On the Optimization of Protvino to ORCA (P2O) Experiment

There is a proposal to send a neutrino beam from the Protvino accelerator complex located in Russia to the detector facility called `Oscillation Research with Cosmics in the Abyss' (ORCA) in the Mediterranean sea to study neutrino oscillation. This is called the P2O experiment which will have a baseline of 2588 km. In this paper, we carry out an optimization study to extract the best possible physics sensitivity of the P2O experiment. In particular, we study the effect of antineutrino run, the role of background as well as the impact of controlling the systematic uncertainties vis-a-vis the statistics.


Introduction
Ambitious and expensive next-generation long-baseline experiments are being proposed to measure the remaining crucial ingredients of the neutrino mass matrix -(i) the sign of ∆m 2  31 aka the neutrino mass hierarchy, (ii) the octant of θ 23 and (iii) CP violation.The Deep Underground Neutrino Experiment (DUNE) [1] has been proposed to be built in USA, Tokai to Hyper-Kamiokande (T2HK) [2] proposal has been made for a long-baseline experiment in Japan and ESSνSB [3] has been put forth as a prospective long-baseline endeavour in Sweden.The CP sensitivity of all these three proposals is very high.DUNE is designed to measure CP violation at around 5σ C.L. with its proposed 3+3 years a e-mail: sandhya@hri.res.inb e-mail: ghoshmonojit@hri.res.inc e-mail: dipyamanpramanik@hri.res.inrun for maximal CP violation 1 .T2HK should be able to discover CP violation at 7σ C.L. in 5+5 years (assuming that the mass hierarchy is known), while ESSνSB's projected sensitivity to CP violation is 8σ from a 5+5 year run.The octant sensitivity at these experiments is also seen to be very good with DUNE, T2HK and ESSνSB promising a 3σ discovery for (θ 23 < 43.5 • and θ 23 > 47.5 • ), (θ 23 < 43 • and θ 23 > 48 • ) and (θ 23 < 41 • and θ 23 > 50 • ), respectively.On the other hand, the hierarchy sensitivity is good only in DUNE where we can expect a 15σ(7.5σ)discovery for δ CP = −90 • (+90 • ) 2 .The ESSνSB set-up is not expected to have any hierarchy sensitivity at all, while for T2HK there is expected to be little hierarchy sensitivity if both the tanks are placed in Japan at a distance of 295 km.In order to alleviate this problem to some extent, there is a proposal to put the second tank of the Hyper-Kamiokande detector in Korea, at a distance of about 1100 km from Tokai [2], bringing in matter effects and hence some hierarchy sensitivity.This proposal is called Tokai to Hyper-Kamiokande Korea (T2HKK) [2].The hierarchy sensitivity for T2HKK proposal though is expected to be not significantly above 5σ C.L. even after 5+5 years of run time.Note that all the projected sensitivity reaches mentioned above are assuming NH to be true.For IH the sensitivity of all experiments are expected to be lower, especially for mass hierarchy.For studies regarding measuring the unknowns in the standard three flavour framework in these future long-baseline experiments see Ref. [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]. 1 By x + y we imply running the experiment for x years in the neutrino mode and y years in antineutrino mode. 2 Throughout the paper we use the acronyms NH for normal hierarchy and IH for inverted hierarchy.
