Short Baseline Neutrino Oscillations
How a new long range gauge interaction can allow a υ oscillation fit to Short Baseline data including LSND and MiniBooNe
19 October, 2007, RETENU ‘07 Ann Nelson, University of Washington and IFT, Universidad Autónoma de Madrid Collaborator: Jon Walsh LiquidScintillatorNeutrinoDetector
• short baseline (30 m) neutrino oscillation experiment at Los Alamos _ _ • νμ from μ decay at rest at energies from 20-53 MeV + νμ from π decay with energies from 60-200 MeV • _ _ • Prob of conversion of νμ to νe =0.264±0.081% • Prob of conversion of νμ to νe =0.26±0.11% LSND cont.
• An Outlier -doesn’t fit into 3 ν oscillation scheme • Even with additional sterile ν’s is difficult to reconcile with other short baseline ν oscillation data
Status of global fits to neutrino oscillations 25 more than 4 v? gives too much Helium: not good for cosmology
Figure 17. The two classes of six four–neutrino mass spectra, (3+1) and (2+2).
3.3σ away from zero. To explain this signal with neutrino oscillations requires a 2 2 mass-squared difference ∆mlsnd 1 eV . Such a value is inconsistent with the mass- squared differences required by solar/KamLAND and atmospheric/K2K experiments within the standard three–flavour framework. In this section we consider four–neutrino schemes, where a sterile neutrino [114, 115, 116] is added to the three active ones to provide the additional mass scale needed to reconcile the LSND evidence. We include in our analysis data from the LSND experiment, as well as from short-baseline (SBL) accelerator [117, 118] and reactor [105, 109, 119] experiments reporting no evidence for oscillations (see Ref. [120] for details of our SBL data analysis). We update our previous four–neutrino analyses (see, e.g., Refs. [121, 122]) by including the most recent solar and KamLAND [15] data, the improved atmospheric neutrino fluxes [32] and latest data from the K2K long-baseline experiment [17].
5.1. A common parameterization for four–neutrino schemes Four–neutrino mass schemes are usually divided into the two classes (3+1) and (2+2), as illustrated in Fig. 17. We note that (3+1) mass spectra include the three–active neutrino scenario as limiting case. In this case solar and atmospheric neutrino oscillations are 2 explained by active neutrino oscillations, with mass-squared differences ∆msol and 2 ∆matm, and the fourth neutrino state gets completely decoupled. We will refer to such limiting scenario as (3+0). In contrast, the (2+2) spectrum is intrinsically different, as the sterile neutrino must take part in either solar or in atmospheric neutrino oscillations, or in both. Neglecting CP violation, neutrino oscillations in four–neutrino schemes are generally described by 9 parameters: 3 mass-squared differences and 6 mixing angles in the lepton mixing matrix [20]. We use the parameterization introduced in Ref. [123], in 2 2 2 terms of ∆msol, θsol, ∆matm, θatm, ∆mlsnd, θlsnd. These 6 parameters are similar to the two-neutrino mass-squared differences and mixing angles and are directly related to the oscillations in solar, atmospheric and the LSND experiments. For the remaining 3 Some SBL ν expts
