Model-independent Approach of the JUNO ⁸B Solar Neutrino Program

Electron neutrino fluxes are produced from thermal nuclear fusion reactions in the solar core, either through the proton–proton (pp) chain or the carbon–nitrogen–oxygen (CNO) cycle. According to their production reactions, the solar neutrino species can be categorized as pp, ⁷Be, pep, ⁸B, hep neutrinos of the pp chain, and the ¹³N, ¹⁵O, and ¹⁷F neutrinos of the CNO cycle. Before reaching the detector, solar neutrinos undergo flavor conversion inside the Sun and Earth during their propagation. Solar neutrino measurements have a long history starting with the measurements done by the Homestake experiment (Davis et al. 1968). Many measurements, such as those of Homestake (Davis et al. 1968), Kamiokande (Hirata et al. 1989), GALLEX/GNO (Anselmann et al. 1993; Altmann et al. 2000), SAGE (Abazov et al. 1991), and SuperKamiokande (SK; Fukuda et al. 1998, 2001), observed the solar neutrino deficit problem: that is, the number of observed neutrinos originating from the Sun was much less than that expected from the standard solar model (SSM). Subsequently, the Sudbury Neutrino Observatory (SNO) provided the first model-independent evidence of solar neutrino flavor conversion using three distinct neutrino interaction channels in heavy water (Chen 1985; Ahmad et al. 2001, 2002; Ahmed et al. 2004; Aharmim et al. 2008, 2013a, 2013b). These reactions are the ν_e sensitive charged current (CC) interaction, all flavor sensitive neutral current (NC) interaction on deuterium, and the elastic scattering (ES) interaction on electrons from all neutrino flavors with different cross sections.

Solar neutrino observations rely on the SSM flux predictions, the neutrino oscillation parameters, and the solar density model, which determine the flavor conversion (Wolfenstein 1978; Mikheev & Smirnov 1985; Zyla et al. 2020). Thus, although SK (Renshaw et al. 2014; Abe et al. 2016) and Borexino (Bellini et al. 2014; Agostini et al. 2020) experiments have made precision measurements on the ⁸B neutrinos via the ES interaction, the evaluation of the total amount of neutrinos produced inside the Sun relies on the input of solar neutrino oscillations (Zyla et al. 2020). The present most precise ⁸B neutrino flux is determined by SNO with a 1σ confidence level uncertainly of around 3.8% (Ahmad et al. 2002; Ahmed et al. 2004; Aharmim et al. 2008, 2013a, 2013b), and it is the only existing model-independent flux measurement. Therefore, a second independent measurement of the total ⁸B neutrino flux with the NC channel (Arafune et al. 1989; Ianni et al. 2005) would be important in answering relevant questions in the field of solar physics. For example, there is the solar abundance problem, in which the SSM based on the solar composition with a higher value of metallicity is inconsistent with the helioseismological measurements (Vinyoles et al. 2017). Note that a recent solar model is able to resolve the discord between the helioseismological and photospheric measurements (Magg et al. 2022), but lively discussions on this topic are still ongoing (Yang 2022; Buldgen et al. 2023).

In contrast, the neutrino oscillation parameters ${\sin }^{2}{\theta }_{12}$ and ${\rm{\Delta }}{m}_{21}^{2}$ have reached the 1σ confidence level uncertainty of around 5% and 15%, respectively, from the current global solar neutrino data (Esteban et al. 2020). The mixing angle ${\sin }^{2}{\theta }_{12}$ is extracted from the comparison of the observed fluxes of pp, ⁷Be, and ⁸B solar neutrinos to their respective total fluxes from the SSM. And the mass squared difference ${\rm{\Delta }}{m}_{21}^{2}$ is measured from both the vacuum–matter transition of the ⁸B neutrino oscillations and the size of the day–night asymmetry. A direct comparison of oscillation parameters from the solar neutrino and reactor antineutrino oscillations is a unique probe of new physics beyond the Standard Model of particle physics. It would be excellent to have a new measurement of solar neutrino oscillations with high precision in this respect. This has triggered a variety of interesting discussions on the prospects of future large neutrino detectors (Beacom et al. 2017; Abe et al. 2018; Capozzi et al. 2019; Abusleme et al. 2021a).

The Jianmen Underground Neutrino Observatory (JUNO) is a 20 kt liquid scintillator (LS) detector located in South China and will start acquiring data by 2024. As a multiple-purpose neutrino experiment, JUNO is unique for solar neutrino detection because of its large target mass, excellent energy resolution, and expected low background levels. With the analysis threshold cut of around 2 MeV for the recoiled electron energies in the ES channel, JUNO can make a high statistics measurement of the flux and spectral shape of ⁸B solar neutrinos and will be able to extract the neutrino oscillation parameters ${\sin }^{2}{\theta }_{12}$ and ${\rm{\Delta }}{m}_{21}^{2}$ (Abusleme et al. 2021a). In addition to the high statistics measurement in the ES channel, the presence of the large mass of the ¹³C nuclei (∼0.2 kt) makes it feasible to detect ⁸B solar neutrinos via CC and NC interactions on ¹³C. By combining the CC, NC, and ES channels, we are able to perform a model-independent measurement of the ⁸B solar neutrino flux and oscillation parameters ${\sin }^{2}{\theta }_{12}$ and ${\rm{\Delta }}{m}_{21}^{2}$, which will add a unique contribution to the global solar neutrino program.

This paper is organized as follows. We illustrate the typical signatures of the CC and NC interactions of ⁸B solar neutrinos and evaluate the corresponding backgrounds in the JUNO detector in Section 2. In Section 3, the physics potential of detecting ⁸B solar neutrinos with different combinations of CC, NC, and ES channels is presented, and the sensitivity to the ⁸B solar neutrino flux, ${\sin }^{2}{\theta }_{12}$ and ${\rm{\Delta }}{m}_{21}^{2}$ is reported. The concluding remarks of this study are presented in Section 4.

The JUNO experiment is building the world's largest LS detector with a total target mass of 20 kt, in which the mass fraction of carbon is 88%. Given that the natural abundance of ¹³C is 1.1%, the total mass of ¹³C reaches 193.6 tons, which is similar to the total deuterium mass of 200 tons for the SNO detector. Considering the preferable cross sections of ¹³C at solar neutrino energies (Fukugita et al. 1988; Suzuki et al. 2012, 2019), the CC and NC solar neutrino rates on ¹³C will be rather sizable in the JUNO detector.