The main reason for lower hierarchy sensitivity in the above mentioned next-generation long-baseline experiments is their shorter baseline.To keep the experiment at the oscillation maximum the corresponding fluxes are made to peak at lower energies.Earth matter effects, which bring in nearly all the mass hierarchy sensitivity in these experiments is linearly proportional to the neutrino energy and hence is not high enough in these experiments, leading to lower hierarchy sensitivity.There is another European experimental proposal with a relatively longer baseline.This proposal is known as the Protvino to ORCA (Oscillation Research with Cosmics in the Abyss) or the P2O experiment [19,20,21].This proposal comprises of shooting a neutrino beam from the Protvino accelerator site in Russia to the ORCA detector in the Mediterranean sea at a distance of 2588 km from the accelerator.The Protvino accelerator site currently houses the U-70 accelerator.The proposal is to upgrade the accelerator to produce 70 GeV protons with a beam power of 450 KW to deliver 4×10 20 protons on target per year.The pions produced from the beam dump create a neutrino beam which is peaked at about 5 GeV, in order to coincide with the oscillation maximum for this baseline.This larger beam energy brings in significant matter effects in the oscillation probability giving P2O a clear edge over the other next-generation experiments in measuring the neutrino mass hierarchy.We will see that even with just one year of running of this experiment, one would measure the neutrino mass hierarchy at more than 3.5σ in the worst possible scenario and greater than 5σ in the best possible case.This extremely high sensitivity of P2O to neutrino mass hierarchy comes also from the megatonscale mass of the ORCA detector as well as the fact that the 2588 km baseline is very close to being bi-magic [22,23].
In this paper we make a detailed study on the optimization of the experimental set-up for measuring the three unknowns in neutrino physics mentioned above.We will look into how the detector systematics and detector backgrounds affect the CP violation and octant of θ 23 sensitivities of this experiment vis-a-vis the number of years of running of the experiment.We find that the hierarchy sensitivity of P2O, especially for NH true, is so high that any deterioration coming from uncontrolled backgrounds and/or systematic uncertainties makes no practical difference and one is ensured a sure shot discovery of the neutrino mass hierarchy within a very short time.The impact of systematics and backgrounds show up when the hierarchy is inverted, nonetheless a clear discovery of mass hierarchy is guaranteed, albeit with slightly higher run time than needed for the NH true case.We will show that the time needed for hierarchy discovery at P2O even with IH true will be significantly shorter than that needed at other competing experiments.On the other hand, the CP violation and octant sensitivity of P2O is seen to be weaker than the corresponding expected sensitivity at competing long-baseline experiments.We will show that these sensitivities can get improved mildly to severely with changes in systematic uncertainties and background.Also, for all cases, we study the impact of adding the antineutrino run to the projected sensitivity at P2O.Note that the P2O collaboration in their first results [19] have shown the sensitivity to hierarchy and CP violation using 3 years run in the neutrino channel only.We find that a small antineutrino run fraction helps in getting rid of parameter degeneracies and helps in improving the expected sensitivity of CP violation and octant of θ 23 .We will quantify each of these aspects in what follows.
The rest of the paper is organised in the following way.In section 2 we spell out our experimental and simulation details.In section 3 we present the main results of our paper assuming NH to be true.In section 4 we present our main findings on what happens when the true hierarchy is inverted instead of normal.Finally in section 5 we compare the sensitivity of the P2O experiment with the other future long-baseline experiments.We conclude in section 6.We also add an appendix to point out an interesting feature about the role of mis-id background in the octant sensitivity.

Experimental and Simulation Details
To simulate the P2O experiment we have taken the experimental configuration as given in [19].As mentioned above the U-70 accelerator located in Protvino accelerator complex 100 km south of Moscow, will be upgraded to produce 70 GeV proton beam with a beam power of 450 KW to deliver 4 × 10 20 protons on target (pot) per year.The neutrinos produced in this accelerator will be detected at ORCA at a distance of 2588 km.At this baseline the first oscillation maxima occurs at 5 GeV in vacuum.We have obtained both the neutrino and antineutrino fluxes from the P2O collaboration and implemented them in the GLoBES [24] software to calculate the events.
The two main event topologies in ORCA are track and cascade.The tracks are almost always produced by ν µ charged current interactions while cascades come from ν e charged current interactions, ν τ charged current interactions as well as neutral current interactions of neutrinos.In our simulations we have simulated track and cascade events for both neutrino and antineutrino  channels by suitably modifying GLoBES.A brief discussion on the backgrounds is in order.Since the tracks come from ν µ charged current interactions alone, the only backgrounds for the disappearance channel come from neutral current backgrounds and mis-id.For appearance channel, backgrounds come from ν τ charged current interactions and neutral current interactions as well as mis-id.We take the numbers for tau and neutral current background for the appearance channel from the P2O proposal [19].The mis-id in appearance channel is varied for optimisation as will be discussed below and throughout the paper.