Channel Experiment Lowest sin2 2θ Best reach in ∆m2 at high ∆m2 sin2 2θ 2 3 3 νµ νe LSND 0.03 eV > 2.5 10− > 1.2 10− → 2 × 3 × 3 KARMEN 0.06 eV < 1.7 10− < 1.0 10− 2 × 3 × 3 NOMAD 0.4 eV < 1.4 10− < 1.0 10− 2 × 1 × 2 νe disappearance Bugey 0.01 eV < 1.4 10− < 1.3 10− 2 × 1 × 2 Chooz 0.0001 eV < 1.0 10− < 5 10− 2 × × 1 νµ disappearance CCFR84 6 eV NA < 2 10− 2 × 1 CDHS 0.3 eV NA < 5.3 10− × Table 5: Results used in 3+2 fit. sin2 2θ limit is 90% CL matrix is also expanded by two rows and two columns. The data that drive the fits are the “short baseline” experiments that provide information on high ∆m2 oscillations, summarized in Tab. 5. The combination of 146 147 152 153 ν¯µ ν¯e (LSND, Karmen II ), νµ νe (NOMAD ), νµ disappearance (CDHS, → 154 → 148 25 CCFR84 ), and νe disappearance (Bugey, CHOOZ ) must all be accommodated within the model. A constraint for Super K νµ disappearance is also included. None of the short baseline experiments except for LSND provide evidence for oscillations beyond 3σ. However, it should be noted that CDHS has a 2σ (statistical and systematic, combined) effect consistent with a high ∆m2 sterile neutrino when the data are fit for a shape dependence, and Bugey has a 1σ pull at ∆m2 1eV2. As a result, these two ∼ experiments define the best fit combination of high and low ∆m2 for the 3+2 model. However, there are acceptable solutions with a combination of low ∆m2 values. The 151 2 2 2 2 best fit, has ∆m14 = 0.92 eV , ∆m15=22 eV , although there are combinations which work with two relatively low ∆m2 values. A wide range of mixing angles can be accommodated, and the best fit has Ue4 = 0.121, Uµ4 = 0.204, Ue5 = 0.036 and Uµ4 = 0.224. The other mixing angles involving the sterile states are not probed by the ν disappearance, ν disappearance and ν ν appearance experiments listed µ e µ → e above. There is 30% compatibility for all other experiments and LSND. Introducing extra neutrinos, including sterile ones, would have cosmological impli- cations, compounded if the extra neutrinos have significant mass (>1 eV). However, there are several ways around the problem. The first is to note that while the best fit requires a high mass sterile neutrino, there are low-mass fits which work within the 3+2 model. The second is to observe that there are a variety of classes of theories where the neutrinos do not thermalize in the early universe.122 In this case, there is no conflict with the cosmological data, since the cosmological neutrino abundance is substantially reduced. If more than one ∆m2 contributes to an oscillation appearance signal, then the data can be sensitive to a CP-violating phase in the mixing matrix. Experimentally, for this to occur, the ∆m2 values must be within less than about two orders of magnitude of one another.
42 September 6, 2007 22:20 WSPC/Trim Size: 9in x 6in for Proceedings noon04
cosmo 9 Status of global fits to neutrino oscil3+1lations 29 2+2
(3+1)NEV NEV+atm+ atm + K2K 1 NEV + atm(1d) 10 10 ] ] 2 2 LSNDLSND global global
[eV LSND DAR [eV LSND DAR 1 0
2 LSND 10 2 LSND m m " !
95% CL 95% 99% CL
95% CL
99% CL
0.1 -1 10
-3 -2 -1 0 0 5 10 15 20 -4 -3 -2 -1 0 10 10 10 10 10 10 10 10 10 2 !" 2 cosmo sin 2#LSND sin 2!LSND
2 Figure 20. Upper bound on sin 2θlsnd from NEV, atmospheric and K2K neutrino Figure 5. Left: Status of the 3+1 oscillation scenario2s. Right:2 Present status of the data in (3+1) schemes. The bound is calculated for each ∆mlsnd using the ∆χ for bounds on the active-st1 ed.ro.if.lTehe daodttemd liniexctoruresrpeondsfrtoothme bousndoalta99r% Ca.Ln. wdithoaut Km2Koasndpuhsinegric neutrino data in one–dimensional atmospheric fluxes. Also shown are the regions allowed at 99% C.L. (2+2)-models. (2 d.o.f.) from global LSND data [113] and decay-at-rest (DAR) LSND data [128].
