Probing nonstandard interactions at Daya Bay
Received: December
Probing nonstandard interactions at Daya Bay
Sanjib Kumar Agarwalla 0 1 2 4 5
Partha Bagchi 0 1 2 4 5
David V. Forero 0 1 2 3 5
Mariam T´ortola 0 1 2 5
0 We explore the
1 Parc Cientific de Paterna, C/ Catedratico Jos ́e Beltr ́an , 2 E46980 Paterna (Val`encia) , Spain
2 Sainik School Post , Bhubaneswar 751005 , India
3 Center for Neutrino Physics , Virginia Tech
4 Institute of Physics , Sachivalaya Marg
5 Open Access , c The Authors
bAHEP Group, Institut de F´ısica Corpuscular  C.S.I.C./Universitat de Val`encia, (NSI) in the production and detection processes of reactor antineutrinos at the Daya Bay experiment. We report for the first time, the new constraints on the flavor nonuniversal and flavor universal chargedcurrent NSI parameters, estimated using the currently released 621 days of Daya Bay data. New limits are placed assuming that the new physics effects are just inverse of each other in the production and detection processes. With this special choice of the NSI parameters, we observe a shift in the oscillation amplitude without distorting the L/E pattern of the oscillation probability. This shift in the depth of the oscillation dip can be caused by the NSI parameters as well as by θ13, making it quite difficult to disentangle the NSI effects from the standard oscillations. correlations between the NSI parameters and θ13 that may lead to significant deviations in the reported value of the reactor mixing angle with the help of isoprobability surface plots. Finally, we present the limits on electron, muon/tau, and flavor universal (FU) NSI couplings with and without considering the uncertainty in the normalization of the total event rates. Assuming a perfect knowledge of the event rates normalization, we find strong upper bounds ∼ 0.1% for the electron and FU cases improving the present limits by one order of magnitude. However, for a conservative error of 5% in the total normalization, these constraints are relaxed by almost one order of magnitude. ArXiv ePrint: 1412.1064
Neutrino Physics; Beyond Standard Model

Data analysis of modern reactor experiments
Bounds on NSI from Daya Bay without normalization error
Constraints on electronNSI couplings
Constraints on muon/tauNSI couplings
Constraints for the flavoruniversal NSI case
Bounds on NSI from Daya Bay with 5% normalization error
Comparing NSI constraints from 217 and 621 days of Daya Bay run
Summary and conclusions
A Effective survival probability with the NSI parameters: εseγ 6= εγd∗e
A.1 Presence of the NSI parameters only at the production stage
A.2 NSI at the source and detector with the same magnitude and different phases 27
1 Introduction 3 4 5
2 Implementing NSI in modern reactor experiments
Effective antineutrino survival probability in reactor experiments
2.3 Impact of the NSI parameters on the effective probability
tineutrino experiments Daya Bay [1–3] and RENO [4] has firmly established the threeflavor
neutrino paradigm [5–7] and signifies an important development towards our understanding
of the structure of the neutrino mass matrix, whose precise reconstruction would shed light
on the underlying new physics that gives rise to neutrino mass and mixing [8–10]. Another
reactor electron antineutrino disappearance experiment: Double Chooz [11, 12], and the
two accelerator electron (anti)neutrino appearance experiments: MINOS [13] (completed)
and T2K [14, 15] (presently running) have also confirmed the nonzero and moderately
to see that with 621 days of data taking and using the merit of identical multidetector
Undoubtedly, this high precision measurement of the 13 mixing angle has speeded up the
search for the neutrino mass ordering and the possible presence of a CPviolating phase in
current and future neutrino oscillation experiments [16–20].
To explain the presence of small neutrino masses and relatively large neutrino mixings
as indicated by neutrino oscillation data, various neutrino mass models have been proposed.
These neutrino mass models come in various categories such as the cases where neutrinos
acquire mass via the popular seesaw mechanism [21–31]. We find also models where
neutrinos get mass radiatively due to the presence of extra Higgs bosons [32–34] or low energy
supersymmetric hybrid models with spontaneous or bilinear breaking of Rparity [35, 36].
The structure of the standard electroweak neutral and charged currents gets affected by the
presence of these mechanisms responsible for the neutrino mass generation [25]. In most of
the cases, in the low energy regime, these effects are known as nonstandard interactions
(NSI). Various extensions of the Standard Model (SM), such as leftright symmetric models
and supersymmetric models with Rparity violation, predict NSI of neutrinos with other
fermions [37–45]. The NSI in these models are usually generated via the exchange of new
massive particles at low energies.
Neutrino NSI may be of chargedcurrent (CC) or neutralcurrent (NC) type, and they
can be classified in two main categories: flavorchanging NSI, when the flavor of the leptonic
current involved in the process is changed, or flavorconserving nonuniversal NSI, when
the lepton flavor is not changed in the process but the strength of the interaction depends
on it, violating the weak universality. In the low energy regime, these new interactions
may be parameterized in the form of effective fourfermion Lagrangians:
LCC−NSI =
LNC−NSI =
NCNSI couplings generally affecting the neutrino propagation in matter (m). Note that in
eqs. (1.1) and (1.2) we have assumed for the new interactions the same Lorentz structure as
for the SM weak interactions, (V±A). Even though more general expressions are possible
within a generic structure of operators, as shown in ref. [46], these are the dominant
contributions for reactor experiments, where we will focus our attention in this work.
