Particle Physics Theory Sub-Group Presentation

1. Particle Physics Theory Sub-Group Presentation Benedict Allbrooke Paul Clarkson Lauren Lewis Jennifer Wallace

2. 2 Generation Case • In some cases is a good approximation – eg. For solar neutrinos. • Mixing matrix relates the weak and mass eigenstates. • Propagates as a QM wave function. • Probability is proportional to the amplitude of the QM wave function squared at a position.

3. 2 Generation Case continued... • Probability of oscillation. • Where θ is the mixing angle, ΔM2is the difference between mass eigenstates squared in eV2, L is the baseline in km, and E is the energy of the neutrino in GeV.

4. 3 Generation Case • 3 generation case relates the three known mass eigenstates to the three known weak eigenstates. • This case can become a combination of 2 generation cases. • Maki-Nakagawa-Sakata (MNS) matrix. • Analogous to CKM matrix for quarks.

5. 3 generation case continued... • Maki-Nakagawa-Sakata (MNS) matrix • α is the Majorana phase • δ is the CP violating phase

6. MNS Explained • If sterile neutrinos are inferred, then the matrix MNS becomes 4x4. • If neutrinos are Majorana, the matrix is not orthogonal. • The matrix is unitary, therefore if all known parameters are found and it is not, new physics must be present.

7. 3 generation probability equations • These are the probabilities ignoring CP violation and considering neutrinos as Dirac particles. • Ref: Neutrino Factories: Physics, Steve Geer, FNAL, 2008.

8. CP violation • P – parity, C - charge conjugation. • The weak force does not conserve either, therefore both are violated. • However, together, CP restores invariance. • If CP is violated, particles and antiparticles have different oscillation probabilities.

9. CP Violation continued... • Neutrinos and antineutrinos have different chiralities, left and right handed respectively. • The weak force coupling depends on handedness. • The CP violating phase δ is inferred by the unitarity of the MNS matrix.

10. Majorana or Dirac? • Majorana particles are the same as their antiparticles, therefore can only be electrically neutral fermions. • Dirac particles are not the same as their antiparticle. • In the MNS matrix, if neutrinos are Dirac, α is zero. • If Majorana, α is the angle between neutrino and antineutrino.

11. Majorana or Dirac continued... • Majorana neutrinos violate lepton number. • Can only be determined through neutrino-less double beta decay. • The see-saw mechanism is a theory that combines both Dirac and Majorana mass terms.

12. See-Saw Mechanism • Way to explain small mass of neutrino by implying corresponding heavy neutrinos. • Heavy neutrinos must be Majorana. • The observable neutrinos are the small neutrinos.

13. Mass Hierarchy • 2 possible schemes for mass eigenstates.

14. Matter Effects • Can be used to determine mass hierarchy. • A=2(√2)GFYeρEV

15. Matter Effects Continued... • Oscillation probabilities different in a vacuum than in matter. • For normal hierarchy, it enhances the probability for neutrino oscillation, and suppress the probability for antineutrino oscillation, and vice-versa for inverted hierarchy. • To investigate, need to run for half of the time with νe & anti-νμand half the time withanti-νe &νμ.

16. Proposal – Detector 1 • Neutrino source energy of 15GeV to increase sensitivity to θ13 measurements. • Baseline of 7300km to minimise CP violating phase. • Beam would go through mantle, increasing matter effects.

17. Proposal – Detector 2 • Off axis detector with a baseline of 3000km, enhances CP violation. • Neutrino energy of 6GeV. • Only goes through crust and not mantle, still has matter effects.

18. Matter Effects and CP Violation • Ref: Neutrino Factories: Physics, Steve Geer, FNAL, 2008.

19. Muon Storage Ring • This shows the inclination of the beams needed for baselines 7300km and 3000km. • This diagram assumes an equilateral triangle.

20. Possible Locations for Detectors Physics with a very long neutrino factory baseline; Raj Gandhi, Walter Winter

21. Running Time • Run the experiment for half of the time with νe & anti-νμ(from μ+ decays) and half the time withanti-νe &νμ(from μ- decays). • Run for two and a half years both ways (if can only run for five years).

