International workshop on dark matter, dark energy and matter- antimatter asymmetry National Tsing Hua University ( 國立清華大學 ) 20–21 November 2009 Electromagnetic

International workshop on dark matter, dark energy and matter-antimatter asymmetry

National Tsing Hua University (國立清華大學 )

20–21 November 2009

Electromagnetic LeptogenesisElectromagnetic Leptogenesis

Sandy S. C. Law (羅上智 )

Chung Yuan Christian University (中原大學 )

In collaboration with:

Nicole Bell (University of Melbourne) & Boris Kayser (Fermilab)

Reference: N. F. Bell et al. Phys. Rev. D78 (2008) 085024 (arXiv:0806.3307 [hep-ph])

International workshop on dark matter, dark energy and matter-antimatter asymmetry, 20-21 Nov 2009, S. Law (CYCU)

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Key problem: Baryon asymmetry of the Universe

Our Universe

matter antimatter

In our universe, matter is more dominant than antimatter.

Studying the acoustic peaks in the CMB spectrum (WMAP collaboration) gives rise to the following baryon-to-photon ratio (assuming Friedmann Universe):

The Standard Model (SM) actually has all the ingredients it needs to create a baryon asymmetry BUT the amount which can be produced is too small new physics required?

Statistical fluctuation? ( too small)

initial conditions? ( unlikely, because of inflation)

large scale separation? ( restricted by causality)

need Baryogenesis


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Overview of Baryogenesis

Basic conditions for baryogenesis (Sakharov, JETP Lett. 5, 24 1967):

baryon number (B) violation

C, CP violation

thermal non-equilibrium

Some models of baryogenesis:

Electroweak Baryogenesis (phase transitions)

GUT Baryogenesis (heavy particle decays)

Baryogenesis via Leptogenesis (heavy lepton decays)

Affleck-Dine (connection to inflation)

others: spontaneous baryogenesis, baryogenesis from black hole evaporation, models with SUSY and extra-dimensions etc…

requires adding (at least two) heavy RH Majorana neutrinos to the SM

Step 1: a lepton asymmetry is created when the RH neutrinos decay out-of-equilibrium in the early universe

L-violation from N R L via the YukawaYukawa coupling

CP-violation at loops level:

thermal non-equilibrium occurs when

Step 2: L asymmetry is then partially converted to B 0.35 L by the non-perturbative electroweak sphalerons

Type-I seesaw to explain the tiny mass of ordinary neutrinos


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Highlights of thermal leptogenesis (standard version)

Leptogenesis (Fukugita et al., PLB174, 45 1986) creates a baryon asymmetry by first generating an excess in lepton:


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Aims and Motivations

The usual leptogenesis scenario is an elegant solution for the baryogenesis problem and the interplay between

asymmetry creation light neutrino massesVS

implies that

In this work, we wish to consider a possible new channel to generate lepton number where

the model has the same particle content as the minimally extended SM of standard leptogenesis

the decay of RH neutrinos still plays a central role

and in doing so, investigate whether such new mechanism is a viable alternative and whether it can significantly alter the standard leptogenesis picture.

High-energy CP violation may be related to the low-energy sector

the leptogenesis scale to be about 109 to 1013 GeV (Davidson et al. 02,

Buchmüller et al. 02).


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Electromagnetic dipole moment couplings

Beside the obvious Yukawa coupling: that can provide a link between the light and heavy neutrinos, another possibility is through dim-5 effective transition moment operators of the form:

magnetic dipole moment electric dipole moment

where , d are dimensionless couplings, F is the electromagnetic field strength

tensor and is the cutoff scale of our effective theory. We assume that these operators are generated by some unspecified new physics at energy beyond .

When written in terms of chiral fields, the most general electromagnetic dipole electromagnetic dipole momentmoment (EMDM) coupling of NR to L is given by


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An EMDM toy model

For better illustration and comparison with standard leptogenesis, we first demonstrate the viability of the dim-5 EMDM interactions between light and heavy neutrinos in generating a lepton asymmetry by including in the Lagrangian:

where PR = (1 + 5) / 2, j = e, , and k = 1, 2, 3.

