Revisiting the LSND anomaly. II. Critique of the data analysis
ABSTRACT This paper, together with a preceding paper, questions the so-called “LSND anomaly”: a 3.8σ excess of ν̅ e interactions over standard backgrounds, observed by the LSND Collaboration in a beam dump experiment with 800 MeV protons. That excess has been interpreted as evidence for the ν̅ μ→ν̅ e oscillation in the Δm2 range from 0.2 eV2 to 2 eV2. Such a Δm2 range is incompatible with the widely accepted model of oscillations between three light neutrino species and would require the existence of at least one light “sterile” neutrino. In a preceding paper, it was concluded that the estimates of standard backgrounds must be significantly increased. In this paper, the LSND Collaboration’s estimate of the number of ν̅ e interactions followed by neutron capture, and of its error, is questioned. The overall conclusion is that the significance of the “LSND anomaly” is not larger than 2.3σ.
EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
17 October 2011
Revisiting the ‘LSND anomaly’ II:
critique of the data analysis
Thispaper, togetherwithaprecedingpaper, questionstheso-called‘LSNDanomaly’: a
3.8 σ excess of ¯ νeinteractions over standard backgrounds, observed by the LSND Collabo-
ration in a beam dump experiment with 800 MeV protons. That excess has been interpreted
as evidence for the ¯ νµ→ ¯ νeoscillation in the ∆m2range from 0.2 eV2to 2 eV2. Such a
∆m2range is incompatible with the widely accepted model of oscillations between three
light neutrino species and would require the existence of at least one light ‘sterile’ neutrino.
In a preceding paper, it was concluded that the estimates of standard backgrounds must be
significantly increased. In this paper, the LSND Collaboration’s estimate of the number
of ¯ νeinteractions followed by neutron capture, and of its error, is questioned. The overall
conclusion is that the significance of the ‘LSND anomaly’ is not larger than 2.3 σ.
The HARP–CDP group
A. Bolshakova1, I. Boyko1, G. Chelkov1a, D. Dedovitch1, A. Elagin1b, D. Emelyanov1,
M. Gostkin1, A. Guskov1, Z. Kroumchtein1, Yu. Nefedov1, K. Nikolaev1, A. Zhemchugov1,
F. Dydak2, J. Wotschack2∗, A. De Min3c, V. Ammosov4†, V. Gapienko4, V. Koreshev4,
A. Semak4, Yu. Sviridov4, E. Usenko4d, V. Zaets4
1Joint Institute for Nuclear Research, Dubna, Russia
2CERN, Geneva, Switzerland
3Politecnico di Milano and INFN, Sezione di Milano-Bicocca, Milan, Italy
4Institute of High Energy Physics, Protvino, Russia
(To be submitted to Phys. Rev. D)
aAlso at the Moscow Institute of Physics and Technology, Moscow, Russia
bNow at Texas A&M University, College Station, USA
cOn leave of absence
dNow at Institute for Nuclear Research RAS, Moscow, Russia
∗Corresponding author; e-mail: email@example.com
arXiv:1112.0907v1 [hep-ex] 5 Dec 2011
This is the second of two papers that argue that the 3.8 σ significance of the ‘LSND anomaly’,
claimed by the LSND Collaboration, cannot be upheld.
The LSND experiment was carried out at the Los Alamos National Laboratory in the years
1993–1998. Its scientific goal was a search for ¯ νµ→ ¯ νeoscillations in the ‘appearance’ mode.
The neutrino fluxes were produced by dumping 800 MeV protons into a ‘beam stop’. While νµ,
¯ νµand νefluxes were abundant, the ¯ νeflux was vanishingly small.
The LSND Collaboration claimed an excess of ¯ νeinteractions over the expectation from
standard backgrounds . This excess was interpreted as evidence for the ¯ νµ→ ¯ νeoscillation
with ∆m2in the range from 0.2 eV2to 2 eV2and came to be known as ‘LSND anomaly’. In
stark conflict with the widely accepted model of oscillations of three light neutrino flavours, the
excess would require the existence of at least one light ‘sterile’ neutrino that does not couple to
the Z boson.