In Table 1, we present the typical CC, NC, and ES detection channels for ⁸B solar neutrinos in the LS medium. For each interaction channel, the reaction threshold is provided, together with the typical experimental signatures, and the expected event numbers for 10 yr of data taking before event selection cuts. The spin and parity of the daughter nuclei at the ground (gnd) or excited state, denoted by the corresponding excited energies, are also provided. The unoscillated ⁸B solar neutrino ν_e flux (5.25 × 10⁶/cm² s⁻¹) is taken from the final result from SNO for this estimation (Aharmim et al. 2013b), and the spectrum is taken from Bahcall et al. (1996) and Bahcall (1997). The cross sections for these exclusive channels are taken from the calculation in Fukugita et al. (1988) and Suzuki et al. (2012, 2019), in which the uncertainties at the level of a few percent are considered to be achievable. Note that the standard Mikheev–Smirnov–Wolfenstein (MSW) effect of solar neutrino oscillations (Wolfenstein 1978; Mikheev & Smirnov 1985) and the neutrino oscillation parameters from Zyla et al. (2020) are used in the calculation of the signals of the CC, NC, and ES channels.

Table 1. Typical CC, NC, and ES Detection Channels of the ⁸B Solar Neutrinos Together with the Final States, Neutrino Energy Threshold, Typical Signatures in the Detector, and Expected Event Numbers with 10 yr of Data Taking

No.	Channels		Threshold	Signal	Event Numbers
			(MeV)		(10 yr)
1		νe +12C → e−+12N(1+; gnd) (Fukugita et al. 1988)	16.827	e−+12N decay (β+, Q = 17.338 MeV)	0.43
1	CC	${\nu }_{e}{+}^{13}{\rm{C}}\to {e}^{-}{+}^{13}{\rm{N}}({\tfrac{1}{2}}^{-};\mathrm{gnd})$ (Suzuki et al. 2012)	2.2	e−+13N decay (β+, Q = 2.22 MeV)	3929
2		${\nu }_{e}{+}^{13}{\rm{C}}\to {e}^{-}{+}^{13}{\rm{N}}({\tfrac{3}{2}}^{-};3.5\,\mathrm{MeV})$ (Suzuki et al. 2012)	5.7	e−+p	2464
4		νx +12C → νx +12C(1+; 15.11 MeV) (Fukugita et al. 1988)	15.1	γ	4.8
3	NC	νx +13C → νx + n+12C(2+; 4.44 MeV) (Suzuki et al. 2019)	6.864	γ + n capture	65
4		${\nu }_{x}{+}^{13}{\rm{C}}\to {\nu }_{x}{+}^{13}{\rm{C}}({\tfrac{1}{2}}^{+};3.089\,\mathrm{MeV})$ (Suzuki et al. 2012)	3.089	γ	14
5		${\nu }_{x}{+}^{13}{\rm{C}}\to {\nu }_{x}{+}^{13}{\rm{C}}({\tfrac{3}{2}}^{-};3.685\,\mathrm{MeV})$ (Suzuki et al. 2012)	3.685	γ	3032
6		${\nu }_{x}{+}^{13}{\rm{C}}\to {\nu }_{x}{+}^{13}{\rm{C}}({\tfrac{5}{2}}^{+};3.854\,\mathrm{MeV})$ (Suzuki et al. 2012)	3.854	γ	2.8
7	ES	νx + e → νx + e	0	e−	3.0 × 105

Note. Note that ν_x with (x = e, μ, τ) denotes all three active flavor neutrinos. The spin and parity of the daughter nuclei at the gnd or excited states, denoted as the corresponding excited energies, are also provided.

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There are no interactions on the ¹²C nuclei for most solar neutrinos because of the high energy threshold. Thus, for the CC channel, we are left with the following two exclusive interactions:

$$\begin{eqnarray}&&{\nu }_{e}{+}^{13}{\rm{C}}\to {e}^{-}{+}^{13}{\rm{N}}\left({\displaystyle \frac{1}{2}}^{-};\mathrm{gnd}\right),\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{\nu }_{e}{+}^{13}{\rm{C}}\to {e}^{-}{+}^{13}{\rm{N}}\left({\displaystyle \frac{3}{2}}^{-};3.502\,\mathrm{MeV}\right),\end{eqnarray} \tag{ 2 }$$

where the final ¹³N is in the ground state and excited ¹³N(3/2⁻; 3.502 MeV) state, respectively. For the first reaction channel, the ground state of ¹³N undergoes a delayed β⁺ decay (Q = 2.2 MeV) with a lifetime of 863 s. The distinct signature for this channel is a coincidence of the prompt electron and delayed positron with stringent time, distance, and energy requirements. The expected number of events for ⁸B solar neutrinos in this coincidence channel is 3929 with 10 yr of data taking. On the other hand, although the channel with an excited ¹³N(3/2⁻; 3.502 MeV) has a comparable cross section as the ground-state channel (Suzuki et al. 2012), the corresponding signature after quenching is a single event since the deexcitation of ¹³N(3/2⁻; 3.502 MeV) is dominated by a proton knockout, and thus, cannot be distinguished from the recoiled electron of the ES channel and the single γ of the NC channel on an event-by-event basis. Therefore, in the coincidence event category, we focus on the CC channel with the ground-state ¹³N and consider the channel with the excited ¹³N(3/2⁻; 3.502 MeV) as a component of the total spectrum of the singles as illustrated in Figure 2.

Among the five listed NC channels, the only one with a coincidence signature is the interaction of ν_x +¹³C → ν_x + n+¹²C, with a prompt γ energy of 4.44 MeV from ¹²C deexcitation and the delayed neutron capture. However, given that the background from the inverse beta decay (IBD) interactions of reactor antineutrinos are overwhelming, where the signal-to-background ratio is at the level of 10⁻⁴, the event rate of this channel is unobservable. In this work, we focus on the NC channels with the signature of single γ deexcitation, among which the NC interaction with the ¹³C deexcited energy of 3.685 MeV:

$$\begin{eqnarray}&&{\nu }_{x}{+}^{13}{\rm{C}}\to {\nu }_{x}{+}^{13}{\rm{C}}\left({\displaystyle \frac{3}{2}}^{-};3.685\,\mathrm{MeV}\right)\end{eqnarray} \tag{ 3 }$$

is the dominant interaction channel and will be used to determine the ⁸B solar neutrino flux via the NC interaction.

