- Email: [email protected]
Comments on reconstruction and origins of the neutrino mass spectrum
Nuclear Physics B (Proc. Suppl.) 87 (2000) 288-290
ELSEVIER
PROCEEDINGS SUPPLEMENTS www.elsevier.nl/locatelnpe
Comments on reconstruction A. Yu. Smirnov
and origins of the neutrino mass spectrum
a
a International Center for Theoretical Physics, Strada Costiera 11, 34100 Trieste, Italy There are two main issues in the present day neutrino physics: (i) Reconstruction of the neutrino mass (and flavor) spectrum and (ii) Identification of origin of the neutrino mass and mixing, or in other terms, implications of the neutrino data for the fundamental theory. Present status and perspectives of the reconstruction are summarized. We comment on the see-saw and the “bulk-brane” mechanisms of neutrino mass generation.
1. Mass and flavors. Recent data on atmospheric neutrinos have further confirmed the existence of maximal or close to maximal flavor mixing [l]. Now, I think, we can expect “anything” from neutrinos. Clearly, the simplest structure of the neutrino spectrum with normal mass hierarchy and small mixing is not realized. So, we should keep an open mind to any unexpected but experimentally possible features of the spectrum: l The mass hierarchy can be normal or inverted. l The spectrum can have a degeneracy: partial (when two mass eigenstates almost coincide) or complete (when all three masses are almost equal). l The neutrino mass matrix can show some new symmetries. l The spectrum can contain more than three states. An important issue is whether neutrino results are consistent with the “quark-1epton” symmetry and Grand Unification [2]. Eventually, we can arrive at one of the two opposite (and by now unexcluded) possibilities: 1). The neutrino mass matrix can be simpler than that in the quark sector. The reason could be that neutrino masses are related to physics at large mass scale (GUT) which has a richer symmetry. 2). Neutrino mass spectrum and mixing can be more complicated than those in the quark sector: due to the smallness of neutrino masses the spectrum can be “polluted” by several different contributions: e.g., see-saw mechanisms, Planck-
scale induced non-renormalizable operators, direct Yukawa couplings, etc. Anyway, in the minimal version there are three mass eigenstates, vi, with masses mi (i = 1,2,3) and three flavor eigenstates v,, a = e, p, 7. The problem is to find mi and distribute (mix) flavors in the mass eigenstates: that is, find Uai admixture of the flavor a! in the eigenstate vi. 2. What do we know? 1. From atmospheric neutrino data we have learned that equal (comparable) admixtures of up and V, are present in one of the mass eigenstates, say us. That is, Up3 N U73 N l/a. 2. Admixture of the ye flavor in us is zero or small: Ue3 < 1. 3. The oscillation solution of the atmospheric neutrino problem adds confidence that the solution of the solar neutrino problem is also related to neutrino masses and mixings. All existing solutions imply the hierarchy of mass splittings: Am?& - Am& << Am2atm * That’s it! We do not know how the ye flavor in two states (and therefore v~, v7) is distributed with small splitting. We do not know whether vs is the lightest state or the heaviest one: the sign Am:,, > 0 of Am:,, 3 rng - rng is unknown. < 0) in the case of normal (inverted) P&9n mass hierarchy. This leads to a significant ambiguity. Even if there is no sterile neutrino and the spectrum has a hierarchical structure, so that we have four schemes which m3=JK, differ by the distribution of the V,-flavor and the value of the splitting Am;,; they correspond to
0920-5632/00/S - seefront matter 0 2000 Elsevier Science B.V. All rights reserved. PI1 SO920-5632(00)00682-4
A. Yu. Smirnov /Nuclear Physics B (Proc. Suppl.) 87 (2000) 288-290
different solutions of the z/o-problem. Four more schemes can be constructed a s s u m ~ i n v e r t e d mass hierarchy: ml ~ m2 ~ x/Am2tm << m3. The number of schemes is doubled if we add spectra with degeneracy: mi >> ~ t m . 2 Even more possibilities appear if a partially degenerate spectrum is considered. Furthermore, there is a smooth transition from a hierarchical to a degenerate spectrum which does not change the oscillation pattern. 3 Major steps. The following results will significantly diminish the ambiguity: Identification of the solution of the solar neutrino problem. There is a good chance that existing and forthcoming experiments will discriminate among the suggested solutions. This will allow one to determine with rather good accuracy the size and the sign (for MSW solutions) of Am~l. Moreover, it will distribute the z/~ flavor in the mass eigenstates ul and v2. For the SMA MSW solution, ue is concentrated in gl with a small admixture in the v2. For all other solutions (LMA MSW, LOW MSW, VO) the mixing is large, which implies comparable admixtures of u~ in states with a small splitting: U~I " U~2. In this case it will be important to determine possible deviations from maximal mixing. Measurements of ]U~3[. It is of great importance not only for fundamental theory but also for astrophysics, especially for physics of supernova neutrinos. JUra[ is also important for the interpretation of the results of the ~ 0 ~ - decay searches. W h a t can we expect? (i) The long-baseline experiments MINOS, CERN-GS and later u-factories, with better sensitivity will improve the CHOOZ bound. (ii) New reactor experiments with better sensitivity to ]Ue3[ are under consideration [3]. (iii) Fhrther studies of the atmospheric neutrinos, in particular, searches for an excess and distortion of the zenith angle distribution of the e-like events can reveal [Ue31-effects. (iv) The /~t3ou searches are sensitive to [Ue3[: In the schemes with a normal mass hierarchy the contribution from the third mass eigenstate to the effective Majorana mass is m~e --
