Status of global fits to neutrino oscillations

J. W. F. Valle; M. A. Tortola; M. Maltoni; T. Schwetz

REVIEW

Status of global fits to neutrino oscillations

M. Maltoni, T. Schwetz, M. A. Tortola, J. W. F. Valle

High Energy Physics - Phenomenology · Submitted 18 May 2004 · 148 references

Pith's verdict: The standard 2004–2007 global neutrino fit: tables are genuinely new work, the θ13 bound is a Δχ² cut rather than a calibrated interval, and the authors say so themselves.

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arXiv IDhep-ph/0405172 (version 6)

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CitationJ. W. F. Valle, M. A. Tortola, M. Maltoni, T. Schwetz. "Status of global fits to neutrino oscillations." arXiv:hep-ph/0405172 (2004). https://pith.science/paper/KHCJWEY4

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Editor's note

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Bottom line: this is the reference global fit for the 2004–2007 era, and the parameter tables are the numbers people actually cited. It is labelled a review, but the fits are new work, not a summary of prior results. Cite it, and cite the appendix version you mean — the paper revises itself in place four times (Tables 1, B1, C1, D1). That is honest but makes a bare 'Table 1' ambiguous, which is my only real usability complaint. Minor, but worth knowing before you put a number in a slide. What is genuinely new: the three-flavour fit with KamLAND 2004, K2K-I+II, three-dimensional atmospheric fluxes and BP04/BS05 solar fluxes; the decomposition of the sin²θ13 bound by data set; and the (2+2) four-neutrino exclusion at 4.9σ via parameter goodness of fit, which holds whether or not LSND is confirmed. That last section is the most robust thing in the paper and does not depend on the contested inputs. The statistical work is better than typical for this genre: pulls treated exactly to all orders rather than expanded, correlated statistical errors for SNO salt, and an explicit cross-check that the atmospheric fit reproduces Super-K's own result. The appendices are unusually candid about their own limits. On the soft spots, the stress-test lands on the mechanism but not on the conclusion. Appendix A.2 footnote ‖ admits the θ13 bound uses 'the naive method' of a Δχ² cut restricted to the physical region, while the KamLAND-only best fit sits at sin²θ13 = −0.13. At a boundary that cut does not carry 3σ coverage, so 0.047 is plausibly too tight and should not be quoted as a calibrated interval. But the 2007 KamLAND sample gives 0.050, so the physics conclusion — θ13 small, solar+KamLAND holding the line where CHOOZ weakens — survives intact. The digitisation of the KamLAND spectrum from a figure is disclosed and largely defused by Appendix D's stability check. Who should read it: anyone doing oscillation phenomenology or long-baseline design in this parameter range. It deserves a serious referee, though the referee's job is mostly to check the boundary treatment and the binning, not the framework.

Referee report

Significance

The paper is a careful and useful synthesis. The statistical machinery is described in enough detail to be reproduced: pull parameters for systematics, an exact treatment of pulls to all orders rather than a first-order expansion (which lets the SNO neutral-current measurement and the SSM boron-flux prediction be fitted on the same footing), correlated statistical errors for the SNO salt data, and an explicit cross-check that the atmospheric fit agrees with the Super-K collaboration's own result. The robustness studies are genuine tests rather than assertions: the NSI fit of Fig. 4 shows the oscillation parameters are stable while bounding epsilon and epsilon-prime, and the solar-fluctuation and transition-moment analyses yield falsifiable limits (|Lambda| < 3.4 x 10^-10 mu_B, and 0.29 x 10^-10 mu_B after three years of Borexino). The parameter-goodness-of-fit treatment of Section 5 is a reproducible and appropriate way to reject (2+2) schemes without dilution by data-point counting. If the numbers hold, the paper fixes the size of the last undetermined leptonic mixing angle and hence the scale of CP-violating effects for the next generation of long-baseline experiments.

Major objections (3)

[Section 4.2, Eq. (17), Table 1, and footnote of Appendix A.2] The headline bound sin^2 theta_13 <= 0.047 at 3 sigma (1 d.o.f.) is obtained by applying a Delta chi^2 = 9 cut to a profile whose minimum lies on the physical boundary. The authors state this plainly in Appendix A.2 (the unconstrained KamLAND best fit sits at sin^2 theta_13 = -0.13, with Delta chi^2 = 3.5 relative to the physical point, 1.75 after the 13C correction) and in the footnote, which calls the procedure naive and notes that a reliable bound would require a Monte Carlo of synthetic data sets. The limitation is acknowledged, but it is not carried through to the presentation: Eq. (17) and Table 1 quote 0.047 without qualification, and Section 4.2 and Fig. 15 then use the solar+KamLAND constraint as the argument that the bound is held where CHOOZ weakens (Delta m^2_atm below about 2 x 10^-3 eV^2). Because a boundary MLE undercovers, 0.047 is plausibly too tight, and the KamLAND resolution within the physical region quoted in Appendix A.2 (sigma about 0.02) is not small compared with the bound. The authors' own Appendix B demonstrates the sensitivity concretely: correcting the 13C background moves the 3 sigma value from 0.047 to 0.051 (Table B1). I ask that the bound be quoted with the calibration caveat alongside Eq. (17), or that the 13C-updated value be promoted to the primary result, or that the Monte Carlo calibration be supplied. The qualitative conclusion that theta_13 is small survives either way; the specific number does not currently carry the stated coverage.
[Appendix A.1 and Fig. A1] The KamLAND spectral information is reconstructed by digitising the ratio plot of Fig. 3 of Ref. [15] into 13 bins of 180 km/E and re-binning in 1/E_prompt, because event-level energies are unavailable outside the collaboration. The authors justify the 1/E binning well, but they also show that the choice is not innocuous: the Delta chi^2 of the low-Delta m^2 minimum changes from 4.0 to 7.5 and that of the high-LMA minimum from 8.5 to 11.3 when going from E_prompt to 1/E_prompt binning. What is not shown is the effect of this choice on the two quantities that the rest of the paper leans on, namely the Delta m^2_sol error bar and the solar+KamLAND contribution to the theta_13 bound. Since the latter is one of the paper's headline results, a systematic check would be proportionate: quote the theta_13 bound and the Delta m^2_sol interval under both binnings, or state explicitly how much of the quoted precision is attributable to the digitisation and binning choice. This is a request for a sensitivity statement, not for a reanalysis.
[Table 1 versus Tables B1, C1, and D1; Abstract and Section 1] The paper's stated purpose is to report the status of global fits, but the main text and abstract present the 2004 numbers as current while Appendices C and D (June 2006 and September 2007) supersede them. Table D1 gives sin^2 theta_13 <= 0.050 at 3 sigma, Delta m^2_31 = 2.4 x 10^-3 eV^2, and sin^2 theta_12 = 0.32, against Table 1's 0.047, 2.2 x 10^-3 eV^2, and 0.30. The abstract's phrase 'the latest KamLAND and K2K updates presented at Neutrino2004' is now factually stale given Appendix D. For a review whose title is 'Status of global fits', the reader is left to reconcile five tables spanning three years of data. I ask that the abstract and introduction be updated to point to the latest appendix, or that a short signposting paragraph be added at the start of Section 4 stating which table is the current result and which are historical. This is a currency and presentation issue rather than a physics error, but it bears directly on what the paper claims to deliver.