Finally, we also consider the ES interaction channel on the electron,

$$\begin{eqnarray}&&{\nu }_{x}+e\to {\nu }_{x}+e,\end{eqnarray} \tag{ 4 }$$

where the signature is a single recoiled electron (Abusleme et al. 2021a). Using all three channels of the CC, NC, and ES interactions, we are able to make a model-independent measurement of the ⁸B solar neutrino flux, ${\sin }^{2}{\theta }_{12}$ and ${\rm{\Delta }}{m}_{21}^{2}$ with JUNO, which is useful in disentangling the solar dynamics and the neutrino oscillation effects. This measurement is expected to be the only model-independent study after the SNO experiment (Ahmad et al. 2001, 2002; Ahmed et al. 2004; Aharmim et al. 2008).

To summarize, in this work, we are going to employ the following three interaction channels for a model-independent approach of the JUNO ⁸B solar neutrino program: (i) the CC detection channel is sensitive to the ν_e component of solar neutrinos, (ii) the NC channel is sensitive to all active neutrino flavors (ν_e , ν_μ , ν_τ ) with identical cross sections, and (iii) the ES channel is also sensitive to all active flavors, but with a preferred cross section for the ν_e flux (i.e., σ(ν_μ/τ ) ≃ 0.17 σ(ν_e )).

2.1.  ν_e +¹³C CC Channel

For the typical coincidence signature of the CC channel, ν_e +¹³C → e⁻+¹³N(1/2⁻; gnd), the energy of the prompt signal is the kinetic energy of the outgoing electron with the reaction threshold of 2.2 MeV. Therefore, there is a one-to-one correspondence between the electron kinetic energy and the initial neutrino energy T_e ≃ E_ν − 2.2 MeV because of the negligible recoil energy of the daughter ¹³N. Meanwhile, the delayed signal is the deposited energy of the positron from the ¹³N β⁺ decay (Q = 2.2 MeV), with a decay lifetime of τ = 863 s. The time and spatial correlation between the prompt and delayed signals provides the distinct feature of the coincidence signature.

In the following, we consider two significant backgrounds for this coincidence signature of the CC channel in this work.

• 1.  
  The first background is the accidental coincidence of two single events. For the visible energy between 2 and 5 MeV, natural radioactivity composes the most significant part of the prompt component of the coincidence candidate, while the prompt background events above 5 MeV come from the muon-induced unstable isotopes and the recoiled electrons of solar neutrino ES interactions. Due to the expected natural radioactivity level in the LS (10⁻¹⁷ g/g ²³⁸U and ²³²Th in the secular equilibrium, 10⁻¹⁸ g/g ⁴⁰K and 10⁻²⁴ g/g ²¹⁰Pb), a requirement on the selection of the prompt energy is to minimize the contribution from these radioactivity events. The delayed component of the accidental background is mainly from the cosmogenic ¹¹C decay (Q = 1.98 MeV) in the energy range of [1, 2] MeV, while the internal LS radioactivity contributes less than 2% compared to that from ¹¹C. If the internal radioactivity is 1–2 orders of magnitude higher than expected, the contribution to the delayed component from the radioactivity would be at the same level as the cosmogenic ¹¹C decay. Note that all the single events in the energy range between 1 and 2 MeV can be accurately measured in situ with future data, and the accidental background can be deduced with the off-time coincidence method. Note that we have neglected the external radioactivity, which can be effectively removed by the proper fiducial volume cut.
• 2.  
  The second background is produced by the correlated prompt and delayed decays of unstable isotopes from the same parent muon. These correlated decays are not considered in the above accidental background. Therefore, the cosmic muon and the corresponding isotope simulations have been performed, and the muon veto strategies of the threefold coincidence are the same as those in Abusleme et al. (2021a). This shows that the prompt signal is mainly from the beta decays of ¹²B, ⁸Li, ⁶He, and ¹⁰C (below 4 MeV), and as expected the delayed signal is from ¹¹C. The muon detection efficiency of the outer water veto can reach as high as 99.5% (Abusleme et al. 2021a). Since the remaining untagged muons are usually located at the edge of the central detector, this muon-induced correlated background can be removed using the fiducial volume cut and is neglected in this work. Note that we have assumed a perfect detector uniformity for these isotopes and used the whole detector region to estimate the background inside the fiducial volume.

We have simulated the signal and backgrounds using the official JUNO simulation software (Zou et al. 2015; Lin et al. 2017). According to the signal characteristics of the CC channel, the accidental background can be calculated with different selection cuts. The final event selection criteria are obtained by optimizing the figure of merit, $S/\sqrt{S+B}$, where S and B stand for the rates of the signal and background, respectively. The optimized event selection cuts of the fiducial volume, prompt and delayed energies, time and spatial correlation cuts, and muon vetos are provided step by step in Table 2, where the efficiencies of the signal and backgrounds are also calculated. In order to avoid possible large contamination from the internal radioactivity and muon-induced ¹⁰C, we select the threshold of the prompt visible energy to 5 MeV for the CC channel, i.e., 5 MeV < E_p < 14 MeV. Meanwhile, the fiducial volume is chosen to be R < 16.5 m to reject the external radioactivity and isotopes, with R being the distance to the detector center. It should be noted that an anticoincidence criterion with a time distance cut of ΔT > 4 ms has been used to reject the IBD interactions of reactor antineutrinos, achieving a rejection power of 100%. Meanwhile, this IBD rejection cut has a negligible impact on the signal because of the much longer lifetime of ¹³N.

Table 2. Efficiencies of Optimized Event Selection Cuts for the Signal and Backgrounds of the ν_e CC Channel [ν_e +¹³C → e⁻+¹³N(1/2⁻; gnd)] Analysis

	Cuts	CC Signal Efficiency	CC Signal	Background for CC Channel
				Solar ES	Muon-induced Isotopes
				Accidental	Accidental	Correlated
⋯	⋯	⋯	3929	⋯	⋯	⋯
Time cut	4 ms < ΔT < 900 s	65%	2554	1010	1013	1012
Energy cut	5 MeV < Ep < 14 MeV	79%	1836	109	1010	109
	1 MeV < Ed < 2 MeV	91%
Fiducial volume cut	R < 16.5 m (Abusleme et al. 2021a)	81%	1487	107	107	108
Vertex cut	Δd < 0.47 m	87%	1293	328	105	106
Muon veto	Muon and TFC veto (Abusleme et al. 2021a)	50%	647	164	53	58
Combined	⋯	17%	647	275

Note. The expected event numbers of the signal and backgrounds for 10 yr of data taking after each cut are also listed. The fiducial volume used in this work corresponds to the effective mass of 16.2 kt. For the energy cuts, E_p and E_d represent the visible energy of prompt and delayed signals. The same muon and threefold-coincidence veto strategies as in Abusleme et al. (2021a) are used for the reduction of muon-induced isotopes.