against a sterile component, since the detailed informations which are needed to use a constraint othnese tdahtaearepporefrssenstomliybnloet av vaGonzalez-Garilaabllue oeutsoidefthtehSueperh-Kecaollvabioerciaartion. e +ut rMaltoniino mass in this sce- nario from th5e.3i.r(3c+1o):nstrornigbly udistfaivoounredtbyoSBtLhdeataenergy density in the Universe which is It is known for a longandtime [12 0,Maltoni,129, 130, 131, 132, 1Schw33, 134] thatetz,(3+1) m aTórss schemetolas ,Valle presently conasretdrisafaivnouered bybthye cocmopasrmisoniocf SmBL idcisarpopewaraancve deatab[1a18c, k11g9]rwoithuthne dLSNrDadiation and large 2 scale structurresulft.oTrhme raeatsoinoisnthadt aint(a3+1[)1sc4he]m.es the relation sin 2θlsnd = 4 de dµ holds, and the parameters de and dµ (see Eq. (19)) are strongly constrained by νe and νµ We show disnappeFaraingce.ex5perimthentes, lelaadintgetso ta dorueblse suuplptrsessioonfof tthhe LeSNDaanmapliltyudse.iIsn of neutrino data Ref. [13LNSD2] it was realized that the up-do wnvsasymmetr y oSBL,cosmobserved in atmospheric µ events 2 in these scenaleardisotosa.n adIdnitiontahl ceonstlreaifnt onadnµ. dThec∆eχn(dtµr) farolm tpheafint teo latmwospehersicu+Km2Kmarize the results data is shown in the right panel of Fig. 19. We find that the use of the new atmospheric from Ref. [13fl]uxeos [n32] atshwell a(s 3K2+K 1da)ta [s17c] ceonsiaderraibolyss;trenwgtheen sthee econsttrhaiantton adµf: ttheer the inclusion of new bound d 0.065 at 99% C.L. decreases roughly a factor 2 with respect to the µ ≤ previous bound d 0.13 [36, 127], as implied by fitting atmospheric data with one– the cosmological bounµ d≤ there is only a marginal overlap at 95% CL be- dimensional fluxes [39] and without K2K. Following Ref. [127] we show in Fig. 20 the 2 tween the alloupwperebdounLd oSn tNheDLSNDreosgcililaotinon aamnplidtudetshin e2θlesndxfcrolmuthde ecodmbirneedganiaolynsis from SBL+ATM of NEV and atmospheric neutrino data. This figure illustrates that the improvement 2 experiments. imTplihedeby rthiegsthrontgepr baounndeoln diµlilsumsosttlry arelteveanst fotrhloweersvatluaestouf ∆smlosnfd. Ftrhome (2+2) scenarios. this figure we see that the bound is incompatible with the signal observed in LSND at the At present, th95e% Cl.oL.wOnelyrmabrgoinaul onvedrlaporengiontshexeist bsetweeernitlhee bocuondmandpgolobnaleLnSNtD dfartoa m the analysis of atmospheric data and the upper bound from the analysis of solar data do not overlap at more than 4 . The figure also illustrates the effect of the inclusion of the SNOII in this conclusion. Alternative explanations to the LSND result include the possibility of CPT violation [15], which implies that the masses and mixing angles of neu- trinos may be different from those of antineutrinos. We have performed an analysis of the existing data from solar, atmospheric, long baseline, reactor and short baseline data in the framework of CPT violating oscillations [2]. The summary of the results of this analysis is presented in Fig. 6, which shows clearly that there is no overlap below the 3 level between the LSND and the all-but-LSND allowed regions. We also note that that the all-but- 2 2 2 LSND region is restricted to ∆m 31 = ∆m LSND 0 02 eV , whereas for 2 2 2 LSND we always have ∆m 31 = ∆m LSND 0 02 eV . Acknowledgments This work was supported in part by the National Science Foundation grant PHY0098527. MCG-G is also supported by Spanish Grants No. FPA-2001- MiniBooNE
• E from 200 to 3000 MeV, average 750 MeV • L ~ 541 m • similar L/E to LSND, but higher E, L • first data with νμ’s does not confirm conventional ν oscillation interpretation of LSND