First taking the same number of energy bins as given in [19], we match the number of events corresponding to three years run in the neutrino mode by introducing energy dependent efficiencies.These efficiencies ensure that the energy dependence of the effective mass is taken into account appropriately.The event spectrum we obtain for NH is given in the left panel of Fig. 1.Then we generate events for IH which perfectly matches with the event spectrum as given in [19] (right panel of Fig. 1).The choice of neutrino oscillation parameters are same as in [19].After matching the events we next match with the χ 2 plots of [19].For this we have taken 20% mis-id background in the appearance channel in addition to the neutral current and tau background shown in Fig. 1.For systematics we have taken an overall normalization error of 5% for disappearance channel signal, 11% error for disappearance channel background and 6% error for appearance channel background.Following [19], there is no systematic uncertainty for appearance channel signal and also we have not considered any systematic error to incorporate shift in the energy scale.Note that ref. [19] does not give any information on antineutrinos, therefore we take the exact same values of the efficiencies, background and systematics for the antineutrino analysis.
In the following sections we will discuss the hierarchy, octant and CP sensitivity of the P2O experiment.As the present data hints the preference of NH over IH, we present our results for NH in detail in the next section.After that we will give the results for IH for some selective values of parameters.

Results for NH
In this section we discuss the capability of the P2O experiment to discover the unknowns in the three flavour standard neutrino oscillations namely neutrino mass hierarchy, octant of the mixing angle θ 23 and measurement of the Dirac type phase δ CP .Our aim of this study will be to find out the optimal configuration of the P2O experiment to discover the above mentioned parameters by considering various combinations of antineutrino exposure, systematic errors and backgrounds.For systematic uncertainty, we only vary the error associated with appearance channel signal and the only background we vary is the mis-id in the appearance channel.This is because in the P2O collaboration study, the systematic error associated with the appearance channel is taken as zero and also the percentage of the mis-id background is not presented.In our χ 2 analysis we have kept fixed the parameters θ 12 = 33.4[25,26,27].

Hierarchy
The hierarchy sensitivity of an experiment is calculated by taking the correct hierarchy in the true spectrum and the wrong hierarchy in the test spectrum.First we study the effect of antineutrino run on the hierarchy sensitivity of the P2O experiment.In Fig. 2 we have plotted hierarchy χ 2 vs δ CP (true).The parameters θ 23 and δ CP has been marginalized in the test.The left/middle/right panel is for θ 23 (true) value of 42 • /45 • / 48 • .In these plots we have assumed a total run-time of six years and we have considered four different combinations of neutrino and antineutrino ratio.
In all the three panels we see that the hierarchy sensitivity is maximum at δ CP = −90 • and minimum at δ CP = +90 • .This is because of the well known hierarchy δ CP degeneracy [28,29].In the case of P2O, this degeneracy is lifted because of the large matter effect.But still the probability in NH corresponding to δ CP = −90 • (+90 • ) is furthest (closest) to the probability in the IH.This is true for both neutrino and antineutrino.To understand the role of antineutrinos we need to understand the behavior of octant degeneracy.It was shown in [30,31] that the main role of the antineutrino is to resolve the octant degeneracy to improve the CP and hierarchy sensitivity in the longbaseline experiments.Therefore, if the wrong hierarchy χ 2 occurs with the wrong octant, then addition of antineutrinos can improve the hierarchy χ 2 by removing the wrong octant solution.That is what is happening for θ 23 = 42 • (left panel).For 6+0, the hierarchy χ 2 occurs with the wrong octant and 5+1 gives better sensitivity than 6+0.In this panel we also note that further addition of antineutrinos decreases the sensitivity.From this we understand that only one year of antineutrino is sufficient to remove the octant degeneracy and further addition of antineutrino only decreases the statistics due its low cross section and smaller flux as compared to the neutrinos.The situation is slightly different for θ 23 = 48 • (right panel).At this true value of θ 23 the hierarchy χ 2 appears with the right octant and thus antineutrino should not help much.That is why we see that the sensitivity is best for 6+0, except few region of δ CP (true).Now let us discuss for θ 23 = 45 • where there is no octant degeneracy (middle panel).Here we see that at δ CP (true) = −90 • , 6+0 and 5+1 have similar sensitivity and with further addition of antineutrinos, sensitivity decreases.Whereas for δ CP (true) = 90 • , 5+1 gives the best sensitivity and the worst sensitivity comes for 3+3 and 6+0.