NSI effects may appear at three different stages in a given neutrino experiment, namely
neutrino production, neutrino propagation from the source to the detector, and neutrino
detection. In a shortbaseline reactor experiment, the effects on the neutrino propagation
are negligible since it happens mainly in vacuum. Therefore, the new generation of
shortbaseline reactor experiments, such as Daya Bay, offers an excellent scenario to probe the
presence of NSI at the neutrino production and detection, free of any degeneracy with
NSI propagation effects. Actually, some work has already been done in the context of
NSI at shortbaseline reactor experiments. In particular, forecasts for the sensitivity of
Daya Bay to NSI have been published, for instance, in ref. [47]. More recently, another
article presented constraints on neutrino NSI using the previous Daya Bay data set [48].
The results derived there are in general agreement with some of the cases we discuss in
section 4. Nevertheless, our paper also studies the phenomenology of some other interesting
cases not considered in ref. [48], and provides a detailed description of the effect of NSI in
the neutrino survival probability. Finally, we also discuss the fragility of the bounds on the
NSI couplings derived using Daya Bay data against the presence of an uncertainty on the
total event rate normalization in the statistical analysis of reactor data.
Given the production and detection neutrino processes involved in shortbaseline
reC.L. bounds on these parameters [49]:
coming from unitarity constraints on the CKM matrix as well as from the nonobservation
of neutrino oscillations in the NOMAD experiment. Here the couplings with different
= εfαfβ0,L + εfαfβ0,R. Other constraints on neutrino NSI
couplings using solar and reactor neutrinos have been given in [50–55]. On the other hand,
NSI have also been studied in the context of laboratory experiments with accelerators in
refs. [53, 56–58], while bounds from atmospheric neutrino data have been presented in
refs. [59, 60]. Recently a forecast for the sensitivity to NSI of the future PINGU detector
has been presented in [61]. Future mediumbaseline reactor experiments like JUNO can
also serve as test bed to look for NSI [62].
This paper is organized as follows. In section 2, we describe the procedure for
implementing the NSI effect in the modern reactor experiments. There, we derive the effective
antineutrino survival probability expressions which we use later to analyze the Daya Bay
data. We also give plots to discuss in detail the impact of the NSI parameters on the
plots. Section 3 describes the numerical methods adopted to analyze the reactor data.
Apart from this, a brief description of the Daya Bay experiment and the important
features of its present data set which are relevant for the fit are also given in this section.
Section 4 presents the constraints on the NSI parameters imposed by the current Daya Bay
data assuming a perfect knowledge of the event rates normalization. Next we derive the
bounds on the NSI parameters taking into account the uncertainty in the normalization of
event rates with a prior of 5% in section 5. In section 6, we compare the constraints on
1The NSI parameters probed in our analysis get contributions from the (V±A) operators in eq. (1.1)
we have dropped the chirality indices all over the paper.
while the redefinition of the antineutrino flavor states is given by:
the NSI parameters obtained with the current 621 days of Daya Bay data with the limits
derived using the previously released 217 days of Daya Bay data. Finally, we summarize
and draw our conclusions in section 7. In appendix A, we give the effective antineutrino
Implementing NSI in modern reactor experiments
According to the usual procedure followed in the nonstandard analyses of reactor data [47,
63], we start by redefining the neutrino flavour states in the presence of NSI in the source
and detection processes. For the initial (at source) and final (at detector) neutrino flavor
states, we have [64–67]:
The normalization factors required to obtain an orthonormal basis can be expressed as:
and the neutrino mixing between flavor and mass eigenstates is given by the usual
expres
The correct normalization of the neutrino states in presence of NSI is a very important
point, required to obtain a total neutrino transition probability normalized to 1.
However, one has to consider that when dealing with a nonorthonormal neutrino basis, the
normalization of neutrino states will affect not only the neutrino survival probability but
also the calculation of the produced neutrino fluxes and detection cross sections. In this
while convoluting the neutrino oscillation probabilities, cross sections, and neutrino fluxes
to estimate the number of events in a given experiment such as Daya Bay. This is due to
the fact that the SM cross sections and neutrino fluxes used in our simulation have been
theoretically derived assuming an orthonormal neutrino basis and therefore they need to be
corrected. Then, from here we can consider the following effective redefinition of neutrino
and antineutrino states:
ν¯αieff = ν¯αi + X εα∗γ ν¯γ i,
s s
where we have dropped the normalization factors that will cancel in the Monte Carlo
simulation of Daya Bay data. From these effective neutrino states we will calculate an
effective neutrino oscillation probability, that will be used all along our analysis. Note that
when we will discuss the features of the probability prior to the simulation of a particular
experiment, we will always refer to the effective probability, that might be greater than one.