• excess of νe’s below 475 MeV, 96 ±17±20, doesn’t fit conventional ν oscillation interpretation _ • currently running with ν’s. 5
QE events) for 475 < Eν < 1250 MeV; however, an ex- at 98% CL two-neutrino appearance oscillations as an cess of events (96 ± 17 ± 20 events) is observed below 475 explanation of the LSND anomaly. The bottom plot of MeV. This low-energy excess cannot be explained by a Fig. 3 shows limits from the KARMEN [2] and Bugey two-neutrino oscillation model, and its source is under [32] experiments. investigation. The dashed histogram in Fig. 2 shows the A second analysis developed simultaneously and with predicted spectrum when the best-fit two-neutrino oscil- the same blindness criteria used a different set of recon- lation signal is added to the predicted background. The struction programs, PID algorithms, and fitting and nor- bottom panel of the figure shows background-subtracted malization processes. The reconstruction used a simpler data with the best-fit two-neutrino oscillation and two model of light emission and propagation. The PID used oscillation points from the favored LSND region. The 172 quantities such as charge and time likelihoods in an- QE oscillation fit in the 475 < Eν < 3000 MeV energy gular bins, Mγγ, and likelihood ratios (electron/pion and range yields a χ2 probability of 93% for the null hypoth- electron/muon) as inputs to boosted decision tree algo- 2 esis, and a probability of 99% for the (sin 2θ = 10−3, rithms [33] that are trained on sets of simulated signal MiniBooNE∆m2 = 4 eV2) best- fiOscillationt point. resultsevents and background events with a cascade-training technique [34]. In order to achieve the maximum sen- sitivity to oscillations, the νµ-CCQE data sample with 2! oscillation two subevents were fit simultaneously with the νe-CCQE analysis threshold 2.5 MiniBooNE datay candidate sample with one subevent. By forming a χ2 expected backgroundg !µ using both data sets and using the corresponding covari- 2.0 BG + best-fit !µ"!e!µ ance matrix to relate the contents of the bins of the two ! background 1.5 µ distributions, the errors in the oscillation parameters that !e background best describe the νe-CCQE candidate data set were well
events / MeV 1.0 constrained by the observed νµ-CCQE data. This pro- 0.5 cedure is partially equivalent to doing a νe to νµ ratio analysis where many of the systematic uncertainties can- cel. data - expected background 0.8 The two analyses are very complementary, with the best-fit !µ"!e second having a better signal-to-background ratio, but 2 2 2 0.6 sin (2$)=0.004, #m =1.0 eV !µ the first having less sensitivity to systematic errors from sin2(2 )=0.2, m2=0.1 eV2 $ # !µ detector properties. These different strengths resulted in 0.4 very similar oscillation sensitivities and, when unblinded, 0.2 yielded the expected overlap of events and very similar excess events / MeV oscillation fit results. The second analysis also sees more 0.0 events than expected at low energy, but with less signif- 300 600 900 1200 1500 3000 icance. Based on the predicted sensitivities before un- reconstructed E (MeV) ! blinding, we decided to present the first analysis as our oscillation result, with the second as a powerful cross- FIG. 2: The top plot shows the number of candidate νe events QE check. as a function of Eν . The points represent the data with sta- tistical error, while the histogram is the expected background In summary, while there is a presently unexplained with systematic errors from all sources. The vertical dashed discrepancy with data lying above background at low line indicates the threshold used in the two-neutrino oscilla- energy, there is