The reported signal at the LSND experiment, when interpreted as neutrino
mixing with $\delta m^2 = 6 \;\rm{eV}^2$, provides evidence for neutrinos with
a cosmologically significant mass. However, attempts to reconcile this
interpretation of the experiment with other hints about neutrino properties
require a (sterile) fourth neutrino and/or an ``inverted'' neutrino mass
hierarchy. An interpretation of the LSND experiment employing $\delta m^2 =
0.3\; \rm{eV}^2$, with three-generation mixing and a ``normal'' neutrino mass
hierarchy, can just barely be reconciled with the negative results of other
laboratory neutrino oscillation experiments and the positive hints of neutrino
oscillation from the solar and atmospheric neutrino problems. Though subject to
test by by future experiments, such a solution allows (but does not demand)
neutrino masses relevant for dark matter.Comment: To be published in Nucl. Phys. B (Proc. Suppl.), in the proceedings
  of "Sources and Detection of Dark Matter in the Universe", held in Santa
  Monica, Feb. 14-16 1996. 5 page

Adeva

Athanassopoulos

Berezhianai

Bilenky

Buskulic

Caldwell

Cardall

Casper

Chen

Christian Y. Cardall

Chun

Enqvist

Fogli

Foot

Fukuda

Fuller

George M. Fuller

Kitamura

Krastev

Kwong

Michael

Montanet

Primack

Qian

Saltzberg

Totsuka

Yasuda

English

arXiv

Crossref

Nuclear Physics B - Proceedings Supplements

Three-generation neutrino mixing and lsnd dark matter neutrinos

The reported signal at the LSND experiment, when interpreted as neutrino mixing with δm2 = 6 eV2, provides evidence for neutrinos with a cosmologically significant mass. However, attempts to reconcile this interpretation of the experiment with other hints about neutrino properties require a (sterile) fourth neutrino and/or an "inverted" neutrino mass hierarchy. An interpretation of the LSND experiment employing δm2 = 0.3 eV2, with three-generation mixing and a "normal" neutrino mass hierarchy, can just barely be reconciled with the negative results of other laboratory neutrino oscillation experiments and the positive hints of neutrino oscillation from the solar and atmospheric neutrino problems. Though subject to test by by future experiments, such a solution allows (but does not demand) neutrino masses relevant for dark matter

