# In vacuo oscillation

1. Apr 10, 2005

### wstevenbrown

Hi, I'm Steve, the new guy. After a long literature search, I have been unable to find any reference to experimental confirmation of neutrinos of any type oscillating in a vacuum. All of the many models under discussion seem to assume that they oscillate, but nowhere have I been able to find a measurement of the mixing angle. There are many, many articles which show measurement of oscillation while passing thru condensed matter-- and none which demonstrate this in vacuo. Can anybody point me at a reference which doesn't simply assume this, or one which measures it? Thanks.

2. Apr 10, 2005

### zefram_c

The closest one can get to a 'pure vacuum' experiment is the measurements done on solar neutrinos - although of course such neutrinos have to pass through the Sun in order to reach us. You can look up the papers by the SNO or SuperKamiokande collaborations for that purpose.

3. Apr 10, 2005

### wstevenbrown

I have sampled those, not exhaustively searched them. One would think, assuming solar emission constant, that the difference between perihelion and aphelion would show the effect, if it exists. One would also have to correct for distance-squared dropoff. Can it be that the statistical universe is still too small?

4. Apr 11, 2005

### Meir Achuz

Some of these references should help.

References for hep-ph/0503079
This information is courtesy of SLAC's SPIRES-HEP preprint index.
Result of SLAC-SPIRES search:
1. hep-ph/0411274 [abs, ps, pdf, other] :
Title: 2004 TASI Lectures on Neutrino Physics
Authors: Andre de Gouvea (Northwestern U.)

2. hep-ex/0104049 [abs, ps, pdf, other] :
Title: Evidence for Neutrino Oscillations from the Observation of Electron Anti-neutrinos in a Muon Anti-Neutrino Beam
Authors: A. Aguilar, L.B. Auerbach, R.L. Burman, D.O. Caldwell, E.D. Church, A.K. Cochran, J.B. Donahue, A. Fazely, G.T. Garvey, R.M. Gunasingha, R. Imlay, W.C. Louis, R. Majkic, A. Malik, W. Metcalf, G.B. Mills, V. Sandberg, D. Smith, I. Stancu, M. Sung, R. Tayloe, G.J. VanDalen, W. Vernon, N. Wadia, D.H. White, S. Yellin
Comments: 71 pages,28 figures, 17 tables
Journal-ref: Phys.Rev. D64 (2001) 112007

3. SLAC database (no arXiv entry):
Title: Review Of Particle Physics. Particle Data Group
First-Author: Eidelman
Journal-ref: Phys.Lett. B592 (2004) 1
4. hep-ph/0412099 [abs, ps, pdf, other] :
Title: Theory of Neutrinos
Authors: R.N. Mohapatra (discussion leader), S. Antusch, K.S. Babu, G. Barenboim, Mu-Chun Chen, S. Davidson, A. de Gouvea, P. de Holanda, B. Dutta, Y. Grossman, A. Joshipura, J. Kersten, Y.Y. Keum, S.F. King, P. Langacker, M. Lindner, W. Loinaz, I. Masina, I. Mocioiu, S. Mohanty, H. Murayama, S. Pascoli, S. Petcov, A. Pilaftsis, P. Ramond, M. Ratz, W. Rodejohann, R. Shrock, T. Takeuchi, T. Underwood, F. Vissani, L. Wolfenstein
Comments: 50 Pages, 10 figures, theory discussion group report to the APS neutrino study. v2 - very minor corrections, references added

5. hep-ph/0503086 [abs, ps, pdf, other] :
Title: Neutrinos Have Mass - So What?
Authors: Andre de Gouvea
Comments: invited brief review, 15 pages, 1 eps figure, typo corrected, reference added
Journal-ref: Mod.Phys.Lett. A19 (2004) 2799-2813