Since the ‘LSND anomaly’ calls the Standard Model of particle physics in a non-trivial way
into question, the MiniBooNE experiment at the Fermi National Accelerator Laboratory set out
to check this result. In the neutrino mode, an oscillation νµ→ νewith parameters compatible
with the LSND claim was not seen . However, first results from running in antineutrino mode
and searching for ¯ νµ→ ¯ νeled the MiniBooNE Collaboration to conclude that their result does
not rule out the ‘LSND anomaly’  that had indeed been observed in the antineutrino mode.
In this situation it appears worthwhile to undertake a critical review of the original results
of the LSND experiment that gave rise to the ‘LSND anomaly’. This is the subject both of this
paper and of a preceding paper .
Although we agree with many of the LSND Collaboration’s approaches and results, in two
areas we disagree with LSND. The first area—which has been discussed in Ref. —concerns
the underestimation of the ¯ νeflux from standard sources. According to our assessment the in-
creased standard background reduces the significance of the ‘LSND anomaly’ from 3.8 to 2.9 σ.
The second area is quantitatively discussed in this paper. It concerns the neglect of a bias and
the underestimation of systematic errors in the isolation of the signal of ∼120 ¯ νe+ p → e++ n
reactions with a correlated γ from neutron capture out of ∼2100 candidate events.
In this section, we recall LSND’s determination of the number of beam-related ¯ νeinteractions
by a fit to the Rγdistribution—the centre piece of the LSND data analysis. Before, we describe
briefly the salient features of the LSND experiment.
The LSND neutrino detector  is a tank filled with liquid scintillator. The amplitude and
the time of arrival of scintillation light and of Cherenkov light are detected by an array of
phototubes (PMTs) on the surfaces of the tank. The reconstruction of the energy and position of
reaction secondaries is solely based on the responses of the phototubes. There is no distinction
between positive and negative electric charges.
The ¯ νeflux is measured through the reaction ¯ νe+ p → e++ n which has a well known cross-
section. The signature is an e+and a delayed 2.2 MeV γ from deuteron creation by the capture
of the neutron on a free proton, n + p → d + γ. The average delay of the γ is ∼186 µs,
determined by the neutron capture cross-section in the scintillator medium.
Besides cuts that enrich beam-induced electrons1)w.r.t. cosmic-ray particles, and a cut that
requires electrons to be inside a fiducial volume that ends 35 cm from the faces of the PMTs,
THE LSND FIT OF THE RγDISTRIBUTION
1)We use the generic term ‘electron’ both for electrons and positrons.
a cut 20 MeV < Ee < 60 MeV2)is applied to qualify as ‘primary electron’. Furthermore,
activities within 1 ms after the primary electron are recorded with a lower trigger threshold not
to miss 2.2 MeV γ’s. The number of such activities can be zero, one, or larger than one.
Despite the cuts to suppress cosmic-ray particles, there remains a large cosmogenic back-
ground. This background is determined in beam-off gates and subtracted after proper normal-
ization from the event numbers observed in beam-on gates. This doubles approximately the
statistical error but introduces no systematic uncertainty.
Integrated over the data taking of the LSND experiment in the years 1993 – 1998, the num-
ber of beam-related ‘primary electrons’ is about 2100. The key issue is how to isolate from
these 2100 events the signal, i.e., the number of events with a correlated 2.2 MeV γ from neu-
tron capture. We recall that the signal claimed by LSND is 117.9 events .
The isolation criterion applied by LSND is the following. “Correlated 2.2 MeV γ from
neutron capture are distinguished from accidental γ from radioactivity by use of the likelihood
ratio, Rγ, which is defined to be the likelihood that the γ is correlated divided by the likelihood
that the γ is accidental. Rγdepends on three quantities: the number of hit PMTs associated with
the γ (the multiplicity is proportional to the γ energy), the distance between the reconstructed γ
position and positron position, and the time interval between the γ and positron (neutrons have
a capture time in mineral oil of 186 µs, while the accidental γ are uniform in time)” (Section
VII.C in Ref. ).