Minor objections (8)

[Abstract] The phrase 'the current worlds' global neutrino data sample' should read 'the current world's global neutrino data sample'.
[Section 3.3, Eq. (8) and Table 1] Eq. (8) gives sin^2 theta_sol = 0.29 from solar+KamLAND, while Table 1 gives sin^2 theta_12 = 0.30 from the global three-flavour fit. A sentence explaining that the difference is the two- versus three-flavour treatment (and the inclusion of atmospheric, K2K, and CHOOZ data) would prevent the reader from reading this as an inconsistency.
[Fig. 6 caption] The caption states that the regions delimited by the lines correspond to solar data, but does not say whether the same solar contours are overlaid in both the 2002 and 2004 panels. Please state this explicitly, since the visual comparison of the two panels is the point of the figure.
[Fig. 14 legend] The legend lists 'Solar' and 'KamLAND' as separate entries alongside 'Total', but the surrounding text discusses 'solar+KamLAND' as a single data set. Please clarify whether the figure shows solar-only and KamLAND-only profiles in addition to their combination, and label them accordingly.
[Section 5.2 and Table 2] Section 5.2 quotes chi^2_PG = 26.1 corresponding to 5.1 sigma, which is a one-degree-of-freedom test in eta_s, whereas Table 2 quotes chi^2_PG = 33.9 for (2+2) with four degrees of freedom and 4.9 sigma. The two numbers are consistent but the text does not distinguish them, and a reader may take them as contradictory. A clause noting that the first is the one-parameter eta_s test of Eq. (21) and the second the four-parameter test of Eq. (22) would remove the ambiguity.
[Appendix D] Typographical: 'No significant improvement has been otained here' should read 'obtained'.
[Section 2.4, Eq. (5)] The NSI bounds -0.03 <= epsilon <= 0.02 and |epsilon'| <= 0.05 are taken from Ref. [50], which used the one-dimensional Bartol flux, while the rest of Section 2 now uses the three-dimensional Honda flux. The footnote acknowledges this, but a sentence in the main text stating that the NSI bounds are not on the same flux footing as the oscillation parameters would help the reader weigh them.
[Appendix A.1] The 2.69 accidental background events added to the lowest energy bin are quoted without an uncertainty. Please state the uncertainty or explain why it is negligible.

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The paper

The paper claims

A single five-parameter fit to all neutrino oscillation data fixes the size of the last unknown mixing angle and with it the scale of CP violation in the lepton sector.

The reading

Three-flavour neutrino oscillations are described by five numbers: two mass-squared differences, three mixing angles. This paper's job is to extract those five numbers, with honest error bars, from every oscillation data set available in mid-2004 — solar rates and spectra, the KamLAND reactor spectrum, Super-K atmospheric zenith distributions, K2K, and the CHOOZ reactor limit — and to say what the result implies for the two small quantities that control whether neutrinos can violate CP. Those quantities are the hierarchy ratio $alpha = Delta m^2_{sol}/Delta m^2_{atm}$ and the mixing angle $theta_{13}$. The paper reports $alpha = 0.035$ with $0.024 leq alpha leq 0.060$ at $3sigma$, and $sin^2theta_{13} leq 0.047$ at $3sigma$ for one degree of freedom. The second number is the one that matters for planning: it says the CP-violating term in the oscillation probability is small, so any future experiment that wants to see leptonic CP violation has to be built to reach it.

What carries the argument

The load-bearing device is a five-dimensional $chi^2$ built from a pull-parameter treatment of every systematic uncertainty, minimised over $(sin^2theta_{12}, sin^2theta_{23}, sin^2theta_{13}, Delta m^2_{21}, Delta m^2_{31})$ and projected onto one- and two-dimensional subspaces. Two approximations make it tractable: $Delta m^2_{sol}$ is set to zero when fitting atmospheric and K2K data, and $Delta m^2_{atm}$ is set to infinity when fitting solar and KamLAND data, which also makes the Dirac CP phase drop out. The pull method is extended in two ways the paper flags as new: it handles correlated statistical errors, needed for the SNO salt data, and it treats each pull parameter exactly rather than to first order, which lets the fit choose its own compromise between the SNO neutral-current measurement and the Standard Solar Model prediction for the boron flux instead of expanding around the predicted value. A separate parameter-goodness-of-fit statistic, built from the sum of the individual data sets' $Delta chi^2$ functions rather than from the total $chi^2$, is what converts the solar-versus-atmospheric tension in four-neutrino schemes into a meaningful rejection level without being diluted by the large number of data points.

Extended reading notes

Core claim

The central claim is that a global three-flavour fit to the 2004 data set returns a consistent, tightly constrained parameter set, and that the bound on $sin^2theta_{13}$ is no longer a CHOOZ monopoly. The best-fit points are $Delta m^2_{21} = 8.1 times 10^{-5}$ eV$^2$, $Delta m^2_{31} = 2.2 times 10^{-3}$ eV$^2$, $sin^2theta_{12} = 0.30$, $sin^2theta_{23} = 0.50$, with $sin^2theta_{13}$ compatible with zero and bounded above at 0.047 ($3sigma$, 1 d.o.f.). The argument for the $theta_{13}$ bound is the paper's most consequential move: the authors show that solar plus KamLAND data alone now give $sin^2theta_{13} leq 0.079$ at $3sigma$, comparable to the CHOOZ-plus-atmospheric-plus-K2K bound of 0.067, and that the two constraints are complementary rather than redundant. Solar data disfavour the large $Delta m^2_{sol}$ that would let a nonzero $theta_{13}$ hide, while KamLAND's spectral distortion pins $Delta m^2_{sol}$ down and breaks the $sin^2theta_{13}$–$sin^2theta_{12}$ degeneracy. The paper also uses the same machinery to rule out four-neutrino schemes: (2+2) spectra fail at $4.9sigma$ from the disagreement between solar and atmospheric data on how much sterile neutrino participates, and (3+1) schemes are strongly disfavoured by short-baseline disappearance data, leaving the LSND anomaly without a satisfactory oscillation explanation.

