 is the CP asymmetry, where

εlα =Γ(Nα → LlΦ)− Γ(Nα → Lc

l Φc)∑

k[Γ(Nα → LkΦ) + Γ(Nα → Lc

kΦc)]

κf ≡ κ(zf ) is the final efficiency factor, where z = mN1/T and

κ(z) =

∫ z

zi

dz′D

D + SdnN1

dz′e−∫ z

z′ dz′′W(z′′)

D = ΓD/Hz (decay and inverse decay), S (scattering) and W (washout).K-factor is defined as K = ΓD(z→∞)/H(z = 1) = m1/m∗, wherem1 = (M†DMD)11/mN1 (effective neutrino mass) andm∗ = (16/3)(π5g∗/5)1/2v2/MPl ' 1.1 meV (equilibrium neutrino mass).Strong washout: K & 3 and weak washout: K 1.

Problems with Vanilla Leptogenesis

Maximal CP asymmetry is given by

εmax1 =

316π

mN1

v2

√∆m2

atm

Lower bound on mN1 : [S. Davidson and A. Ibarra, Phys. Lett. B 535, 25 (2002); W. Buchmuller, P. Di Bari and M. Plumacher, Nucl.

Phys. B 643, 367 (2002)]

mN1 > 6.4× 108 GeV(

η∆B

6× 10−10

)(0.05 eV√

∆m2atm

)κ−1

f

Experimentally inaccessible mass range!

Also leads to a lower limit on the reheat temperature Trh & 109 GeV.

In many SUSY scenarios, need Trh . 106 − 109 GeV to avoid the Gravitinoproblem. [J. R. Ellis, J. E. Kim, D. V. Nanopoulos, Phys. Lett. B 145, 181 (1984); K. Kohri, T. Moroi and A. Yotsuyanagi, Phys. Rev. D 73,

123511 (2006); V. S. Rychkov and A. Strumia, Phys. Rev. D 75, 075011 (2007)]

Resonant Leptogenesis

• Resonant Leptogenesis

×NαNα

LCl

Φ†

(a)

×Nα Nβ

Φ

L LCl

Φ†

(b)

×Nα

L

Nβ

Φ†

LCl

Φ

(c)

Importance of self-energy effects (when |mN1 −mN2| ≪ mN1,2)[J. Liu, G. Segre, PRD48 (1993) 4609;

M. Flanz, E. Paschos, U. Sarkar, PLB345 (1995) 248;L. Covi, E. Roulet, F. Vissani, PLB384 (1996) 169;

...

J. R. Ellis, M. Raidal, T. Yanagida, PLB546 (2002) 228.]

Importance of the heavy-neutrino width effects: ΓNα

[A.P., PRD56 (1997) 5431; A.P. and T. Underwood, NPB692 (2004) 303.]

Warsaw, 22–27 June 2014 Flavour Covariance in Leptogenesis A. Pilaftsis

Heavy Majorana neutrino self-energy effects on the leptonic CP-asymmetry(ε-type) become dominant [M. Flanz, E. Paschos and U. Sarkar, Phys. Lett. B 345, 248 (1995); L. Covi, E. Roulet and F.

Vissani, Phys. Lett. B 384, 169 (1996)] and resonantly enhanced, even up to order 1, when∆mN ∼ ΓN mN1,2 . [A. Pilaftsis, Nucl. Phys. B 504, 61 (1997); Phys. Rev. D 56, 5431 (1997)]

The quasi-degeneracy can be naturally motivated as due to approximate breakingof some symmetry in the leptonic sector.

Heavy neutrino mass scale can be as low as the EW scale. [A. Pilaftsis and T. Underwood, Phys.

Rev. D 72, 113001 (2005)]

A potential testable scenario of leptogenesis, with implications at both Energy andIntensity Frontiers.

RL Basics

Flavor-diagonal Boltzmann equations:

nγHN

zdηNα

dz=

(1− ηN

α

ηNeq

)∑l

γNαLlΦ

nγHN

zdδηL

l

dz=∑α

(ηNα

ηNeq− 1)δγNα

LlΦ− 2

3δηL

l

∑k

[γLlΦ

LckΦ

c + γLlΦLkΦ

+ δηLk(γLkΦ

Lcl Φ

c − γLkΦLlΦ

)]where δγNα

LlΦ= εlα

∑k γ

NαLkΦ

and γNαLΦ ≡

∑l γ

NαLlΦ

=m3

Nαπ2z K1(z)ΓNα .

Total decay width is given by

ΓNα =mNα

16π

[(h† h)αα + (hc† hc)αα

].

