Neutrino Oscillation Phenomenology: Exploring the Physics of Neutrinos

1. Neutrino Oscillation Phenomenology Boris Kayser Pontecorvo SchoolSeptember, 2019 NASA Hubble Photo

2. 1 Spin: 1 1 1 1 Without the neutrino, angular momentum would not be conserved. 2 2 2 2 What Are Neutrinos Good For? Energy generation in the sun starts with the reaction — Uh, oh ……

3. The Neutrinos Neutrinos and photons are by far the most abundant known elementary particles in the universe. There are 340 neutrinos/cc. The neutrinos are spin – 1/2, electrically neutral, leptons. The only known forces they experience are the weak force and gravity. This means that they do not interact with other matter very much at all. Thus, neutrinos are difficult to detect and study. Their weak interactions are successfully described by the Standard Model.

4. The Neutrino Revolution(1998 – …) Neutrinos have nonzero masses! Leptons mix!

5. The 2015 Nobel Prize in Physics went to TakaakiKajita and Art McDonald for the experiments that proved this. Sudbury Neutrino Observatory,Canada Super– Kamiokande, Japan

6. The discovery of neutrino mass and leptonic mixing comes from the observation of neutrino flavor change (neutrino oscillation).

7. The Physics of Neutrino Oscillation — Preliminaries

8.  e  W W W   e The Neutrino Flavors There are three flavors of charged leptons: e ,  ,  There are three known flavors of neutrinos: e, ,  We define the neutrinos of specific flavor, e, , , by W boson decays:

9. e e  Detector   e but not   As far as we know, when a neutrino of given flavor interacts and turns into a charged lepton, that charged lepton will always be of the same flavor as the neutrino. Lederman Schwartz Steinberger The weak interaction couples the neutrino of a given flavor only to the charged lepton of the same flavor.

10. Neutrino Flavor Change (“Oscillation”) If neutrinos have masses, and leptons mix, we can have — • Give a  time to change character, and you can have • e • The last 21 years have brought us compelling evidence that such flavor changes actually occur.  e W  e  Detector Long Journey for example:

11. 3 (Mass)2 2 1 Flavor Change Requires Neutrino Masses There must be some spectrum of neutrino mass eigenstates i: Mass (i)  mi

12. Flavor Change Requires Leptonic Mixing The neutrinos e,,of definite flavor (W ee or  or ) must be superpositions of the mass eigenstates: |> = U*i |i> . Neutrino offlavor Neutrino of definite mass mi = e, , or  “PMNS” Leptonic Mixing Matrix i Pontecorvo The leptonic mass eigenstates are e, μ, τ, and ν1, ν2, ν3.

13. Notation: l denotes a charged lepton. le  e, l, l . Since the only charged lepton couples to is lα, the3must be orthogonal. To make up 3 orthogonal , we must have at least 3 i. Unless some imasses are degenerate, all i will be orthogonal. Then — This says that U is unitary, but note the unitary U may not be 3 x 3.

14. defined by . Leptonicmixing is easily incorporated into the Standard Model (SM) description of the lW interaction. For this interaction, we then have — Semi-weak coupling Left-handed LSM Taking mixing into account The SM interaction conserves the Lepton Number L,

15. The Meaning of U W+ W+ Caution: The 3 x 3 U may not be unitary. Please talk about leptonicmixing, not neutrino mixing. The e row of U: The linear combination of neutrino mass eigenstates that couples to e. The 1 column of U: The linear combination of charged-lepton mass eigenstates that couples to 1 .

16. How Neutrino Oscillation In Vacuum Works

17. l (e.g. ) l (e.g. )  Amp W W Target Source l l  i Amp = i W W Target Source Neutrino Oscillation (Approach of B.K. and Stodolsky) () ()

18. l l  i Amp i W W Target Source = Coordinates of detection point, taking source point as (0, 0) Momentum and energy of νi

19. Neutrino sources are ∼ constant in time. Averaged over time, the interference is — unlessE2 = E1. Only neutrino mass eigenstates witha common energy E are coherent. (Stodolsky)

20. For each mass eigenstate νi, . Then the plane-wave factor is — Irrelevant overall phase factor

21. l l  i Amp i W W Target Source Then — =

22. Probability of Neutrino Oscillation in Vacuum where . Neutrino flavor change implies neutrino mass!

23. Neutrinos vs. Antineutrinos A difference between the probabilities of these two oscillations in vacuum would be a leptonicviolation of CP invariance. Assuming CPT invariance — Probability

24. In neutrino oscillation, CP non-invariance comes from phases in the leptonic mixing matrix U. ( ) ( ) ( )

25. The plane-wave treatment of neutrino oscillation is not completely correct, . since The expression for the oscillation probability resulting from this treatment is wrong at very large L. But a wave packet treatment shows that the plane-wave expression is correct under almost all circumstances. 