The said likelihoods for correlated and accidental γ’s are obtained from respective distribu-
hereinFig.1. Inthefollowing, werefertothesedistributionsas‘basedistributions’. Anactivity
within 1 ms after the primary electron is only accepted if three criteria are met: ∆r ≤ 250 cm,
8 µs ≤ ∆t ≤ 1 ms, and 21 ≤ Nhits ≤ 60. If all three criteria are met, the product of the
probabilities of the observed ∆r, ∆t and Nhitsis calculated both for the correlated and the ac-
cidental distributions, and then their ratio Rγ. If at least one of the three criteria is not met, the
likelihood ratio Rγis artificially set to zero3). If there are several accepted activities, the activity
with the largest Rγis chosen (Section III.F in Ref. ). The resulting Rγdistribution of the
data is shown as black dots with (statistical) error bars in Fig. 14 in Ref. , reproduced here in
The prominent peak of the Rγdistribution in the first bin reflects the many events with no
accepted activity within 1 ms after the primary electron.
The Rγdistribution of the data is then fitted with a linear combination of two Rγhypotheses:
γ’s. The former is obtained by generating triplets [∆r, ∆t, Nhits] according to the respective
distributions for correlated γ’s, and then calculating Rγ. The latter is analogously obtained by
generating triplets [∆r, ∆t, Nhits] according to the respective distributions for accidental γ’s,
and then calculating Rγ. By construction, the Rγdistribution of correlated γ’s favours large
values of Rγwhile the Rγdistribution of accidental γ’s favours small values of Rγ. In addition,
for either hypothesis an estimate was made of the probability of meeting all three criteria on
∆r, ∆t and Nhits(termed ‘efficiency’ by LSND).
Then, according to LSND, a χ2minimization determines a signal (termed ‘beam excess’ by
LSND) of 117.9 ± 22.4 events with a correlated γ out of about 2100 candidate events (Section
VII.D in Ref. ).
2)The maximum energy of a ¯ νein the decay of a muon at rest is 52.8 MeV.
3)LSND make no statement about lower and upper limits of Rγ; in our analysis values of Rγbelow 0.051 are
set to 0.051, and values above 199 are set to 199.
0 25 50 75100125150175 200225
0200 400600 8001000
2530354045 50 5560
Correlated DistributionUncorrelated Distribution
Fig. 1: “Distributions for correlated 2.2 MeV γ (solid curves) and accidental γ (dashed curves). The top
plot shows the distance between the reconstructed γ position and positron position, ∆r, the middle plot
shows the time interval between the γ and positron, ∆t, and the bottom plot shows the number of hit
phototubes associated with the γ, Nhits.” (Figure and its caption copied from Fig. 10 in Ref. .)
Fig. 2: “The Rγdistribution for events that satisfy the selection criteria for the primary ¯ νµ→ ¯ νeoscilla-
tion search.” (Figure and its caption copied from Fig. 14 in Ref. .)
This procedure, while a priori adequate, is criticized below on several accounts. The results
of the procedure depend on the correctness of the ‘base distributions’ and the ‘efficiencies’
of correlated and accidental γ’s, both not discussed in the LSND papers. A contribution of
positrons from12Ngsbeta decays that are interpreted as correlated γ’s, has been neglected.
With a view to gaining insight into the salient features of the LSND fit of the Rγdistribution by
an emulation, Table 1 gives the numerical values of the bin contents in the double-logarithmic
Fig. 2 as obtained by a plot digitization program.
EMULATION OF THE LSND FIT OF THE RγDISTRIBUTION
Table 1: Numerical values of the bin contents in Fig. 2 for the Rγdistributions of correlated γ’s, acci-
dental γ’s, and of the data including errors.