Effective antineutrino survival probability in reactor experiments
tance L from source to detector is defined as:
Pν¯αs→ν¯βd = hν¯βd exp (−i H L)ν¯αi .
s 2
In terms of the neutrino mass differences and mixing angles, this transition probability in
vacuum may be written as:
where Δmj2k = mj2 − m2k. In the case of standard oscillations, Yαjβ is defined as:
In presence of NSI, however, according to the definition of neutrino states in eq. (2.2), this
expression is modified as follows [63]:
Yαβ ≡ Uβ∗j Uαj + X εsα∗γ Uβ∗j Uγj + X εηd∗βUη∗j Uαj + X εsα∗γ εηd∗βUη∗j Uγj .
j
is produced at the source and a positron is detected inside the detector, one has to replace
by splitting the new couplings into its absolute value and its phase:
Now expanding the various terms of the general transition probability as given in eq. (2.8)
Pν¯es→ν¯ed = Pν¯SeM→ν¯e + PnNoSnIosc + PoNscSIatm + PoNscSIsolar
where the Standard Model (SM) contribution is given by
Pν¯SeM→ν¯e = 1 − sin2 2θ13 c122 sin2 Δ31 + s122 sin2 Δ32 − c143 sin2 2θ12 sin2 Δ21,
effective survival probability in eq. (2.12) can be written as:
+ εede2 + εsee2 + 2εedeεee cos(φede − φsee) (2.14)
s
+2εedeεee cos(φede +φsee)+2εseμεμe cos(φseμ +φdμe)+2εseτ ετe cos(φseτ +φτde),
s d d
PoNscSIatm = 2 ns13s23 hεseμ sin(δ − φseμ) − εdμe sin(δ + φdμe)i
+ s13c23 εeτ  sin(δ − φseτ ) − ετe sin(δ + φτde)i
h s d
− s23c23 εeμετe sin(φseμ + φτde) + εeτ εμe sin(φseτ + φdμe)i
h s d s d
− c223εeτ ετe sin(φseτ + φτde) − s223εeμεμe sin(φseμ + φdμe)o sin (2Δ31)
s d s d
−4 ns13s23 hεseμ cos(δ − φseμ) + εdμe cos(δ + φdμe)i
+ s13c23 εeτ  cos(δ − φseτ ) + ετe cos(δ + φτde)i
h s d
+ s23c23 εeμετe cos(φseμ + φτde) + εeτ εμe cos(φseτ + φdμe)i
h s d s d
+ c223εeτ ετe cos(φseτ + φτde) + s223εeμεμe cos(φseμ + φdμe)o sin2 (Δ31) , (2.15)
s d s d
−c23(εeμ sin φseμ + εμe sin φdμe)
s d
as given in ref. [46], with a good agreement between the calculated probabilities here and
there. However, as it can be seen in the expressions above, here we also include new
corrections will be discussed later in the paper. In eq. (2.15), note the presence of a term
can affect the L/E dependence of the probability in the presence of neutrino NSI.
In this work2 we assume that, likewise the mechanisms responsible for production (via
each other, this is also true for the associated NSI [46, 47]. This assumption allows us to
write εsγ = εd∗ ≡ εγ eiφγ where we drop the universal e index for simplicity. With these
γ
assumptions, eq. (2.12) takes the form (keeping the terms upto the second order in small
2In the appendix, we have given the effective probability expressions for the physical situations where
also modify the L/E pattern of the oscillation probability due to the shift in its energy. A detailed analysis
of the Daya Bay data under such scenarios will be performed in [69].
non−oscillat{ozry NSI terms
−4{s23εμ2 + c223ετ 2 + 2s23c23εμετ cos(φμ − φτ )} sin2 Δ31
2
−4{2s13[s23εμ cos (δ − φμ) + c23ετ  cos(δ − φτ )]} sin2 Δ31.
Pν¯es→ν¯ed ' 1 − sin2 2θ13 c122 sin2 Δ31 + s122 sin2 Δ32 − c143 sin2 2θ12 sin2 Δ21
For this special case of NSI parameters, there is no linear sinedependent term in eq. (2.17)
and two striking features are emerging from the effective probability expression which are
responsible for a change in the oscillation amplitude. First we can see the presence of some
nonoscillatory NSI terms which are independent of L and E and are given by
and, second, there is a shift in the effective 13 mixing angle due to oscillatory NSI terms
which can be written as
s13 → s123 + s223εμ2 + c223ετ 2 + 2s23c23εμετ  cos(φμ − φτ )
2
These two features, which are brought about by the NSI parameters, are responsible for
a shift in the oscillation amplitude without distorting the L/E pattern of the oscillation
probability as can be clearly seen from figure 1 and figure 2 that we will discuss in the next
section. Eq. (2.19) suggests that it will be quite challenging to discriminate the effect of
note that there are some CP conserving terms in eq. (2.19) which come into the picture
due to the presence of NSI parameters. One of the most important consequences of the
new nonoscillatory NSI terms (see eq. (2.18)) is that they can cause a flavor transition at
is known as “zerodistance” effect [46, 70]. In modern reactor experiments, this effect can
be probed using the near detectors which are placed quite close to the source.