Through this dim-5 term, the heavy RH neutrinos can now decay into a light neutrino and a photon in the early universe

This decay is L-violating and has a reaction rate given by

where Mk is the mass of the k th heavy neutrinos and


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An EMDM toy model (cont.)

Analogous to the standard version, we expect the leading contribution to the CP asymmetry to come from the interference between the tree-level process and the 1-loop corrections with on-shell intermediate states:

To ascertain whether leptogenesis is possible, the key quantity of interest is the CP asymmetry in the decays of Nk :

vertex correction self-energy correction

Through explicit computation, one finds that the interference is given by

Since the complex matrix is arbitrary, this expression is in general nonzero, showing that leptogenesis is possible via the EMDM term.


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A more realistic EMDM leptogenesis model

To construct an effective theory that is realistic, we only employ EMDM operators that are SM gauge invariant. The most economical of which are of dim-6 (Bell et al.

PRL95 151802, 2005):

where is the SM Higgs doublet, B and W are the U(1)Y and SU(2)L field

tensors, and i’s are the SU(2) generators. is assumed to be beyond the electro

weak scale. After spontaneous symmetry breaking, these operators will become the transition moments of N and .

The previous setup is simple and can demonstrate the viability of leptogenesis through EMDM like interactions, it is however unrealistic and incompatible with the SM.

In the early universe, however, such term can induce a 3-body decay process for the heavy RH neutrino:


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A more realistic EMDM leptogenesis model (cont.)

For simplicity, we just consider one of the decay channels:

It is not hard to show that a nonzero lepton asymmetry can be produced when we consider the interference between this tree-level process and, for example, these high-order graphs:

(k m)

The expressions of the 3-body decay rate and the CP asymmetry have a similar form to those derived previously (taking k =1 and summing over j):


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Connection to light neutrino masses

Recall that in standard leptogenesis with Yukawa couplings, light neutrino masses can be generated by the type I seesaw type I seesaw mechanism.

a realisation of the seesaw mass term

where coupling h also controls leptogenesis scale.

In electromagnetic leptogenesis, although the Yukawa term may be switched off (hence, no neutrino mass at the lowest order), radiative corrections involving the EMDM operators can generically induce neutrino mass terms (Davidson et al. 05, Bell

et al. 05, 06).

contribution to neutrino Dirac mass contribution to light neutrino Majorana mass


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Connection to light neutrino masses (cont.)

Without knowing the UV completion of the theory, there is no model independent way of calculating the exact size of these radiative contributions. However, using naïve dimensional analysis, an estimate of them can be obtained.

For the induced Dirac mass term:

Type I seesaw

For the induced light Majorana mass term:

These expressions signify that the typical interplay between asymmetry generation and neutrino mass as in standard leptogenesis is again at play here but via coupling instead.

c.f.


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Standard vs. Electromagnetic leptogenesis

It is evident that the leptogenesis model based on EMDM operators mentioned results in expressions that are largely similar to that of standard case where Yukawa couplings are involved.

Setting k = 1 and summing over j, we present the comparison between the two:

YukawaYukawa ElectromagneticElectromagnetic


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The N1-leptogenesis parameter space

Consider a hierarchical RH neutrino spectrum with M1 < M2 < M3 . In this case, the

asymmetry produced will be predominantly due to the decay of N1, the lightest RH neutrinos.

Even in this simplified picture, to see if the correct amount of baryon asymmetry can be produced, one needs some quantitative understanding of:

This is because when N2,3 decays out-of-equilibrium, there will be some L-violating scattering processes involving N1 that are in equilibrium. As a result, any excess L created from N2,3 would be washed out.

the dilution (dilution (dd)) due to the conversion from excess L to B from sphalerons as well as expansion of the Universe

the size of size of (the CP asymmetry parameter)

the interplay between NR's production rate and ΔL ≠ 0 scattering

processes (i.e. washout) efficiency factor (efficiency factor ()) for L production


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The N1-leptogenesis parameter space (cont.)

Combining the above three factors, the produced baryon asymmetry is given by:

B d = O(10 10)

dd dilution factor: from analysis of photons production rate, relativitistic degrees of freedom and electroweak sphalerons O(10 2) for most scenarios.

raw CP asymmetry: from explicit calculations of the loop diagrams and interference terms. It can be highly dependent on the neutrino mass model employed.