0.050 – 0.106
0.106 – 0.226
0.226 – 0.480
0.480 – 1.02
1.02 – 2.17
2.17 – 4.61
4.61 – 9.80
9.80 – 20.8
20.8 – 44.3
44.3 – 94.1
94.1 – 200
(1932 ± 79)
20.54 ± 8.65
6.00 ± 7.63
20.98 ± 7.84
26.04 ± 7.45
10.07 ± 5.54
12.50 ± 5.45
10.07 ± 4.85
6.00 ± 3.89
14.23 ± 4.49
18.43 ± 5.13
For the size of the bin contents and the logarithmic scale, the contents of the first Rγbin
(and, if applicable, theirerrors) cannot be read off precisely. The values usedin our fit emulation
are shown in brackets in Table 1. Thereby, for the two hypothesis distributions use was made of
the statement that the correlated and accidental ‘efficiencies’ for Rγ> 1 are quoted by LSND
as 0.51 and 0.012, respectively (Table IX in Ref. ).
The results for the ‘beam excess’ from our fits of the data points shown in Fig. 2 are listed in
Table 2. Fit No. 2, which is our emulation of the LSND fit, gives the result 112.5 ± 21.6 events
which is to compared with the published LSND result, listed as Fit No. 1, of 117.9±22.4 events.
In view of the numerical uncertainties of the contents of the first Rγbins, we consider our Fit
No. 2 a satisfactory emulation of Fit No. 14). Fit No. 2 is graphically shown in Fig. 3.
The first important aspect of our emulation is that it nearly reproduces the total error of
the ‘beam excess’ (21.6 w.r.t. to 22.4 published by LSND) by taking into account merely the
statistical errors of the data points shown in Fig. 2. We recall that the error of 22.4 events was
used by LSND to calculate the significance of the ‘LSND anomaly’. We note that in comparison
4)The (unreadable) error of the first Rγbin does not matter much: the fit result of 112.5 ± 21.6 events changes
to 112.4±21.5 for an error equal to the square root of the bin content, and to 112.8±21.6 for an error three times
the square root of the bin content.
Fig. 3: Emulation of the fit of the LSND Rγdistribution with the sum of the hypotheses for correlated
(hatched) and accidental (open) γ’s.
Table 2: Fits of LSND data shown in Fig. 2
No. of events with corr. γ
117.9 ± 22.4 (19.0%)
112.5 ± 21.6 (19.2%)
116.7 ± 22.1 (18.9%)
103.1 ± 20.2 (19.6%)
105.7 ± 20.5 (19.4%)
Result published by LSND in Ref. 
Our emulation of the LSND fit
Fit No. 2 without 1st Rγbin
Rγhypotheses from Fig. 10 in Ref. 
Fit No. 3 without 1st Rγbin
The prominent spikes in the first Rγbin of Fig. 2, caused by the ‘efficiencies’ of correlated
and uncorrelated γ’s, raise questions on respective uncertainties and their effect on the ‘beam
excess’ and its error.
Following LSND’s nomenclature, the ‘efficiency’ of correlated and uncorrelated γ’s is de-
fined as the probability to find a respective γ that meets three criteria: distance ∆r ≤ 250 cm,
timedelay8µs≤ ∆t ≤1mswithrespecttotheprimaryelectron, andpulseheight20≤ Nhits≤
60. The numerical values of these efficiencies are, for Rγ> 1, 0.51 for correlated γ’s and 0.012
for accidental γ’s, respectively. Both values are quoted by LSND with an error of 7% (Table IX
in Ref. ).
First, we show that especially the numerical value of the ‘efficiency’ of correlated γ’s is
important for the ‘beam excess’ and its error.
The content of the first bin consists almost exclusively of events that have no accepted
delayed γ. Therefore, the content of the first bin does not contribute to the fit’s purpose of
discriminating between correlated and accidental γ’s. So why did LSND include the first Rγ
bin into the fit? Omitting the first Rγbin reduces the number of data bins from 11 to 10, and
reduces the degrees of freedom from 9 to 8, but preserves fully the potential of discriminating
between correlated and uncorrelated γ’s. The result for the ‘beam excess’ is 116.7±22.1 events
(Fit No. 3 in Table 2) where an ‘efficiency’ of correlated γ’s of 0.51 for Rγ > 1 has been
used. This result which bypasses the reading uncertainty of the data content of the first bin, is
remarkably close to LSND’s result for the bin excess from their 11-bin fit, 117.9 ± 22.4 (Fit
No. 1 in Table 2), and proves that our emulation of the LSND fit makes sense.