For definiteness, in this work we have restricted our analysis to the following choices
of the NSI parameters:
• Lepton number conserving nonuniversal NSI parameters which depend on the flavor
characterizing the violation of weak universality. Under this category, we study the
following two cases:
1. Considering only the NSI parameters εe and φe which are associated with ν¯e. In
the presence of these flavor conserving NSI parameters, eq. (2.17) takes the form:
new nonoscillatory NSI terms appearing at the survival probability produce a
This expression will be very useful to discuss the behavior of the effective
prob
2. Considering only the NSI parameters εμ and φμ which are associated with ν¯μ.
In the presence of these flavor violating NSI parameters, eq. (2.17) takes the
e →ν¯ed ' Pν¯SeM→ν¯e + 2εμ2 − 4{s23εμ2 + 2s13s23εμ cos(δ − φμ)} sin2 Δ31. (2.22)
2
the effective survival probability will be exactly the same as eq. (2.22) with the
in the neutrino transition probability may be interpreted as a global redefinition
• Lepton number conserving universal NSI parameters which do not depend on flavor.
in eq. (2.17) takes the form:
−4{ε2 + 2s23c23ε2 + 2s13ε cos(δ − φ)(s23 + c23)} sin2 Δ31. (2.24)
In this case, the effective mixing angle in the presence of oscillatory and
nonoscillatory NSI terms will be given by:
As stated above, the expressions given in this subsection to illustrate the shift in the
effective reactor angle in the presence of NSI, eqs. (2.21), (2.23) and (2.25), contain only
first order corrections in the NSI couplings. Note, however, that terms of second order
will briefly discuss the relevance of second order corrections in our analysis. Clearly, these
corrections to the effective neutrino probability are only significant in the cases where first
7.6 × 10−5
2.55 × 10−3
the right panel. In both the panels, the solid black lines depict the probability without new physics
involved (SM case).
it is straightforward to evaluate the size of the second order terms for the three cases under
study. Taking into account the baselines and neutrino energies probed at the Daya Bay
experiment, we find that second order corrections (for vahishing first order corrections) are
one order of magnitude smaller than for the two other cases, comes from the smallness of
the coefficient responsible for second order corrections in the expression of the effective
1 2
2 sin2 Δ31 − s23 , very close to zero for the energies and baselines studied
in Daya Bay. This result can be observed in the correlation plots in figures 3 and 4 (see
dashed blue line) in section 2.4. There, one sees that second order corrections are small but
visible for electronNSI and flavouruniversal case, while they are almost negligible for the
muon/tauNSI case. The impact of the second order corrections over the results presented
in this work is discussed in section 7.
Impact of the NSI parameters on the effective probability
Now we will study the possible impact of the NSI parameters at the effective probability
level. Table 1 depicts the benchmark values of the various oscillation parameters that are
considered to generate the oscillation probability plots. These choices of the oscillation
parameters are in close agreement with the bestfit values that have been obtained in the
recent global fits of the world neutrino oscillation data [5–7]. Here we would like to mention
and the NSImodified threeflavor oscillation effective probability as a function of the
electron antineutrino energy with a sourcedetector distance of 1.58 km. In the left panel of
eq. (2.20)). The solid black line shows the standard oscillation probability without the NSI
terms (see eq. (2.13)). The other four lines have been drawn considering particular choices
probability is less compared to the standard value because the contribution from the
nonthen the oscillation probability is above the standard value because the contribution from
most of the energies of interest. This is the sign of the nonunitarity effects [68, 72–75],
caused by the presence of neutrino NSI at the source and detector of reactor experiments.
In the right panel of figure 1, the band shows the changes in the effective probability after
the NSI terms have a nontrivial L/E dependency. The standard oscillation probability
without the NSI terms is shown by the solid black line and the other four lines have been
(more) compared to the standard value for almost all the choices of neutrino energy as
light grey region. In figure 2, the solid black line depicts the standard probability without
Energy [MeV]
km for the flavoruniversal NSI case (see section 2.2 for details). The dark salmon region shows the
without new physics involved (SM case).
considering the NSI parameters. The other four lines in this plot display the effective
oscilin the figure legends. It is quite clear from eq. (2.24) that the nonoscillatory terms
dominate over the oscillatory terms in the flavoruniversal NSI case. Therefore, the dark salmon
region of figure 2 closely resembles the left panel of figure 1 where we consider the NSI
to draw the isoprobability surface plots. Left panel of figure 3 shows the isoprobability
oscillation probability without considering the NSI parameters as given by eq. (2.13). Now
increase the overall probability (see eq. (2.20)). Then, we need to increase the value of
for (δ − φμ,τ ) = 90◦ or 90◦ in the right panel of figure 3.