Unstable particle mixing effects are accounted for by the resummed Yukawacouplings [A. Pilaftsis and T. Underwood, Nucl. Phys. B 692, 303 (2004); A. Pilaftsis, Phys. Rev. D 78, 013008 (2008)]

hlα = hlα − i∑β,γ

|εαβγ |hlβ

×mα(mαAαβ + mβAβα) − iRαγ [mαAγβ(mαAαγ + mγAγα) + mβAβγ(mαAγα + mγAαγ)]

m2α − m2

β+ 2im2

αAββ + 2iIm(Rαγ)[m2α|Aβγ |2 + mβmγRe(A2

βγ)]

,

where Rαβ =m2α

m2α − m2

β+ 2im2

αAββand all transition amplitudes are evaluated

on-shell with p2 = m2Nα ≡ m2

α.

Key Diagrams

Nβ(p, s)

Φ(q)

Lk(k, r)

[hc] βk

nΦ(q)[nLr (k)]

kl Nα(p, s)

Φ(q)

Ll(k, r)

[hc]lα

Nβ(p, s)

Φc(q)

[Lc(k, r)]l

hlβ

nΦ(q)[nLr (k)]

kl Nα(p, s)

Φc(q)

[Lc(k, r)]k

h αk

Figure : Decay and Inverse Decay.

Nβ(p)

Φ(q2)

Ln(k2, r2)

Φ(q1)

Lk(k1, r1)

hnβ [hc] β

knΦ(q1)[n

Lr1(k1)]

kl

Nα(p)

Φ(q1)

Ll(k1, r1)

Φ(q2)

Lm(k2, r2)

[hc]lα h αm

Nβ(p)

Φc(q2)

[Lc(k2, r2)]m

Φ(q1)

Lk(k1, r1)

[hc] βm [hc] β

knΦ(q1)[n

Lr1(k1)]

kl

Nα(p)

Φ(q1)

Ll(k1, r1)

Φc(q2)

[Lc(k2, r2)]n

[hc]lα [hc]nα

Figure : ∆L = 0 and ∆L = 2 scattering.

RL Basics

In the narrow-width approximation, the collision rates for the ∆L = 0 and ∆L = 2scatterings are given by [F. Deppisch and A. Pilaftsis, Phys. Rev. D 83, 076007 (2011)]

γLkΦLlΦ

=∑α,β

(γNα

LΦ + γNβLΦ

)(

1− 2imNα−mNβΓNα+ΓNβ

) 2(

h∗lαhc∗kαhlβ hc

kβ + hc∗lα h∗kαhc

lβ hkβ

)[(h†h)αα + (hc† hc)αα + (h†h)ββ + (hc† hc)ββ

]2 ,

γLkΦLc

l Φc =

∑α,β

(γNα

LΦ + γNβLΦ

)(

1− 2imNα−mNβΓNα+ΓNβ

) 2(

h∗lαh∗kαhlβ hkβ + hc∗lα hc∗

kαhclβ hc

kβ

)[(h†h)αα + (hc† hc)αα + (h†h)ββ + (hc† hc)ββ

]2 .

Flavor-dependent CP-asymmetry is given by

εlα =|hlα|2 − |hc

lα|2∑k

(|hkα|2 + |hc

kα|2) =

|hlα|2 − |hclα|2

(h†h)αα + (hc† hc)αα.

In the two heavy-neutrino flavor limit, reduces to

εlα ≈Im[(h∗lαhlβ)(h†h)αβ

](h†h)αα(h†h)ββ

(m2

Nα − m2Nβ

)mNαΓ

(0)Nβ(

m2Nα − m2

Nβ

)2+(

mNαΓ(0)Nβ

)2 .

Analytic Solution

In terms of the K-factor Kα = ΓNα/(ζ(3)HN),

ηNα

ηNeq− 1 ' 1

Kαz(attractor solution).

In the kinematic regime z > zα1 ≈ 2K−1/3α ,

dδηLl

dz= z2K1(z)

(εl −

23

zKeffl δη

Ll

),

where Keffl = κl

∑α KαBlα ≡ κlKl is the effective washout parameter due to 2↔ 2

scatterings, and κl ≡∑

k

(γ

LlΦLc

kΦc +γ

LlΦLkΦ

)+γ

LlΦLc

l Φc−γ

LlΦLlΦ∑

α γNαLΦ Blα

.

In the regime z > zl2 ≈ 2(Keff

l )−1/3, the lepton asymmetry can be approximated by

δηLl (z) ' 3

2εl

Keffl z.

up to a point z = zl3 ≈ 1.25 ln(25Keff

l ), beyond which it freezes out.