26. — Comments —

31. For β ≠ α, Important Special Cases Three Flavors 31

32. Two waves of different frequencies, and their CP interference. (—) (—) (—) (—) (—) 32

35. e involves or e e W W e e e e e +2GFNe, e VW = –2GFNe, e This raises the effective mass of e, and lowers that of e. Neutrino Flavor Change In Matter Coherent forward scattering via this W-exchange interaction leads to an extra interaction potential energy — Electron density Fermi constant

36. The matter effect — — Grows with neutrino energy E — Is sensitive to Sign(m2) — Reverses when  is replaced by  The fractional importance of matter effects on an oscillation involving a vacuum splitting m2 is — [2GFNe] / [m2/2E] . Vacuum energy Interaction energy This last is a “fake CP violation” that has to be taken into account in searches for genuine CP violation.

37. Evidence For Flavor Change Evidence of Flavor Change Compelling Compelling Compelling Compelling “Interesting” Neutrinos Solar Reactor(Long-Baseline) Atmospheric Accelerator(Long-Baseline) Accelerator, Reactor, and Radioactive Sources(Short-Baseline)

38. What We Have Learned

39. 3 3 m2atm 2 2 m2sol m2sol } } 1 1 The (Mass)2 Spectrum Which way? or (Mass)2 m2atm Inverted Normal ~ ~ m2sol = 7.6 x 10–5 eV2, m2atm = 2.5 x 10–3 eV2 Are there more mass eigenstates?

40. 3 m2big How far above zero is the whole pattern? (Mass)2 2 m2little 1 ?? 0 Constraints On the Absolute Scale of Neutrino Mass Known Known Neutrino masses are tiny Cosmology, under certain assumptions m(i) < 0.17 eV Alli Tritium beta decay Oscillation Mass[Heaviest i] > m2big > 0.05 eV

41. Measurements of the tritium βenergy spectrum bound the average neutrino mass — (Farzan & Smirnov) (Mainz & Troitzk) (Lecture by Kathrin Valerius) Presently:

42. Leptonic Mixing Mixing means that — |> = U*i |i> . Neutrino offlavor Neutrino of definite mass mi = e, , or  i |i> = Ui | > .  (ifU is unitary) Inversely, Flavor- fraction of i = |Ui|2 . When a i interacts and produces a charged lepton, the probability that this charged lepton will be of flavor  is |Ui|2.

43. } 2 3 m2sol 1 m2atm or (Mass)2 m2atm 2 } m2sol 3 1 [|Ui|2] [|Ui|2] e [|Uei|2] Experimentally, the flavor fractions are — Inverted Normal

44. Observations We Can Use To Understand The Flavor Fractions

45. The Disappearance of Atmospheric νμ  Detector  Cosmic ray Isotropy of the > 2 GeV cosmic rays + Gauss’ Law + No  disappearance  ––––––– = 1 . But Super-Kamiokande finds for E > 1.3 GeV — ~  (Up) (Down)

46. Half the long distance traveling nμ disappear The nμfrom nearby do not disappear z   Super-Kamiokande

47. 3 3 m2atm 2 2 m2sol m2sol } } 1 1 At Eν> 1.3 GeV, in — or m2atm the solar splitting is largely invisible. Then— 1 At large L/E

48. Reactor e have E 3 MeV, so if L  1.5 km, will be sensitive to — Reactor – Neutrino Experiments and |Ue3|2 = sin2θ13 but not to — .

49. Then — Measurements by the Daya Bay, RENO, and Double CHOOZ reactor neutrino experiments, (and by the T2K accelerator neutrino experiment) |Ue3|2≅ 0.02 (Lecture by Yifang Wang)

50. The Change of Flavorof Solar νe Nuclear reactions in the core of the sun produce e. Only e. • The Sudbury Neutrino Observatory (SNO) measured, for the high-energy part of the solar neutrino flux: • sol d  e p p  e • sol d   n p  e+  + remains a )  From the two reactions, e e+  +  ——————— = 0.301 ± 0.033 For solar neutrinos, P(e  e) = 0.3