case with the help of isoprobability surface contours. In the left panel, we consider four
are the same for 90◦ and 90◦ choices of phases (see the dashed blue lines) because the phases
and the baseline L = 1.58 km.
it enhances the overall oscillation probability to a great extent even for a small value of
reduce the contribution coming from the standard survival oscillation probability. Right
flavoruniversal NSI case, the contribution from the nonoscillatory NSI terms dominates
features emerging from the extreme right panel of figure 7 (see later in section 4) where
give a negative contribution to the neutrino survival probability that, to be compensated,
requires an enhancement of the standard survival probability by reducing the value of
Data analysis of modern reactor experiments
Reactor antineutrinos are produced by the fission of the isotopes 235U, 239Pu, 241Pu and
238U contributing to the neutrino flux with a certain fission fraction fk. Reactor
antineuis a delayed coincidence between two gamma rays: one coming from the positron (prompt
signal) and the other coming from the neutron capture in the innermost part of the
antineutrino detector (AD), containing gadoliniumdoped liquid scintillator. The light created is
collected by the photomultipliers (PMTs) located in the outermost mineral oilregion. The
The expected number of IBD events at the dth detector, Td, can be estimated summing
up the contributions of all reactors to the detector:
Td =
X Trd =
Z ∞
where Np is the number of protons in the target volume, Ptrh is the reactor thermal power,
d denotes the efficiency of the detector and hEki is the energy release per fission for a given
isotope k taken from ref. [76]. The neutrino survival probability Pee depends also on the
we use the parameterization given in ref. [77] as well as the new normalization for reactor
taken from ref. [79].
Daya Bay experiment
Daya Bay is a reactor neutrino experiment with several antineutrino detectors (ADs),
arranged in three experimental halls (EHs). Electron antineutrinos are generated in six
in the EHs. The effective baselines are 512 m and 561 m for the near halls EH1 and EH2
and 1579 m for the far hall EH3 [2]. With this nearfar technology Daya Bay has minimized
the systematic errors coming from the ADs and thus provided until now the most precise
determination of the reactor mixing angle. In the last Neutrino conference, Daya Bay has
reported its preliminary results considering 621 days of data taking combining their results
for two different experimental setups [3]: one with six ADs as it was published in ref. [2]
and the other after the installation of two more detectors, eight ADs in total. This new
combined data set has four times more statistics in comparison with the previous Daya
Bay results. Thus, the precision in the determination of the reactor mixing angle has been
improved, and it is now of the order of 6%.
In this work we will consider the most recent data release by the Daya Bay
Collaboration described above and we will concentrate on the total observed rates at each detector,
Md − Td 1 + anorm + Pr ωrdαr + ξd + βd
r=1 r
Here Td corresponds to the theoretical prediction in eq. (3.1), Md is the measured number
contribution of the rth reactor to the dth AD number of events, determined by the
baselines Lrd and the total thermal power of each reactor. The pull parameters, used to
the reactor, detector and background uncertainties with the corresponding set of errors
the quadratic sum of the background uncertainties taken from ref. [3]. Finally, we also
consider an absolute normalization factor anorm to account for the uncertainty in the total
in the normalization of reactor antineutrino fluxes. In our analysis we will follow two
different approaches concerning this parameter. In section 4 we will take it equal to zero,
assuming perfect knowledge of the events normalization. This hypothesis will be relaxed in
section 5, where we will allow for a nonzero normalization factor in the statistical analysis,
being determined from the fit to the Daya Bay data. As we will see, the results obtained
in our analysis are strongly correlated with the treatment of the total normalization of
reactor neutrino events in the statistical analysis of Daya Bay data and therefore it is of
crucial importance to do a proper treatment of this factor.
Bounds on NSI from Daya Bay without normalization error
In this section we will present the bounds on the NSI couplings we have obtained using
current Daya Bay reactor data. In all the results, we have assumed maximal 23 mixing
and we have marginalized over atmospheric splitting with a prior of 3%. For definiteness
will discuss the bounds arising from Daya Bay data in comparison with existing bounds. We
Constraints on electronNSI couplings
According to the expression in eq. (2.20), the effective survival probability in the case
when only NSI with electron antineutrinos are considered is independent of the standard
Our results are presented in figure 5. From the left panel in this figure, we can confirm
the behaviors shown by the isoprobability curves in the section 2.4, namely, the presence
regions correspond to 68% (black dashed line), 90% (green line) and 99% C.L. (red line) for 2 d.o.f.
by one order of magnitude:
no bound can be obtained from reactor data.
Concerning the determination of the reactor mixing angle, the presence of the
NSI
The same interval is obtained for the two panels at figure 5 and it also coincides exactly
with the allowed range in absence of NSI. In consequence, we can say that the reactor angle
determination by Daya Bay is robust in this specific case.