Analytic Solution

independently of the initial conditions (see Fig. 1). In thisregime, the BE (4.33) becomes

d!Ll

dz¼ z2K1ðzÞ

!"l $

2

3zKl!Ll

"; (4.35)

with "l ¼P3

#¼1 "#l and Kl ¼P3

#¼1 K#B#l. We mayinclude the numerically significant RIS-subtractedcollision terms proportional to !Ll

in (4.27), by rescalingKl ! $lKl % Keff

l , where

$l %

Pk¼e;%;&

ð'Ll!LCk!y þ 'Ll!

Lk!Þ þ 'Ll!

LCl!y $ 'Ll!

Ll!

P3#¼1 '

N#

L!B#l

¼ 2X3

#;(¼1

ð "h)y#l

"h)l( þ "h)Cy

#l"h)Cl( Þ½ð "h)y "h)Þ#( þ ð "h)Cy "h)CÞ#(( þ ð "h)y

#l"h)l( $ "h)Cy

#l"h)Cl( Þ2

½ð "h) "h)yÞll þ ð "h)C "h)CyÞll(½ð "h)y "h)Þ## þ ð "h)Cy "h)CÞ## þ ð "h)y "h)Þ(( þ ð "h)Cy "h)CÞ(((

)!1$ 2i

mN#$mN(

#N#þ #N(

"$1: (4.36)

In determining the scaling factor $l, we have assumed that!Ll

* !Lk!lin (4.18), which is a valid approximation

within a given R‘L scenario under study. Note that ifonly the diagonal # ¼ ( terms representing the RIS con-tributions are considered in the sum, $l reaches its maxi-mum value, i.e. $l ¼ 1þOð"2

l Þ. We also have checkedthat in the Ll-conserving limit of the theory, the parameter$l vanishes, as it should.

As is illustrated in Fig. 1, the solution !Llto (4.35)

exhibits different behavior in the three kinematic regimes,characterized by the specific values of the parameterz ¼ mN=T:

zl2 + 2ðKeffl Þ$1=3; zl3 + 1:25 lnð25Keff

l Þ: (4.37)

For z values in the range zl2 < z < zl3, the solution !Llmay

well be approximated by

!LlðzÞ ¼ 3

2

"l

Keffl z

: (4.38)

For z > zl3, the lepton-number density !Llfreezes out and

approaches the constant value !Ll¼ ð3"lÞ=ð2Keff

l zl3Þ.2The general behavior of !Ll

in the different regimes isdisplayed in Fig. 1.In this paper we only consider R‘L scenarios, for which

the washout is strong enough, such that the critical tempera-ture zc ¼ mN=Tc where the baryon asymmetry !B decou-ples from the lepton asymmetries!Ll

is situated in the lineardropoff or constant regime. Specifically, we require that

zc > 2K$1=3# ; zc > 2ðKeff

l Þ$1=3; (4.39)

for all heavy-neutrino species N# ¼ N1;2;3 and lepton fla-vors l ¼ e, %, &. As a consequence, the baryon asymmetry!B becomes relatively independent of the initial values of!Ll

and !N#. In this case, taking into account all factors in

(4.29), (4.30), and (4.38), the resulting BAU is estimatedto be

!B ¼ $ 28

51

1

27

3

2

X

l¼e;%;&

"l

Keffl minðzc; zl3Þ

+ $3 , 10$2X

l¼e;%;&

"l

Keffl min½mN=Tc; 1:25 lnð25Keff

l Þ( :

(4.40)

We note that the formula (4.40) provides a fairly goodestimate of the BAU !B to less than 20%, in the applicableregime of approximations given by (4.39) forKeff

l * 5 for aright-handed neutrino mass scale of the order of the electro-weak scale. Hence, to account for the observed BAU !obs

Bgiven in (4.31), lepton asymmetries "l * 10$7 are required.In the next section, we present numerical estimates of the

z1 z2 z3zc

N1

L

10 2 10 1 100 101 102

10 10

10 9

10 8

10 7

10 6

10 5

10 4

z

L,

N

FIG. 1 (color online). Numerical solutions to BEs (4.32) and(4.35) for "!N1

¼ !N1=!eq

N $ 1 and !L&, respectively, in a R&L

model with mN ¼ 220 GeV, K1 ¼ 106, Keff& ¼ 102, "& ¼ 10$6

and zc ¼ mN=Tc ¼ 1:6.

