Electromagnetic Leptogenesis at TeV scale. Sudhanwa Patra

Transcription

1 Electromagnetic Leptogenesis at TeV scale Sudhanwa Patra Physical Research Laboratory, INDIA Collaboration with Debjyoti Choudhury, Namit Mahajan, Utpal Sarkar 25th Feb, 2011 Sudhanwa Patra, NuHorizon-IV, HRI p. 1/22

2 Baryogenesis via Leptogenesis The key idea of Baryogenesis via Leptogenesis is to First create an excess of L, and then turn it into an excess of B Creating an excess of L: requires L and CP violating processes that will go out of thermal equilibrium at some stage during the evolution of the Universe (Sakharov s conditions revisited). L and CP violating interactions. Extensions to the SM. out of thermal equilibrium condition. fast expansion rate H. In standard leptogenesis scenario, CP and L violating interactions originate from the Yukawa terms in the Lagrangian: L = l L hφn R 1 2 Nc R M N R Yukawa term connects the light and heavy neutrino. Majorana mass term violates L-number. Complex Yukawa coupling (h) is the source of CP-violation and Majorana mass terms violate lepton number. The asymmetry in L generated can be partially converted into an asymmetry in B via electroweak sphaleron interactions. Sudhanwa Patra, NuHorizon-IV, HRI p. 2/22

3 Some Fundamental issues in Leptogenesis The seesaw mechanism and the associated mechanism of leptogenesis are very attractive means to explain the origin of the small neutrino masses and the baryon asymmetry of the universe. In standard leptogenesis, there exists heavy right handed neutrino of mass close to GUT scale10 15 GeV and its out-of-equilibrium decay creates a net lepton asymmetry which, subsequently, gets converted into the observed baryon asymmetry via the sphaleron interactions. At the same time, the inclusion of the right handed (Majorana) fields can explain the observed smallness of light neutrinos through the so-called seesaw mechanism Although the aforementioned scheme is theoretically very attractive, it suffers from the lack of direct detectability, e.g. at high-energy colliders, such as the LHC or ILC, or in any other foreseeable experiment. A phenomenologically interesting solution to this problem may be obtained within the framework of resonant leptogenesis (RL) where one can lower down the scale upto 100 GeV. Characterized by the presence of two (or more) nearly degenerate heavy Majorana neutrinos, in such scenarios the corrections to the self-energies play a pivotal role in determining the lepton asymmetry. Indeed, if the mass difference be comparable to their decay widths, the resonant enhancement could render asymmetries to be as large as O(1). Sudhanwa Patra, NuHorizon-IV, HRI p. 3/22

4 Thermal Leptogenesis First studied in Fukugita and Yanagida 86. They have calculated the lepton asymmetry as ε 1 3 [ M 1 Im M T D M ] νm D [ ] 16π v 2 M T D M D For Hierarchal case M 1 << M 2 << M 3, GeV M GeV Barbieri 00, Davidson-Ibarra 02 In case of Resonant Leptogenesis,N i spectrum is Quasi-degenerate (M 1 M 2 << M 3 ) M GeV Pascos, Sarkar 96; Pilaftsis 98, Pilaftsis etal 04.. Absolute bound on M 1 > 2.6 GeV Hambye etal 08; 03. The same analysis can be done fermion triplet at TeV scale. One is more careful in this case since gauge scattering of fermion triplet can significantly alter the scenario of leptogenesis Recently a phenomenologically interesting proposal has been given by Kayser et al, which is named as Electromagnetic leptogenesis Sudhanwa Patra, NuHorizon-IV, HRI p. 4/22

5 Electromagnetic leptogenesis Recently a very interesting possibility of electromagnetic leptogenesis has been proposed, wherein the source of CP violation has been identified with the electromagnetic dipole moment(s) of the neutrino(s) Kayser et al, PRD 08 There are dipole operator between light(ν)-light(ν) neutrinos, heavy(n)-heavy(n) neutrinos and light(ν)-heavy(n) neutrinos. We are interested in the dipole moment coupling of the last type. The general form of such dipole couplings is given by ν Lj λ jk σ αβ N Rk F αβ, where F αβ denotes the U(1) field strength tensor. The aforementioned dimension-five operators are, presumably, generated by some new physics operative beyond the electroweak scale. WithCP -violation being encoded in the structure of the dipole moments, the decays of heavier neutrinos to lighter ones and a photon, can, in principle, lead to a lepton asymmetry in the universe. Although the proposal is a very interesting one, so far it has not been incorporated in any realistic model. A guiding principle in our quest is that the new physics should be at the TeV scale so as to render the model testable at the LHC or future Linear Colliders. Sudhanwa Patra, NuHorizon-IV, HRI p. 5/22