289
2 m. ]Ue3] 2 ~A~T~at
(v) Studies of the supernova neutrinos have a unique sensitivity to [Ue3[. Values of [Ue3[ as small as 10 -2 can produce an observable effect in the ue or Pe energy spectrum [4]. Determination of the sign of Am~tm, 2 that is, identification of the type of mass hierarchy. Matter effects are sensitive to the sign of A m a 2t m • Therefore, the determination of the sign requires: (a) non-zero [U¢3[ (usual matter affects re-channels of oscillations only); (b) study of matter effects in the electron neutrino channels; (c) possibility to distinguish effects in v~ and #e channels. (One can compare the matter effects for ve or P~ or for mixed beam of known composition with vacuum oscillation effects or compare the effects in v~ and p~ channels.) This will be possible with (i) atmospheric neutrinos; (ii) LBL experiments and experiments at u-factories, (iii) supernova neutrinos where, depending on the hierarchy type, strong transitions occur in either v~ or P~ channel [4]. The fi~/o~-decay mass, me~, strongly depends on the mass hierarchy type: in the case of inverted hierarchy [5], it can be as large as mee .-.
CP-violation. Perspectives of discovery of CPviolation in neutrino oscillations depend significantly on the solution of the solar neutrino problem and on the existence of new neutrino states. New neutrinos. There are two motivations for an introduction of sterile neutrinos: 1) To explain the atmospheric neutrino data via vu +4 us - oscillations. This allows one to rescue a concept of fermion families with small interfamily mixing: the flavor mixing is small; the large vu mixing is that with the sterile neutrino which has no analogy in the quark sector. (ii) To reconcile the LSND result with the oscillation solutions of the solar and atmospheric neutrino problems. One point should be emphasized: the LSND result implies that either solar or atmospheric neutrino problems (or both) should be solved by conversion to sterile states. So, one should observe signatures of sterile neutrinos in the solar or/and atmospheric neutrinos. Inversely, establishing that both solar and atmo-
290
A. Yu. Smirnov /Nuclear Physics B (Proc. Suppl.) 87 (2000) 288-290
spheric neutrinos undergo flavor conversion (as the dominant mode) will testify against an oscillation interpretation of the LSND result. The last statement can be checked soon: there are already data which disfavor the u~ ~ us interpretation of atmospheric neutrino data. The SNO experiment will test the ue --+ v8 solution of the v® problem [6]. In schemes with four neutrinos, predictions for the fl~0~-decay mass are modified [5]. 4. S e e - s a w or b u l k - b r a n e ?
It is believed that the smallness of neutrino mass is related to neutrality of neutrinos. The two mechanisms which realize this connection use the fact that the right-handed neutrinos, uR, are singiets of the SM symmetry group. In the celebrated see-saw mechanism, smallness of the neutrino mass is explained by the existence of a large mass scale: the fact that vR are singiets means that their Majorana masses MR are unprotected by the symmetry and therefore can be large. This leads to: m~ ~ ( h v ) 2 / M R ,
(1)
where h is the Yukawa coupling and v is the electroweak scale. Does the smallness of the neutrino mass testify via the see-saw for Grand Unification (see [2])? In fact, the atmospheric neutrino result with h ,,~ 1 gives MR ,,, 1014 GeV - two orders of magnitude smaller then GUT scale M G U T ~ 1016GeV (see an analysis for 3 generations in [7]). At least one MR can be obtained closer to MGUT, if one takes into account mixing between generations. However, there is no direct relation between MR and MGUT, SO that even equality M R = MGUT can be misleading. Predictions of light neutrino masses and mixing depend substantially on the structure of the righthanded neutrino mass matrix/~)/R [7]. Some information about/tT/R can be obtained from studies of (i) leptogenesis which can lead via sphaleron effects to observable baryon asymmetry, (ii) proton decays in the context of GUT [8]. In the bulk-brahe mechanism proposed recently [9] the smallness of neutrino mass is related to the existence of large extra compact dimensions
(R _< 0.1 mm). The components uR, being singlets, can propagate in the bulk of the extra dimensions. According to the bulk-brane mechanism, standard model fields are localized on a 3 dimensional brane (wall) embedded in the bulk of N compact extra dimensions. Gravitons and some other particles (singlets of SM group) can propagate in the bulk. The effective width of the brane is inversely proportional to the fundamental scale of quantum gravity: ,~ 1 / M ! ( M I >_ 10 TeV). All couplings of the brahe particles, in particular vL, with bulk particles (vR in our case) are suppressed by a universal factor M I / M p I which is just the degree of overlap of the wave functions which reside in the bulk and on the brane. In particular, the Dirac mass formed by uL and vR will be m = (hvMF)/Mm.