Cardall, Christian Y

Fuller, George M

eScholarship - University of California

UC San DiegoUC San Diego Previously Published WorksTitleThree-generation neutrino mixing and lsnd dark matter neutrinosPermalinkhttps://escholarship.org/uc/item/2ht6x62hJournalNuclear and Particle Physics Proceedings, 51(2)ISSN2405-6014AuthorsCardall, Christian YFuller, George MPublication Date1996-11-01DOI10.1016/s0920-5632(96)00510-5 Peer reviewedeScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaNuclear Physics B (Proc. Suppl.) 51B (1996) 259-263 Three-generation neutrino mixing and LSND dark matter neutrinos Christian Y. Cardall and George M. Fuller a aDepartment of Physics, University of California, San Diego, La Jolla, California 92093-0319 The reported signal at the LSND experiment, when interpreted as neutrino mixing with bm* = 6 eV*, provides evidence for neutrinos with a cosmologically significant mass. However, attempts to reconcile this interpretation of the experiment with other hints about neutrino properties require a (sterile) fourth neutrino and/or an “inverted” neutrino mass hierarchy. An interpretation of the LSND experiment employing 6m2 = 0.3 eV2, with three- generation mixing and a “normal” neutrino mass hierarchy, can just barely be reconciled with the negative results of other laboratory neutrino oscillation experiments and the positive hints of neutrino oscillation from the solar and atmospheric neutrino problems. Though subject to test by by future experiments, such a solution allows (but does not demand) neutrino masses relevant for dark matter. 1. ACCOMODATING LSND DARK MATTER NEUTRINOS: “UNNATURAL” SCHEMES Based on the first year of data, a possible signal in the LSND experiment at Los Alamos has been reported [l]. Results from the second year of data confirm this signal [2]. An early and oft-quoted interpretation of this signal was that it repre- sents c, * V, mixing, with Sm2 z 6 eV2 and sin2 20 z 5 x 10w3. The motivations for the selec- tion of these mixing parameters are twofold: (1) compatibility with the negative results of other accelerator or reactor experiments (see Fig. 3 of Ref. [l]); and (2) the cosmologically interest- ing neutrino mass of 2.5 eV, which fits well into coldfhot dark matter models that seem to sat- isfy many observational constraints on large-scale structure formation [3]. Many attempts to reconcile the LSND result with neutrino oscillation solutions to the solar and atmospheric neutrino problems have been made [4]. These have at least one of two “un- natural” features: a fourth neutrino, and/or an inverted neutrino mass hierarchy. A fourth neutrino is required when three differ- ent independent mass differences are used, e.g., ~?4imD = 6 eV2, Sm&,,os z 10v2 eV2, and Wolar = low5 eV* or lo-i0 eV2. From mea- surements of the width of the 2, boson, it is known that only three neutrino species partici- pate in electroweak interactions [5]. Therefore, a fourth neutrino would have to be “sterile,” having no standard model interactions. Since a V~ t) v, solution to the atmospheric neutrino problem is restricted by big-bang nucleosynthesis considera- tions [6], the sterile neutrino typically makes its appearance in a u, t) v, small-angle MSW solu- tiorrto the solar neutrino problem. An inverted neutrino mass hierarchy is one in which the neutrino mass eigenvalue most closely associated with the u, is heavier than those asso- ciated with the vfi or uT, or the mass eigenvalue associated with the V~ is heavier than that associ- ated with the u,. The requirement of an inverted hierarchy arises from considerations of supernova r-process nucleosynthesis [7]. For the typical mix- ing parameters associated with the LSND experi- ment cited above, an MSW resonant transforma- tion increases the average energy of the u, popu- lation in the post core-bounce supernova environ- ment. This drives the material around the super- nova remnant proton-rich, precluding synthesis of the r-process elements. This problem does not occur with an inverted mass hierarchy in which the u, is the heaviest neutrino. In this case, an MSW resonant transformation increases the av- erage energy of the V, population, enhancing the neutron-rich conditions required for successful T- process nucleosynthesis. Should the existence of sterile neutrinos or an inverted neutrino mass hierarchy be designated 0920-5632/96/$15.00 Copyright 01996 Elsevier Science B.V. All rights reserved. PIISO920-5632(96)00510-5 260 C. P Cardall, G.M. Fuller/Nuclear Physics B (Proc. Suppi.) S/B (1996) 259-263 “unnatural”? After all, we expect the existence of particles beyond the standard model, and we have no solid reason to assume that the genera- tional mass pattern of the neutrinos should follow that of the corresponding charged leptons. The relevant point is that before assuming that the positive hints of neutrino mixing-LSND and the solar and atmospheric neutrino problems-point to things significantly different than what is ex- pected from the standard model, schemes more in harmony with our experience from the standard model should be pushed to their limits first. 