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We illustrate in Figure 1 the expected prompt visible energy spectra of the selected signal and residual backgrounds in the CC channel after the optimized cuts. The expected number of selected signals is 647 for 10 yr of data taking is shown as the purple line. The fiducial volume used in this work corresponds to the effective mass of 16.2 kt. The accidental background with solar neutrino ES interactions as the prompt signal is illustrated as the green line and contributes 164 background events, which will be fully correlated with the solar neutrino ES signal in the following global analysis. In contrast, the muon-induced isotopes contribute 111 background events (depicted as the red line of Figure 1), which are from both the accidental coincidence (53 events) and correlated background (58 events). Therefore, we can achieve an excellent $S/\sqrt{S+B}$ ≃ 21, offering an excellent prospect for future experimental measurements. As a comparison, a preliminary study assessing the feasibility of detecting solar neutrinos via the CC interactions on ¹³C in the Borexino experiment has been previously reported in the thesis of Ghiano (2012), where an upper limit for the number of the solar neutrino CC interaction ¹³C was established, constrained by the limited event statistics.

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Finally, the expected event number of hep solar neutrinos in the CC channel is about 15 for 10 yr of data taking, but only three events are beyond the spectral tail of ⁸B solar neutrinos. Thus, it would be difficult to detect the hep solar neutrinos with the CC interaction on ¹³C, and the signal from the hep solar neutrinos will be neglected in this work.

2.2. v_x+¹³C NC Channel

The typical signature for the NC event, ν_x +¹³C → ν_x +¹³C(3/2⁻; 3.685 MeV) is a monoenergetic γ with an energy of 3.685 MeV, convoluted with the energy resolution of ${\sigma }_{E}/E=3 \% /\sqrt{E\ (\mathrm{MeV})}$ for the JUNO detector. The expected visible energy spectra of all single event sources for 10 yr of data taking with the same energy-dependent fiducial volume cuts as in Abusleme et al. (2021a) are shown in Figure 2. The blue and green curves represent singles from the ν_x +¹³C NC and ν_x + e ES channels, respectively. The purple curve includes the ν_e +¹³C → e⁻+¹³N(3/2⁻; 3.502 MeV) channel and the residual singles of the ν_e +¹³C → e⁻+¹³N(1/2⁻; gnd) channel after the coincidence cut. The anticoincidence criterion successfully reduces residual singles from reactor antineutrino IBD interactions to a negligible level. These residuals are due to cases where prompt and delayed signals appear in the same 1 μs readout window. The red curve represents the single events from natural radioactivity and muon-induced unstable isotopes (Abusleme et al. 2021a). The brown curve includes the ${\bar{\nu }}_{e}+e$ ES and ${\bar{\nu }}_{x}{+}^{13}{\rm{C}}$ NC channels from reactor antineutrinos. The NC events rate from reactor antineutrinos is less than 0.2% of that from solar neutrinos. The black curve is the summation of all the components. Note that the discontinuities at 3 and 5 MeV are caused by the energy-dependent fiducial volume cuts which are, from low to high energies, R < 13 m for [2, 3] MeV, R < 15 m for [3, 5] MeV, and R < 16.5 m for the energies larger than 5 MeV. The upper right insert plot is illustrated for the energy range between 3 and 5 MeV in the linear scale, where a clear peak from the solar neutrino NC channel can be seen above the continuous spectra from solar neutrino ES interactions and the other backgrounds, demonstrating the promising prospect for the observation of the NC channel at JUNO. After all the cuts the number of signal events in the NC channel is 738 for 10 yr of data taking.

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2.3.  ν_x + e ES Channel

2.4. Day–Night Asymmetry

The MSW effect can cause solar neutrino event rate variations as a function of the solar zenith angle when the neutrinos propagate through Earth (Carlson 1986; Baltz & Weneser 1987, 1988; Krastev & Petcov 1988; Akhmedov et al. 2004; Blennow et al. 2004; de Holanda et al. 2004; Liao 2008; Long et al. 2013), and result in the day–night asymmetry of the solar neutrino observation, in which the signal rate in the night is higher than that in the day, due to ν_e regeneration inside Earth.

In this work, in addition to the visible energy spectra of the CC, NC, and ES channels, we also consider the day–night asymmetry to constrain the neutrino oscillation parameters. The location of JUNO (i.e., 112°31'05'' E and 22°07'05'' N (Abusleme et al. 2022a)) is used in the day–night asymmetry calculations, and the two-dimensional visible energy and zenith angle spectra are employed. For illustration, we show in Figure 3 the ratios of solar neutrino signal event rates with and without considering the terrestrial matter effects as the function of the zenith angle θ_z . The red and blue solid lines denote the ES and CC channels, respectively. In comparison, the dashed lines denote the respective averages over the whole zenith angle range. The ratios of the day–night average (R_A), daytime (R_D), and nighttime (R_N) are also illustrated in the first three bins. The error bars are quoted as the statistical uncertainties of the signal and backgrounds. The blue shaded regions with different colors from left to right are used to denote the zenith angle ranges passing through the crust, mantle, and core of Earth, respectively. The day–night asymmetry, defined as (R_D − R_N)/R_A, is predicted to be −3.1% and −1.6% for the CC and ES channels respectively. The energy ranges of the CC and ES channels are [5, 14] MeV and [2, 16] MeV, respectively. Given that all the neutrino flavors can be detected through the NC channel, no day–night asymmetry exists in the NC detection. Note that the magnitude of the day–night asymmetry strongly depends on the value of ${\rm{\Delta }}{m}_{21}^{2}$. If ${\rm{\Delta }}{m}_{21}^{2}$ is decreased from the KamLAND measurement 7.5 × 10⁻⁵ eV² (Gando et al. 2013) to 6.1 × 10⁻⁵ eV² of the global solar neutrino data (Esteban et al. 2020), the absolute values of the day–night asymmetry also increase to −4.2% and −2.2% for the CC and ES channels, respectively.