(2)
For M I = 10 TeV, h = 1 this gives m ,,~ 10 -4 eV. On the brane, the bulk neutrino will manifest itself as an infinite tower of Kaluza-Klein states with masses m n = n / R (n = O, + l , 4-2...). Thus, usual neutrinos are mixed by the universal mass term (2) with an infinite number of sterile neutrinos. R = 0.1 mm gives mt ,,~ 2 . 1 0 -3 eV. One possible application of these results is the solution of the solar neutrino problem via ve conversion to bulk states [10]. The first serious check of this possibility will be done soon by the SNO experiment. REFERENCES
1. M. Nakahata, these proceedings; F. Ronga, these proceedings. 2. G. Altarelli, hep-ph/0001024. 3. L. Mikaelyan, hep-ex/9910042. 4. A. S. Dighe, hep-ph/9912414, hepph/9907423. 5. C. Giunti, hep-ph/9912427. 6. J.N. Bahcall, P. I. Krastev, A. Yu. Smirnov, hep-ph/9911248 7. E. Kh. Akhmedov, hep-ph/0001041. 8. Y. Achiman, hep-ph/9911314. 9. N. Arkani-Hamed et al., hep-ph/9811448, K. R. Dienes et al, hep-ph/9811428. 10. G. Dvali, A. Yu. Smirnov, hep-ph/9904211.
ELSEVIER
PROCEEDINGS SUPPLEMENTS www.elsevier.nl/locatelnpe
Comments on reconstruction A. Yu. Smirnov
and origins of the neutrino mass spectrum
a
a International Center for Theoretical Physics, Strada Costiera 11, 34100 Trieste, Italy There are two main issues in the present day neutrino physics: (i) Reconstruction of the neutrino mass (and flavor) spectrum and (ii) Identification of origin of the neutrino mass and mixing, or in other terms, implications of the neutrino data for the fundamental theory. Present status and perspectives of the reconstruction are summarized. We comment on the see-saw and the “bulk-brane” mechanisms of neutrino mass generation.
1. Mass and flavors. Recent data on atmospheric neutrinos have further confirmed the existence of maximal or close to maximal flavor mixing [l]. Now, I think, we can expect “anything” from neutrinos. Clearly, the simplest structure of the neutrino spectrum with normal mass hierarchy and small mixing is not realized. So, we should keep an open mind to any unexpected but experimentally possible features of the spectrum: l The mass hierarchy can be normal or inverted. l The spectrum can have a degeneracy: partial (when two mass eigenstates almost coincide) or complete (when all three masses are almost equal). l The neutrino mass matrix can show some new symmetries. l The spectrum can contain more than three states. An important issue is whether neutrino results are consistent with the “quark-1epton” symmetry and Grand Unification [2]. Eventually, we can arrive at one of the two opposite (and by now unexcluded) possibilities: 1). The neutrino mass matrix can be simpler than that in the quark sector. The reason could be that neutrino masses are related to physics at large mass scale (GUT) which has a richer symmetry. 2). Neutrino mass spectrum and mixing can be more complicated than those in the quark sector: due to the smallness of neutrino masses the spectrum can be “polluted” by several different contributions: e.g., see-saw mechanisms, Planck-
scale induced non-renormalizable operators, direct Yukawa couplings, etc. Anyway, in the minimal version there are three mass eigenstates, vi, with masses mi (i = 1,2,3) and three flavor eigenstates v,, a = e, p, 7. The problem is to find mi and distribute (mix) flavors in the mass eigenstates: that is, find Uai admixture of the flavor a! in the eigenstate vi. 2. What do we know? 1. From atmospheric neutrino data we have learned that equal (comparable) admixtures of up and V, are present in one of the mass eigenstates, say us. That is, Up3 N U73 N l/a. 2. Admixture of the ye flavor in us is zero or small: Ue3 < 1. 3. The oscillation solution of the atmospheric neutrino problem adds confidence that the solution of the solar neutrino problem is also related to neutrino masses and mixings. All existing solutions imply the hierarchy of mass splittings: Am?& - Am& << Am2atm * That’s it! We do not know how the ye flavor in two states (and therefore v~, v7) is distributed with small splitting. We do not know whether vs is the lightest state or the heaviest one: the sign Am:,, > 0 of Am:,, 3 rng - rng is unknown. < 0) in the case of normal (inverted) P&9n mass hierarchy. This leads to a significant ambiguity. Even if there is no sterile neutrino and the spectrum has a hierarchical structure, so that we have four schemes which m3=JK, differ by the distribution of the V,-flavor and the value of the splitting Am;,; they correspond to