2. ACCOMODATING LSND NEUTRI- NOS: A “NATURAL” SCHEME We seek to construct a “natural” scheme of neutrino mass and mixing that reconciles all known hints about neutrino properties. Such a “natural” scheme would involve only three neu- trino flavors, and would not have an inverted neu- trino mass hierarchy. We would expect such a solution to take advantage of the possibilities of three-generation mixing, rather than simply con- sisting of a set of two-flavor neutrino mixings that have been “stitched together.” In particular, the atmospheric neutrino problem could involve both up +) u, and u,, +) u, mixing. In using only three neutrinos, one is immedi- ately faced with the problem mentioned earlier, i.e. three independent mass differences. To ac- comodate a neutrino mixing solution to the so- lar neutrino problem, a small mass difference is required: &&,, z lo-’ eV2 or 10-l’ eV2 for MSW and “just-so” vacuum oscillation solutions, respectively [8]. These scales for the mass differ- ence cannot be altered much. In the case of the MSW solution, a mass level crossing is the basis of the whole effect, and so the mass difference is essentially determined by solar parameters. The “just so” vacuum oscillation solution requires that the earth-sun distance be on the order of the neu- trino oscillation length; thus the mass difference for this solution is determined as well. There may be a little more freedom in the neu- trino mass differences used to explain the LSND signal and the atmospheric neutrino problem, however. In particular, we consider the possibil- ity of explaining both LSND and the atmospheric neutrino data with a single common mass differ- ence in the range Gmztmos LSX,, z 0.2 - 0.4 eV2. This is an order of magnitude smaller than the mass difference usually associated with the LSND signal, and an order of magnitude larger than that usually associated with atmospheric neutrinos. Is the use of a common mass difference for LSND and atmospheric neutrinos feasible? Fig. 3 of Ref. [l] shows that 6m&,os, LSND z 0.2 - 0.4 eV2 is compatible with the negative results of other accelerator and reactor experiments. How- ever, the claimed zenith-angle dependance of the atmospheric neutrino data seem to imply a smaller mass difference, bm&,os = lop2 eV2, with a 90% C.L. upper limit of about 0.1 eV” [9]. We note that the statistical significance of this fit has been questioned [lo]. According to another analysis, of the Kamiokande multi-GeV data, %kos 2 0.25 eV2 is excluded at 90% C.L., and 6m&,os > 0.47 eV2 is excluded at 95% C.L. [ll]. Thus Sm~tmos,LSND z 0.3 eV2 would be allowed at 95% C.L. Next we turn to a discussion of the mixing an- gles. The neutrino flavor eigenstates, u,, can be written as a linear combination of mass eigen- states, vi: (1) where U,, are elements of a unitary mixing ma- trix U. We take U to be a standard parametriza- tion of the Cabbibo-Kobayashi-Maskawa (CKM) matrix involving three mixing angles and a CP violating phase [ 121. The mass differences indicated above satisfy c5mfol,, << Gm&,os, LSND. A useful approxima- tion in this case is the ‘Lone mass scale domi- nance” (OMSD) limit, in which we neglect c5m$,,ar relative to Sm?&,s LsND. The discussion is con- siderably simplified in this limit, as the results from two-flavor interpretations of neutrino mix- ing experiments can be directly converted to the three-neutrino OMSD interpretation [13]. For two-neutrino vacuum oscillations, the survival probability P is given by P = 1 - sin2 20 sin2 (1.27?) , C. Y Cardall, GM Fuller/Nuclear Physics B (Proc. Suppl.) 5lB (1996) 259-263 261 where L is the path length (in km) of a neu- trino initially in a flavor eigenstate at L = 0, E is the neutrino energy in GeV, and 6m2 (= 6m2 atmos, LsND) is in eV. The two-flavor mixing angle is 8. In the OMSD limit, we have the follow- ing correspondence between the two-flavor mixing angle and the elements of the three-flavor mixing matrix: sin2 28 ti 41~Cls121~~S12 (wp.), (3) sin2 28 e 4]Uo1s]2(1 - ]Uas12) (disapp.); (4) for appearance and disappearance experiments, respectively. For the parametrization of U in Ref. [12], we have I&l2 = sin2 013, (5) lqL312 = cos2 fill3 sin2 e23, (6) IUT312 = ~05~ 813 c~~2 e23. (7) Notice that the mixing angle 1312 and the CP- violating phase do not appear in the oscillation probability. Thus 6m2 and the mixing angles 01s and 82s are the only parameters needed to describe three-flavor mixing involving the larger mass difference (Smztmos, LSND) in the OMSD case. Fig. 1 shows the allowed ranges of the mix- ing angles 61s and 02s. Each panel corresponds to a different value of Gmztmos LSND. This figure shows that a small area of the f?is and 023 plane is available for Gm&mos LsND M 0.3 - 0.4 eV2 which explains the LSND signal, provides a solution to the atmospheric neutrino problem, and does not conflict with the negative results of other accel- erator and reactor experiments. For small val- ues of &-which are indicated by the solution in Fig. l-the small angle MSW solution to the solar neutrino problem is essentially unaffected P61. Thus it appears that there is an essentially unique solution that can simultaneously explain the LSND signal and solve the solar and atmo- spheric neutrino problems, all without introduc- ing sterile neutrinos. We have shown elsewhere that existing limits