From these three panels we see that the minimum hierarchy sensitivity for six year running of the experiment is always greater than 10σ, irrespective of the antineutrino exposure.
Next we study the effect of background and systematics on hierarchy sensitivity.In Fig. 3, we have presented the hierarchy χ 2 vs systematic uncertainty for the four combinations of background.This we give just for one year neutrino exposure of the P2O experiment and for δ CP (true) = +90 • and θ 23 (true) = 42 • .As the χ 2 is minimum for this value of δ CP and NH true, this gives the most conservative configuration of the experiment.From this plot we understand that the sensitivity does not vary much with the systematic uncertainty.For all the four combinations of the background, hierarchy sensitivity falls only within 1σ when systematic is varied from 1% to 20%.On the other hand we observe that the sensitivity depends greatly on the amount of background.For 5% systematic error, the sensitivity goes from 5.5σ to 7.5σ when background decreases from 20% to 5%.However, it is very important to note from this plot that whatever be the systematic error or the background, P2O has hierarchy sensitivity always more than 5σ, even with one year neutrino run.This can be attributed to two facts: (i) huge matter effect enable P2O to have a very large sensitivity and (ii) the baseline for P2O is close to the bi-magic baseline [22,23] for which the hierarchy sensitivity gets enhanced at a particular energy.

Octant
Octant sensitivity of an experiment is calculated by taking the correct octant in the true spectrum and wrong octant in the test spectrum.We first study the effect of antineutrinos in the determination of the octant.In Fig. 4, we have presented octant sensitivity for different combination of neutrino and antineutrino ratio, taking the total run-time of six years.In the left and middle panel we have presented the results as a function of δ CP (true) and in the right panel we have given our results as a function of θ 23 (true).The left and middle panel are for θ 23 in the lower octant (θ 23 = 42 • ) and higher octant (θ 23 = 48 • ), respectively.In the right panel, true value of δ CP = −90 • which is the present best-fit value of this parameter.In all the panels θ 23 has been marginalized in the opposite octant and δ CP has been marginalized in its full range.Hierarchy is also marginalized.