2The onset of the freeze-out is defined as the position zl3 wherethe relative slope of (4.35) drops below 1, i.e. when j!0

Ll=!Ll

j ¼2=3ðzl3Þ3K1ðzl3ÞKeff

l ¼ 1. The solution to this equation can beanalytically expressed in terms of the Lambert W function, towhich zl3 in (4.37) proves to be an excellent interpolatingapproximation over the wide range of values Keff

l + 2$ 1010.

FRANK F. DEPPISCH AND APOSTOLOS PILAFTSIS PHYSICAL REVIEW D 83, 076007 (2011)

076007-12

[F. Deppisch and A. Pilaftsis, Phys. Rev. D 83, 076007 (2011)]

Flavordynamics of RL

Flavor effects important for the time-evolution of lepton asymmetry in RL models.Two sources of flavor effects, due to

Heavy neutrino Yukawa couplings h αl .[A. Pilaftsis, PRL 95, 081602 (2005); T. Endoh, T. Morozumi and Z.-h. Xiong, PTP 111, 123 (2004); P. Di Bari, NPB 727, 318 (2005);

S. Blanchet, P. Di Bari, D. A. Jones and L. Marzola, JCAP 1301, 041 (2013)]

Charged lepton Yukawa couplings y kl . [R. Barbieri, P. Creminelli, A. Strumia and N. Tetradis, NPB 575, 61 (2000); A.

Abada, S. Davidson, F. -X. Josse-Michaux, M. Losada and A. Riotto, JCAP 0604, 004 (2006); E. Nardi, Y. Nir, E. Roulet and J. Racker, JHEP

0601, 164 (2006); S. Blanchet and P. Di Bari, JCAP 0703, 018 (2007)]

Lead to three distinct physical phenomena: mixing, oscillation and (de)coherence.

Fully flavor-covariant formalism essential to capture consistently all flavor effects.

Within the semi-classical Boltzmann framework, we promote individual numberdensities to number density matrices (the so-called ’density matrix’ formalism).[G. Sigl and G. Raffelt, Nucl. Phys. B 406, 423 (1993)]

Obtain manifestly flavor-covariant transport equations.[PSBD, P. Millington, A. Pilaftsis and D. Teresi, Nucl. Phys. B 886, 569 (2014)]

Flavor Covariant Formalism

Unitary flavor transformations:

Ll → V ml Lm, L†,l → V l

m L†,m, NR,α → U βα NR,β , N†,αR → Uα

β N†,βR .

The Lagrangian

−LN = h αl LlΦ NR,α + NC

R,α [MN ]αβ NR,β + H.c.

is invariant if h αl → V ml Uα

β h βm , [MN ]αβ → Uα

γ Uβδ [MN ]γδ.

Flavor-covariant quantization, e.g.

Ll(x) =

∫p,s

[(2EL(p))−

12

] i

l

([e−ip·x] j

i[u(p, s)] k

j bk(p, s) +[eip·x] j

i[v(p, s)] k

j d†k (p, s))

Matrix number densities: [nL] ml ∝ 〈b†,m bl〉, [nL] m

l ∝ 〈d†l dm〉, [nN ] βα ∝ 〈a†,β aα〉

Necessary to consider generalized discrete symmetries C,P, T, e.g.

dl = (bl)C ≡ G†,lm(bl)

C with G = V VT.

Number densities transform as (nL)C = (nL)T, (nN)C = (nN)T(nN , nN not independent)

Define CP-“even” and CP-“odd” quantities:

nN =12

(nN + nN), δnN = nN − nN , δnL = nL − nL.

Flavor Covariant Transport Equations

nX(t) ≡ 〈nX (t; ti)〉t = Trρ(t; ti) nX (t; ti)

.

Markovian master equation for number density matrices:

ddt

nX(k, t) ' i〈 [HX0 , nX(k, t)] 〉t −

12

∫ +∞

−∞dt′ 〈 [Hint(t′), [Hint(t), nX(k, t)]] 〉t.

For charged-lepton and heavy-neutrino matrix number densities, we find:

ddt

[nLs1s2 (p, t)] m

l = − i[EL(p), nL

s1s2 (p, t)] m

l+ [CL

s1s2 (p, t)] ml

ddt

[nNr1r2 (k, t)] β

α = − i[EN(k), nN

r1r2 (k, t)] β

α+ [CN

r1r2 (k, t)] βα + Gαλ [C

Nr2r1 (k, t)] λ

µ Gµβ

Collision terms are of the form

[CLs1s2 (p, t)] m

l ⊃ −12

[Fs1s r1r2 (p, q, k, t)] n βl α [Γs s2r2r1 (p, q, k)] m α

n β ,

where F = nΦ nL ⊗(1− nN) − (

1 + nΦ) (

1− nL)⊗ nN are the statistical tensors, andΓ are the rank-4 absorptive rate tensors describing heavy neutrino decays and inversedecays.

