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 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) (arXiv: [hep-ph])

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 1 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

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 2 Overview of Baryogenesis Basic conditions for baryogenesis ( Sakharov, JETP Lett. 5, ): 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 Yukawa  L-violation from N R   L  via the Yukawa 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 International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 3 Highlights of thermal leptogenesis (standard version) Leptogenesis ( Fukugita et al., PLB174, ) creates a baryon asymmetry by first generating an excess in lepton:

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 4 Aims and Motivations The usual leptogenesis scenario is an elegant solution for the baryogenesis problem and the interplay between asymmetry creationlight neutrino masses VS 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 10 9 to GeV ( Davidson et al. 02, Buchmüller et al. 02 ).

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 5 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 momentelectric 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 . electromagnetic dipole moment When written in terms of chiral fields, the most general electromagnetic dipole moment (EMDM) coupling of N R to L is given by

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 6 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 P R = (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 M k is the mass of the k th heavy neutrinos and

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 7 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 N k : vertex correctionself-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.

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 8 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. PRL , 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 electroweak 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:

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 9 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)(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 ):

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 10 Connection to light neutrino masses type I seesaw Recall that in standard leptogenesis with Yukawa couplings, light neutrino masses can be generated by the 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 masscontribution to light neutrino Majorana mass

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 11 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.

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 12 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: YukawaElectromagnetic

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 13 The N 1 -leptogenesis parameter space Consider a hierarchical RH neutrino spectrum with M 1 < M 2 < M 3. In this case, the asymmetry produced will be predominantly due to the decay of N 1, 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 N 2,3 decays out-of-equilibrium, there will be some L-violating scattering processes involving N 1 that are in equilibrium. As a result, any excess L created from N 2,3 would be washed out. dilution ( d )  the dilution ( d ) due to the conversion from excess  L  to  B  from sphalerons as well as expansion of the Universe size of   the size of  (the CP asymmetry parameter) efficiency factor (  )  the interplay between N R 's production rate and ΔL ≠ 0 scattering processes (i.e. washout)  efficiency factor (  ) for L production

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 14 The N 1 -leptogenesis parameter space (cont.) Combining the above three factors, the produced baryon asymmetry is given by:  B  d   = O(10  10 ) d d 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 M 1  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 ):

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 15 The N 1 -leptogenesis parameter space (cont.)   efficiency factor: from studying the interplay between different non-equilibrium processes (N 1 production vs. washout) using a network of Boltzmann equations. Combining the above three factors, the produced baryon asymmetry is given by:  (Buchmüller, Di Bari, Plümacher, 02) : effective neutrino mass It is related to the decay parameter and is a measure of how strongly N 1 couples to the thermal plasma.  B  d   = O(10  10 )

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 15 The N 1 -leptogenesis parameter space (cont.)   efficiency factor: from studying the interplay between different non-equilibrium processes (N 1 production vs. washout) using a network of Boltzmann equations. Combining the above three factors, the produced baryon asymmetry is given by:  (Buchmüller, Di Bari, Plümacher, 02) weak washout strong washout It is related to the decay parameter and is a measure of how strongly N 1 couples to the thermal plasma. : effective neutrino mass  max  0.18  B  d   = O(10  10 )

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 15 The N 1 -leptogenesis parameter space (cont.)   efficiency factor: from studying the interplay between different non-equilibrium processes (N 1 production vs. washout) using a network of Boltzmann equations. Combining the above three factors, the produced baryon asymmetry is given by:  (Buchmüller, Di Bari, Plümacher, 02) region favored by light neutrino oscillation data typically,   O(10  2 ) Therefore, with d,   O(10  2 ), successful leptogenesis requires |  |  O(10  6 )  B  d   = O(10  10 )

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 16 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(10  2 eV). the scale of M 1 must be of order greater than 10 9 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

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 17 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 K 1  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:

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 18 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(10  11  B ), such induced moments are too small to be of any concerns.

International workshop on dark matter, dark energy and matter-antimatter asymmetry, Nov 2009, S. Law (CYCU) 19 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. electromagnetic 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 electromagnetic interactions between the light and heavy neutrinos: dim-5: SM Higgs 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 Higgs. Thus, the connection to light neutrino mass turns out to be inevitable. dim-6:

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