on two-flavor mixing parame- ters based on supernova r-process nucleosynthesis can be applied to the three-flavor mixing case in the OMSD limit [17]. We conclude that the above solution has a small enough mass difference that supernova r-process production is not adversely affected [7]. Cold+hot dark matter models, with about 20% of the dark matter comprised of two species of -2.5 eV neutrinos, are reported to fit large-scale structure data well [3]. Choosing bm&,, M 0.3 - 0.4 eV2 no longer directly implies the exis- tence of neutrinos with this mass. Since neutrino oscillations are only sensitive to neutrino mass d$erences, however, all of the neutrino masses can be offset from zero to provide a neutrino mass sum - 5 eV. In such a scheme the neutrino masses would be nearly degenerate, a possibility consid- ered in Refs. [18].l It should be noted that the putative solution in Fig. 1 is fragile. We have already mentioned that the mass difference Gm&,os LSND z 0.3 - 0.4 eV2 is allowed at 95% C.L., but not at 90% C.L. A similar situation exists for the mixing angles: the contours in Fig. 1 (except the atmospheric neu- trino solution contours) are 95% C.L. contours. At 90% C.L., the LSND detection band shrinks and the exclusion region from other accelerator and reactor experiments expands, and the solu- tion in Fig. 1 virtually disappears. We have sought a “natural” solution, but in the end it still has what might be considered some “unnatural” features. For example, we have taken 6m2,e,I M 6rnz v >> 6m2, v , in anal- ogy with the hierarch;-of mass dikerences of the charged leptons. For the charged leptons, this hierarchy of mass differences arises naturally from the hierarchy of the masses themselves, i.e. rn3 << rn: << m2,. However, the offset of neu- trino masses from zero required to make the neu- trino masses sum to about 5 eV for cold+hot dark matter models causes the absolute masses to have roughly similar magnitudes, in contrast to the masses of the charged leptons. Another unnatural feature of this putative “natural)’ solution is that several of the off- diagonal elements of the mixing matrix U have relatively large magnitudes. This is in contrast ‘Note that with all three neutrino masses offset from zero, the OMSD limit (which applies to mass d@erences) can still apply, even if the masses themselves are “nearly degenerate.” 262 C. Y Cardall, G.M. Fuller/Nuclear Physics B (Proc. Suppl.) 51B (1996) 259-263 10’ 2 ,.,’ -2 1 ,>.’ 2 ,:’ I .,- ,:’ 10-l ,:’ , _ . :’ -------------+-- ,:’ _------_--__- 10-z ~r:,~:~~---~~ . n7 ._----- --- Figure 1. Allowed regions of the mixing angles 013 and 823, for four values of the dominant mass difference. The region between the solid lines is the 95% C.L. detection of LSND [14]. The region inside the long dashed lines is excluded by accelerator/reactor 95% C.L. limits [13]. The region enclosed by the short dashed lines represents a solution to the sub-GeV atmospheric neutrino data [15]. to the quark mixing case [12]. It has been recog- nized previously that a three-neutrino oscillation explanation of the LSND experiment requires this unusual feature [ 191. Large off-diagonal terms will generally be present whenever oscillation proba- bilities are large, and neutrino oscillation expla- nations of the atmospheric neutrino anomaly and the LSND data both invoke relatively large oscil- lation probabilities. 3. FUTURE TESTS Fortunately, the prospects are good for test- ing the last remaining three-neutrino solution that explains the LSND signal and solves the solar and atmospheric neutrino problems. The LSND experiment continues to run. A compa- rable experiment, KARMEN, is receiving an up- grade that within a few years should provide ei- C. E Cardall, G.M. Fuller/Nuclear Physics B (Proc. Suppl.) 5lB (1996) 259-263 263 ther a confirmation or refutation of the LSND signal [20]. Super-Kamiokande will provide much better statistics on the claimed zenith-angle de- pendance of the atmospheric neutrino data [21]. Super-Kamiokande and SNO may also be able to distinguish solar neutrino solutions involving sterile neutrinos from solutions involving only ac- tive neutrino flavors [22]. A null result at the San Onofre reactor experiment [23] would not rule out the “natural” solution proposed here; on the other hand, a detection of neutrino oscillations at San Onofre could not be accounted for by our solution. However, proposed long-baseline accel- erator experiments will probe the entire region of parameter space favored by the atmospheric neu- trino sub-GeV data [13,24] and could thus provide the crucial test. Supported by grants NSF PHY95-03384 and NASA NAG5-3062 at UCSD. REFERENCES 1. C. Athanassopoulos et al. (LSND Collabora- tion), Phys. Rev. Lett. 75, 2650 (1995). 2. C. Athanassopoulos et aE. (LSND Collabora- tion), preprint LA-UR-96-1326, 1996. 3. J. R. Primack, J. Holtman, A. Klypin, and D. 0. Caldwell, Phys. Rev. Lett. 74, 2160 (1995). 4. G. M. Fuller, J. R. Primack, and Y.-Z. Qian, Phys. 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Three-generation neutrino mixing and LSND dark matter neutrinos

Three-generation neutrino mixing and LSND dark matter neutrinos

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