6. hep-ph/0407155 [abs, ps, pdf, other] :
Title: Normal vs. Inverted Hierarchy in Type I Seesaw Models
Authors: Carl H. Albright (Northern Illinois U. and Fermilab)
Comments: 10 pages including 1 figure; improved version with additional illustration of results for whole class of models with charged lepton mass matrices diagonal in flavor space; accepted for publication in Physics Letters B
Journal-ref: Phys.Lett. B599 (2004) 285-293

7. hep-ph/0405172 [abs, ps, pdf, other] :
Title: Status of global fits to neutrino oscillations
Authors: M. Maltoni, T. Schwetz, M.A. Tortola, J.W.F. Valle
Comments: 41 pages, 22 figures, 2 tables. Updated version of two, three and four-neutrino oscillation analyses including new K2K and solar neutrino data as well as detailed analysis of the KamLAND results and their impact on constraining theta_13. Accepted review for publication in the Focus Issue on Neutrino Physics of New Journal of Physics" edited by F. Halzen, M. Lindner, and A. Suzuki; v4: short appendix added providing updated results which take into account a new background source in Kamland data
Journal-ref: New J.Phys. 6 (2004) 122

8. hep-ph/0411252 [abs, ps, pdf, other] :
Title: Earth Matter Effects at Very Long Baselines and the Neutrino Mass Hierarchy
Authors: Raj Gandhi, Pomita Ghoshal, Srubabati Goswami, Poonam Mehta, S Uma Sankar

9. hep-ph/0408070 [abs, ps, pdf, other] :
Title: Untangling CP Violation and the Mass Hierarchy in Long Baseline Experiments
Authors: Olga Mena, Stephen Parke (Fermilab)
Comments: 15 pages, Latex, 4 postscript figures. Submitted to New Journal of Physics, Focus on Neutrino Physics'' issue
Journal-ref: Phys.Rev. D70 (2004) 093011

10. hep-ph/0403068 [abs, ps, pdf, other] :
Title: Prospects of accelerator and reactor neutrino oscillation experiments for the coming ten years
Authors: P. Huber, M. Lindner, M. Rolinec, T. Schwetz, W. Winter
Comments: 38 pages, 13 figures, Eqs. (1) and (5) corrected, small corrections in Figs. 8, 9, and Tab. 4, discussion improved, ref. added, version to appear in PRD, high resolution figures are available at this http URL
Journal-ref: Phys.Rev. D70 (2004) 073014

11. hep-ph/0301210 [abs, ps, pdf, other] :
Title: The Complementarity of Eastern and Western Hemisphere Long-Baseline Neutrino Oscillation Experiments
Authors: Hisakazu Minakata (Tokyo Metropolitan), Hiroshi Nunokawa (Estadual Paulista), Stephen Parke (Fermilab)
Comments: 21 pages, Latex, 3 postscript figures
Journal-ref: Phys.Rev. D68 (2003) 013010

12. hep-ph/0210192 [abs, ps, pdf, other] :
Title: Oscillation Physics with a Neutrino Factory
Authors: M.Apollonio et al. (CERN working group on oscillation physics at the Neutrino Factory)
Comments: 105 pages, to appear on the CERN Yellow Report on the Neutrino Factory Warning: to accomplish arXiv submission rules on file sizes (650M against the original compressed version of 2.5G), figures in this paper have been converted to bitmap, thus resulting in a worse quality. A better-quality version of this paper can be found in www.cern.ch/campanel/main.ps for comments: Mario.Campanelli@cern.ch (editor)

13. hep-ph/0501037 [abs, ps, pdf, other] :
Title: Resolving parameter degeneracies in long-baseline experiments by atmospheric neutrino data
Authors: P. Huber, M. Maltoni, T. Schwetz

14. hep-ph/0407336 [abs, ps, pdf, other] :
Title: A question of hierarchy: matter effects with atmospheric neutrinos and anti-neutrinos
Authors: D. Indumathi, M.V.N. Murthy
Comments: 36 pages revtex with 14 eps figures; new section on statistical significance when detector resolution is included
Journal-ref: Phys.Rev. D71 (2005) 013001