Collision Rates for Decay and Inverse Decay

nΦ [nL] kl [γ(LΦ → N)] l β

k α

L

Φ

Nβ Nα

[hc] βk

[hc]lα

↓

Nβ(p, s)

Φ(q)

Lk(k, r)

[hc] βk

nΦ(q)[nLr (k)]

kl Nα(p, s)

Φ(q)

Ll(k, r)

[hc]lα

Collision Rates for 2 ↔ 2 Scattering

nΦ [nL] kl [γ(LΦ → LΦ)] l n

k m

Φ

L

ΦLn Lm

hnβ h α

m

[hc] βk [hc]lα

Nβ Nα

↓

Nβ(p)

Φ(q2)

Ln(k2, r2)

Φ(q1)

Lk(k1, r1)

hnβ [hc] β

knΦ(q1)[n

Lr1(k1)]

kl

Nα(p)

Φ(q1)

Ll(k1, r1)

Φ(q2)

Lm(k2, r2)

[hc]lα h αm

Application to Resonant Leptogenesis

Classical statistics: 1± nX ' 1.

Kinetic equilibrium.

Degenerate spin degrees of freedom.

Small deviation from equilibrium for charged leptons: [nL] ml + [nL] m

l ' 2 nLeq δ

ml .

Unstable particle mixing accounted for by resummed Yukawa couplings:h αl → h αl . [A. Pilaftsis and T. Underwood, Nucl. Phys. B 692, 303 (2004)]

[γNLΦ]

m β

l α ∝ hmαh βl + [hc]m

α[hc] βl

[δγNLΦ]

m β

l α ∝ hmαh βl − [hc]m

α[hc] βl .

Thermal RIS-subtraction to avoid double counting.[E. W. Kolb and S. Wolfram, Nucl. Phys. B 172, 224 (1980)]

Charged-lepton decoherence processes involving the RH charged leptons (otherscan be ignored by virtue of the KMS relation).

Final Rate Equations

HN nγ

zd[ηN ] β

α

dz= − i

nγ

2

[EN , δη

N] β

α+[Re(γN

LΦ)] β

α− 1

2 ηNeq

ηN , Re(γN

LΦ) β

α

HN nγ

zd[δηN ] β

α

dz= − 2 i nγ

[EN , η

N] β

α+ 2 i

[Im(δγN

LΦ)] β

α− i

ηNeq

ηN , Im(δγN

LΦ) β

α

− 12 ηN

eq

δηN , Re(γN

LΦ) β

α

HN nγ

zd[δηL] m

l

dz= − [δγN

LΦ]m

l +[ηN ] α

β

ηNeq

[δγNLΦ]

m β

l α +[δηN ] α

β

2 ηNeq

[γNLΦ]

m β

l α

− 13

δηL, γLΦ

LcΦc + γLΦLΦ

m

l− 2

3[δηL]

nk

([γLΦ

LcΦc ]k m

n l − [γLΦLΦ ]

k mn l

)− 2

3

δηL, γdec

m

l+ [δγback

dec ] ml

Final Rate Equations: Mixing

HN nγ

zd[ηN ] β

α

dz= − i

nγ

2

[EN , δη

N] β

α+[Re(γN

LΦ)] β

α− 1

2 ηNeq

ηN , Re(γN

LΦ) β

α

HN nγ

zd[δηN ] β

α

dz= − 2 i nγ

[EN , η

N] β

α+ 2 i

[Im(δγN

LΦ)] β

α− i

ηNeq

ηN , Im(δγN

LΦ) β

α

− 12 ηN

eq

δηN , Re(γN

LΦ) β

α

HN nγ

zd[δηL] m

l

dz= − [δγN

LΦ]m

l +[ηN ] α

β

ηNeq

[δγNLΦ]

m β

l α +[δηN ] α

β

2 ηNeq

[γNLΦ]

m β

l α

− 13

δηL, γLΦ

LcΦc + γLΦLΦ

m

l− 2

3[δηL]

nk

([γLΦ

LcΦc ]k m

n l − [γLΦLΦ ]