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In this section, we study the physical potential for the model-independent measurement of ⁸B solar neutrinos using the CC, NC, and ES channels. Based on the typical event signatures, the full solar neutrino data can be separated into correlated and single event data sets. As discussed in the previous section, all three interaction channels from ⁸B solar neutrinos contribute to the single event data set, while the correlated data set includes events from both the CC channel and the accidental coincidence of the ES channel.

In this analysis, we consider the following systematic uncertainties. First, the uncertainty of detection efficiency is estimated to be 2% (Abusleme et al. 2021a), which is fully correlated with the the signal and background components of each data set, but uncorrelated between the coincidence and single event data samples. Second, the current uncertainty of the ¹³C cross sections from the model calculation is at the level of several percent (Fukugita et al. 1988; Suzuki et al. 2012, 2019), but the precision could be reduced to 1% or better with large-scale modern shell-model calculations (Barrett et al. 2013). Therefore, the uncertainties for the ¹³C CC and NC interaction are taken as 1% for the current study. A 0.5% cross-section uncertainty is used for the ES channel (Tomalak & Hill 2020). Third, the shape of the uncertainty of ⁸B solar neutrinos is taken from Bahcall et al. (1996) and Bahcall (1997), and the uncertainties for the radioactive and muon-induced backgrounds are the same as those in Abusleme et al. (2021a), namely, 1% for ²³⁸U, ²³²Th, and ¹²B decays, 3% for ⁸Li and ⁶He decays, and 10% for ¹⁰C and ¹¹Be decays. A 2% uncertainty is used for the single event from the reactor antineutrino ES interaction. In this work, we treat the ⁸B solar neutrino flux as a free parameter since we are performing a model-independent measurement. Only in the scenario of combining with the SNO flux measurement, an uncertainty of 3.8% is used as an informative prior.

The standard Poisson-type χ² method using the Asimov data set (Zyla et al. 2020) is employed to estimate the sensitivity to measure the ⁸B solar neutrino flux and the oscillation parameters sin² θ₁₂ and ${\rm{\Delta }}{m}_{21}^{2}$, where different pull parameters are included in the χ² function to account for the systematic uncertainties described in this section. More technical details on the construction of the χ² function are provided in the Appendix. In order to identify the contribution of each interaction channel, we divide the whole data sets into the correlated events, the single events within [3.5, 4.1] MeV, and the single events outside [3.5, 4.1] MeV, which correspond to the CC, NC, and ES measurements respectively.

In Figures 4–6, we illustrate the two-dimensional allowed ranges and the marginalized one-dimensional curves on the sensitivity of the ⁸B neutrino flux, ${\sin }^{2}{\theta }_{12}$ and ${\rm{\Delta }}{m}_{21}^{2}$, of which Figure 4 shows the comparison of the ES and ES+NC measurements, Figure 5 for the comparison the ES+NC and ES+NC+CC measurements, and Figure 6 for the comparison of the JUNO and JUNO + SNO flux measurements. In addition, a summary of relative uncertainties on the ⁸B neutrino flux, ${\sin }^{2}{\theta }_{12}$ and ${\rm{\Delta }}{m}_{21}^{2}$, from the model-independent approach is provided in Figure 7. Several important observations and comments are presented as follows.

• 1.  
  The NC measurement is accomplished based on the single events within [3.5, 4.1] MeV, where the background events are from the singles of ES and CC interactions of ⁸B solar neutrinos, together with the natural radioactivity and muon-induced unstable isotopes. The standard MSW effect of solar neutrino oscillations is used in the calculation of ES and CC interactions and the oscillation parameters sin² θ₁₂ and ${\rm{\Delta }}{m}_{21}^{2}$ are marginalized. The ⁸B solar neutrino flux can be obtained with an accuracy of 10.6% with the NC measurement, which is comparable to the level of 8.6% from the NC measurement of the SNO Phase III data (Aharmim et al. 2013a).
• 2.  
  The ES measurement is based on the single events outside the energy range of [3.5, 4.1] MeV, in which the dominant background is from the natural radioactivity and muon-induced unstable isotopes, which are summarized in Figure 2 and more details can be found in Abusleme et al. (2021a). In the model-independent approach of the ES measurement, the ⁸B neutrino flux and two oscillation parameters, sin² θ₁₂ and ${\rm{\Delta }}{m}_{21}^{2}$, are simultaneously constrained, where the relative uncertainties are derived as ${}_{-8 \% }^{+11 \% }$, ${}_{-17 \% }^{+17 \% }$, and ${}_{-25 \% }^{+45 \% }$, respectively. The uncertainties of sin² θ₁₂ and ${\rm{\Delta }}{m}_{21}^{2}$ are larger than those obtained in Abusleme et al. (2021a) by including the 3.8% SNO flux measurement because of the strong correlation between the flux and oscillation parameters in the model-independent approach. When adding the JUNO NC measurement, the accuracy of the ⁸B neutrino flux can be improved to the level of ${}_{-5.5 \% }^{+6.0 \% }$, and the uncertainties of sin² θ₁₂ and ${\rm{\Delta }}{m}_{21}^{2}$ are also improved to ${}_{-10 \% }^{+10 \% }$, and ${}_{-21 \% }^{+31 \% }$, respectively.
• 3.  
  The CC measurement with the correlated events alone cannot simultaneously determine the ⁸B neutrino flux and oscillation parameters because of the high visible energy threshold. However, combining the CC measurement with the single events of the NC+ES channels will help break the correlation and possible degeneracy among different parameters, where the accuracy of the ⁸B neutrino flux can be further improved to 5%, while those of ${\sin }^{2}{\theta }_{12}$ and ${\rm{\Delta }}{m}_{21}^{2}$ are ${}_{-8 \% }^{+9 \% }$, and ${}_{-17 \% }^{+25 \% }$, respectively.
• 4.  
  The expected 5% precision of the ⁸B neutrino flux obtained with all three detection channels is much better than that of 11.6% from the latest prediction of the SSM (Vinyoles et al. 2017). This will be the only model-independent measurement after those of SNO (Aharmim et al. 2013b). In addition, the uncertainties of ${\sin }^{2}{\theta }_{12}$ and ${\rm{\Delta }}{m}_{21}^{2}$ from the ⁸B neutrino measurement at JUNO are at the levels of ${}_{-8 \% }^{+9 \% }$ and ${}_{-17 \% }^{+25 \% }$, respectively, which is comparable to the levels of ${}_{-5 \% }^{+5 \% }$, and ${}_{-11 \% }^{+20 \% }$ from the latest results of combined SK and SNO solar neutrino data (Super-Kamiokande Collaboration et al. 2023). Considering that the reactor antineutrino measurement from JUNO will obtain sub-percent levels of ${\sin }^{2}{\theta }_{12}$ and ${\rm{\Delta }}{m}_{21}^{2}$ in the near future (Abusleme et al. 2022b), measurements of these parameters from future solar neutrino data would be important to test the charge, parity, and time reversal symmetry of fundamental physics and resolve the possible discrepancy between the neutrino and antineutrino oscillation channels.
• 5.  
  Within the spirit of the model-independent approach, one can also include the 3.8% ⁸B neutrino flux measurement from SNO as an informative prior, where even better precision levels of the flux and oscillation parameters can be achieved. In this scenario, the expected accuracy of the ⁸B solar neutrino flux would reach the level of 3%, and sin² θ₁₂ and ${\rm{\Delta }}{m}_{21}^{2}$ can be constrained with the precision of ${}_{-6.5 \% }^{+7.5 \% }$, and ${}_{-15 \% }^{+19 \% }$, respectively. These measurements are comparable to those from the current global solar neutrino data and would provide unique information to the future solar neutrino program.
• 6.  
  It is noteworthy that the signal event statistics, detection efficiency, and cross-section uncertainties are the most crucial factors that affect the detection potential of the CC and NC detection channels. If the cross-section uncertainties are 10%, instead of 1% assumed in this work, the uncertainty of the ⁸B neutrino flux will become ${}_{-6 \% }^{+6 \% }$.
• 7.  
  In the CC detection channel, the observed energy of the prompt electron is directly related to the incoming neutrino energy, making it crucial to lower the prompt energy threshold to investigate the predicted increase in the solar neutrino survival probability at lower energies. For this analysis, we set a conservative prompt energy threshold at 5 MeV to optimize the trade-off between signal detection efficiencies and background contamination. Regarding the accidental background, radioactivity is the primary source of the prompt signal below 3.5 MeV, where stringent background control measures are essential, as outlined in Abusleme et al. (2021b). Conversely, solar neutrino ES events become the leading prompt signal above 3.5 MeV. For the prompt energy range of 3.5–5 MeV, the cosmogenic correlated background is significantly higher than in the region above 5 MeV, as depicted in Figure 1, while the signal efficiency is considerably lower between 3.5 and 5 MeV, due to the multiplicity cut. Additional technical details in this regard will be reported elsewhere in the future.