15. hep-ph/0305152 [abs, ps, pdf, other] :
Title: Atmospheric Neutrino Oscillations, theta(13) and Neutrino Mass Hierarchy
Authors: J. Bernabeu, Sergio Palomares-Ruiz (Valencia U.), S. T. Petcov (SISSA, Trieste & INFN, Trieste)
Journal-ref: Nucl.Phys. B669 (2003) 255-276

16. hep-ph/0501184 [abs, ps, pdf, other] :
Title: Supernova neutrinos can tell us the neutrino mass hierarchy independently of flux models
Authors: V. Barger, Patrick Huber, Danny Marfatia

17. hep-ph/0412100 [abs, ps, pdf, other] :
Title: Identifying the neutrino mass hierarchy with supernova neutrinos
Authors: M. Kachelriess, R. Tomas
Comments: 10 pages, 11 figures. Based on talks given at Quarks04 and 5th Rencontres du Vietnam

18. hep-ph/0303210 [abs, ps, pdf, other] :
Title: Detecting the Neutrino Mass Hierarchy with a Supernova at IceCube
Authors: A.S.Dighe, M.T.Keil, G.G.Raffelt (MPP, Munich)
Comments: 19 pages, 6 Figs, final version accepted by JCAP, some references added
Journal-ref: JCAP 0306 (2003) 005

19. hep-ph/0302033 [abs, ps, pdf, other] :
Title: Probing the neutrino mass hierarchy and the 13-mixing with supernovae
Authors: C.Lunardini, A.Yu.Smirnov
Comments: LaTeX, 56 pages, 12 figures; a few clarifications added; typos corrected. Version to appear in JCAP
Journal-ref: JCAP 0306 (2003) 009

20. hep-ph/0209117 [abs, ps, pdf, other] :
Title: Long Baseline Neutrino Experiments and the LOW solution -- What is Left to Do and How Well Can It Be Done
Authors: Gabriela Barenboim, Andre de Gouvea (Fermilab)

21. hep-ph/0002064 [abs, ps, pdf, other] :
Title: The Dark Side of the Solar Neutrino Parameter Space
Authors: Andre de Gouvea (CERN), Alexander Friedland, Hitoshi Murayama (UC Berkeley, LBNL)
Comments: 4 pages, 3 figures, uses psfig. Fixed typos in Eq. (3). An imprecise comment in the footnote removed
Journal-ref: Phys.Lett. B490 (2000) 125-130

22. hep-ex/0503053 [abs, pdf] :
Title: NOvA Proposal to Build a 30 Kiloton Off-Axis Detector to Study Neutrino Oscillations in the Fermilab NuMI Beamline
Authors: The NOvA Collaboration, D. Ayres, et al

23. hep-ex/0210005 [abs, ps, pdf, other] :
Title: Letter of Intent to build an Off-axis Detector to study numu to nue oscillations with the NuMI Neutrino Beam
Authors: D. Ayres et.al

24. hep-ph/0303081 [abs, ps, pdf, other] :
Title: Very Long Baseline Neutrino Oscillation Experiment for Precise Measurements of Mixing Parameters and CP Violating Effects
Authors: M.V. Diwan, D. Beavis, Mu-Chun Chen, J. Gallardo, R.L. Hahn, S. Kahn, H. Kirk, W. Marciano, W. Morse, Z. Parsa, N. Samios, Y. Semertzidis, B. Viren, W. Weng, P. Yamin, M. Yeh, W. Frati, K. Lande, A.K. Mann, R.Van Berg, P. Wildenhain, J.R. Klein, I. Mocioiu, R. Shrock, K.T. McDonald
Journal-ref: Phys.Rev. D68 (2003) 012002