excellent agreement between data and tion analysis. Also shown are the best-fit oscillation spec- prediction in the oscillation analysis region. If the oscil- trum (dashed histogram) and the background contributions lations of neutrinos and antineutrinos are the same, this from νµ and νe events. The bottom plot shows the number of events with the predicted background subtracted as a func- result excludes two neutrino appearance-only oscillations QE as an explanation of the LSND anomaly at 98% CL. tion of Eν , where the points represent the data with total errors and the two histograms correspond to LSND solutions at high and low ∆m2. We acknowledge the support of Fermilab, the Depart- ment of Energy, and the National Science Foundation. A single-sided raster scan to a two neutrino We thank Los Alamos National Laboratory for LDRD appearance-only oscillation model is used in the energy funding. We acknowledge Bartoszek Engineering for the QE range 475 < Eν < 3000 MeV to find the 90% CL limit design of the focusing horn. We acknowledge Dmitri Top- 2 2 − 2 corresponding to ∆χ = χlimit χbestfit = 1.64. As tygin, Anna Pla, and Hans-Otto Meyer for optical mea- shown by the top plot in Fig. 3, the LSND 90% CL al- surements of mineral oil. This research was done using lowed region is excluded at the 90% CL. A joint analysis resources provided by the Open Science Grid, which is as a function of ∆m2, using a combined χ2 of the best supported by the NSF and DOE-SC. We also acknowl- fit values and errors for LSND and MiniBooNE, excludes edge the use of the LANL Pink cluster and Condor soft- 6
10-3 10-2 10-1 1 102 102 [4] B. T. Cleveland et al., Astrophys. J. 496, 505 (1998). sin2(2") upper limit [5] J. N. Abdurashitov et al., Phys. Rev. C 60, 055801 (1999). MiniBooNE 90% C.L.y MiniBooNE 90% C.L. sensitivity [6] W. Hampel et al., Phys. Lett. B 447, 127 (1999). BDT analysis 90% C.L. MiniBooNE, 10 10 [7] S. Fukuda et al., Phys. Lett. B 539, 179 (2002). [8] Q. R. Ahmad et al., Phys. Rev. Lett. 87, 071301 (2001); )
4 Q. R. Ahmad et al., Phys. Rev. Lett. 89, 011301 (2002); /c Karmen, 2 S. N. Ahmed et al., Phys. Rev. Lett. 92, 181301 (2004). 1 1 [9] K. Eguchi et al., Phys. Rev. Lett. 90, 021802 (2003); | (eV 2 T. Araki et al., Phys. Rev. Lett. 94, 081801 (2005). m ! | [10] K. S. Hirata et al., Phys. Lett. B 280, 146 (1992); Bugey Y. Fukuda et al., Phys. Lett. B 335, 237 (1994). 10-1 LSND 90% C.L. 10-1 [11] Y. Fukuda et al., Phys. Rev. Lett. 81, 1562 (1998). LSND 99% C.L. [12] W. W. M. Allison et al., Phys. Lett. B 449, 137 (1999). versus [13] M. Ambrosio et al., Phys. Lett. B 517, 59 (2001). [14] M. H. Ahn et al., Phys. Rev. Lett. 90, 041801 (2003). [15] D. G. Michael et al., Phys. Rev. Lett. 97, 191801 (2006). [16] M. Sorel, J. M. Conrad, and M. H. Shaevitz, Phys. Rev. LSND MiniBooNE 90% C.L.y D 70, 073004 (2004). KARMEN2 90% C.L. [17] T. Katori, A. Kostelecky and R. Tayloe, Phys. Rev. D 10 Bugey 90% C.L. 10 74, 105009 (2006). [18] S. Kopp, Phys. Rept. 439, 101 (2007). )
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End of story? /c 2 149 (1997). 1 1 [20] S. Agostinelli et al., Nucl. Instrum. Meth. A506, 250 | (eV 2 (2003). m ! | [21] J. R. Sanford and C. L. Wang, Brookhaven National Lab- oratory, AGS internal reports 11299 and 11479 (1967) 10-1 10-1 (unpublished). [22] M. G. Catanesi et al. [HARP Collaboration], arXiv:hep- LSND 90% C.L. ex/0702024; T. Abbott et al., Phys. Rev. D45, 3906 LSND 99% C.L. (1992); J. V. Allaby et al., CERN 70-12 (1970); 10-2 10-2 D. Dekkers et al., Phys. Rev. 137, B962 (1965); 10-3 10-2 10-1 1 sin2(2") G. J. Marmer et al., Phys. Rev. 179, 1294 (1969); T. Eichten et al., Nucl. Phys. B44, 333 (1972); A. Aleshin et al. et al. FIG. 3: The top plot shows the MiniBooNE 90% CL limit , ITEP-77-80 (1977); I. A. Vorontsov , ITEP- (thick solid curve) and sensitivity (dashed curve) for events 88-11 (1988). with 475 < EQE < 3000 MeV within a two neutrino oscilla- [23] D. Casper, Nucl. Phys. Proc. Suppl. 