Constraints on muon/tauNSI couplings
In this subsection we present the results obtained considering only the NSI parameters
associated with muon and tau neutrinos. As we have discussed in section 2.2, in this case,
see eq. (2.22). Therefore, it is enough to consider in our calculations the effective phase
The results corresponding to this particular case are shown in figure 6. Here again we
can see how the regions presented in the left panel of the figure agree with the behavior
0.012 0.024 0.036 0.048
0.012 0.024 0.036 0.048
180◦ and 180◦. The regions correspond to 68% (black dashed line), 90% (green line), and 99%
C.L. (red line) for 2 d.o.f.
shown in the isoprobability plots (right panel of figure 3) where there is an
anticorrelacompensated by a shift of the preferred value of the reactor mixing angle toward smaller
while the obtained bound for the NSI coupling is the following
In this case reactor data can not improve the present constraints on the NSI couplings at
eq. (1.3), and we get a limit of the same order of magnitude of the ones derived at ref. [49].
However, in both cases the limits have been derived using different data and assumptions,
and therefore, they can be regarded as complementary bounds coming from different data
is allowed to vary. In this case, a wider range in the reactor mixing angle is allowed:
The reason is that, in addition to the anticorrelation shown in the left panel, a correlation
is negative. Note, however, that both correlations are not symmetric, what results in
conventions for the lines is the same as in figure 5
in the redefinition of the effective reactor angle in the presence of NSI given in eq. (2.23).
Nevertheless, even though there is a wider allowed region in the reactor angle, the bound
is set to zero, namely:
Constraints for the flavoruniversal NSI case
Here we present the results obtained under the hypothesis of flavoruniversal NSI, that
is, we assume all NSI couplings are present and they take the same value. Therefore, we
entering in the calculations. In this case, the effective survival probability is given by the
have considered four different cases in our analysis: one with all the phases set to zero, two
cases varying only one of the phases with the other set to zero and a last case varying the
two phases simultaneously. Our results are presented at figure 7.
The left panel in figure 7 shows the tight constraint obtained for the magnitude of the
The same behavior is also present in the middle panel of figure 7, where the Dirac phase
by the nonoscillatory term in eq. (2.25). Under this assumption, we obtain the following
bound on the magnitude of the flavoruniversal coupling:
the one obtained in the standard case, and therefore the Daya Bay determination is barely
different values, a completely different behavior results, as it is shown in the right panel of
therefore the first order expression in eq. (2.25) can not satisfactory explain the degeneracy
As commented above, the presence of flavor universal NSI implies that the reactor mixing
angle may be compatible with zero. Nevertheless, the degeneracy between the mixing angle
with accelerator longbaseline neutrino experiments. A global analysis of neutrino data
assuming the simultaneous presence of NSI in reactor and accelerator neutrino data would
be very useful for this purpose. Besides solving the degeneracy, the combined analysis
might provide further constraints on the NSI couplings as well as improve the agreement
in ref. [80–82]. However, since the production, detection and propagation of neutrinos is
quite different in both kind of experiments, a global analysis would require a very detailed
study with many new physics parameters involved, besides the consideration of a specific
model for NSI. In any case, this point is out of the scope of the present analysis and it will
be considered elsewhere.
Finally, let us comment that we have also considered the case of flavoruniversal NSI
with all the phases different from zero. However, we have not presented the results obtained
therefore no information on any of the parameters can be extracted from the analysis of
Daya Bay data. All the results obtained in this section are summarized in table 2. Needless
table, we have marginalized over the NSI couplings over a wide range. Similarly, to place
electrontype NSI coupling
muon or tautype NSI couplings
universal NSI couplings
without considering any uncertainty in the normalization of reactor event rates in the statistical
analysis (anorm = 0).
Bounds on NSI from Daya Bay with 5% normalization error
In the previous section, we have not considered any normalization error in the statistical
analysis of Daya Bay reactor data. This means that we have assumed a perfect knowledge of
the event normalization at the experiment, disregarding the presence of uncertainties in the
flux reactor normalization or in the detection cross section, among others. This procedure
has been followed in most of the previous phenomenological analyses of Daya Bay data in
presence of NSI, see for instance ref. [47]. In the more recent work at ref. [48], the authors
have considered small uncertainties in the reactor flux and in the detector properties,
although they did not take into account an uncertainty in the overall normalization of the
event rates. Needless to say that a more detailed analysis of reactor data can not ignore the
of Daya Bay data using the expression defined at eq. (3.2), where a free normalization
factor is considered in order to account for the uncertainties in the total event number
normalization. This point is very relevant in the study of NSI with reactor experiments,
since the uncertainty in the event normalization presents a degeneracy with the
zerodistance effect due to NSI. In consequence, the far over near technique exploited by Daya
Bay in order to reduce the dependence upon total normalization does not work equally
fine in the presence of NSI, where the nonoscillatory zerodistance effect, simultaneously
present at near and far detectors, does not totally cancel. Actually, in the standard model
case without NSI, the number of events expected at the near detector is given by:
NNSMD ' N (1 + anorm)PeSeM(L = 0) = N (1 + anorm) ,
while, in the presence of NSI, the event number at the near detector is calculated as follows:
NNNDSI ' N (1 + anorm)PeNeSI(L = 0) = N (1 + anorm)(1 + f (ε))
Here anorm controls the normalization of far and near detector events in the fit and, together
to zero, we artificially increase the power of Daya Bay data to constrain the zerodistance
effect due to NSI, getting nonrealistic strong bounds on the NSI couplings. On the other
hand, we can not leave the factor anorm totally free in our statistical analysis, as it is usually
done in the standard Daya Bay analysis, where the factor is kept small thanks to the far
over near technique. Actually, we have found that leaving the normalization factor totally
free, and due to the degeneracy with the NSI couplings, it could achieve very large values,
of the order of 1020%. For this reason it is necessary the use of a prior on this magnitude.