25. hep-ex/0106019 [abs, ps, pdf, other] :
Title: The JHF-Kamioka neutrino project
Authors: Y.Itow, T.Kajita, K.Kaneyuki, M.Shiozawa, Y.Totsuka, Y.Hayato, T.Ishida, T.Ishii, T.Kobayashi, T.Maruyama, K.Nakamura, Y.Obayashi, Y.Oyama, M.Sakuda, M.Yoshida, S.Aoki, T.Hara, A.Suzuki, A.Ichikawa, T.Nakaya, K.Nishikawa, T.Hasegawa, K.Ishihara, A.Suzuki, A.Konaka

26. hep-ex/0402041 [abs, ps, pdf, other] :
Title: A New Nuclear Reactor Neutrino Experiment to Measure theta 13
Authors: K. Anderson, et al
Comments: 167 pages, 57 figures, 125 authors, 40 Institutions White Paper Report on Using Nuclear Reactors to search for a value of theta 13

27. hep-ph/0112074 [abs, ps, pdf, other] :
Title: The LMA MSW Solution of the Solar Neutrino Problem, Inverted Neutrino Mass Hierarchy and Reactor Neutrino Experiments
Authors: S.T. Petcov, M. Piai
Comments: Results and conclusions unchanged. Few clarifying remarks, footnotes and few references added. Version to be published in Phys. Lett. B
Journal-ref: Phys.Lett. B533 (2002) 94-106

28. hep-ph/0306017 [abs, ps, pdf, other] :
Title: Precision Neutrino Oscillation Physics with an Intermediate Baseline Reactor Neutrino Experiment
Authors: Sandhya Choubey, S.T. Petcov, M. Piai
Journal-ref: Phys.Rev. D68 (2003) 113006

29. SLAC database (no arXiv entry):
Title: A Novel Concept For A Anti-Nu/E / Nu/E Neutrino Factory: The Beta Beam
First-Author: Zucchelli
Journal-ref: Phys.Lett. B532 (2002) 166
30. hep-ex/0302007 [abs, ps, pdf, other] :
Title: Physics Reach of the Beta Beam
Authors: Mauro Mezzetto
Comments: Invited talk at the Nufact02 Workshop, Imperial College of Science, Technology and Medicine, London, July 2002
Journal-ref: J.Phys. G29 (2003) 1771-1776

31. hep-ph/0312068 [abs, ps, pdf, other] :
Title: Neutrino oscillation physics with a higher $\gamma$ $\beta$-beam
Authors: J. Burguet-Castell, D. Casper, J.J. Gomez-Cadenas, P.Hernandez, F.Sanchez
Comments: An error corrected, conclusions unchanged. Revised version to appear in Nuclear Physics B
Journal-ref: Nucl.Phys. B695 (2004) 217-240

5. Apr 11, 2005

### Haelfix

There is indeed a difference between perihelion and aphelion, but its not quite for the reasons you might expect.

The dynamics of neutrino oscillations in dense mediums is a bit of an art form, and usuallly not taught at all outside of specialist circles as its rather technical.

In general you end up with a validation of the MSW effect

6. Apr 11, 2005

### wstevenbrown

"There is indeed a difference between perihelion and aphelion, but its not quite for the reasons you might expect."

And... is this documented? I have special anti-jargon hip-boots.

The precise reason for my original question was to discriminate between matter-induced effects (MSW, etc.) and 'intrinsic' oscillation, which should take place in the proper time of the particle, and therefore be dependent on total energy. Was my question unclear? Steve

PS BTW Meir, thanx for ref. list. I already had most of them, except for the SN articles, which may be very useful. S

7. Apr 11, 2005

### Haelfix

I mean its way beyond our present capabilities to somehow do away with MSW corruption in an experiment hence you have to include that effect. However, the good fit to the data that a MSW model gives is a good indication that yes indeed neutrinos mix in vacuo. I mean the entire premise of that model is in that very basic fact; you simply would not observe such a thing if they never mixed. Moreover massless neutrino models are disfavored by something like 5 sigma.