Load-bearing premise

The KamLAND spectral information is read off a published ratio plot rather than from event-level data, so every KamLAND-derived number in the paper, including the $Delta m^2_{sol}$ best fit and the solar-plus-KamLAND share of the $theta_{13}$ bound, rests on that digitisation.

Editorial extensions

If this is right

If $sin^2theta_{13} lesssim 0.05$, the CP-violating term in the long-baseline $nu_e to nu_mu$ appearance probability is suppressed by roughly this factor, so a next-generation superbeam or beta-beam must be designed around a small $theta_{13}$, not a large one.
The lower bound on $Delta m^2_{atm}$ from K2K, combined with the $Delta m^2_{atm}$-independent solar-plus-KamLAND bound on $theta_{13}$, prevents the CHOOZ limit from degrading at the low $Delta m^2_{atm}$ values implied by the new three-dimensional atmospheric fluxes.
Because $alpha$ is measured to be about 0.03, the sub-leading three-flavour corrections to atmospheric and long-baseline oscillations are small but not negligible, and the combination $alpha sin 2theta_{12} = 0.032$ (range 0.022 to 0.054) is the quantity a long-baseline experiment actually constrains.
The (2+2) four-neutrino explanation of LSND is excluded independently of whether LSND itself is confirmed, because the rejection comes from solar and atmospheric data disagreeing about the sterile fraction.
The oscillation interpretation of solar data survives departures from the Standard Solar Model, from random radiative-zone density fluctuations, and from sub-leading spin-flavour precession, up to the magnetic moment bounds the paper derives.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper's own later appendices show how much the headline numbers move with new data: by the 2007 update the $3sigma$ bound on $sin^2theta_{13}$ relaxes from 0.047 to 0.050 and the best fit shifts to a slightly nonzero 0.007. A reader should treat the 2004 numbers as a snapshot of a fit that was still being re-run, not as a fixed constant of nature.
The claim that solar plus KamLAND contributes materially to the $theta_{13}$ bound depends on a spectral-shape argument in KamLAND rather than on a rate. That makes the bound sensitive to the shape of the reactor flux and the energy-scale calibration in a way that the CHOOZ bound is not, so the two constraints are less independent than their separate listing suggests.
If the fit prefers a slightly negative $sin^2theta_{13}$ when the physical region is not imposed — as Appendix A.2 reports, at $Delta chi^2 approx 3.5$ before the $^{13}$C background correction — then the quoted upper bound is being set partly by a downward fluctuation, and a future experiment with better statistics could move the central value up without contradicting anything here.
The pattern that emerges, with two large angles, one small angle, and a hierarchy ratio near 0.03, is exactly the regime in which the CP-violating asymmetry is largest relative to the matter-induced fake asymmetry, so the smallness of $theta_{13}$ is bad news for statistics but not necessarily for the cleanliness of a CP measurement.

Original abstract

We review the present status of global analyses of neutrino oscillations, taking into account the most recent neutrino data including the latest KamLAND and K2K updates presented at Neutrino2004, as well as state-of-the-art solar and atmospheric neutrino flux calculations. We give the two-neutrino solar + KamLAND results, as well as two-neutrino atmospheric + K2K oscillation regions, discussing in each case the robustness of the oscillation interpretation against departures from the Standard Solar Model and the possible existence of non-standard neutrino physics. Furthermore, we give the best fit values and allowed ranges of the three-flavour oscillation parameters from the current worlds' global neutrino data sample and discuss in detail the status of the small parameters $\alpha \equiv \Dms/\Dma$ as well as $\sin^2\theta_{13}$, which characterize the strength of CP violating effects in neutrino oscillations. We also update the degree of rejection of four-neutrino interpretations of the LSND anomaly in view of the most recent developments.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.12 · human participants 0.02 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.34 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v6. Results and the main claim are underlined; show every role.

We review the present status of global analyses of neutrino oscillations, taking into account the most recent neutrino data including the latest KamLAND and K2K updates presented at Neutrino2004, as well as state-of-the-art solar and atmospheric neutrino flux calculations. We give the two-neutrino solar + KamLAND results, as well as two-neutrino atmospheric + K2K oscillation regions, discussing in each case the robustness of the oscillation interpretation against departures from the Standard Solar Model and the possible existence of non-standard neutrino physics. Furthermore, we give the best fit values and allowed ranges of the three-flavour oscillation parameters from the current worlds' global neutrino data sample and discuss in detail the status of the small parameters $\alpha \equiv \Dms/\Dma$ as well as $\sin^2\theta_{13}$, which characterize the strength of CP violating effects in neutrino oscillations. We also update the degree of rejection of four-neutrino interpretations of the LSND anomaly in view of the most recent developments.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We review the present status of global analyses of neutrino oscillations, taking into account the most recent neutrino data including the latest KamLAND and K2K updates presented at Neutrino2004, as well as state-of-the-art solar and atmospheric neutrino flux calculations.	contribution 0.91	0.49	0.07	asserted 0.70
s1	We give the two-neutrino solar + KamLAND results, as well as two-neutrino atmospheric + K2K oscillation regions, discussing in each case the robustness of the oscillation interpretation against departures from the Standard Solar Model and the possible existence of non-standard neutrino physics.	contribution 0.82	0.81	0.08	asserted 0.87
s2	Furthermore, we give the best fit values and allowed ranges of the three-flavour oscillation parameters from the current worlds' global neutrino data sample and discuss in detail the status of the small parameters $\alpha \equiv \Dms/\Dma$ as well as $\sin^2\theta_{13}$, which characterize the strength of CP violating effects in neutrino oscillations.	result 0.68	0.83	0.19	asserted 0.99
s3	We also update the degree of rejection of four-neutrino interpretations of the LSND anomaly in view of the most recent developments.	contribution 0.70	0.74	0.08	asserted 0.84

What kind of paper the classifier reports this is: review 1.00 · evidence from analysis of existing data 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v6

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Allowed (sin2 θatm, ∆m2 atm) regions at 90%, 95%, 99%, and 3σ C.L. for 2 d.o.f. The regions delimited by the lines correspond to atmospheric data only, while for the colored regions also K2K data are added. The best fit point of atmospheric (atmospheric + K2K) data is marked by a triangle (star). Also shown is the ∆χ 2 as a function of sin2 θatm and ∆m2 atm, minimized with respect to the undisplayed parameter. 2.2. The K2K accelerator experiment The KEK to Kamioka (K2K) long-baseline neutrino oscillation experiment [16] probes the νµ disappearance oscillation channel in the same r

**Figure 2.** Allowed K2K regions in the (sin2 θatm, ∆m2 atm) plane at 90%, 95%, 99%, and 3σ C.L. for 2 d.o.f. The hollow lines delimit the region determined from the atmospheric data only. The star (triangle) corresponds to the K2K (atmospheric) best fit point. statistically compatible both with our previous result [30] and the value obtained by the new Super-K L/E analysis [33]. Let us remark that the K2K constraint on ∆m2 atm from below is important for future long-baseline experiments, since the performance of such experiments is drastically affected if ∆m2 atm were in the lower part of the 3