Recent reevaluations of the reactor antineutrino flux indicate an uncertainty on the total
flux of about 3% [77, 83]. However, an independent analysis in ref. [84] claims that this
uncertainty may have been underestimated due to the treatment of forbidden transitions
in the antineutrino flux evaluation, and proposes a total uncertainty of 4%. Since the total
normalization errors may also include uncertainties coming from other sources, we follow
the conservative approach of taking a total uncertainty on the reactor event normalization
To illustrate the differences with respect to the results obtained in the previous section,
assuming no uncertainties in the event rate normalization, here we have considered only
the cases where all phases are set to zero.3 The results obtained with these assumptions
are presented in figure 8 and table 3. In the left panel of figure 8 we present the allowed
this case, the range for the reactor mixing angle is rather similar to the one shown in the
left panel of figure 5:
still slightly better than the one at eq. (1.3)):
the right panel of figure 8. In this case, the allowed range for the reactor mixing angle is
a bit enlarged with respect to the previous one:
due to the presence of NSI oscillation terms driven by the new physics couplings with muon
and tau antineutrinos. As commented above, the loss of sensitivity to the NSI couplings is
and, therefore, second order corrections are not relevant.
assuming 5% uncertainty on the total event rate normalization of Daya Bay events. The conventions
for the lines is the same as in figure 5.
with a 5% uncertainty on the total event normalization.
due to the degeneracy between the normalization uncertainty and the zerodistance terms
induced by the presence of NSI. In this way, a larger value of the NSI parameters can
be compensated with a nonzero normalization factor anorm, without spoiling the good
agreement with experimental reactor data.
Finally, the middle panel of figure 8 shows the results obtained when only NSI with
muon or tau antineutrinos are considered. In this case, the cancellation between the
norThe bound on the NSI coupling is given by:
Comparing NSI constraints from 217 and 621 days of Daya Bay run
The new highprecision data from Daya Bay with 621 days of running time [3] has improved
the impact of the four time more statistics that the Daya Bay experiment has accumulated
the new (old) 621 (217) days of Daya Bay data. Here all the phases are considered to be zero and
with the help of eight ADs in comparison with the previously released Daya Bay data set
with six ADs. Now it would be quite interesting to see how much we can further constrain
the allowed ranges for these NSI parameters under consideration using the new 621 days of
Daya Bay data in comparison with the old 217 days of Daya Bay run. In figure 9, we
compare the performance of the current and the previous data sets of Daya Bay in constraining
In both the panels, the solid (dashed) lines portray the results with the new (old) 621 (217)
days of Daya Bay data. For the sake of illustration, we have only chosen the cases of NSI
phases to be zero. In particular, we have focused on the situations which are presented in
sections 4.1 and 4.2, where we do not consider the normalization uncertainty on the reactor
the current data, the improvement in constraining the allowed parameter space between
parameters using the previous (current) 217 (621) days of Daya Bay data. Here all the
phases are considered to be zero. We do not consider the normalization uncertainty on the
same while analyzing 621 days of Daya Bay data. This feature is also there in the case
two when we consider the current 621 days of Daya Bay data compared to its previous
compared to the old data set. These results suggest that the future data from the Daya Bay
(621) days of Daya Bay data. Here all the phases are considered to be zero. We also do not consider
Current (621 days)
Previous (217 days)
Current (621 days)
Previous (217 days)
electrontype NSI parameters
muon or tautype NSI parameters
universal NSI parameters
Current (621 days)
Previous (217 days)
Current (621 days)
Previous (217 days)
Current (621 days)
Previous (217 days)
Current (621 days)
Previous (217 days)
Current (621 days)
Previous (217 days)
(621) days of Daya Bay data. Here we allow the phases or their certain combinations to vary freely.
experiment with more statistics is going to play an important role to further constrain the
allowed parameter space for the NSI parameters. There are also marginal improvements
parameters obtained using the old 217 days and new 621 days of Daya Bay data allowing
the phases or their certain combinations to vary freely as we consider in table 2 in section 4.