112, 161 (2002). ν et al. tion model. Also shown is the limit from the boosted decision [24] A. Aguilar-Arevalo , in preparation. QE [25] D. Ashery et al., Phys. Rev. C 23, 2173 (1981). tree analysis (thin solid curve) for events with 300 < Eν < 3000 MeV. The bottom plot shows the limits from the KAR- [26] H. Ejiri, Phys. Rev. C 48, 1442 (1993); F. Ajzenberg- MEN [2] and Bugey [32] experiments. The MiniBooNE and Selove, Nucl. Phys. A506, 1 (1990); G. Garvey private Bugey curves are 1-sided upper limits on sin2 2θ correspond- communication. ing to ∆χ2 = 1.64, while the KARMEN curve is a “unified [27] D. Rein and L. M. Sehgal, Annals Phys. 133, 79 (1981). approach” 2D contour. The shaded areas show the 90% and [28] CERN Program Library Long Writeup W5013 (1993). et al. 99% CL allowed regions from the LSND experiment. [29] B. C. Brown , IEEE Nuclear Science Symposium Conference Record 1, 652 (2004). [30] D. Rein and L. M. Sehgal, Phys. Lett. B 104, 394 (1981). [31] T. Goldman, private communication. ware in the analysis of the data. [32] B. Achkar et al., Nucl. Phys. B434, 503 (1995). [33] B. P. Roe et al., Nucl. Instrum. Meth. A543, 577 (2005); H. J. Yang, B. P. Roe, and J. Zhu, Nucl. Instrum. Meth. A555, 370 (2005); H. J. Yang, B. P. Roe, and J. Zhu, [1] C. Athanassopoulos et al., Phys. Rev. Lett. 75, 2650 Nucl. Instrum. Meth. A574, 342 (2007). (1995); 77, 3082 (1996); 81, 1774 (1998); A. Aguilar et al., [34] Y. Liu and I. Stancu, arXiv:Physics/0611267 (to appear Phys. Rev. D 64, 112007 (2001). in Nucl. Instrum. Meth.). [2] B. Armbruster et al., Phys. Rev. D 65, 112001 (2002). [3] E. Church et al., Phys. Rev. D 66, 013001 (2002). Beyond standard neutrinos • Neutrinos are unique! • Only SM particle which can mix with “dark” (sterile) fermions • Oscillations sensitive to GUT scale • Oscillations sensitive to extremely feeble new interactions • Neutrinos have history of surprises $8)#>'(?)1@6),)1A)A.(,# Summer MiniBooNE !"#$%&'('()"*+,#-"#(#-).""
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!"#$%&'()*#+,-.%,%#/,.0)12.3&##############4)53(,678(3(,#9:;#######################<= What if LSND is ν physics? some others considered so far: various combinations of 1 • more than 3+1 [1] T. Schwetz, arXiv:0710.2985 [hep-ph]. • CPV [2] J. Dent, H. Pas, S. Pakvasa and T. J. Weiler, arXiv:0710.2524 [hep-ph]. [3] H. Nunokawa, S. J. Parke and J. W. F. Valle, arXiv:0710.0554 [hep-ph]. new background for νe’s [4] D. Majumdar, arXiv:0708.3485 [hep-ph]. • [5] J. A. Harvey, C. T. Hill and R. J. Hill, arXiv:0708.1281 [hep-ph]. [6] C. Giunti and M. Laveder, arXiv:0707.4593 [hep-ph]. • νe disappearance [7] X. Q. Li, Y. Liu and Z. T. Wei, arXiv:0707.2285 [hep-ph]. [8] S. Goswami and W. Rodejohann, arXiv:0706.1462 [hep-ph]. increased background [9] J. C. Montero and V. Pleitez, arXiv:0706.0473 [hep-ph]. • [10] S. M. Bilenky, F. von Feilitzsch and W. Potzel, arXiv:0705.0345 [hep-ph]. • more exotic [11] M. Maltoni and T. Schwetz, arXiv:0705.0107 [hep-ph]. Motivation for our model
➡We focus on essential differences between LSND, MiniBooNE experiments, take results at face value _ ➡Consider physics which_ is intrinsically different for ν’s versus ν’s ➡anomalous energy dependence ➡Note: MiniBooNE, LSND, CDHS all have oscillation baselines through matter ➡suggests: new physics MSW-like effect A new light gauge boson?