k mn l

)− 2

3

δηL, γdec

m

l+ [δγback

dec ] ml

Final Rate Equations: Oscillation

HN nγ

zd[ηN ] β

α

dz= − i

nγ

2

[EN , δη

N] β

α+[Re(γN

LΦ)] β

α− 1

2 ηNeq

ηN , Re(γN

LΦ) β

α

HN nγ

zd[δηN ] β

α

dz= − 2 i nγ

[EN , η

N] β

α+ 2 i

[Im(δγN

LΦ)] β

α− i

ηNeq

ηN , Im(δγN

LΦ) β

α

− 12 ηN

eq

δηN , Re(γN

LΦ) β

α

HN nγ

zd[δηL] m

l

dz= − [δγN

LΦ]m

l +[ηN ] α

β

ηNeq

[δγNLΦ]

m β

l α +[δηN ] α

β

2 ηNeq

[γNLΦ]

m β

l α

− 13

δηL, γLΦ

LcΦc + γLΦLΦ

m

l− 2

3[δηL]

nk

([γLΦ

LcΦc ]k m

n l − [γLΦLΦ ]

k mn l

)− 2

3

δηL, γdec

m

l+ [δγback

dec ] ml

Notice:

O(h4) in total lepton asymmetry.Hence, different from the ARSmechanism, which is an O(h6) effect.[E. Akhmedov, V. Rubakov, A. Smirnov, PRL 81, 1359 (1998);T. Asaka and M. Shaposhnikov, PLB 620, 17 (2005);B. Shuve and I. Yavin, arXiv:1401.2459 [hep-ph]]

Final Rate Equations: Charged Lepton Decoherence

HN nγ

zd[ηN ] β

α

dz= − i

nγ

2

[EN , δη

N] β

α+[Re(γN

LΦ)] β

α− 1

2 ηNeq

ηN , Re(γN

LΦ) β

α

HN nγ

zd[δηN ] β

α

dz= − 2 i nγ

[EN , η

N] β

α+ 2 i

[Im(δγN

LΦ)] β

α− i

ηNeq

ηN , Im(δγN

LΦ) β

α

− 12 ηN

eq

δηN , Re(γN

LΦ) β

α

HN nγ

zd[δηL] m

l

dz= − [δγN

LΦ]m

l +[ηN ] α

β

ηNeq

[δγNLΦ]

m β

l α +[δηN ] α

β

2 ηNeq

[γNLΦ]

m β

l α

− 13

δηL, γLΦ

LcΦc + γLΦLΦ

m

l− 2

3[δηL]

nk

([γLΦ

LcΦc ]k m

n l − [γLΦLΦ ]

k mn l

)− 2

3

δηL, γdec

m

l+ [δγback

dec ] ml

Captures three distinct physical phenomena: mixing, oscillation and decoherence.

RL from ‘First Principles’

Use Kadanoff-Baym equations for an exact description of quantum transportphenomena.To define number densities, often have to perform a gradient expansion intime-derivatives.Implicitly discards absorptive transitions.We perform a perturbative loopwise truncation of the KB equations using aperturbative approach to non-equilibrium QFT. [P. Millington and A. Pilaftsis, Phys. Rev. D 88, 085009 (2014)]

Confirm that mixing and oscillation are distinct phenomena, and both are ofsimilar magnitude in RL. [PSBD, P. Millington, A. Pilaftsis and D. Teresi, Nucl. Phys. B, to appear (2014)]

Field-Theoretic Transport PhenomenaMixing and Oscillations

0.2 0.5 110-8

10-7

10-6

z = mNêT

dhL

dhL

dhmixL

dhoscL

Combination ”÷L = ”÷Losc + ”÷L

mix yields a factor of 2 enhancementcompared to the isolated contributions for weakly-resonant RL.

Testing TeV-scale Leptogenesis at Energy Frontier

Through detection of a heavy neutrino (Majorana/(pseudo)-Dirac).q

q′

W+

ℓ+

Nℓ+

W− j

j

q

q′

W+

l+

Nl−

W+l+

ν

There are additional t-channel infra-red enhanced contributions which areimportant for LHC. [PSBD, A. Pilaftsis, U. K. Yang, Phys. Rev. Lett. 112, 081801 (2014)]

q

q′W+

γ

ℓ+

ℓ+

N

j

j

q

q′

W+

γ

j

j

W−

ℓ+

N

q

q′q′

γ

j

j

W+

ℓ+

N

q

q′

q′′

γ

j

j

W+ℓ+

N

Discovery of LNV at the LHC would rule out high-scale leptogenesis.[F. Deppisch, J. Harz and M. Hirsch, Phys. Rev. Lett. 112, 221601 (2014)]