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In this work, we have studied the physics potential of detecting ⁸B solar neutrinos at JUNO, in a model-independent manner by using the CC, NC, and ES detection channels. Because of its largest-ever mass of ¹³C and the expected low background level, excellent signal-to-background ratios can be achieved. Thus, ⁸B solar neutrinos will be observable in all three interaction channels.

We have performed detailed evaluations of the background budgets and signal efficiencies of the CC, NC, and ES channels at JUNO. With optimized selection strategies, we find that the expected ⁸B neutrino rates of the CC and NC channels are ${ \mathcal O }(100)$ interactions per year after the event selection. It turns out that the signal event statistics, detection efficiency, and cross-section uncertainties are the most crucial factors that affect the detection potential of these two channels. We have carried out a combined analysis of both the coincidence and single events from all three detection channels, and shown that the ⁸B solar neutrino flux, ${\sin }^{2}{\theta }_{12}$ and ${\rm{\Delta }}{m}_{21}^{2}$, can be measured to ±5%, ${}_{-8 \% }^{+9 \% }$, and ${}_{-17 \% }^{+25 \% }$, respectively. When combined with the SNO flux measurement, the world's best precision of 3% can be achieved for the ⁸B neutrino flux.

In the history of solar neutrino experiments, the NC measurement is unique in decoupling the neutrino flux and oscillation parameters, and enabling the model-independent approach of the solar neutrino program. SNO has been the only solar neutrino experiment in the past to achieve this goal, and JUNO would be the second one. In this work, we have demonstrated the feasibility of ⁸B solar neutrino measurements at JUNO, which, together with other large solar neutrino detectors (Beacom et al. 2017; Abe et al. 2018; Capozzi et al. 2019), will open a new era of solar neutrino observation and may uncover new directions for neutrino physics and solar physics.

We are grateful for the ongoing cooperation from the China General Nuclear Power Group. This work was supported by the Chinese Academy of Sciences, the National Key R&D Program of China, the CAS Center for Excellence in Particle Physics, Wuyi University, and the Tsung-Dao Lee Institute of Shanghai Jiao Tong University in China, the Institut National de Physique Nucléaire et de Physique de Particules (IN2P3) in France, the Istituto Nazionale di Fisica Nucleare (INFN) in Italy, the Italian-Chinese collaborative research program MAECI-NSFC, the Fond de la Recherche Scientifique (F.R.S-FNRS) and FWO under the "Excellence of Science—EOS" in Belgium, the Conselho Nacional de Desenvolvimento Científico e Tecnològico in Brazil, the Agencia Nacional de Investigacion y Desarrollo and ANID—Millennium Science Initiative Program—ICN2019_044 in Chile, the Charles University Research Center and the Ministry of Education, Youth, and Sports in Czech Republic, the Deutsche Forschungsgemeinschaft (DFG), the Helmholtz Association, and the Cluster of Excellence PRISMA+ in Germany, the Joint Institute of Nuclear Research (JINR) and Lomonosov Moscow State University in Russia, the joint Russian Science Foundation (RSF) and National Natural Science Foundation of China (NSFC) research program, the MOST and MOE in Taiwan, the Chulalongkorn University and Suranaree University of Technology in Thailand, University of California at Irvine, and the National Science Foundation in the US.