6 A Realistic Model Retaining the gauge symmetry of the SM, the extra fields are three right-handed singlet fieldsn ir and a singly charged vector-like fermione. a singly charged scalar (H + ) and a pair of Higgs doublets (Σ, D). Fields, their quantum number under the SM gauge group SU(3) C SU(2) L U(1) Y and discrete symmetry Z 2. Field SU(3) C SU(2) L U(1) Y Z 2 Fermions Q L (u,d) T L (3, 2, 1/6) + u R (3, 1, 2/3) + d R (3, 1, -1/3) + l L (ν, e) T L (1, 2, -1/2) + e R (1, 1, -1) + E L (1, 1, -1) - E R (1, 1, -1) - N R (1, 1, 0) - Scalars Φ (1, 2, +1/2) + Σ (1, 2, +1/2) - D (1, 2, +1/2) - H + (1, 1, +1) + Sudhanwa Patra, NuHorizon-IV, HRI p. 6/22

7 At this stage, we are faced with a problem generic to electromagnetic leptogenesis. νν andn N are allowed but both the Dirac mass Nl and the magnetic moment Nl are forbidden along with the term N lφ. But the effective N l coupling has to be allowed (so as to allow the mandatory N ν +). This will be taken care of by introducing a softz 2 symmetry breaking term. After the soft breaking of the discrete symmetry, the required interactions will be allowed, which will generate the neutrino mass, magnetic moment and resonant leptogenesis successfully. Also, NlΦ needs to be highly suppressed on two counts, to ensure that the light neutrino mass, accruing from the seesaw mechanism, is not too large and to prevent then from decaying dominantly tol+φ. While this could, nominally, be ensured by invoking some symmetry wherein the photon and the Φ transform differently, such an assignment would adversely impact the phenomenology of the charged particles. We rather choose to introduce a discretez 2 symmetry. All the mass scales has been restricted around 100 GeV-10 TeV, so these extra particles also have masses of TeV range. H +,Σ,D don t take any vev at this level.. Sudhanwa Patra, NuHorizon-IV, HRI p. 7/22

8 Yukawa terms and scalar potential While the Yukawa Lagrangian for the quarks remains unchanged from the SM, that for the leptonic sector can be written as L Yuk [ y H N R E L H + +y Σ l L ΣE R +y D l L DE R ] + h Σ l L ΣNR +h D l L DNR +y e l L Φe R +h.c. + [ ] 1 2 (N R) C M N N R M E E R E L +h.c. (1) The scalar potential can be parametrized as V(Φ,Σ,D,H + ) = µ 2 Φ Φ 2 +m 2 2 Σ 2 +m 2 3 D 2 +m 2 h H 2 +λ 1 Φ 4 +λ 2 Σ 4 + λ 3 D 4 +λ h H 4 +λ ΦH (Φ Φ) H 2 +λ DH (D D) H 2 + λ ΣH (Σ Σ) H 2 +λ DΣH (D Σ) H 2 + λ ΦΣ 2 [ ] (Φ Σ) 2 +h.c. + λ DΦ (D Σ)(Φ Φ)+f 1 (Φ Φ)(D D)+f 2 (Φ Φ)(Σ Σ) + f 3 Φ D 2 +f 4 Φ Σ 2 +f 5 (D D)(Σ Σ)+f 6 D Σ 2 + [ µ s Σ D(H + ) +h.c. ]. (2) Sudhanwa Patra, NuHorizon-IV, HRI p. 8/22

9 Adding a soft-term These termsn l+ andnν mass term can be generated only when thez 2 is broken. Rather than break it spontaneously, and thereby risk domain walls, we choose to break it explicitly, but only through a soft term. We introduce the relevant soft-term as V soft = µ 2 soft Φ D +... (3) without going into the origin this terms. This has the advantage of obviating any domain wall problem while eliminating any qualitative changes to the rest of the phenomenology. The scale of the soft symmetry breakingµ soft needs to be significantly lower than the electroweak symmetry breaking scale. This naturally leads to a large gradation in the vacuum expectation values, namely D, Σ Φ. This will then give us the Dirac mass term Nl and the magnetic moment term Nl, as required for the present model. This will also generate the unwanted term NlΦ due to the mixing of D and Σ with Φ, but this interaction will be suppressed by a factor of D / Φ, which if O(10 3 ), is consistent with the light neutrino mass. Sudhanwa Patra, NuHorizon-IV, HRI p. 9/22