Testing TeV-scale Leptogenesis at Intensity Frontier

Observable BP1 BP2 BP3 Exp. Limit

BR(µ→ eγ) 4.5× 10−15 1.9× 10−13 2.3× 10−17 < 5.7× 10−13

BR(τ → µγ) 1.2× 10−17 1.6× 10−18 8.1× 10−22 < 4.4× 10−8

BR(τ → eγ) 4.6× 10−18 5.9× 10−19 3.1× 10−22 < 3.3× 10−8

BR(µ→ 3e) 1.5× 10−16 9.3× 10−15 4.9× 10−18 < 1.0× 10−12

RTiµ→e 2.4× 10−14 2.9× 10−13 2.3× 10−20 < 6.1× 10−13

RAuµ→e 3.1× 10−14 3.2× 10−13 5.0× 10−18 < 7.0× 10−13

RPbµ→e 2.3× 10−14 2.2× 10−13 4.3× 10−18 < 4.6× 10−11

|Ω|eµ 5.8× 10−6 1.8× 10−5 1.6× 10−7 < 7.0× 10−5

〈m〉 [eV] 3.8× 10−3 3.8× 10−3 3.8× 10−3 < (0.11–0.25)

[PSBD, P. Millington, A. Pilaftsis and D. Teresi, Nucl. Phys. B 886, 569 (2014)]

TeV-scale Leptogenesis in Left-Right Seesaw

Common lore: MWR > 18 TeV for successful leptogenesis. [J.-M. Frere, T. Hambye and G. Vertongen,

JHEP 0901, 051 (2009)]

True only in the Minimal LRSM with generic YN . 10−5.5.

In the class of TeV-scale LRSM with large MD elements [PSBD, C.-H. Lee and R. N. Mohapatra, Phys.

Rev. D 88, 093010 (2013)], including flavor effects substantially lowers the leptogenesis boundto MWR & 3 TeV. [PSBD, C.-H. Lee and R. N. Mohapatra, Phys. Rev. D 90, 095012 (2014)]

10-4 10-3 10-2 0.1 110-11

10-10

10-9

10-8

10-7

Y

|ηΔL(zc)|

MWR= 3 TeV

MWR= 4 TeV

MWR= 6 TeV

MWR= 8 TeV

MWR= 10 TeV

|ηobsΔL | = 2.47× 10-8

2 4 6 8 1010-12

10-11

10-10

10-9

10-8

10-7

10-6

MWR(TeV)

|ηΔL(zc)|

δM = 15 MeV

δM = 1 MeV

δM = 100MeV

δM = 1 GeV

δM = 10 GeV

|ηobsΔL | = 2.47× 10-8

Possible correlations of the lepton asymmetry with LFV is an interesting probe ofTeV-scale leptogenesis in these models.

Conclusion

Leptogenesis provides an attractive link between two seemingly disparate piecesof evidence for BSM physics, namely, neutrino mass and baryon asymmetry.

Resonant Leptogenesis provides a way to test this idea in laboratory experiments.

Flavor effects play a crucial role in obtaining a realiable estimate of the leptonasymmetry.

A fully flavor-covariant formalism essential to describe consistently all flavoreffects.

Provides a complete and unified description of Resonant Leptogenesis, capturingthree physically distinct phenomena:

resonant mixing between heavy neutrinos,coherent oscillations between heavy-neutrino flavors,quantum decoherence effects in the charged-lepton sector.

Mixing and oscillation are both important and should be taken into account in RLcalculations.

TeV-scale leptogenesis leads to testable effects at both Energy and Intensityfrontiers.

Backup slides

Minimal Model of Resonant τ -Genesis

Consider a minimal model of Resonant τ -Genesis. [A. Pilaftsis, Phys. Rev. Lett. 95, 081602 (2005)]

Yukawa couplings break the O(3)-symmetry to (almost) U(1)Le+Lµ × U(1)Lτ :

h =

0 ae−iπ/4 aeiπ/4

0 be−iπ/4 beiπ/4

0 0 0

+δh, where δh =

εe 0 0εµ 0 0

ετ κ1e−i(π4 −γ1) κ2ei(π4 −γ2)

From type-I seesaw formula: Mν ' − v2

2 h M−1N hT = 0 in the limit δh→ 0.

To satisfy neutrino oscillation data, require

a2 =2mN

v2κN

(Mν,11 −

M2ν,13

Mν,33

), b2 =

2mN

v2κN

(Mν,22 −

M2ν,23

Mν,33

),

ε2e =

2mN

v2

M2ν,13

Mν,33, ε2

µ =2mN

v2

M2ν,23

Mν,33, ε2

τ =2mN

v2 Mν,33 .

where κN ≡ 18π2 ln

(µXmN

) [2κ1κ2 sin(γ1 + γ2) + i(κ2

2 − κ21)].