To understand the role of antineutrinos in resolving octant degeneracy, first we have to understand how octant degeneracy occurs in neutrinos and antineutrinos.It has been shown in [32,29] that for the neutrino channel octant degeneracy occurs at (δ CP = −90 • , LO)  with (δ CP = +90 • , HO) and for the antineutrino channel octant degeneracy occurs at (δ CP = +90 • , LO) with (δ CP = −90 • , HO).This is the reason why a balanced run of antineutrino is always important to have significant octant sensitivity.The above discussion explains why for 42 • octant sensitivity is maximum for 6+0 at δ CP = +90 • and minimum for δ CP = −90 • (left panel).With the addition of antineutrino run the sensitivity for δ CP = +90 • decreases and sensitivity for δ CP = −90 • increases.From the plot we also realise that the best sensitivity is achieved for 5+1.For this exposure, the octant sensitivity of χ 2 = 4(5.5)can be obtained for δ CP = −90 • (+90 • ).For θ 23 = 48 • we notice that the sensitivity is maximum for 6+0 at δ CP = −90 • and decreases as antineutrino is added to the neutrino data (middle panel).Whereas for δ CP = +90 • all the combinations of the antineutrino run give almost equal sensitivity.Note that the sensitivity in the higher octant is smaller than the sensitivity in the lower octant.This is due to the fact that for the higher octant, the denominator in the χ 2 is higher than the denominator in the χ 2 for lower octant.Here the octant sensitivity is around χ 2 = 4(3.5)for δ CP = −90 • (+90 • ).The right panel shows octant sensitivity for different values of θ 23 for δ CP = −90 • .From the plot we see that up to θ 23 = 38 • in the lower octant, 6+0 gives the worst octant sensitivity and up to θ 23 = 42 • , 5+1 give the best octant sensitivity.For higher octant all the four combination give almost equal sensitivity.From this plot we conclude that with the current background and systematics, P2O can resolve octant at 3σ for θ 23 values except 40 • (39 • ) < θ 23 < 49 • for 3+3 (5+1) run.
From the above discussion we realize that 5+1 would be the best combination for P2O to determine the octant sensitivity for both LO and HO.But even for this best combination, a maximum χ 2 of 4 can be achieved at the present best-fit of δ CP and θ 23 which is −90 • and 42 • & 48 • .Next we study the effect of background and systematics in octant sensitivity with the neutrino to antineutrino ratio of 5:1.
In Fig. 5, we have presented the run-time to achieve a sensitivity of a certain confidence level as a function of background for different combination of systematic uncertainties.This we give for θ 23 = 42 • and δ CP = −90 • .From the figure we see that there is no effect of background and systematics to achieve 1σ sensitivity as the required run-time remains almost fixed to almost 1 year for all the values of systematics and background.To achieve 2σ sensitivity run-time keep increasing as we increase the systematics for a fix value of background.For the most optimistic case (i.e., 0% systematic error), the required run-time increases from 4.5 years to 7 years to achieve a 2σ octant sensitivity when the background increases from 5% to 20%.potential is defined as the capability to distinguish a value of δ CP from the CP conserving values of 0 • and 180 • .To study the role of antineutrinos, in Fig. 6, we have plotted sensitivities for four different combinations of neutrino to antineutrino ratio.The left/middle/right panel is for θ 23 = 42 • /45 • /48 • .In these figures we have marginalized over θ 23 and hierarchy in the test.The effect of octant degeneracy can be seen for (θ 23 , δ CP ) combination of (42 • , −90 • ) and (48 • , +90 • ) from the shape of the curves.This is because for the pure neutrino run (i.e., 6+0) the CPV χ 2 occurs in the wrong octant for (42 • , −90 • ) and (48 • , +90 • ).Therefore addition of antineutrino run is supposed to help in the sensitivity by removing the octant degeneracy.From the panel we understand that for (42 • , −90 • ), all the combinations of antineutrino run gives almost same sensitivity and for (48 • , +90 • ), the sensitivity keeps improving with the addition of antineutrino data.However from the shape of the curves it is also clear that even with the addition of antineutrino runs, the octant degeneracy is not completely removed.For the other two combinations i.e., (42 • , −90 • ) and (48 • , = 90 • ) we note that 6+0 and 5+1 give the best sensitivity, respectively.The middle panel shows the CPV sensitivity without any octant degeneracy.From this panel we note that addition of antineutrino run helps in improving the CPV sensitivity.For δ CP = −90 • , all the combinations of the antineutrino run gives similar sensitivity and for δ CP = +90 • , 6+0 provides the best sensitivity.From the discussion we can also conclude that the antineutrino run is important for CPV discovery and 5+1 will be the best option for P2O.It is also important to note that irrespective of the combination of the antineutrino run, the CPV discovery is always less than 3σ for all the three combinations of θ 23 .