10 Neutrinos Mass There is no Dirac neutrino mass at tree level. once the soft-breaking term is included, the field D may receive a non-zero vev which is 0.1 GeV. This, in turn, gives a Dirac mass to the neutrinos viz. M D = h D D = h D v D. (4) This, together with the Majorana mass termm N for the heavy right-chirality fields, gives rise to a light neutrino Majorana mass via type-i seesaw mechanism, viz. m ν = M D M 1 N M D (5) For the choice of parameters we are interested, M D 10 3 h D v 10 4 GeV, for Φ = v 100 GeV and h D 0.001, This gives the correct magnitude of the light neutrino masses m ν GeV 0.01 ev. The hierarchy of masses could be obtained because of the different values of the elements of the matricesm N andh D. Sudhanwa Patra, NuHorizon-IV, HRI p. 10/22

11 Estimation of EMDM coupling (λ) 5-Dimensional EMDM operator: L EM = λ jk ν j σ αβ P R N k F αβ +h.c. Feynman diagrams which estimate the effective EMDM coupling strength between light neutrino ν and heavy neutrinos N are: D D N k H + H + E Σ ν j N k H + E Σ Σ ν j (a) (b) D H + Σ N k E ν j (c) Sudhanwa Patra, NuHorizon-IV, HRI p. 11/22

12 Bound on EMDM coupling (λ) The effective dimension-5 coupling constant λ can thus be expressed in a simple form under the assumption of almost equal mass for the particles in the loop (M E M H M Σ M eq ) as: λ = y Σ y H µ s v D 64π 2 M 3 eq For a representative reasonable sets of parameters: M N TeV,M eq TeV, y Σ = y H 1,µ s 100 GeV andv D = 0.1 GeV, the EMDM coupling strength which is responsible for electromagnetic leptogenesis is found to beλ GeV 1.. The masses ofσandd is greater than than the mass of RH neutrinom N, so thatn R can not decay intoν +Dorν +Σ.. For successful leptogenesis, the size of the EMDM coupling should be constrained by the out of equilibrium condition.. Γ = λ λ 4π M3 N < H = 1.7 g MN 2 M Pl From this the upper bound on the EMDM couplings reads as λ 2 < (M N /TeV) Sudhanwa Patra, NuHorizon-IV, HRI p. 12/22

13 CP-asymmetry for EM leptogenesis We would like to check the viability of lepton asymmetry generation for such setup. Hence, it is sensible to calculate the CP asymmetry parameter for this decay: ε k,j Γ (N k +ν j ) Γ (Nk + ν j ) Γ (Nk +ν j ) +Γ (Nk + ν j ) The lowest order contribution to decay rate is Γ(N 1 ν) = (λ λ) 11 4π M 3 1 Interference of the effective tree level and one loop diagrams required for this calculation. N k N k N m ν j ν n ν j Sudhanwa Patra, NuHorizon-IV, HRI p. 13/22

14 Baryon asymmetry via EM Leptogenesis The CP-asymmetry is ε i = 1 (λ λ) ii (λ λ) mm m i Im[ (λ λ) 2 im The CP-asymmetry is non-zero only if the EMDM coupling matrix λ is complex. ] (M 2 m M2 i )M iγ m (M 2 m M2 i )2 +M 2 i Γ2 m the intermediate states of the loop diagrams go on-shell. For resonant condition where M 2 M 1 Γ 1 /2 we found maximum CP-asymmetry, i.e, ε 1. We are interested the case where M 2 M 1 >> Γ 1 /2. For this ε 1 = 1 2π(λ λ) 11 M 2 m m 1 Im [ ] (λ λ) 2 1m R where R M 1 M 1 M 2. One need mass splitting of M 1 M to account for ε 10 5 for successful leptogenesis. This lepton asymmetry will get converted into baryon asymmetry via Sphaleron transition. Sudhanwa Patra, NuHorizon-IV, HRI p. 14/22

15 Evolution of lepton asymmetry parameter The Boltzmann equations relevant in this model are dy N1 dz dy B L dz [ ] = {D(z)+S(z)} Y N1 Y eq N (6) 1 [ = ǫ N1 D(z) Y N1 Y eq N 1 ] W(z)Y B L (7) There are four classes of processes which contribute to the different terms of the equations: decays, inverse decays, L = 1 scatterings and L = 2 processes mediated can be written as by heavy neutrinos YNeq K 0.1 Y N K 0.01 K z Sudhanwa Patra, NuHorizon-IV, HRI p. 15/22

16 Numerical Estimation of Y B The Boltzmann equations are numerically solved to give the present baryon asymmetry of the Universe 1 Y B Y N Y B Y eq Y N z Here we have plotted Y B vs z. One can see that the final baryon asymmetry found to be consistent with the WMAP data. Sudhanwa Patra, NuHorizon-IV, HRI p. 16/22