Fit No. 3 is graphically shown in Fig. 4.
Our 10-bin fit sharpens the argument that the LSND fit result comprises little systematic
error margin, if at all. Already the error of 7% quoted by LSND for the ‘efficiency’ of correlated
γ’s (which will be disputed below) would increase, quadratically added, the 22.1 error of our
10-bin fit to 23.6 which alone (other systematic errors still ignored) exceeds already the total
error of 22.4 quoted by LSND.
As far as the statistical error is concerned, there is no appreciable gain from the inclusion
into the fit of the data in the first Rγbin. As for the systematic error, while the 7% uncertainty
of the ‘efficiency’ of correlated γ’s cannot be avoided, the propagation of the 7% systematic
uncertainty on the ‘efficiency’ of accidental γ’s into the error of the ‘beam excess’ could be
While we consider in retrospect a 10-bin fit as the better choice, we limit ourselves in the
further discussion to the 11-bin fit since this type of fit was LSND’s choice and underlies the
The ‘efficiencies’ are in an 11-bin fit an integral part of the two hypothesis distributions for
correlated and uncorrelated γ’s. The numerical values of the ‘efficiencies’, in particular the one
of correlated γ’s, have a direct impact on the ‘beam excess’ and its error.
Where do the ‘efficiency’ values and their errors come from? Can the values quoted by
LSND be understood? It is surprising that the values are quoted in LSND’s final physics paper
(Table IX in Ref. ), however, nowhere in this paper is their origin discussed. The only hint
can be found in an earlier paper that quotes intermediate results (Section III.F in Ref. ): “The
efficiency for producing and detecting a 2.2 MeV correlated γ within 2.5 m, with 21–50 PMT
hits, and within 1 ms was determined to be 63 ± 4% using the solid curve of Fig. 5. This
efficiency is the product of the probability that the γ trigger is not vetoed by a veto shield signal
within the previous 15.2 µs (82 ± 1%), the data acquisition livetime (94 ± 3%, lower for γ’s
than for primary events), the requirement that the γ occurs between 8 µs and 1000 µs after the
Fig. 4: 10-bin fit of the LSND Rγdistribution with the sum of the hypotheses for correlated (hatched)
and accidental (open) γ’s.
primary event (95±1%), the requirement that the γ has between 21 and 50 hit PMTs (90±4%),
and the requirement that the γ reconstructs within 2.5 m of the primary event (96±2%)”. From
this we can conclude that the efficiency for correlated γ’s stated in LSND’s final physics paper,
0.51 (±7%) for Rγ> 1, is in part determined by data acquisition properties, and in part by the
‘base distributions’ of ∆r, ∆t and Nhits.
While we must assume that the data acquisition properties such as livetime, and experi-
mental conditions such as the rate of accidental γ’s, were understood and correctly taken into
account, we shall dispute below some of the ‘base distributions’ and their impact on the ‘effi-
In this section, we shall assess systematic uncertainties of the ‘base distributions’ that were
published by LSND  and reproduced in Fig. 1.
Why did LSND publish smooth functions in their final physics paper  and not data and
Monte Carlo distributions, respectively, as they did in their earlier paper on intermediate re-
sults ? This question is the more appropriate as there are interesting differences between the
two presentations, not discussed by LSND anywhere in their papers, to which we shall return
We note also that systematic uncertainties of the ‘base distributions’ are nowhere discussed
in LSND papers.
Our discussion will concentrate on LSND’s final base distributions since these were claimed
to underlie their final results. We note that the distributions shown in Fig. 1 are computer-drawn
functions. We have reproduced the LSND ‘base distributions’ with a plot digitization program.
They are referred to below as HARP–CDP ‘base distributions’ and used to emulate the Rγfit
hypotheses for correlated and accidental γ’s.
ON UNCERTAINTIES OF THE ‘BASE DISTRIBUTIONS’
∆t is the time delay between the primary electron and the subsequent correlated or accidental γ.