And yes indeed you can get values for the mixing angle and delta mass squared etc through a conglomeration of various means. Afaik the experimental bounds are still pretty ugly, and model dependant of course (I think the four mixing scenario is favored though). I believe they are pretty dependant too on stellar modeling so thats another potential complication.

You are probably looking for a fullon comprehensive experimental survey of solar neutrino experiments. Perhaps one of the links above will give it to you.

8. Apr 11, 2005

### Stefan Udrea

massless neutrinos

Hello.

quote:
<<Moreover massless neutrino models are disfavored by something like 5 sigma.>>
What do you mean by that ? What does sigma stand for ?
I was told that,in the recent years, some experiments proved that the neutrinos have mass ; you seem to be saying that this is only more likely, but not a fact proven 100 %.

9. Apr 11, 2005

### wstevenbrown

"I mean the entire premise of that model is in that very basic fact; you simply would not observe such a thing if they never mixed."

Precisely the point-- a model-dependent assumption, not an experimentally demonstrated fact-- and it really doen't matter which model is being talked about.

"There is indeed a difference between perihelion and aphelion, but its not quite for the reasons you might expect."

What is the difference? What reasons are given, and by whom? I'm not trying to be a PIA here, but the literature is pretty difficult to search on this particular question. Everybody includes in vacuo oscillation in their assumption set; apparently, nobody has quantified it. It's enough to make me wish for the next supernova (more than 5 KPc away). Steve

10. Apr 12, 2005

### Haelfix

Here is a review article I've used before, its fairly comprehensive and the latter sections go through a lot of the experimental data and what they find.

http://arxiv.org/PS_cache/hep-ph/pdf/0202/0202058.pdf

Im afraid you're not going to find what you are looking for though, perhaps atmospheric neutrino data is more along the lines of what you would want.
Neutrinos are notoriously difficult to detect due to their weak cross sections with matter, which is why you want large sources of them (like from the sun) and a huge bath of stuff occupying a large volume in order to see just a few chemical reactions.

Hell even their very existance historically was purely indirect! They were inferred by energetics (missing momentum). I do however think the evidence is pretty compelling that they do mix and are massive. Theoretically it makes good sense, and its hard to envision a model where they don't and we still see what we see.

Last edited: Apr 12, 2005
11. Apr 13, 2005

### Stefan Udrea

Thank you , Haelfix.
Tough lecture :yuck:

12. Apr 16, 2005

### wstevenbrown

[sigh] another lovely equation for the in vacuo oscillation, with enough unknown/unconstrained parameters to render it unmeaningful.

Assume, for the sake of discussion, that the total neutrino flux at the solar surface is relatively constant, or at least stochastically so. We represent it by the ordered sextuplet (e, anti-e, mu, anti-mu, tau, anti-tau). Somewhere on earth, and not necessarily at the same location, we have large detectors for each type. At each detector , the detection data are binned according to zenith angle, recoil energy and distance from Sol at time of reception. By comparing only within identical zenith angles and recoil energies, we should be able to notice a smooth shift in the neutrino spectrum. After correcting for inverse-square signal dropoff (which only affects the amplitude of the signal, not its spectral distribution), any residual variation in a "sufficiently large" sample space should be directly attributable to smooth variations caused by L-sub-vac, the oscillation length in a vacuum, with respect to Earth’s orbital distance.

Assuming only that solar spectrum is long-term constant, the detection efficiency at each detector can be factored out or, just as usefully, expressed as a ratio of some other detector.

The reason for additional binning by recoil energy is that oscillations take place in the proper time of the particle. At higher energies = higher velocities, the oscillation length appears longer due to the slowdown of the particle’s clock WRT ours.

Discounting for the moment our inability to distinguish taus and sterile variants, there still should be smooth variation in the flavors we can see. The only remaining difficulty is, how large is “sufficiently large”?