0920-5632/00/S - seefront matter 0 2000 Elsevier Science B.V. All rights reserved. PI1 SO920-5632(00)00682-4
A. Yu. Smirnov /Nuclear Physics B (Proc. Suppl.) 87 (2000) 288-290
different solutions of the z/o-problem. Four more schemes can be constructed a s s u m ~ i n v e r t e d mass hierarchy: ml ~ m2 ~ x/Am2tm << m3. The number of schemes is doubled if we add spectra with degeneracy: mi >> ~ t m . 2 Even more possibilities appear if a partially degenerate spectrum is considered. Furthermore, there is a smooth transition from a hierarchical to a degenerate spectrum which does not change the oscillation pattern. 3 Major steps. The following results will significantly diminish the ambiguity: Identification of the solution of the solar neutrino problem. There is a good chance that existing and forthcoming experiments will discriminate among the suggested solutions. This will allow one to determine with rather good accuracy the size and the sign (for MSW solutions) of Am~l. Moreover, it will distribute the z/~ flavor in the mass eigenstates ul and v2. For the SMA MSW solution, ue is concentrated in gl with a small admixture in the v2. For all other solutions (LMA MSW, LOW MSW, VO) the mixing is large, which implies comparable admixtures of u~ in states with a small splitting: U~I " U~2. In this case it will be important to determine possible deviations from maximal mixing. Measurements of ]U~3[. It is of great importance not only for fundamental theory but also for astrophysics, especially for physics of supernova neutrinos. JUra[ is also important for the interpretation of the results of the ~ 0 ~ - decay searches. W h a t can we expect? (i) The long-baseline experiments MINOS, CERN-GS and later u-factories, with better sensitivity will improve the CHOOZ bound. (ii) New reactor experiments with better sensitivity to ]Ue3[ are under consideration [3]. (iii) Fhrther studies of the atmospheric neutrinos, in particular, searches for an excess and distortion of the zenith angle distribution of the e-like events can reveal [Ue31-effects. (iv) The /~t3ou searches are sensitive to [Ue3[: In the schemes with a normal mass hierarchy the contribution from the third mass eigenstate to the effective Majorana mass is m~e --
289
2 m. ]Ue3] 2 ~A~T~at
(v) Studies of the supernova neutrinos have a unique sensitivity to [Ue3[. Values of [Ue3[ as small as 10 -2 can produce an observable effect in the ue or Pe energy spectrum [4]. Determination of the sign of Am~tm, 2 that is, identification of the type of mass hierarchy. Matter effects are sensitive to the sign of A m a 2t m • Therefore, the determination of the sign requires: (a) non-zero [U¢3[ (usual matter affects re-channels of oscillations only); (b) study of matter effects in the electron neutrino channels; (c) possibility to distinguish effects in v~ and #e channels. (One can compare the matter effects for ve or P~ or for mixed beam of known composition with vacuum oscillation effects or compare the effects in v~ and p~ channels.) This will be possible with (i) atmospheric neutrinos; (ii) LBL experiments and experiments at u-factories, (iii) supernova neutrinos where, depending on the hierarchy type, strong transitions occur in either v~ or P~ channel [4]. The fi~/o~-decay mass, me~, strongly depends on the mass hierarchy type: in the case of inverted hierarchy [5], it can be as large as mee .-.
