SM predicts massless neutrinos

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1 MASSIVE NEUTRINOS

2 SM predicts massless neutrinos What is the motivation for considering neutrino masses? Is the question of the existence of neutrino masses an isolated one, or is connected to other outstanding questions of particle physics? What sort of tests can be performed to know wheater the neutrinos have masses?

3 TOP-DOWN APPROACH: THEORETICAL MOTIVATIONS IN PARTICLE PHYSICS n R s are not introduced in the SM just because one wants to predict massless neutrinos. Gauge symmetry of e.m. interactions massless photons For massless n no such symmetry principle in SM Masslessness of n unsatisfactory from a theoretical point of view Many GUT s predict neutrino masses

4 BOTTOM-UP APPROACH: MOTIVATIONS FROM ASTROPHYSICS 1939: Bethe listed the chain of reactions responsible for burning hydrogen into helium in stellar cores. In these reactions, some electon neutrinos are produced. Since they interact weakly, they leave the star without any hindrance, bringing information about stellar core. Solar neutrino problem: Experiments detect only 1/3 of the flux of n e expected from detailed calculations. Neutrino oscillations? n e produced in weak process is not a mass eigenstates, but a superposition of different mass eigenstates. One the passage from the Sun to the Earth, the n e can partially oscillate to some other flavor, producing the solar n e deficit. ALL NEUTRINOS CANNOT BE MASSLESS

5 EVIDENCE OF NEUTRINO OSCILLATIONS

6 Lot of effort since 60s Finally convincing evidence for neutrino oscillation Neutrinos appear to have tiny but finite mass

7 QUESTIONS RELATED TO NEUTRINO MASS Neutrino mixing: gauge eigenstates would be a superposition of the mass eigenstates. Non-trivial leptonic mixing matrix V Generational lepton numbers L e, L m, L t, cannot remain global symmetries Possible CP violation in the leptonic sector [the leptonic mixing matrix V can be complex] Neutrinos Antineutrinos? Dirac or Majorana particles? Neutrino stability. Do neutrinos decay?

8 Neutrinos have mass They have mass. Can t go at speed of light. What is this right-handed particle? New particle: right-handed neutrino (Dirac) Old anti-particle: right-handed anti-neutrino (Majorana) 8

9 Dirac neutrino Dirac field of the electron. 4 basic spinors e L, e R e - e L, e R e + e L e R, e R?? By boosting to a different Lorentz frame, one cannot see a different charge on a particle! The boosted observer sees e R With massive neutrinos one can mimic the electron situation, postulating two more states n R and n L. The boosted observator will see a n R when we see a n L. Neutrino will be a Dirac particle with 4 complex degree of freedom

10 Majorana neutrino Can we not do without postulating the two new spinor states? Can t the boosted observed see the state n R? Unlike the electrons, n L and n R have both zero electric charge. They differ only by lepton number (L) But lepton number is not a global symmetry. It does not govern the dynamics. Nothing of sacred about it! If it is broken, n L and n R can be the boosted counterparts of one another. These two spinors can thus constitute the left and righthanded projections of the same fermionic field. Neutrinos will be two-components Majorana fields A Majorana neutrino is its own antiparticle

11 Difference btw Majorana and Weyl neutrino Both are two component spinors, but A Weyl neutrino is massless. n L moves at speed of light. No observer can overtake it and view if as a r.h. object. So a r.h. counterpart of n L is not necessary to obtain a Lorentz covariant picture. Similarly a n R does not require its l.h. counterpart. They could have different lepton number to distinguish themselves. A Majorana neutrino has mass. But n n. So the r.h. component of n L can be n R or n R. Similarly, n L n L. That is why only n L and n R suffice. They can Lorentz transformed to each other. Neutrino cannot have any additive quantum number. The self-conjugacy is the reason why a Majorana particle has half as many degrees of freedom as a Dirac particle.

A Gedanken experiment to distinguish between a Dirac and a Majorana neutrino Suppose that it were practically possible to put at rest a massive n m with spin-down in the middle of the room.