**Figure 3.** Effective flavour-changing NSI operator. feature in most neutrino mass models [51] and can be of two types: flavour-changing (FC) and non-universal (NU). These interactions (called NSI for short) may be schematically represented as effective dimension-6 terms of the type εGF , as illustrated in

**Figure 4.** Atmospheric neutrino oscillation parameters from [50] fitted in the presence of non-standard interactions using the Bartol flux [39]. We show the behaviour of the χ 2 as a function of the four parameters ∆m2 atm (upper left), sin2 2θatm (lower left), the FC parameter ε (upper right), and the NU parameter ε ′ (lower right). In each panel the χ 2 is minimized with respect to the three undisplayed parameters. In the left panels we show also the pure oscillation case (OSC), with ε and ε ′ set to zero. oscillations allows to set strong bounds on NSI. From the right panels of

**Figure 5.** Allowed regions from all solar neutrino data at 90%, 95%, 99%, and 3σ C.L. for 2 d.o.f. in the plane of sin2 θsol and ∆m2 sol. The regions delimited by the curves correspond to the BP00 SSM [63], whereas for the colored regions the BP04 SSM [31] has been used. Also shown is ∆χ 2 as a function of sin2 θsol and ∆m2 sol, minimized with respect to the undisplayed parameter. The labeled contours denote constant CC/NC ratio in the SNO experiment. given in Ref. [64], are ruled out. Despite the fact that the BP04 model does not imply any significant change in the solar neutrino parameters

**Figure 6.** Allowed regions from KamLAND data at 90%, 95%, 99%, and 3σ C.L. for 2 d.o.f. for the 2002 data sample [14] (left panel) and the latest 766.3 ton-year data sample [15] (right panel). The regions delimited by the lines correspond to solar data. The KamLAND best fit points are marked with a star, the solar best fit point with a dot. problem, which in this way has been singled out as the only viable one. Before this experiment we had a very complex pattern of alternative oscillation solutions like LOW, SMA, or VAC, see e.g., Refs. [35, 36]. All of these are completely ruled out by the…

**Figure 7.** Allowed regions from combined solar and KamLAND data at 90%, 95%, 99%, and 3σ C.L. for 2 d.o.f.. The regions shown with lines correspond to solar data only, from

**Figure 8.** Effect of random matter density fluctuations with a correlation length of L0 = 100 km on the electron-neutrino survival probability for LMA oscillations. ∆m2 sol ≃ 1.4 × 10−4 eV2 at 3σ (see e.g., Ref. [30]) is now ruled out with a ∆χ 2 = 22.1 with respect to the global minimum, which corresponds to an exclusion at about 4.3σ for 2 d.o.f.. Notice also that the day/night data are treated as previously [30, 36]. An improved analysis of the day/night asymmetry data along the lines followed by the Super-K collaboration in Ref. [70] would lead to an even more pronounced rejection of the

**Figure 9.** Solar neutrino oscillation parameters with an arbitrary noise amplitude and a correlation length L0 = 100 km from combining solar data with 2002 KamLAND data (left panel) and 2004 KamLAND data (right panel). The contour lines refer to solar data only. helioseismic bounds turn out to be insensitive to fluctuations whose size is as small as those to which neutrinos are sensitive [74, 75] typically several hundreds of km. Second, recent studies have shown how such solar density fluctuations can arise near the solar equatorial plane in the presence of magnetic fields deep within the…

**Figure 10.** Bounds on random matter density fluctuations for a correlation length of L0 = 100 km from solar neutrino data, solar + KamLAND data, and solar data for oscillation parameters fixed at the best fit point. fluctuations are strongly constrained if the correlation length lies in the range of several hundred km. Comparing the curves for free and fixed oscillation parameters one notes that the bounds on fluctuations have already become rather stable, a situation that may still improve when the accuracy on ∆m2 sol and θsol gets improved by future neutrino experiments. Because oscillations…

**Figure 11.** Contours of the 90% C.L. bound on |Λ| in units of 10−10µB from combined solar and reactor data (left panel) and after 3 years of Borexino data-taking (right panel). The gray (light) shaded region is the 3σ LMA region obtained in the global analysis of solar neutrino data (best fit point marked with a triangle), whereas the green (dark) one corresponds to the 3σ region obtained after including the KamLAND results (best fit point marked with a star). The dashed line in the right panel corresponds to Pe1 = 0.5 for 7Be neutrinos, and shows the strongest attainable limit. Borexino is…

**Figure 12.** Projections of the allowed regions from the global oscillation data at 90%, 95%, 99%, and 3σ C.L. for 2 d.o.f. for various parameter combinations. Also shown is ∆χ 2 as a function of the oscillation parameters sin2 θ12,sin2 θ23,sin2 θ13, ∆m2 21, ∆m2 31, minimized with respect to all undisplayed parameters. 4.2. The small parameters α ≡ ∆m2 sol/∆m2 atm and θ13 Genuine three–flavour effects are associated to the mass hierarchy parameter α ≡ ∆m2 sol/∆m2 atm and the mixing angle θ13. In particular, in a three–neutrino scheme CP violation disappears in the limit where two neutrinos…

**Figure 13.** ∆χ 2 from global oscillation data as a function of α ≡ ∆m2 sol/∆m2 atm and α sin 2θ12. 10-2 10-1 sin2 θ 13 0 5 10 15 20 ∆χ 2 Atm + K2K + Chooz Solar + KamLAND Total Solar KamLAND 3σ 90% CL

**Figure 14.** ∆χ 2 profiles projected onto the sin2 θ13 axis, for solar, KamLAND, solar+KamLAND, atmospheric+K2K+CHOOZ, and for the global data. experiments (see, e.g., Refs. [26, 27, 40]). In

**Figure 15.** Upper bound on sin2 θ13 (1 d.o.f.) from solar+KamLAND+CHOOZ data as a function of ∆m2 atm. The dashed (solid) curve corresponds to the 90% (3σ) C.L. bound, the thin curves have been obtained with 2002 KamLAND data, whereas the thick curves follow from the recent 2004 KamLAND update. The light (dark) shaded region is excluded by CHOOZ data alone at 90% (3σ) C.L. The horizontal line corresponds to the best fit value of ∆m2 atm from atmospheric + K2K data given in Eq. (2), and the hatched regions are excluded by atmospheric + K2K data at 3σ according to Eq. (3). ∆m2 31 from…