22. What we can measure and how • Θ13 can be measured by looking at νe νμand ν‾e ν‾μin appearance mode. • This is also true for the reverse channels. • Sensitivity for this should be down to the order of 10-4 . • Mass hierarchy and the CP violating phase can be evaluated by looking at the difference between appearances of neutrinos and antineutrinos.

23. What we can measure and how continued... • Δm232 can be measured from the dip in νμand ν‾μ. • Matter effects will enhance or suppress the dip depending upon it being inverted or normal. • The disappearance of νμwill give a greater measurement of Δm221 and θ12 . • If there is an excess of νe, sterile neutrinos can be inferred.

24. What we can not measure • If θ13 is too small then it will only be possible to set an upper limit on the parameter. • If θ13 is too small then it will not be possible to measure the CP violating phase. • We will not be able to quantify the Majorana phase though may find hints that neutrinos are Majorana.

25. Flux incident on detector • Opening angle of neutrino factory, θ=0.1/γμ. • Radius of beam at baseline L given by L tan(θ) • Source distributed as a 2D Gaussian with normalised equation: X is horizontal position, y is vertical position. σ is the standard deviation.

26. Flux incident on detector continued... • Model full beam width as 5σ. • Gives σ=0.34km for 7300km baseline.

27. Flux incident on detector continued... Probability for one neutrino passing through a certain area: For a square detector of side length 2a:

28. Predicted results • Modelled vacuum oscillations in ROOT to determine probabilities of oscillation • Introduced other oscillation mechanisms such as matter effects • Consider experimental parameters such as detection rate, source flux and efficiency • This gives predictions of detectable events to look at uncertainties on any measurements

29. Predicted results graphs Enhanced by Matter effects Suppressed by Matter effects

30. Implications for other physics • Extra dimensions • See saw mechanism • SUSY • String theory • Dark matter • Leptogenesis • Neutrino communications

31. Thank you for listening. Any questions?

32. Neutrinoless Double Beta Decay (additional page) Shows that neutrinos are majorana. Need a nuclei that is stable against other types of decay. Example 76Ge, τ~1028 years. Can also determine the mass of the neutrino.

33. Leptogenesis(additional slide) N may have energies up to the GUT scale. In the early universe N decays into leptons and Higgs bosons. If CP is violated then the rates of decay will be different. In SM no. of baryons minus no. of leptons conserved. Excess Lepton no. could convert to excess baryon no. Therefore, explaining the asymmetry in the universe.

34. Implications on other physics (additional slide) Extra Dimensions and String Theory: Neutrinos can move through extra dimensions from the three brane we are familiar with. Explains tiny mass and weak interactions. Neutrino Communications: SETI search for extra terrestrial communications. Could one day be used on earth similar to radio waves. Advantages is they can pass through matter and are very fast. Disadvantage is that they are hard to detect. Dark Matter: Non-baryonic dark matter contains neutrinos. Made of sterile neutrinos?

35. See saw Mechanism • Introduces a heavy right handed neutrino for each light left handed neutrino. • Acquire mass through Dirac mass term on same order as electroweak scale ~ 102GeV. • Small masses of left-handed Majorana neutrinos created through pushing mass of right handed neutrino to super high enery scale.

36. Sterile Neutrinos • Hypothetical particles – postulated due to LSND. • LSND – had excess of ve. • Sterile neutrino needed to oscillate very weakly into mainly ve. • Two different mass schemes for extra Δm2. • MiniBoone in general did not find excess of ve.

37. 7300km Baseline • Appearance probability for ve→vµ in matter. • Where Ref: hep-ph/0301257, “Neutrino Factories and the “magic” baseline”

38. 7300km Baseline continued… • When ΔA=nπ, only the first term remains therefore CP violating term has no effect. • 1st non-trivial solution is when (√2)GFneL=2π. • Gives magic baseline equation of: • Corresponds to 7300km between Fermilab and Gran Sasso.

39. 3000km Baseline • Optimal for CP violating phase. • Can distinguish between θ13 and δ by comparing wrong sign muons and binning energy of signal.

40. Total Flux through detector • For detector at 7300km, side length after dead zone taken off: 20m • Fraction of Flux on target: 5.195 E-4 • Yearly flux on target: • 5.195E17 X Efficiency of vμ type • 5.195E17 X Efficiency of ve type • Efficiency =used side length of storage ring ÷ total circumference of storage ring