12 A Gedanken experiment to distinguish between a Dirac and a Majorana neutrino Suppose that it were practically possible to put at rest a massive n m with spin-down in the middle of the room. If accelerated up to relativistic energies in the up direction, when it hits the roof can produce a m - through a CC interaction. If accelerated up to relativistic energies in the down direction, when it hits the floor it can produce a m + (if it is a Majorana particle) or have no interaction (if it is a Dirac particle). Coming to realistic experiments, we will show that oscillation experiments cannot discriminate Majorana from Dirac neutrinos. The only realistic hope of experimentally discriminating Majorana from Dirac neutrino masses is based on the fact that Majorana masses violate lepton number, maybe give a signal in the future neutrinoless double beta decay experiments.

14 LEPTON NUMBER The absence of a conserved lepton number is evident from the fact that Dirac neutrinos have L=+1 and Dirac antineutrinos have L=-1. Since in Majorana case neutrinos and antineutrinos are the same object, it is clear that there cannot be a conserved lepton number. However, since neutrino masses are very small, it is possible to assign to charged leptons and neutrinos an effective total lepton number which is conserved in all the processes that are not sensitive to the Majorana mass of neutrinos. In these processes, neutrinos can be considered massless. We have that neutrinos with negative helicity have L eff =+1 and neutrinos with positive helicity L eff =-1, in agreement with the convention of calling an antineutrino a neutrino with positive helicity. Conservation of effective lepton number in all interactions which are not sensitive to neutrino mass. If Majorana mass term is considered as a perturbation of the massless Lagrangian, it generates transitions with D L eff =±2

15 DIRAC MATRICES To show the feautres that are characteristic of Dirac, Weyl and Majorana fields, it is convenient to introduce different Dirac matrix representations that are related by unitary transformations. We adopt the convention Dirac representation

16 Weyl representation

17 Majorana representation Because the field is real in nature, it is convenient to adopt the representation so that all the components of the Dirac equation are also real.

18 MASSLESS NEUTRINOS We work in the Weyl representation. The two-components Weyl spinors are defined by where y is the Dirac spinor

19 Charge conjugation is defined by with the choice Then charge conjugation is

20 The kinetic termin is written The Majorana field is defined by the Majorana condition that Imposed on a four-component spinor Let us define the two fields by These fields obviously satisfy the Majorana condition, and are taken as Majorana fields.

21 Conversely, The kinetic term can be written

22 MASSIVE MAJORANA NEUTRINOS The Lagrangian with a mass term for a Majorana field is given by by omitting the term for the w field. We assume that m is real. Defining satisfies the Majorana condition in an extendend sense The kinetic term reads

23 Writing We obtain Here, the mass M is complex, but its phase can be absorbed into the phase of y L The second term breaks the lepton number carried by y L

24 MASSIVE DIRAC NEUTRINOS If there are two Weyl fields as we can construct a mass term If m ii =0 the lepton number L i -L j is conserved. If we define the two fields y L and y R by We obtain the conventional Dirac mass term for the Dirac field The kinetic term is given by

25 MASSIVE NEUTRINOS IN WEINBERG-SALAM THEORY We can introduce a Dirac mass term if n R exists in addition to n L which is induced by giving the Higgs field f 0 a vacuum-expectation value through the Yukawa coupling If there is no n R, the Majorana mass term is the only mass term that gives the neutrino mass. Since term is is a SU(2) triplet (as T=T 3 =1), the simplest possible mass and the neutrino mass is given by. The Lagrangian is non-renormalizable, and M is an effective mass. The form of the Lagrangian gives a hint to how the neutrino mass is realized, as

26 SEE-SAW MECHANISM The seesaw mechanism is perhaps the simplest model that leads an effective operator ll ff within a renormalisable class of interactions. Let us assume that the mass term is given by f f n L n R M X n R n L When the heavy field (M>> < f >) is integrated out, this gives diagram

27 Equivalently, this is obtained by diagonalising the mass matrix n L n R nl n R where the two rows (coloumn) refer to left- and right-handed neutrinos and the Dirac mass m = f < f > induces mixing between the two sector Then (We have reversed the sign of m nl, using the degree of freedom for the phase factor) The attractive feature of this model is that the smallness of the neutrino mass can be understood in terms of a large-mass scale M, which often appears in higher unification theories.