The ∆t ‘base distributions’ for 8 µs ≤ ∆t ≤ 1 ms are uncontroversial, and so are the pertinent
contributions to the ‘efficiencies’ of correlated and accidental γ’s.
The ∆t distribution of accidental γ’s is flat since we understand that any number of γ’s was
recorded that fell into the window 8 µs ≤ ∆t ≤ 1 ms (the choice of the one with the largest Rγ
among them does not depend on ∆t). Because of this requirement—that is nowhere discussed
in the LSND papers—, it would have been worthwhile to demonstrate experimentally that the
∆t distribution of accidental γ?s was indeed flat.
The ∆t distribution of correlated γ’s is claimed by LSND as exponentially falling with
a mean time delay of 186 µs. We checked the latter with a Monte Carlo program that tracks
1 MeV neutrons (the average energy of neutrons released in the signal reaction ¯ νe+ p → e++ n)
from creation until capture by a free proton in the LSND detector5). Salient results are shown
in Figs. 5 and 6. The average time to reach the epithermal energy of 10 keV is 16.0 ns and
hence negligibly small in comparison to the average time of 15.0 µs to reach the thermal energy
of 0.022 eV. The bulk of the time is spent between subsequent elastic scatterings at thermal
energy. We find the time delay distribution until capture exponentially falling with an average
of 196.1 µs, slightly larger than 186 µs.
The ∆t ‘base distributions’
5)We are indebted to K. N¨ unighoff from the Forschungszentrum J¨ ulich GmbH for making available to us an
extensive compilation of neutron cross-sections on free protons.
Fig. 5: Distribution of time delays between the creation in the LSND scintillator medium of a 1 MeV
neutron and the transition to the epithermal energy of 10 keV.
This time delay solely depends on the average speed of a thermal neutron and its capture
cross-section. At thermal energy level, the hydrogen atoms in the LSND detector medium,
mineral oil, are not free but bound which increases the capture cross-section with respect to
the one for free hydrogen atoms. This increase—which entails a decrease of the average time
delay—depends on the energy levels of vibrational states of the hydrogen atom in the mineral
oil molecule and is hard to estimate. LSND do not state where their expectation of 186 µs
comes from, but they state in an earlier paper that they measured the average time delay as
188±3 µs (Section III.B and Fig. 1 in Ref. ) with cosmic-ray neutrons. This is possible since
the neutron’s ∆t distribution is nearly independent of the initial neutron energy (other than the
neutron’s ∆r distribution, discussed below). We acknowledge this measurement, conclude that
the hydrogen atom in mineral oil is quasi-free, and use LSND’s average time delay of 186 µs in
Other than LSND’s ∆t ‘base distributions’, their ∆r ‘base distributions’ cause major concerns.
In an infinite medium, the ∆r distribution of accidental γ’s should smoothly rise with (∆r)2.
In the finite fiducial volume of the LSND detector, the actual distribution must fall below this
The ∆r ‘base distributions’
Fig. 6: Distribution of time delays between the creation in the LSND scintillator medium of a 1 MeV
neutron and its capture on a free proton.
Fig. 7: Normalized distributions of the distance ∆r for accidental γ’s: as published by LSND (full line),
and a variant (dotted line).
functional dependence, especially at large ∆r. Indeed, this is seen in Fig. 2 in Ref.  which
shows measured data, but is not seen in Fig. 10 in LSND’s final physics paper  (reproduced
experimental data. We consider that at large ∆r LSND’s parametrization of the ∆r distribution
of accidental γ’s is unphysical.
There is a second reason why LSND’s final ∆r distribution of accidental γ’s cannot be
quite right: the ‘hot spot’ of radioactivity in the upstream bottom portion of the LSND detector,
prominently visible in Fig. 3 in Ref.  and discussed there in Section III.D.2. Yet there is no
mention of this ‘hot spot’ in LSND’s final physics paper .
LSND’s ∆r distribution for accidental γ’s is compared in Fig. 7 with a variant that we
consider equally likely to represent the situation.