17 Magnetic Moment of the heavy RH neutrinos The expression for transition magnetic moment for heavy neutrinos H H N k E Nj c N k E c Nj c (a) (b) E c E N k H Nj c N k H Nj c (c) (d) µ Njk = M [ 64π 2 (Y H ) km (Y H ) mj ] [ I(MH 2,M2,ME 2 ) I(M2 E,M2,MH 2 )] Such large magnetic moments can enhance the production cross section of TeV scale right-handed neutrinos though the Drell-Yan process,e + e, Z N j N k (j k), Sudhanwa Patra, NuHorizon-IV, HRI p. 17/22 which is within the reach of the future linear collider (ILC)..

18 Production of RH neutrino at ILC or LHC The differential cross-section for the process,e + e, Z N k N j (k j) ( ) dσ dω = α2 1 4M2 1 F 1 + 4s s 8sin 4 P ZZ F 2 2θ W ( (1 4sin 2 ) θ W )tanθ W + sin 2 P Z F 3 2θ W ) F 1 = µ 2 N s sin2 θ (1+ 4M2, s F 2 = 1+cos 2 θ 4M2 s sin 2 θ + µ 2 N s tan2 θ W [ sin 2 θ + 4M2 s F 3 = 4µ 2 N s [ sin 2 θ + 4M2 s P ZZ = s 2 (s M 2 Z )2 +Γ 2 M 2 Z ( 1+cos 2 θ )], P Z = ( 1+cos 2 θ )], s(s M 2 Z ) (s M 2 Z )2 +Γ 2 M 2 Z Sudhanwa Patra, NuHorizon-IV, HRI p. 18/22

19 Plot of cross-section versus COM energy The cross section is shown as a function of heavy Majorana neutrino mass M and here we have varied the center of collider energy as M = 500,700,800,1000 GeV Σ fb S Sudhanwa Patra, NuHorizon-IV, HRI p. 19/22

20 Left-Right model with Spontaneous CP-violation In left-right models with spontaneous CP-violation [Mu Chun Chen and Mahanthappa, PRD 2005], predicts vanishing contribution to lepton asymmetry from N νφ. argument[m D ] e iα k, α k is the physical phase which is the source of CP-violation. ε N 3 [ M 1 Im M T D Mν M D] [ ] 16π v 2 M T D M D The argument of M ν e+2iα k and hence, the quantity Im [ M T D M ν M D] is real leading to a vanishing contribution to ε N. Also CP-asymmetry coming from both RH neutrino decay and Higgs triplet decay as [Mu Chun Chen and Mahanthappa, PRD 2007], ε ε N +ε sin(2α k +α L )C It is interesting to note that if α L = 2α k, then the lepton asymmetry vanishes. In this case, electromagnetic leptogenesis is the only contribution to account matter-antimatter asymmetry of the Universe. Left-right mixing will play a crucial role in this case. Sudhanwa Patra, NuHorizon-IV, HRI p. 20/22

21 Left-Right model with Spontaneous CP-violation Interference between 2 one loop diagram will give non-zero CP-asymmetry W a W a W a Ψ k l c l Ψ j Ψ k l c l Ψ j (1) (2) One can write the mixing matrix between the left-right handed sector as U = ( cosζ sinζ e +iα k sinζe iα k cosζ ) (8) ε EM sinζ, where tan2ζ = 2kk v 2 R v2 L One can get the correct lepton asymmetry for TeV scale (Also valid for hierarchical RH neutrino mass) Still few things need to be addressed carefully. Sudhanwa Patra, NuHorizon-IV, HRI p. 21/22

22 CONCLUSION It is possible to explain non-zero light neutrino mass and generate a baryon asymmetry of the universe through leptogenesis at the TeV scale, where the CP violation comes from the electric dipole moment of the neutrinos. Resonant electromagnetic leptogenesis a viable alternative for achieving successful leptogenesis and requires a TeV scale Right Handed neutrino. The correct amount of baryon asymmetry could be generated through resonant enhancement, when the two of the right-handed neutrinos are almost degenerate. In this model light neutrino masses originate from the seesaw mechanism, although the right-handed neutrinos have Majorana masses of the order of TeV. In minimal left-right models with spontaneous CP-violation, electromagnetic leptogenesis is the cleanest scenario to account the matter-antimatter asymmetry of the present universe. crucially depends on the left-right mixing. large magnetic moments can enhance the production cross section of TeV scale right-handed neutrinos though the Drell-Yan process,e + e,z N i N j (i j), which is within the reach of the future linear collider (ILC). Sudhanwa Patra, NuHorizon-IV, HRI p. 22/22