If the various consortia and soi-disant collaborations share data, there are conclusions to be drawn. Steve

13. Apr 27, 2005

### Nereid

Staff Emeritus
(A belated) Welcome to Physics Forums, wstevenbrown!

I assume you check John Bahcall's home page regularly? You might also have a chance to buttonhole an attendee or five at the next relevant neutrino conference (I don't know, off the top of my head, when/where that will be), or quizz the posters long distance.

14. Apr 30, 2005

### wstevenbrown

I asked my original question of an expert. The answer I received was not to the question I asked, so I presume it was filtered thru a secretary or lab assistant. Nevertheless, here it is:

As far as I understand, you proposed analysis has been done in a
combined way using a more general description for the propagation of the
neutrinos that includes both vacuum and matter effects. The bottom line
is that the existing experiments show clearly evidence for matter
effects and that vacuum effects will show up in an isolated way only in
future experiments at low energies.

John Bahcall

I remain curious why the question I asked hits everyone skew-wise, and never gets past their assumption set. Best regards-- Steve

15. Apr 30, 2005

### Nereid

Staff Emeritus
Would you consider re-framing the question, to reduce the possibility of it getting trapped and re-formatted in 'the assumption set'?

16. May 1, 2005

### Haelfix

"Discounting for the moment our inability to distinguish taus and sterile variants, there still should be smooth variation in the flavors we can see. "

Why do you think it needs to be smooth at all, it might be in a vacuum but certainly not in matter! Again you *will* find a variation (by a variation I mean delta epsilon = 0 is disfavored by several standard deviations in a root mean square parameter space survey), and hence you will find some constraints on the bounds of the various vacuum mixing angles but again there are model dependencies implicit in the calculation. And yes the proper length of the oscillation is important when you have detectors set up, but this is all well understood and implicit in the models, not to mention rather irrelevant as the detector lengths tend to be large. All this is in the paper I linked too earlier.

17. May 1, 2005

### wstevenbrown

"Why do you think it needs to be smooth at all, it might be in a vacuum but certainly not in matter!"

If you read my proposition carefully, you will note that binning the data by zenith angle and recoil energy causes all matter effects to cancel. I'm simply tired of seeing the in vacuo component treated as an integration constant. If it exists, it is measurable. What will be measured is changes in the observed solar neutrino spectrum which depend solely on distance from Sol.

I believe I will take Nereid's suggestion to recast the question in more comprehensible form, so as to be unmistakably clear, instead of running into everyone's expectation values. You may not hear from me for awhile on this subject. Best regards-- Steve

18. May 1, 2005

### Haelfix

"If you read my proposition carefully, you will note that binning the data by zenith angle and recoil energy causes all matter effects to cancel./"

Yes and im saying that does not follow and you would have to prove that assertion very carefully (and when you look at it carefully you will realize it can't work). Moreover matter effects are not simply an integration constant.

19. May 1, 2005

### Nereid

Staff Emeritus
Another suggestion if I may ... in your OP, you said: "oscillation while passing thru condensed matter -- and none which demonstrate this in vacuo" (my emphases). I'm curious as to what you'd count as 'in vacuo', and where 'condensed matter' ends ... as you know, there are no 'true vacuums' (even the most rarified radio bubble of an AGN contains some baryons, and there are neutrinos and (presumably) DM everywhere). For the purposes of your enquiry, is the 'condensed matter' that we earthlings usually think of (in OOMs, a range of 3, ~0.1 to 10 g/cc) what you have in mind? You seem to be interested in proton/nucleon densities (e.g. per m^3), but it's quite unclear (to me, at least).

BTW, if you don't like using the WRAP quote tags button (that's the one on the right, like a speech bubble), you can type in [ quote] and [/ quote] (without the spaces, of course) - it will make your posts easier to read (by clearly distinguishing what you said from what what the person you're quoting said).

20. May 1, 2005

### Spin_Network

May I suggest you read this first:http://arxiv.org/abs/hep-ph?0503028