The ∆r distribution for accidental γ’s is rather insensitive to the spatial resolution of the
reconstructed position of the accidental γ. The variant shown in Fig. 7 has been generated with
a spatial resolution of σ = 35 cm.
The ∆r distribution of accidental γ’s could experimentally be well determined by recording
γ-compatible events in randomly opened gates, and calculating ∆r w.r.t. a randomly chosen
location within the fiducial volume. It would have been worthwhile to present the result in
LSND’s final physics paper.
The cut ∆r ≤ 250 cm that contributes to the ‘efficiency’ of accidental γ’s will have a
different effect for the two distributions shown in Fig. 7.
Nowweturntothe∆r distributionofcorrelatedγ’s. Thisdistributionstemsfromaconvolu-
tion of (i) the distribution of the distance of the neutron emitted in the reaction ¯ νe+ p → e++ n
between its point of creation and its point of capture, (ii) the spatial resolution of the recon-
structed point of creation, and (iii) the spatial resolution of the reconstructed position of the
2.2 MeV γ.
Our result on the first of these three distributions is shown in Fig. 8. The average ∆r
between the point of creation of a 1 MeV neutron and the point of its capture is 11.4 cm. This is
consistent with expectation from neutron diffusion theory which stipulates that thermal neutrons
are captured at an average distance of 2√Ddiff· λabs∼ 4.7 cm, were Ddiff = 0.144 cm is the
neutron diffusion coefficient and λabs= 38.4 cm is the mean free path in mineral oil. While
these numbers hold in the limit of free protons, we recall our conclusion from Section 4.1 that
the hydrogen atom in mineral oil is quasi-free. The increase from 4.7 cm to 11.4 cm stems
from the neutron’s movement during slowing down from 1 MeV kinetic energy to the average
thermal energy of 0.022 eV. We note that there is no discussion in the LSND papers of the
distribution of the distance ∆r of the neutron between creation and capture.
The point of neutron creation is reconstructed as the position of the primary electron. LSND
state the average spatial resolution as 14 cm (Section II.E in Ref. ).
The spatial resolution of 2.2 MeV γ’s is recognized to be important by LSND, however
they do not specify the resolution. The only statement that can be found reads as “the most
likely distance was reduced from 74 cm [with a previous reconstruction algorithm] to 55 cm”
(Section IV in Ref. ). A peak position of 55 cm suggests a spatial resolution of approximately
35 cm when taking the said convolution into account. This is considerably smaller than the
estimate of 54 cm which is 14 cm multiplied by?33/2.2, where 33 MeV is the average primary
resolution of 2.2 MeV γ’s.
We note that all three distributions that are convoluted into the ∆r distribution of correlated
γ’s, come from Monte Carlo simulation and cannot be verified by data in an unbiased manner.
In particular, cosmic-ray neutrons have much higher energy and bias ∆r towards larger values
by virtue of the decreasing scattering cross-section above 1 MeV energy. For the 2.2 MeV
photons from the capture of cosmic-ray neutrons, there is no unbiased reference point for the
calculation of ∆r.
We compare in Fig. 9 the ∆r distribution claimed by LSND with with a variant that we
consider equally likely to represent the situation.
As both the LSND ∆r distribution for correlated γ’s and our respective distribution tend
toward zero at large ∆r, the cut ∆r ≤ 250 cm will not cause much difference on the ‘efficiency’
of correlated γ’s.
electron energy above the threshold of 20 MeV. So there is quite some uncertainty on the spatial
While the ∆r distributions of correlated and accidental γ’s cause major concerns, the Nhits
distributions cause minor concerns. This is because the pertinent Nhitsdistribution can be ex-
perimentally verified with high statistical precision from the measurement of 2.2 MeV γ’s from
the capture of cosmic-ray neutrons6), and from the measurement of accidental γ’s in randomly
The Nhits‘base distributions’
6)Clean samples of 2.2 MeV γ’s from neutron capture could be ascertained through the observation of an expo-
nentially falling ∆t distribution with an average of 186 µs.
Fig. 8: Distribution of distances between the point of creation in the LSND scintillator medium of a
1 MeV neutron and the point of capture on a free proton.