First we discuss the CP violation (CPV) discovery potential of the P2O experiment. CP violation discovery
We next focus on the effect of background and systematics in the CPV sensitivity of P2O.In Fig. 7 we have plotted the time required to achieve a CPV sensitivity of a certain confidence level vs the background for different combination of the systematic uncertainty.This we have done for θ 23 = 42 • and δ CP = −90 • .The curves are for equal ratio of neutrino and antineutrino combination.From the plot we see that to achieve 1σ sensitivity, P2O requires around 1 year of running, irrespective of the value of systematic and background.The effect of systematic and background comes into the picture to achieve a sensitivity at a higher confidence level.To achieve a 2σ CPV discovery, P2O will require around 3.5 years if the background is 5% and 5.5 years if the background is 20%.This is true irrespective of the systematic error.From the figure we also note that the systematic uncertainty starts to play some role when P2O tries to achieve a CPV sensitivity of 3σ as the curves for different systematic errors tends to separate from each other.Here we observe that the required runtime of P2O is more than 10 years to achieve a 3σ CPV discovery if background is more than 7.5%.
At this point we want to stress the fact that although P2O will achieve a 5σ hierarchy sensitivity in less than 1 year, it can only achieve a 2σ CPV and  octant sensitivity in 8 years of run-time.As we mentioned earlier the hierarchy sensitivity at this baseline is enhanced due to larger matter effect and bi-magic property.But the longer baseline also causes the fluxes to fall significantly due to the 1/L 2 dependence.This was also the case for the LBNO proposal for the Pyhasalmi baseline of 2290 km [33,34,35,36,37,38].Therefore, to achieve a better octant and CP sensitivity, one needs more beam power from the accelerator and/or more running years.
Let us now turn to how precisely P2O will be able to measure a value of δ CP .To study this, in Fig. 8 we have plotted the CP resolution for each value of true δ CP for θ 23 (true) = 45 • .We define CP resolution by 0.5 × allowed range of δ CP values at 1 σ/360.In this figure we have marginalized over θ 23 and hierarchy in the test.This we have presented for four combination of antineutrino runs.From this figure we understand that the best CP resolution is achieved for the 5+1 combination.For this combination a δ CP can be measured within 40/28/27 degrees uncertainty for δ CP (true) = −90 • , 0 • / + 90 • .

Discussion for Sensitivity in IH
In this section we discuss the sensitivity of the P2O experiment in IH.In Fig. 9 we present the hierarchy sensitivity for θ 23 = 45 • .In the left panel, we have given the sensitivity vs δ CP (true) for a total run-time of six years.As for the case of NH, here also we have divided the run-time for four combination of neutrino and antineutrino ratio.Here we see that the maximum sensitivity appears at δ CP = −90 • and the minimum sensitivity occurs at δ CP = +90 • .This is due to the hierarchy-δ CP degeneracy which we have discussed earlier.From this figure we observe that the minimal antineutrino run re-  quired to obtain the best hierarchy sensitivity is 1 year for δ CP = −90 • and 2 years for δ CP = +90 • .However, irrespective of the antineutrino run, for 6 years of running the hierarchy sensitivity is always greater than 10σ for all the values of δ CP .In the right panel of Fig. 9, we have shown the variation of the hierarchy sensitivity with respect to background and systematics for a runtime of 1+0.This we do for δ CP = −90 • for which the sensitivity in IH is minimum.This will give the most conservative estimate.From this we note that the effect of systematics is more stronger in IH as compared to NH.This plot shows that to achieve a 5σ sensitivity, the systematic error can be allowed to increase from 9% to 13% if the background decreases from 20% to 5%.Next let us discuss the octant sensitivity of the P2O experiment in IH.The octant sensitivity of the P2O experiment for IH is very poor.We have checked that for a total run-time of six years, the octant sensitivity in pure neutrino run (i.e., 6+0) is negligible for both θ 23 = 42 • and 48 • .This is because of the fact the neutrino probability is smaller in IH for neutrinos as compared to NH.At both the above mentioned true values, the best octant sensitivity comes for 3+3 combination but the octant χ 2 does not rise above 3.