28 SEE-SAW MODELS FOR NEUTRINO MASSES n : light l.h. Majorana neutrino N : heavy r.h. Majorana neutrino Hierarchy problem: mantaining separate the two mass scales

29 EFFECTIVE FIELD THEORY APPROACH Generic new physics too heavy for being directly studied manifests at low energy as non renormalizable operators (NRO), suppressed by heavy scales. NRO give small corrections, suppressed by powers of E= L, to physics at low energy E, that is therefore well described by a renormalizable SM theory. The introduction of NRO is how the Fermi scale made its first appearance. History might repeat now. Adding NRO to the SM Lagrangian, L e ; L m ; L t ;B are no longer accidentally conserved: Dim 5 operator (n mass) Dim 6 operator (violate B-L, proton decay)

30 Rem: How to determine the dimension of an operator The action must be dimensionless to be Lorentz invariant [x] = (energy) -1 [L] = (energy) 4 D=4 Scalar field D f = 1, each derivative introduces dimension 1 Vector field D A = 1 Spinor field D y = 3/2

31 NEUTRINO MASS & DIM-5 OPERATORS Let us contruct an SU(2) L X U(1) Y theory of neutrino mass. Since n L resides inside the lepton doublet l L, without any detailed analysis we can see that a dimension-5 operator is required: Schematically l L l L contains the desired neutrino bilinear but it carries hypercharge Y = =-2; on the other hands the Higgs doublet f carries hypercharge Y=+1, and so the lowest dimensional operator we can form is of the form llff with dimensions 3/2+3/2+1+1=5. Many O d>4 op.s with SM fields but O d=5 is UNIQUE! v v n a n b l ab depends on the model l ab ~O(1), M~M GUT, v=v EW m n ~10-3 D=5 operator violates lepton number n must be Majorana

32 TREE-LEVEL REALIZATION OF THE SEE-SAW MECHANISM Type I See-Saw N R fermionic singlet Type II See-Saw D scalar triplet Type III See-Saw t R fermionic triplet Linearly prop to Y D suppressed by m/m 2 Minkowski, Gell-Mann, Ramond, Slansky, Yanagida, Glashow, Mohapatra, Senjanovic, Magg, Wetterich, Lazarides, Shafi, Mohapatra, Senjanovic, Schecter, Valle, Foot, Lew, He, Joshi, Ma, Roy,, Bajc, Nemevsek, Senjanovic, Dorsner, Fileviez-Perez

33 Suggests existence of high scales To obtain Λ m 3 ~(Dm 2 atm) 1/2 Λ~10 15 GeV! Hints at physics of very high scales Neutrino mass may be probing unification 62

34 NEUTRINO MASS IN GRAND UNIFIED THEORIES G SU(3) C x SU(2) L x U(1) Y SU(3) C x U(1) Q energy M X M W

35 SU(4) x SU(2) L x SU(2) R SO(10) SU(5) SU(4) x SU(2) x U(1) SU(3) x SU(2) x U(1) In the minimal version of SU(5) no n R and B-L conservation. Massless n R. Mass term by hand (like in SM) SO(10) B-L gauge symmetry to be broken at some scale Room for n R! n naturally acquire mass

36 NEUTRINOLESS DOUBLE BETA DECAY If neutrinos are Majorana particles is possible the neutrinoless double beta decay (0n2b) Violation of lepton number of two units (DL=2)

Testing leptogenesis at the LHC

Santa Fe Summer Neutrino Workshop Implications of Neutrino Flavor Oscillations Santa Fe, New Mexico, July 6-10, 2009 Testing leptogenesis at the LHC ArXiv:0904.2174 ; with Z. Chacko, S. Granor and R. Mohapatra