**Figure 16.** Sections of the three–dimensional allowed regions in the (sin2 θsol, ∆m2 sol) plane at 90%, 95%, 99% and 3σ C.L. for 3 d.o.f. for various sin2 θ13 values from solar data (lines) and solar+KamLAND data (colored regions). The local minima in each plane from solar+KamLAND (solar only) data are marked by filled (open) dots. Let us discuss in some more detail the constraint on sin2 θ13 from solar data, which emerges from a subtle interplay of various solar neutrino observables. In

**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 mass-squared difference ∆m2 lsnd ∼ 1 eV2 . Such a value is inconsistent with the masssquared 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…

**Figure 18.** Parameter dependence of the different data sets in our parameterization. parameters we use ηs, ηe and dµ. These quantities are defined by ηα = X i |Uαi| 2 with i ∈ solar mass states, (18) dα = 1 − X i |Uαi| 2 with i ∈ atmospheric mass states, (19) where α = e, µ, τ, s. Note that in (2+2) schemes the relation ηα = dα holds, whereas in (3+1) ηα and dα are independent. The physical meaning of these parameters is the following: ηα is the fraction of να participating in solar oscillations, and (1 − dα) is the fraction of να participating in oscillations with ∆m2 atm (for further…

**Figure 19.** Left: ∆χ 2 as a function of ηs from solar data before the SNO saltphase results, from current solar data, and from solar+KamLAND data. Middle: ∆χ 2 sol, ∆χ 2 atm+k2k+sbl and ¯χ 2 global as a function of ηs in (2+2) oscillation schemes. The dashed line corresponds to atmospheric and K2K data only (without SBL data). Right: ∆χ 2 atm+k2k as a function of dµ. 5.2. (2+2): ruled out by solar and atmospheric data The strong preference for oscillations into active neutrinos in solar and atmospheric oscillations [36] leads to a direct conflict in (2+2) oscillation schemes. We will now show…

**Figure 20.** Upper bound on sin2 2θlsnd from NEV, atmospheric and K2K neutrino data in (3+1) schemes. The bound is calculated for each ∆m2 lsnd using the ∆χ 2 for 1 d.o.f. The dotted line corresponds to the bound at 99% C.L. without K2K and using one–dimensional atmospheric fluxes. Also shown are the regions allowed at 99% C.L. (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 these data are presently not available outside the Super-K collaboration. 5.3. (3+1): strongly disfavoured…

Figures reproduced from arXiv:hep-ph/0405172 by the authors.

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Forward citations

Cited by 46 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Running Neutrino Mass Parameters in See-Saw Scenarios
hep-ph 2005-01 accept novelty 7.0 of 10

Approximate one-loop renormalization group equations are derived for neutrino masses, lepton mixings and CP phases above the see-saw scales, with software for numerical evolution and estimates showing corrections comp...
Prospects for measuring neutrino mass with 21-cm forest
astro-ph.CO 2025-01 conditional novelty 6.0 of 10

Using an analytic halo model, the authors forecast that 21-cm forest observations with SKA-LOW could constrain the total neutrino mass to about 0.1 eV, potentially distinguishing neutrino mass hierarchies.
Status of neutrino oscillations 2018: first hint for normal mass ordering and improved CP sensitivity
hep-ph 2017-08 conditional novelty 6.0 of 10

Combining 2017-18 reactor, long-baseline and atmospheric neutrino data, the global fit disfavours inverted mass ordering at 3.4 sigma and excludes the CP phase near pi/2 at more than 4 sigma.
Heavy Neutrinos and Lepton Flavour Violation in Left-Right Symmetric Models at the LHC
hep-ph 2012-06 conditional novelty 6.0 of 10

At 14 TeV and 30 fb^-1 the LHC can probe right-handed neutrino mixing elements down to about 0.3 for W_R masses up to 3.5 TeV, and unlike mu to e gamma it is not suppressed by small heavy-neutrino mass splittings.
Neutrinos from WIMP Annihilations Obtained Using a Full Three-Flavor Monte Carlo Approach
hep-ph 2007-09 conditional novelty 6.0 of 10

Oscillation-driven flavor mixing changes the muon-neutrino yield from solar WIMP annihilations by factors of a few, up or down depending on the annihilation channel, while Earth-based annihilations show almost no osci...

Show 41 more citing papers

A Survey of Lepton Number Violation Via Effective Operators
hep-ph 2007-08 accept novelty 6.0 of 10

Requiring each of 129 lepton-number-violating effective operators to generate the observed neutrino mass fixes its cutoff scale, and that scale predicts which experiments can see it.
Non-standard neutrino interactions in reactor and superbeam experiments
hep-ph 2007-08 accept novelty 6.0 of 10

Approximate analytic formulas plus GLoBES simulations show that non-standard neutrino interactions can bias or fake theta-13 measurements in reactor and superbeam experiments, and that combining the two can reveal the effect.
Cosmological parameters from combining the Lyman-alpha forest with CMB, galaxy clustering and SN constraints
astro-ph 2006-04 accept novelty 6.0 of 10

Adding Lyman-alpha forest power spectra to WMAP3, supernovae and galaxy clustering gives sum of neutrino masses below 0.17 eV at 95 percent confidence, no running of the spectral index, and an effective neutrino numbe...
Neutrino-induced Electroweak Symmetry Breaking in Supersymmetric SO(10) Unification
hep-ph 2006-04 conditional novelty 6.0 of 10

Neutrino couplings and large right-handed sneutrino masses enable radiative electroweak symmetry breaking in SO(10) models, reconciling Yukawa unification with the measured bottom quark mass and b to s gamma rate.
Leptonic Charged Higgs Decays in the Zee Model
hep-ph 2006-04 conditional novelty 6.0 of 10

Charged Higgs decays in the general Zee model can have a muon channel enhanced over the tau channel by up to 10^4, changing how these particles should be searched for at colliders.
Physics potential of the CERN-MEMPHYS neutrino oscillation project
hep-ph 2006-03 accept novelty 6.0 of 10

This simulation study shows the CERN-MEMPHYS Beta Beam plus Super Beam program would be competitive with, and in several respects better than, the proposed T2HK experiment, and could halve running time by combining ne...
Family Symmetry and Single Right-Handed Neutrino Dominance in Five Dimensions
hep-ph 2006-03 conditional novelty 6.0 of 10

Five-dimensional versions of the see-saw mechanism can restore single right-handed neutrino dominance in U(1) family symmetry models, with explicit parameter sets matching observed neutrino data.
Predicting neutrino parameters from SO(3) family symmetry and quark-lepton unification
hep-ph 2005-06 conditional novelty 6.0 of 10

A unified SO(3) family symmetry and Pati-Salam model predicts neutrino mixing angles and the oscillation phase in terms of quark mixing parameters, with the reactor angle predicted at about 3.06 degrees.
Novel Supersymmetric SO(10) Seesaw Mechanism
hep-ph 2005-06 conditional novelty 6.0 of 10