Like in table 4, here also we do not take into account the normalization uncertainty on
even if we allow the phases to vary freely, we obtain better limits on the NSI parameters
with the new data set as compared to the previous 217 days of Daya Bay data, except
Summary and conclusions
The success of the currently running Daya Bay, RENO, and Double Chooz reactor
anaccuracy signifies an important advancement in the field of modern neutrino physics with
nonzero mass and threeflavor mixing. With this remarkable discovery, the neutrino
oscillation physics has entered into a highprecision era opening up the possibility of observing
subdominant effects due to possible new physics beyond the Standard Model of particle
physics. At present, undoubtedly the Daya Bay experiment in China is playing a leading
and an important role in this direction. The recent highprecision and unprecedentedly
copious data from the Daya Bay experiment has provided us an opportunity to probe the
existence of the nonstandard interaction effects which might crop up at the production
point or at the detection stage of the reactor antineutrinos.
In this paper for the first time, we have reported the new constraints on the flavor
nonuniversal and also flavor universal NSI parameters obtained using the currently released
621 days of Daya Bay data. While placing the bounds on these NSI parameters, we have
assumed that the new physics effects are just inverse of each other in the production and
special case, we have discussed in detail the impact of the NSI parameters on the effective
antineutrino survival probability expressions which we ultimately use to analyze the Daya
Bay data. With this special choice of the NSI parameters, we have observed a shift in the
oscillation amplitude without altering the L/E pattern of the oscillation probability. This
shift in the depth of the oscillation dip can be caused due to the NSI parameters and as well
Before presenting the final results, we have studied the correlations between the NSI
paramquite useful to understand the final bounds on the NSI parameters that we have obtained
from the fit. Since the shape of the oscillation probability is not distorted with the special
choice of the NSI parameters considered in this paper, an analysis based on the total event
rate at the Daya Bay experiment is sufficient to obtain the limits on the NSI parameters.
As far as the flavor nonuniversal NSI parameters are concerned, first we have
consida perfect knowledge of the normalization of the event rates, the current Daya Bay data
freely in the fit. We have also observed that the determination of the 13 mixing angle is
quite robust in this specific case and it is almost independent of the issue of uncertainty in
coincides exactly with the allowed range in absence of NSI. Next we turn our attention to
fect knowledge of the event rates normalization, the current Daya Bay data sets a limit of
case when we do not consider any uncertainty in the normalization of event rates, the upper
One of the novelties of this work is the inclusion of correction terms of second order in
second order corrections at the effective probability level has been analyzed in section 2.2
as well as in the discussion of the probability and correlation plots in section 2.3 and
relevant for the flavouruniversalNSI case, as commented in section 4.3.
One of the interesting studies that we have performed in this paper is the comparison
of the constraints on the NSI parameters placed with the current 621 days of Daya Bay data
with the limits obtained using the previously released 217 days of Daya Bay run. In this
analysis, all the phases are considered to be zero and the normalization of events is also kept
data compared to its previous 217 days data. This comparative study reveals the merit of
the huge statistics that Daya Bay has already accumulated. It also suggests that the future
highprecision data from the Daya Bay experiment with enhanced statistics is inevitable
to further probe the subleading effects in neutrino flavor conversion due to the presence
of the possible NSI parameters beyond the standard threeflavor oscillation paradigm.
S.K.A. acknowledges the support from DST/INSPIRE Research Grant [IFAPH12],
Department of Science and Technology, India. The work of D.V.F. and M.T. was supported
by the Spanish grants FPA201122975 and MULTIDARK CSD200900064 (MINECO) and
PROMETEOII/2014/084 (Generalitat Valenciana). This work has also been supported by
the U.S. Department of Energy under award number DESC0003915.
In this appendix, we present the effective probability expressions for the physical scenarios
depth of the first oscillation maximum but they also modify the L/E pattern of the
probability due to the shift in its energy. We have already mentioned that a detailed analysis
of the Daya Bay data considering such interesting physical cases will be performed in [69].
Presence of the NSI parameters only at the production stage
Here we assume that the NSI parameters only affect the production mechanism of the
antineutrinos in the reactor experiment. It allows us to write (dropping the universal
With this assumption, we get the effective neutrino survival probability as follows:
−4s13 [s23εμ cos(δ − φμ) + c23ετ  cos(δ − φτ )] sin2 (Δ31)
NSI at the source and detector with the same magnitude and different
In this case, we assume that the magnitude of the NSI parameters is the same at the
production and detection level, but the phases associated with the NSI parameters are
different at the source and detector. Under this situation, we can write:
Under this assumption, the effective neutrino survival probability takes the form:
where the nonstandard terms are given by:
+ εe2 h1 + cos(φed − φse) + cos(φed + φe)
PoNscSIatImIb = 2 ns13s23εμ hsin(δ −φsμ)−sin(δ +φdμ)i+s13c23ετ  hsin(δ −φτs )−sin(δ + φτ )
−s223εμ2 sin(φsμ + φμ) − c223ετ 2 sin(φτs + φτ )
d d
− c23s23εμετ  hsin(φτs + φdμ) + sin(φsμ + φτd)io
−4ns13s23εμhcos(δ −φsμ)+cos(δ +φdμ)i+c23s13ετ hcos(δ −φτs )+cos(δ +φτd)i
This article is distributed under the terms of the Creative Commons
Attribution License (CCBY 4.0), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited.
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