• Anomaly free candidate is gauged B-L (with 3 sterile ‘right handed’ neutrinos) _ • MSW analog effect is opposite for ν, ν 2 2 • MSW analog effect ~ E ρ g /MV • ρ nonzero and similar for LSND, MiniBooNE -5 • g must be < ~10 to agree with precision expts, eg ge-2 • MV must also be tiny to give big enough effect, < ~keV • flavor diagonal for active neutrinos⇒no MSW effect? Spontaneous B-L violation and Majorana ν masses a “mini seesaw” with • ν N eV mass singlet N’s 0 λ H ν λ, g, λ′〈ϕ〉are small M = T ! " • λ H λ# φ N ! ! " ! " " 〈 〉 • nonzero ϕ M†M H E + +V required for active- ≈ 2E sterile mixing VI 0 • may allow for V = − 3 compatibility with 0 VI3 cosmology ! " Anomalous matter effect
effective mass2 matrix for neutrino oscillations: m2 mM M2 = e f f mM 4VE + M2 + m2 ! " • m≡ λ〈H〉~0.2 - 0.4 eV, 3 nearly degenerate eigenvalues govern large mixing angle LBL oscillations in matter at high energy • V ≡ B-L potential, (negative)positive for (anti)ν’s, ~ 10-8-10 -9 eV • M≡ λ〈ϕ〉~1-2 eV, M2 ~ 4VE in MiniBooNE low energy region Heavy ν’s mix with Effective Energy dependent mixing angle
• ϑ ≈ m M/(4 VE+ M2) • bigger for anti neutrinos (negative V) • for neutrinos smaller at high energy m2 mM M2 = e f f mM 4VE + M2 + m2 ! " Effects of B-L potential -9 • eg m=.3 eV, M1 =1 eV, M2 heavy, V= .3 10 0.0030
0.0025 antineutrinos 0.0020 μ -e 0.0015 oscillation probability0.0010 neutrinos at 30 m 0.0005
20 40 60 80 100
Energy (MeV) Effects of B-L potential
-9 • eg m=.3 eV, M1 =1 eV, M2 heavy, V= 0.3 10
0.005
μ -e 0.004 antineutrinos oscillation 0.003 probability 0.002 at 500 m 0.001 neutrinos
200 400 600 800 1000
Energy (MeV) Strategy
• fix mixing angles in m to solar, atmospheric values, with Θ13=0, take M diagonal⇒ only 2 eigenvalues of M affect oscillations involving νe • scan V, m, M1, M2 for fit to LSND, MiniBooNe, CHOOZ,CDHS • for points that fit, predict oscillation results for MiniBooNE anti neutrinos NeutrinoModelNumerics.nb 13
Here is a histogram for each M2 of the predicitons for MiniBooNE anti - neutrinos (at low E). Note that although the total oscillations at MiniBooNE will be lower than this, there should still be substantial oscillations seen for almost all points. Table Histogram MBantiPrediction n , n, 1, 10
350 Preliminar100y Prediction for large low energy 300 anti neutrino @oscillations at MiniBooNE@ @@ DDD 8 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 0.35 30 25 25 25 20 20 20 15 15 , 15 , , 10 10 10 5 5 5 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 0.35 25 25 25 20 20 20 15 15 15 , , 10 10 10 5 5 5 > 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.05 0.1 0.15 0.2 0.25 0.3 0.35 The minimum anti - neutrino low E oscillation probability at MiniBooNE from the fit points, for each value of M2. The smalles value is 3.4 %, which should give rise to visible oscillations at MiniBooNE. Table Min MBantiPrediction n , n, 1, 10 0.0384367, 0.0342595, 0.0381392, 0.0381149, 0.0381068@ @, 0.0380987, 0.0380987@@ DDD, 0.03809078 , 8 < Summary • If taken at face value, LSND anomaly requires dramatic new physics • A new B-L force? • gauge boson mass ~ keV • sterile neutrinos at eV • miniseesaw for neutrino mass • nearly degenerate light neutrinos • no 0νββ decay • energy dependent, lepton sign dependent matter effect • large signal for MiniBooNE antineutrinos