In supersymmetric SO(10) with broken D-parity, an induced left-handed triplet vacuum expectation value cancels the B-L scale out of the neutrino mass formula, so the B-L scale can be TeV while neutrino masses stay small.
Relic neutrino decoupling including flavour oscillations
hep-ph 2005-06 accept novelty 6.0 of 10

Three-flavour oscillations leave the effective neutrino number at 3.046 but raise the total helium-4 shift from neutrino heating to about 2.1e-4, with the oscillation-only part roughly three times smaller than an earl...
p-Wave Dominant Majorana Dark Matter and Its Self-Interactions in a Gauged $U(1)_{L_\mu - L_\tau}$ Model
hep-ph 2025-12 unverdicted novelty 5.0 of 10

A gauged U(1)_{Lμ-Lτ} model generates nearly degenerate Majorana dark matter whose self-interactions via a light scalar mediator set the relic density, resolve core-cusp anomalies, and fit LZ direct detection plus muo...
Probing neutrino transition magnetic moments with coherent elastic neutrino-nucleus scattering
hep-ph 2019-05 conditional novelty 5.0 of 10

Coherent neutrino-nucleus scattering data and projections constrain the three Majorana transition magnetic moments, with future reactor detectors projected to surpass the Borexino limit by about a factor of three.
Dirac Neutrinos and Dark Matter Stability from Lepton Quarticity
hep-ph 2016-06 conditional novelty 5.0 of 10

A Z4 discrete lepton-number symmetry is proposed to make neutrinos Dirac and to stabilize a scalar WIMP dark matter candidate, with the stability argument worked out but the relic abundance only asserted.
Predicting charged lepton flavor violation from 3-3-1 gauge symmetry
hep-ph 2015-02 conditional novelty 5.0 of 10

In a 3-3-1 gauge model with inverse seesaw, the Yukawa couplings that drive charged lepton flavor violation are fixed by neutrino oscillation parameters up to one overall scale, yielding testable ratios of decay branc...
CMB power spectrum parameter degeneracies in the era of precision cosmology
astro-ph.CO 2012-01 accept novelty 5.0 of 10

CAMB's default high-accuracy settings are accurate enough that Planck-era CMB parameter degeneracies are broken by physical effects (lensing, the integrated Sachs-Wolfe effect, recombination geometry) rather than nume...
A model for trimaximal lepton mixing
hep-ph 2008-09 conditional novelty 5.0 of 10

A seesaw model based on softly broken Delta(27) symmetry enforces trimaximal lepton mixing without vacuum alignment, and yields one extra relation tying the deviation from tri-bimaximal mixing to the neutrino mass ratio.
Hints of theta_13>0 from global neutrino data analysis
hep-ph 2008-06 conditional novelty 5.0 of 10

Combining atmospheric, solar, reactor, and accelerator neutrino data yields sin^2(theta_13) = 0.016 +/- 0.010, a roughly 90% confidence hint that the last unknown neutrino mixing angle is nonzero.
Limits on nu_e and anti-nu_e disappearance from Gallium and reactor experiments
hep-ph 2007-11 conditional novelty 5.0 of 10

Combined fits to Gallium source and Bugey/Chooz reactor data give a weak, mutually compatible hint of electron neutrino disappearance with sin-squared-two-theta between 0.02 and 0.08 and delta-m-squared near 1.8 eV sq...
Sneutrino cold dark matter, a new analysis: relic abundance and detection rates
hep-ph 2007-09 conditional novelty 5.0 of 10

Sneutrino dark matter survives current direct-detection limits once a right-handed sneutrino field suppresses the Z coupling, and such models predict antiproton, antideuteron and gamma-ray fluxes within reach of PAMEL...
Decaying warm dark matter and neutrino masses
astro-ph 2007-05 conditional novelty 5.0 of 10

WMAP three-year CMB data are consistent with a thermally produced keV majoron of mass 0.12-0.17 keV and lifetime above 250 Gyr supplying all the dark matter.
CKM and Tri-bimaximal MNS Matrices in a SU(5) x (d)T Model
hep-ph 2007-05 conditional novelty 5.0 of 10

An SU(5) grand unified model with a double-tetrahedral family symmetry reproduces near tri-bimaximal neutrino mixing and realistic quark mixing, and predicts theta_13 approximately theta_c divided by 3 sqrt(2).
Sterile neutrino oscillations after first MiniBooNE results
hep-ph 2007-05 accept novelty 5.0 of 10

No sterile-neutrino scheme with one, two, or three eV-scale states gives a consistent global fit to short-baseline neutrino data once the first MiniBooNE results are included, although CP violation in a (3+2) scheme r...
Phenomenology with Massive Neutrinos
hep-ph 2007-04 accept novelty 5.0 of 10

Three-neutrino oscillations describe the world's neutrino data, with updated mixing parameters and new bounds on exotic physics.
How astrophysical neutrino sources could be used for early measurements of neutrino mass hierarchy and leptonic CP phase
hep-ph 2006-04 accept novelty 5.0 of 10

Astrophysical neutrino flavor ratios could enhance early measurements of the neutrino mass hierarchy and CP phase when combined with reactor and beam experiments.
Are solar neutrino oscillations robust?
hep-ph 2004-06 conditional novelty 5.0 of 10

Allowing non-standard neutrino interactions makes the solar mixing angle ambiguous, with a degenerate dark-side solution at sin²θ_sol = 0.70, though the simplest down-quark-only version is excluded by atmospheric and ...
Updated Global 3+1 Analysis of Short-BaseLine Neutrino Oscillations
hep-ph 2017-03 conditional novelty 4.0 of 10

Adding NEOS, MINOS, and IceCube data to a 3+1 sterile-neutrino fit narrows the allowed mixing parameters to three small Δm2 islands and makes the appearance-disappearance tension tolerable only after dropping MiniBooN...
Probing light sterile neutrino signatures at reactor and Spallation Neutron Source neutrino experiments
hep-ph 2017-02 conditional novelty 4.0 of 10

A sensitivity study finds that TEXONO and COHERENT coherent neutrino-nucleus scattering data could probe eV-scale sterile neutrino mixing at a level competitive with LSND and MiniBooNE.
Towards a cosmological neutrino mass detection
astro-ph.CO 2015-09 accept novelty 4.0 of 10

Combining a Stage-4 CMB lensing experiment with DESI BAO should reach a 1-sigma neutrino mass sum uncertainty of 15 to 19 meV, enough for a 4-sigma detection of the 60 meV minimum, provided large-scale CMB polarizatio...
Update of Short-Baseline Electron Neutrino and Antineutrino Disappearance
hep-ph 2012-10 conditional novelty 4.0 of 10