CP-violation. Perspectives of discovery of CPviolation in neutrino oscillations depend significantly on the solution of the solar neutrino problem and on the existence of new neutrino states. New neutrinos. There are two motivations for an introduction of sterile neutrinos: 1) To explain the atmospheric neutrino data via vu +4 us - oscillations. This allows one to rescue a concept of fermion families with small interfamily mixing: the flavor mixing is small; the large vu mixing is that with the sterile neutrino which has no analogy in the quark sector. (ii) To reconcile the LSND result with the oscillation solutions of the solar and atmospheric neutrino problems. One point should be emphasized: the LSND result implies that either solar or atmospheric neutrino problems (or both) should be solved by conversion to sterile states. So, one should observe signatures of sterile neutrinos in the solar or/and atmospheric neutrinos. Inversely, establishing that both solar and atmo-
290
A. Yu. Smirnov /Nuclear Physics B (Proc. Suppl.) 87 (2000) 288-290
spheric neutrinos undergo flavor conversion (as the dominant mode) will testify against an oscillation interpretation of the LSND result. The last statement can be checked soon: there are already data which disfavor the u~ ~ us interpretation of atmospheric neutrino data. The SNO experiment will test the ue --+ v8 solution of the v® problem [6]. In schemes with four neutrinos, predictions for the fl~0~-decay mass are modified [5]. 4. S e e - s a w or b u l k - b r a n e ?
It is believed that the smallness of neutrino mass is related to neutrality of neutrinos. The two mechanisms which realize this connection use the fact that the right-handed neutrinos, uR, are singiets of the SM symmetry group. In the celebrated see-saw mechanism, smallness of the neutrino mass is explained by the existence of a large mass scale: the fact that vR are singiets means that their Majorana masses MR are unprotected by the symmetry and therefore can be large. This leads to: m~ ~ ( h v ) 2 / M R ,
(1)
where h is the Yukawa coupling and v is the electroweak scale. Does the smallness of the neutrino mass testify via the see-saw for Grand Unification (see [2])? In fact, the atmospheric neutrino result with h ,,~ 1 gives MR ,,, 1014 GeV - two orders of magnitude smaller then GUT scale M G U T ~ 1016GeV (see an analysis for 3 generations in [7]). At least one MR can be obtained closer to MGUT, if one takes into account mixing between generations. However, there is no direct relation between MR and MGUT, SO that even equality M R = MGUT can be misleading. Predictions of light neutrino masses and mixing depend substantially on the structure of the righthanded neutrino mass matrix/~)/R [7]. Some information about/tT/R can be obtained from studies of (i) leptogenesis which can lead via sphaleron effects to observable baryon asymmetry, (ii) proton decays in the context of GUT [8]. In the bulk-brahe mechanism proposed recently [9] the smallness of neutrino mass is related to the existence of large extra compact dimensions
(R _< 0.1 mm). The components uR, being singlets, can propagate in the bulk of the extra dimensions. According to the bulk-brane mechanism, standard model fields are localized on a 3 dimensional brane (wall) embedded in the bulk of N compact extra dimensions. Gravitons and some other particles (singlets of SM group) can propagate in the bulk. The effective width of the brane is inversely proportional to the fundamental scale of quantum gravity: ,~ 1 / M ! ( M I >_ 10 TeV). All couplings of the brahe particles, in particular vL, with bulk particles (vR in our case) are suppressed by a universal factor M I / M p I which is just the degree of overlap of the wave functions which reside in the bulk and on the brane. In particular, the Dirac mass formed by uL and vR will be m = (hvMF)/Mm.
(2)
For M I = 10 TeV, h = 1 this gives m ,,~ 10 -4 eV. On the brane, the bulk neutrino will manifest itself as an infinite tower of Kaluza-Klein states with masses m n = n / R (n = O, + l , 4-2...). Thus, usual neutrinos are mixed by the universal mass term (2) with an infinite number of sterile neutrinos. R = 0.1 mm gives mt ,,~ 2 . 1 0 -3 eV. One possible application of these results is the solution of the solar neutrino problem via ve conversion to bulk states [10]. The first serious check of this possibility will be done soon by the SNO experiment. REFERENCES
1. M. Nakahata, these proceedings; F. Ronga, these proceedings. 2. G. Altarelli, hep-ph/0001024. 3. L. Mikaelyan, hep-ex/9910042. 4. A. S. Dighe, hep-ph/9912414, hepph/9907423. 5. C. Giunti, hep-ph/9912427. 6. J.N. Bahcall, P. I. Krastev, A. Yu. Smirnov, hep-ph/9911248 7. E. Kh. Akhmedov, hep-ph/0001041. 8. Y. Achiman, hep-ph/9911314. 9. N. Arkani-Hamed et al., hep-ph/9811448, K. R. Dienes et al, hep-ph/9811428. 10. G. Dvali, A. Yu. Smirnov, hep-ph/9904211.