Input model parameters: mN , κ1, κ2, γ1, γ2.

Benchmark Points

Parameters BP1 BP2 BP3

mN 120 GeV 400 GeV 5 TeVγ1 π/4 π/3 3π/8γ2 0 0 π/2κ1 4× 10−5 2.4× 10−5 2× 10−4

κ2 2× 10−4 6× 10−5 2× 10−5

a (7.41− 5.54 i)× 10−4 (4.93− 2.32 i)× 10−3 (4.67 + 4.33 i)× 10−3

b (1.19− 0.89 i)× 10−3 (8.04− 3.79 i)× 10−3 (7.53 + 6.97 i)× 10−3

εe 3.31× 10−8 5.73× 10−8 2.14× 10−7

εµ 2.33× 10−7 4.3× 10−7 1.5× 10−6

ετ 3.5× 10−7 6.39× 10−7 2.26× 10−6

Observable BP1 BP2 BP3 Exp. Limit

BR(µ→ eγ) 4.5× 10−15 1.9× 10−13 2.3× 10−17 < 5.7× 10−13

BR(τ → µγ) 1.2× 10−17 1.6× 10−18 8.1× 10−22 < 4.4× 10−8

BR(τ → eγ) 4.6× 10−18 5.9× 10−19 3.1× 10−22 < 3.3× 10−8

BR(µ→ 3e) 1.5× 10−16 9.3× 10−15 4.9× 10−18 < 1.0× 10−12

RTiµ→e 2.4× 10−14 2.9× 10−13 2.3× 10−20 < 6.1× 10−13

RAuµ→e 3.1× 10−14 3.2× 10−13 5.0× 10−18 < 7.0× 10−13

RPbµ→e 2.3× 10−14 2.2× 10−13 4.3× 10−18 < 4.6× 10−11

|Ω|eµ 5.8× 10−6 1.8× 10−5 1.6× 10−7 < 7.0× 10−5

〈m〉 [eV] 3.8× 10−3 3.8× 10−3 3.8× 10−3 < (0.11–0.25)

Lepton Asymmetry for BP 2

-∆ΗL

+∆ΗL

-∆ΗobsL

mN = 400 GeV

zc0.2 1 10 2010-9

10-8

10-7

10-6

10-5

z = mNT

±∆Η

L

total, ΗinN=0, ∆Ηin

L=I


L=0

total, ΗinN=Ηeq

N , ∆ΗinL=0

N diag., ΗinN=Ηeq

N , ∆ΗinL=0

N diag., analytic

L diag., ΗinN=Ηeq

N , ∆ΗinL=0

N, L diag., ΗinN=Ηeq

N , ∆ΗinL=0

BP 2: Lepton Flavor Content

-dhobsL

mN = 400 GeV

zc0.2 1 10 2010-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

z = mNT

¨dhlmL

¨ -dhtt

L

+dhmm

L

-dheeL

¨dhtm

L ¨¨dh

teL ¨

¨dhmeL ¨

BP 2: Heavy Neutrino Flavor Content

mN = 400 GeV

zc0.2 1 10 2010-14

10-12

10-10

10-8

10-6

10-4

10-2

100

¨h abNh eqN

-d

ab¨

h11N heq

N - 1

h22N heq

N - 1

h33N heq

N - 1

¨h12N heq

N ¨¨h13

N heqN ¨

¨h23N heq

N ¨

BP 1

-∆ΗL

+∆ΗL

-∆ΗobsL

mN = 120 GeV

zc0.2 1 10 2010-9

10-8

10-7

10-6

10-5

10-4

z = mNT

±∆Η

L


L=I


L=0

total, ΗinN=Ηeq

N , ∆ΗinL=0

N diag., ΗinN=Ηeq

N , ∆ΗinL=0

N diag., analytic

L diag., ΗinN=Ηeq

N , ∆ΗinL=0


N , ∆ΗinL=0

BP 3

-∆ΗL

+∆ΗL

-∆ΗobsL

0.2 1 10 2010-8

10-7

10-6

10-5

10-4

10-3

z = mNT

±∆Η

L

mN = 5 TeV total, ΗinN=0, ∆Ηin

L=I


L=0

total, ΗinN=Ηeq

N , ∆ΗinL=0

N diag., ΗinN=Ηeq

N , ∆ΗinL=0

N diag., analytic

L diag., ΗinN=Ηeq

N , ∆ΗinL=0


N , ∆ΗinL=0

tev-scale leptogenesis scenarios · 12/11/2014 · sphaleron interactions. [s. yu. khlebnikov, m....

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