In this appendix, we present the technical details of the sensitivity study employed in this work. A Poisson-type least squares function, denoted as χ², is defined as follows:

$$\begin{eqnarray}&&\begin{array}{l}{\chi }^{2}={\chi }_{\mathrm{stat}}^{2}(\mathrm{CC})+{\chi }_{\mathrm{stat}}^{2}(\mathrm{NC})+{\chi }_{\mathrm{stat}}^{2}(\mathrm{ES})+{\chi }_{\mathrm{syst}}^{2}\\ \,=\,2\times \displaystyle \sum _{i=1}^{10}\left[\displaystyle \sum _{{j}_{{\rm{C}}}=1}^{90}\left({N}_{\mathrm{pre}}^{{\rm{C}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}})-{N}_{\mathrm{obs}}^{{\rm{C}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}})+{N}_{\mathrm{obs}}^{{\rm{C}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}})\cdot \mathrm{log}\displaystyle \frac{{N}_{\mathrm{obs}}^{{\rm{C}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}})}{{N}_{\mathrm{pre}}^{{\rm{C}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}})}\right)\right.\\ \,+\,\left.\displaystyle \sum _{{j}_{{\rm{S}}}=1}^{140}\left({N}_{\mathrm{pre}}^{{\rm{S}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{S}}}})-{N}_{\mathrm{obs}}^{{\rm{S}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{S}}}})+{N}_{\mathrm{obs}}^{{\rm{S}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{S}}}})\cdot \mathrm{log}\displaystyle \frac{{N}_{\mathrm{obs}}^{{\rm{S}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{S}}}})}{{N}_{\mathrm{pre}}^{{\rm{S}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{S}}}})}\right)\right]\\ \,+\,{\left(\displaystyle \frac{{\varepsilon }_{X}^{\mathrm{ES}}}{{\sigma }_{X}^{\mathrm{ES}}}\right)}^{2}+{\left(\displaystyle \frac{{\varepsilon }_{X}^{\mathrm{NC}}}{{\sigma }_{X}^{\mathrm{NC}}}\right)}^{2}+{\left(\displaystyle \frac{{\varepsilon }_{X}^{\mathrm{CC}}}{{\sigma }_{X}^{\mathrm{CC}}}\right)}^{2}+\displaystyle \sum _{{k}_{{\rm{C}}}}{\left(\displaystyle \frac{{\varepsilon }_{{\rm{B}}}^{{k}_{{\rm{C}}}}}{{\sigma }_{{\rm{B}}}^{{k}_{{\rm{C}}}}}\right)}^{2}+\displaystyle \sum _{{k}_{{\rm{S}}}}{\left(\displaystyle \frac{{\varepsilon }_{{\rm{B}}}^{{k}_{{\rm{S}}}}}{{\sigma }_{{\rm{B}}}^{{k}_{{\rm{S}}}}}\right)}^{2}\\ \,+\,{\left(\displaystyle \frac{{\varepsilon }_{\mathrm{eff}}^{{\rm{C}}}}{{\sigma }_{\mathrm{eff}}^{{\rm{C}}}}\right)}^{2}+{\left(\displaystyle \frac{{\varepsilon }_{\mathrm{eff}}^{{\rm{S}}}}{{\sigma }_{\mathrm{eff}}^{{\rm{S}}}}\right)}^{2}+{\left({\varepsilon }_{{\rm{s}}}\right)}^{2},\end{array}\end{eqnarray} \tag{ A1 }$$

where ${\chi }_{\mathrm{stat}}^{2}(\mathrm{CC})$, ${\chi }_{\mathrm{stat}}^{2}(\mathrm{NC})$, and ${\chi }_{\mathrm{stat}}^{2}(\mathrm{ES})$ are statistical parts of the CC, NC, and ES channels in the χ² function, respectively. These components are presented in the second and third rows of Equation (A1). The index j_C ranges from 1–90 for the CC measurement, representing the energy range from 5–14 MeV with an equal bin width of 0.1 MeV. For the NC measurement, j_S ranges from 16–21, while for the ES measurement, j_S spans from 1–15 and 22–140 covering the energy range of 2–16 MeV with an equal bin width of 0.1 MeV. The predicted numbers of signal and background events, ${N}_{\mathrm{pre}}^{{\rm{C}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}})$ and ${N}_{\mathrm{pre}}^{{\rm{S}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{S}}}})$, are calculated for the ith zenith angle bin and the j_Cth or j_Sth visible energy bin of the correlated and single event samples, respectively,

$$\begin{eqnarray}\begin{array}{rcl}{N}_{\mathrm{pre}}^{{\rm{C}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}} & = & (1+{\varepsilon }_{\mathrm{eff}}^{{\rm{C}}}){S}_{\mathrm{pre}}^{\mathrm{CC}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}})\\ & & +\displaystyle \sum _{{k}_{{\rm{C}}}}^{}(1+{\varepsilon }_{{\rm{B}}}^{{k}_{{\rm{C}}}}){B}_{\mathrm{pre}}^{{k}_{{\rm{C}}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}}),\end{array}\end{eqnarray} \tag{ A2 }$$

$$\begin{eqnarray}\begin{array}{rcl}{N}_{\mathrm{pre}}^{{\rm{S}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{S}}}}) & = & (1+{\varepsilon }_{\mathrm{eff}}^{{\rm{S}}})[{S}_{\mathrm{pre}}^{\mathrm{NC}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}})\\ & & +{S}_{\mathrm{pre}}^{\mathrm{ES}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}})]\\ & & +\displaystyle \sum _{{k}_{{\rm{S}}}}^{}(1+{\varepsilon }_{{\rm{B}}}^{{k}_{{\rm{S}}}}){B}_{\mathrm{pre}}^{{k}_{{\rm{S}}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{S}}}}),\end{array}\end{eqnarray} \tag{ A3 }$$

where ${S}_{\mathrm{pre}}^{\mathrm{CC}}$, ${S}_{\mathrm{pre}}^{\mathrm{NC}}$, and ${S}_{\mathrm{pre}}^{\mathrm{ES}}$ represent the two-dimensional spectra of the ⁸B neutrino signals in the CC, NC, and ES channels, respectively, incorporating the fiducial volume and signal efficiencies. The projections of these spectra onto the visible energy axis are depicted in Figure 1 for the CC channel and Figure 2 for the NC and ES channels. Meanwhile, ${B}_{\mathrm{pre}}^{{k}_{{\rm{C}}}}$ and ${B}_{\mathrm{pre}}^{{k}_{{\rm{S}}}}$ correspond to the background components in the correlated and single event samples, respectively, with their visible energy spectra illustrated in the same figures. The calculations of the ⁸B neutrino signal spectra in the CC, NC, and ES channels are as follows:

$$\begin{eqnarray}\begin{array}{rcl}{S}_{\mathrm{pre}}^{\mathrm{CC}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}}) & = & {{\rm{\Phi }}}_{{}^{8}{\rm{B}}}\times \left[(1+{\varepsilon }_{{\rm{s}}}{\delta }_{{E}_{\nu }}^{{\rm{S}}}){S}_{{}^{8}{\rm{B}}}({E}_{\nu })\right.\\ & & \times {P}_{{ee}}({\theta }_{12},{\rm{\Delta }}{m}_{21}^{2},{E}_{\nu },{\theta }_{z}^{i})\\ & & \times \ \left.(1+{\varepsilon }_{X}^{\mathrm{CC}})\otimes {\sigma }_{\mathrm{CC}}({E}_{\nu },{E}_{e})\otimes {M}_{}({E}_{e},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}})\right],\end{array}\end{eqnarray} \tag{ A4 }$$