Combined Gallium, reactor, solar and neutrino-carbon data remain compatible with a fourth, sterile neutrino at the electron-volt scale with sin^2(2 theta_ee) about 0.03 to 0.2 and Delta m^2_41 above about 0.5 eV^2 at 95% CL.
Global status of neutrino oscillation parameters after Neutrino-2012
hep-ph 2012-05 accept novelty 4.0 of 10

A global fit to 2012 neutrino data fixes sin-squared theta-13 at about 0.025 and excludes theta-13 = 0 at 10.2 sigma, while the atmospheric angle theta-23 shows only a marginal preference for non-maximal mixing.
Implications of 3+1 Short-Baseline Neutrino Oscillations
hep-ph 2011-11 conditional novelty 4.0 of 10

Adding KARMEN and LSND neutrino-carbon scattering to a 3+1 sterile-neutrino global fit lowers the preferred mass splitting to about 1 eV and yields beta-decay and double-beta mass ranges of 0.1-0.7 eV and 0.01-0.1 eV.
Status of 3+1 Neutrino Mixing
hep-ph 2011-09 conditional novelty 4.0 of 10

Adding updated MiniBooNE antineutrino and new MINOS neutral-current data to a global 3+1 sterile-neutrino fit yields a best point near 5.6 eV squared, with appearance and disappearance data only marginally compatible ...
3+1 and 3+2 Sterile Neutrino Fits
hep-ph 2011-07 conditional novelty 4.0 of 10

Global fits of short-baseline neutrino data favor eV-scale sterile neutrinos but fail a parameter goodness-of-fit test at the 10^-6 to 10^-4 level.
Global neutrino data and recent reactor fluxes: status of three-flavour oscillation parameters
hep-ph 2011-03 accept novelty 4.0 of 10

Combining solar, atmospheric, reactor and long-baseline neutrino data with the revised reactor antineutrino flux, the global three-flavour fit finds only a 1.8 sigma hint for nonzero theta13, with the significance hin...
Statistical Significance of the Gallium Anomaly
hep-ph 2010-06 conditional novelty 4.0 of 10

Accounting for the uncertainty in the neutrino detection cross section, the Gallium radioactive-source deficit stands at about 3.0 sigma, and a short-baseline oscillation fit is favored over no oscillations at about 2...
Physics at a future Neutrino Factory and super-beam facility
hep-ph 2007-10 conditional novelty 4.0 of 10

A common-tool simulation ranks the Neutrino Factory, beta-beam and super-beam against each other, and finds the winner depends on how large the unmeasured mixing angle theta-13 turns out to be.
2020 Global reassessment of the neutrino oscillation picture
hep-ph 2020-06 unverdicted novelty 3.0 of 10

Updated global fit of neutrino oscillation data gives precise measurements of mixing parameters with a 2.5 sigma preference for normal mass ordering.
Neutrino oscillations and Non-Standard Interactions
hep-ph 2017-10 conditional novelty 3.0 of 10

A review argues that a new 5-10 MeV gauge boson can generate sizeable non-standard neutrino matter effects without violating current experimental bounds, though the anomaly-cancellation route to the largest effects re...
Three-flavour neutrino oscillation update
hep-ph 2008-08 conditional novelty 3.0 of 10

Global three-flavour neutrino data remain consistent with zero θ13, with sin²θ13 bounded below 0.035 at 90% CL in the 2008 analysis and 0.034 in the 2010 update.
Non Thermal Features in the Cosmic Neutrino Background
astro-ph 2006-03 unverdicted novelty 1.0 of 10

A review of current cosmological bounds on distortions of the cosmic neutrino background, concluding that present data only weakly constrain non-thermal features and future experiments will tighten some, but not all, ...
Massive neutrinos and cosmology
astro-ph 2006-03 accept novelty 1.0 of 10

A detailed review of how cosmological observations bound the sum of neutrino masses through the free-streaming suppression of small-scale structure, and of future sensitivity forecasts.

How later papers used it

121 later papers cite it

Evidence: substantial. 102 of the citing papers share no author with it, and 54 of those carry a confident label from Pith's citation classifier.

Pith read 35 of the 191 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

18 later papers by other authors are listed below: 18 used its data or values.

Uses its data or values 18 of 52 papers with this label

Used the results of the combined analysis given in this paper's Table I.

Gravity Effects on Neutrino Masses in Split Supersymmetry (2009) · 1.00 · paraphrased: the licence does not allow quoting
Used the central values from this paper's global fit for the mixing angles and neutrino squared mass differences, setting theta13 at its upper limit.

Flavor Violating Transitions of Charged Leptons from a Seesaw Mechanism of Dimension Seven (2010) · 1.00 · paraphrased: the licence does not allow quoting
Imposed this paper's neutrino physics constraints at the 1 sigma level in its numerical analysis.

Radiative seesaw: Warm dark matter, collider and lepton flavour violating signals (2008) · 0.93 · paraphrased: the licence does not allow quoting
Plotted the allowed atmospheric and solar regions corresponding to the values summarized in this paper's table.

Neutrino Mass (2007) · 0.85 · paraphrased: the licence does not allow quoting
Used this paper's global fit of mixing parameters for the relative oscillation amplitudes.

Determination of the Neutrino Mass Hierarchy at an Intermediate Baseline (2008) · 1.00 · paraphrased: the licence does not allow quoting
Used the 3 sigma ranges of the five oscillation parameters presented in this paper's Table 1.

Hybrid textures in minimal seesaw mass matrices (2008) · 1.00 · paraphrased: the licence does not allow quoting
Used the 3 sigma values of the oscillation parameters presented in this paper's Table 1.

Minimal Seesaw Textures with Two Heavy Neutrinos (2008) · 0.99 · paraphrased: the licence does not allow quoting
Used this paper's best-fit values for neutrino masses to obtain the ranges of R.

Radiative and flavor-violating transitions of leptons from interactions with color-octet particles (2009) · 1.00 · paraphrased: the licence does not allow quoting
Fit neutrino mass squared differences to this paper's best fit values.

Supersymmetric seesaw type II: CERN LHC and lepton flavour violating phenomenology (2008) · 1.00 · paraphrased: the licence does not allow quoting
Took five experimental data given at 3 sigma by this paper as low energy constraints in its numerical analysis.

Bridges of Low Energy observables with Leptogenesis in mu-tau Reflection Symmetry (2008) · 1.00 · paraphrased: the licence does not allow quoting
Used this paper's squared mass differences at 3 sigma confidence level.

Determining the Neutrino Mass Hierarchy with Cosmology (2009) · 0.93 · paraphrased: the licence does not allow quoting
Used this paper's best fit values and 2 sigma allowed ranges of the measured oscillation parameters.