For M1 O(10 10 GeV), then O(10

6).

A useful ballpark estimate of the maximum CP asymmetry (assuming hierarchical light neutrino spectrum) is given by (Davidson & Ibarra, 02):


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efficiency factor: from studying the interplay between different non-equilibrium processes (N1 production vs. washout) using a network of Boltzmann equations.


(Buchmüller, Di Bari, Plümacher, 02)

: effective neutrino mass

It is related to the decay parameter

and is a measure of how strongly N1 couples to the thermal plasma.

B d = O(10 10)


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weak washout

strong washout

It is related to the decay parameter

and is a measure of how strongly N1 couples to the thermal plasma.

: effective neutrino massmax 0.18

B d = O(10 10)


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region favored by light neutrino oscillation datatypically, O(10 2)

Therefore, with d, O(10 2), successful leptogenesis requires

|| O(10 6)

B d = O(10 10)


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The electromagnetic leptogenesis scenario

Given the similarity with the standard scenario, we take || O(10 6) as a starting condition for sufficient CP asymmetry leading to successful baryogenesis.

If the EMDM operator dominates the creation of the resulting lepton asymmetry,

one can have an order-of-magnitude estimate of :

where we’ve ignored the matrix structure of and used m = O(102 eV).

the scale of M1 must be of order greater than 109 GeV, akin to standard

leptogenesis

the presence of factor implies only a mild RH neutrino mass

hierarchy would be acceptable

From this, it is clear that


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The electromagnetic leptogenesis scenario (cont.)

For example, suppose we adopt a moderate hierarchy:

and take EMDM couplings of order:

It is then clear that a sufficient CP asymmetry of || O(10 6) can be obtained.

It will lead to a decay parameter of about K1 0.3

i.e. and washout is neither very strong nor weak.

So qualitatively speaking, this setup can achieve successful baryogenesis.

With these parameters, the contributions to the light neutrino Majorana masses are given by:

which are compatible with the oscillation data.

Furthermore, if we set the lightest RH neutrino to be:


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Light neutrino transition dipole moments

Finally, we note that the EMDM operators discussed can induce effective dipole moment interactions between two ordinary light neutrinos via

two-loop diagrams (dominant contribution: ~ 1/)

e.g.

mixing between light and heavy neutrinos (sub-dominant contribution: ~1/2)

Given that the current experimental limits (Beacom et al. 99, Raffelt 99, Borexino, Texono

collaborations) which are of O(1011B), such induced moments are too small to be of

any concerns.


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Summary and Conclusions

Leptogenesis is an elegant solution to the baryogenesis problem where the matter-antimatter asymmetry originates from the L- and CP-violating decays of the postulated heavy RH neutrinos.

Our interests here is to investigate an alternative type of L- and CP-violating decay for the RH neutrinos other than the typical Yukawa couplings. In particular, we’ve concentrated on the electromagneticelectromagnetic interactions between the light and heavy neutrinos:

dim-5:

We aim to construct a model using only the particle content of the minimally extended SM. As a result, the gauge invariant dim-6 EMDM operator must couple to the SM HiggsSM Higgs. Thus, the connection to light neutrino mass turns out to be inevitable.

dim-6:


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Summary and Conclusions (cont.)

Because the EMDM operators can contribute to the light neutrino masses via radiative corrections, the interplay between neutrino mass and asymmetry generation as seen in the standard leptogenesis remains.

Overall, we can conclude that

successful leptogenesis is possible via the L-violating EMDM operators discussed; providing an additional channel for dynamical generation of the matter-antimatter asymmetry of the Universe;

the electromagnetic leptogenesis scenario is largely similar to that of the standard Yukawa-based mechanism, and that the RH neutrino must be of scale beyond 1010 GeV;

the fact that the EMDM picture also have strong connection to the light neutrino sector, implies that the CP-violating couplings in leptogenesis may manifest itself in the low-energy sector, which further motivates the studies of CP violation in light neutrino oscillations.

Documents

International workshop on dark matter, dark energy and matter- antimatter asymmetry National Tsing Hua University ( 國立清華大學 ) 20–21 November 2009 Electromagnetic