$$\begin{eqnarray}&&\begin{array}{l}{S}_{\mathrm{pre}}^{\mathrm{NC}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}})={{\rm{\Phi }}}_{{}^{8}{\rm{B}}}\times \left[(1+{\varepsilon }_{{\rm{s}}}{\delta }_{{E}_{\nu }}^{{\rm{S}}}){S}_{{}^{8}{\rm{B}}}({E}_{\nu })\right.\\ \quad \left.\times (1+{\varepsilon }_{X}^{\mathrm{NC}})\otimes {\sigma }_{\mathrm{NC}}({E}_{\nu },{E}_{\gamma })\otimes {M}_{}({E}_{\gamma },{E}_{\mathrm{vis}}^{{j}_{{\rm{S}}}})\right],\end{array}\end{eqnarray} \tag{ A5 }$$

$$\begin{eqnarray}\begin{array}{rcl}{S}_{\mathrm{pre}}^{\mathrm{ES}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}}) & = & {{\rm{\Phi }}}_{{}^{8}{\rm{B}}}\times \left\{(1+{\varepsilon }_{{\rm{s}}}{\delta }_{{E}_{\nu }}^{{\rm{S}}}){S}_{{}^{8}{\rm{B}}}({E}_{\nu })\right.\\ & & \times \,{{\rm{\Sigma }}}_{\alpha }\left[{P}_{e\alpha }({\theta }_{12},{\rm{\Delta }}{m}_{21}^{2},{E}_{\nu },{\theta }_{z}^{i})\right.\\ & & \times \left.\left.(1+{\varepsilon }_{X}^{\mathrm{ES}})\otimes {\sigma }_{\mathrm{ES}}^{{\nu }_{\alpha }}({E}_{\nu },{E}_{e})\right]\otimes {M}_{}({E}_{e},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}})\right\}.\end{array}\end{eqnarray} \tag{ A6 }$$

The ⁸B neutrino signal spectra for the CC, NC, and ES channels are calculated by multiplying the ⁸B neutrino spectrum ${S}_{{}^{8}{\rm{B}}}$ with the neutrino oscillation probability P_{e α} (where α equals e or μ + τ), and then convolving the resulting product with the differential interaction cross sections (namely, σ_CC, σ_NC, and ${\sigma }_{\mathrm{ES}}^{{\nu }_{\alpha }}$) as well as with the detector response matrix M. The neutrino oscillation probability P_{e α} includes both the standard MSW flavor conversion and terrestrial matter effects, and is a function of the neutrino energy E_ν and the zenith angle ${\theta }_{z}^{}$, calculated within the three-neutrino oscillation framework. The detector response matrix M accounts for the effects of energy resolution and energy nonlinearity, as described in Abusleme et al. (2021a). The observed spectra ${N}_{\mathrm{obs}}^{{\rm{C}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{C}}}})$ and ${N}_{\mathrm{obs}}^{{\rm{S}}}({\theta }_{z}^{i},{E}_{\mathrm{vis}}^{{j}_{{\rm{S}}}})$ are obtained from the corresponding predicted spectra by applying the true values of the ⁸B neutrino flux ${{\rm{\Phi }}}_{{}^{8}{\rm{B}}}$, oscillation parameters ${\sin }^{2}{\theta }_{12}$, and ${\rm{\Delta }}{m}_{21}^{2}$, and assuming negligible contributions from nuisance parameters. Note that, as discussed in Section 2, the ⁸B solar neutrino interactions may also contribute to the background components ${B}_{\mathrm{pre}}^{{k}_{{\rm{C}}}}$ (e.g., the green line in Figure 1, the purple line in Figure 2), In such instances, all correlations between the signal and background components are accounted for in the χ² function.

The nuisance parameters ${\varepsilon }_{X}^{m}$ (m = CC, NC, ES), ${\varepsilon }_{{\rm{B}}}^{k}$, ${\varepsilon }_{\mathrm{eff}}^{n}$ (n = C, S) account for systematic uncertainties associated with the cross section, the backgrounds, and the detection efficiency, respectively, as discussed in the manuscript. The parameter ${\delta }_{{E}_{\nu }}^{{\rm{S}}}$ represents the 1σ fractional variation of the ⁸B neutrino energy spectrum, as detailed in Bahcall et al. (1996) and Bahcall (1997), while ε_s denotes the magnitude of the ⁸B neutrino spectral uncertainty. A summary of the nuisance parameters and their corresponding uncertainties within the χ² function is summarized in Table 3. For the sensitivity study that produced the results shown in Figures 4–7, we selected data sets from one or a combination of the CC, NC, and ES measurements. We then activated the relevant nuisance parameters to account for systematic uncertainties in the corresponding χ² function. During the calculation of the allowed regions for each analysis, the displayed parameters (one or two of the fitting parameters ${{\rm{\Phi }}}_{{}^{8}{\rm{B}}}$, θ₁₂, and ${\rm{\Delta }}{m}_{21}^{2}$) were fitted, while all other physical and nuisance parameters were marginalized. The critical values of Δχ² for various confidence levels are sourced from Zyla et al. (2020).

Table 3. Description of the Nuisance Parameters and the Associated Uncertainties in the χ² Function

Sys.	Description of the Pull Term	Uncertainty
${\varepsilon }_{X}^{\mathrm{ES}}$, ${\varepsilon }_{X}^{\mathrm{NC}}$, ${\varepsilon }_{X}^{\mathrm{CC}}$	Cross section for the CC, NC, and ES channels	1%, 1%, 0.5%
${\varepsilon }_{\mathrm{eff}}^{{\rm{C}}}$, ${\varepsilon }_{\mathrm{eff}}^{{\rm{S}}}$	Detector efficiency	2% (Abusleme et al. 2021a)
${\varepsilon }_{{\rm{B}}}^{{k}_{{\rm{C}}}}$, ${\varepsilon }_{{\rm{B}}}^{{k}_{{\rm{S}}}}$	Rate for the kCth or kSth background component	1%–10%, same as Abusleme et al. (2021a)
εs	8B neutrino energy spectrum	Bahcall et al. (1996), Bahcall (1997)

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