An intermediate gamma beta-beam neutrino experiment with long baseline (2008) · 0.92 · paraphrased: the licence does not allow quoting
Used this paper's constraints on sin^2(2theta13), sin^2(2theta23) and sin^2(2theta12) to identify a viable region.

A Model of Lepton Masses from a Warped Extra Dimension (2008) · 0.82 · paraphrased: the licence does not allow quoting
Set the oscillation parameters to this paper's values.

Dark matter at DeepCore and IceCube (2011) · 1.00 · paraphrased: the licence does not allow quoting
Used this paper's global fit to all neutrino data for a limit on sin^2(thetaR).

Leptoquarks: Neutrino masses and accelerator phenomenology (2007) · 0.96 · paraphrased: the licence does not allow quoting
Chose parameters so that this paper's solar and atmospheric neutrino data are fitted in the correct way.

Spontaneous R-parity violation: Lightest neutralino decays and neutrino mixing angles at future colliders (2008) · 0.88 · paraphrased: the licence does not allow quoting
Used this paper's known neutrino masses and mixing angles to find f_126.

Flavor Physics in SO(10) GUTs with Suppressed Proton decay Due to Gauged Discrete Symmetry (2008) · 0.99 · paraphrased: the licence does not allow quoting
Required viable models to agree with this paper's neutrino oscillation parameters falling within the 2 sigma ranges.

Differentiating Neutrino Models on the Basis of $\theta_{13}$ and Lepton Flavor Violation (2008) · 0.85 · paraphrased: the licence does not allow quoting

How the literature uses it

118 arXiv papers cite this in 189 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 3 papers

I give the allowed ranges of the three--flavour oscillation parameters from the current worlds' global neutrino data sample, their best fit values and discuss the small parameters DeltaM_solar/DeltaM_atm and sin^2 theta_13, which characterize the strength of CP violation in neutrino oscillations.

Physics of Massive Neutrinos · 1.00
We determine the current best fit values and allowed ranges for the three-flavor oscillation parameters, discussing the relevance of each individual data set as well as the complementarity of different data sets.

Status of neutrino oscillations I: the three-neutrino scenario · 0.88
The up-to-date best fit values and allowed ranges of the three-flavour oscillation parameters are determined from these data.

Status of three-neutrino oscillations after the SNO-salt data · 0.83

Papers citing it · 88 sentences without a confident label

Contests it 1 paper

This practice has been violated in recent papers [ref] claiming that the anomalous oscillatory time modulation of the electron-capture decays [equation] observed in a GSI experiment [ref] is due to neutrino mixing (see Refs. [ref] ).

Rates of Processes with Coherent Production of Different Particles and the GSI Time Anomaly · Introduction · contest 0.83

Uses its method or tool 1 paper

Relevant data about neutrinos and their parents was extracted for each event, and fed to a modified version of WimpSim in order to simulate neutrino interaction and propagation to a detector (either IceCube/DeepCore or Super-K) [ref] .[For propagation, we use the default WimpSim parameters: $θ_12 = 33.2^∘$, $θ_13 = 0.0^∘$, $θ_23 = 45.0^∘$, $δ= 0.0$, $Δm_21^2 = 8.1 ×10^-5 eV^2$ and $Δm_31^2 = 2.2 ×10^-3 eV^2$ [ref] , but our results are not particularly sensitive to the exact choice of these parameters.] To validate this method, we confirmed that the cross sections and branching ratios given by MadGraph agreed with those from analytic expressions for $2 →2$ annihilations in the static limit (e.g., from [ref] ).

Neutrinos from Off-Shell Final States and the Indirect Detection of Dark Matter · $WW^∗$ · 0.99

Uses its data or values 51 papers

[ref] , given in Table I.

Gravity Effects on Neutrino Masses in Split Supersymmetry · Results and Predictions · 1.00
The solar, atmospheric and reactor neutrino experiments have measured the mass squared differences and mixing angles [ref] as shown in Table [ref].

Neutrino mass matrix in triplet Higgs models with $A_4$ symmetry · Introduction · 0.99
For the mixing angles and the neutrino squared mass differences we use the central values from the global fit in Ref. [ref] : $sin^2θ_12=0.32$, $sin^2θ_23=0.50$, $Δm^2_21=7.6×10^-5 ^2$, $|Δm^2_31|=2.4×10^-3 ^2$, and set $θ_13$ at its upper limit, $sin^2θ_13=0.05$.

Flavor Violating Transitions of Charged Leptons from a Seesaw Mechanism of Dimension Seven · Numerical analysis · 1.00

Compares with it 1 paper

In Fig. [ref] we show the results of our previous atmospheric neutrino analysis from Refs. [ref] including data from the first phase of the Super-Kamiokande experiment, compared to the new analysis included in this update, based on the Super-Kamiokande data from all three phases of the experiment.

Global neutrino data and recent reactor fluxes: status of three-flavour oscillation parameters · Super-Kamiokande I+II+III data · 1.00

Cites it as support 2 papers

Indeed, recent combinations of solar and KamLAND data prefer $θ_13>0$, although weakly [ref] .

Hints of theta_13>0 from global neutrino data analysis · Introduction · 0.97
In this paper we consider 3+1 four-neutrino schemes, since 2+2 four-neutrino schemes are disfavored by the combined constraints on active-sterile transitions in solar and atmospheric neutrino experiments [ref] .

Short-Baseline Electron Neutrino Disappearance, Tritium Beta Decay and Neutrinoless Double-Beta Decay · Introduction · 0.98

Cites it as background 21 papers

The GALLEX [ref] and SAGE [ref] solar neutrino detectors (see Refs. [ref] ) have been tested in so-called "Gallium radioactive source experiments" which consist in the detection of electron neutrinos produced by intense artificial $^51Cr$ and $^37Ar$ radioactive sources placed inside the detectors.

Limits on nu_e and anti-nu_e disappearance from Gallium and reactor experiments · Gallium · 0.82
Let us now present the results of the global analysis combining all data mentioned in the previous sections [ See also Refs. [ref] for previous experimental references.].

Global neutrino data and recent reactor fluxes: status of three-flavour oscillation parameters · Global 3-neutrino analysis and status of $θ_13$ · 0.90
where $U_MNS^st$ is the physically measurable matrix which includes the Majorana phases in the standard form [ref] , U_MNS^st = ( -c_12c_13 s_12c_13 s_13e^-iδ -s_12c_23-c_12s_23 s_13e^iδ -c_12c_23-s_12s_23 s_13e^iδ s_23c_13 -s_12s_23-c_12c_23s_13e^iδ -c_12s_23-s_12c_23s_13e^iδ c_23c_13 )×diag (e^iα_1, e^i α_2, 1).

Neutrino mass matrix in triplet Higgs models with $A_4$ symmetry · The Higgs triplet model with $A_4$ symmetry · 0.83

Discussion

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