We have presented the results for CPV discovery potential of P2O taking different ratio of neutrino and antineutrino run for IH in Fig. 10 with a total run-time of 6 years taking θ 23 = 45 • .In the left panel we have given the CPV discovery sensitivity as a function of δ CP (true).From both the plot we see that antineutrino helps to improve the sensitivity and all the combination of antineutrino run give almost equal sensitivity.For δ CP = ±90 • , a sensitivity of more than 2σ is obtained.In the right panel of Fig. 10 we have given the required run-time to obtain a certain CPV discovery sensitivity as a function of background for different values of systematics.This we have done taking equal ratio of neutrinos and antineutrinos.The true value of δ CP is −90 • .Similar to the NH case, there is no effect of systematics and background to achieve a sensitivity of 1σ as it requires around 1 year for all the three curves.But unlike NH, the effect of systematics is prominent in IH to achieve a sensitivity of 2σ.For the most conservative case (i.e., 10% systematic uncertainty), time required to gain 2σ sensitivity rises from 4 years to 6.5 years when background increases from 5% to 20%.It is also possible to achieve a 3σ sensitivity within 10 year of running if the background is less than 7.5% and systematics in appearance signal channel is absent.
Finally, in Fig. 11 we have given the CP resolution capability in IH for θ 23 = 45 • taking different neutrino and antineutrino combinations for a total run-time of six years.From the figure we see that the best sensitivity is obtained for 3+3 combination and a value of δ CP (true) = −90 • , 0 • and +90 • can be measured within 30%

Comparison of P2O with Other Future Long-baseline Experiments
In this section we compare the sensitivity of the P2O experiment with the other future long-baseline experiments which are DUNE, T2HK and T2HKK.
In Fig. 12 we compare the hierarchy, octant and CP violation sensitivity of the above mentioned experiments in the left, middle and right panel, respectively, for NH.We have taken a total run time of 10 years for all the four experiments.As described in the letter of intents, for DUNE (T2HK/T2HKK) we have taken the 1:1 (1:3) ratio for neutrino and antineutrino run.For P2O we have taken the most optimized 8+2 configuration with two choices of background i.e., 20% (blue curve) and 5% (black curve).The choices of true values are mentioned in the figures.For hierarchy sensitivity we see that P2O wins over all the other experiments even with 20% background.But for octant, P2O has the worst sensitivity among the given experiments for 20% background.However with 5% background, the sensitivity of P2O is comparable to T2HK, for θ 23 values closer to maximal.For CPV, P2O and T2HK have comparable sensitivity for δ CP = +90 • for 20% background in P2O, while P2O is better than T2HK for 5% background.On the other hand, for δ CP = −90 • , P2O has the worst sensitivity for both the choices of background.

Conclusion
There is a proposal (P2O) to upgrade the Protvino accelerator complex to produce a 70 GeV proton beam with a beam power of 450 kW and use it to produce and send a neutrino beam to the ORCA detector in the Mediterranean sea at a distance of 2588 km.The beam will be peaked at about 5 GeV to produce at oscillation maximum at ORCA.The preliminary sensitivity reach of this experiment to neutrino mass hierarchy and CP violation has been presented by the P2O collaboration for 3 years of running of the experiment in the neutrino channel.In this paper, we have performed a detailed optimisation study of P2O for all three neutrino physics parameters measurable at long-baseline experimentsneutrino mass hierarchy, CP violation and octant of θ 23 .The optimisation is done with respect to (i) neutrino vs antineutrino run-time, (ii) detector systematic uncertainties, (iii) total running time of the experiment and (iv) backgrounds coming from mis-id in the appearance channel.
We started by matching our simulated number of events as well a χ 2 with the results presented by the P2O collaboration [19] for 3 years run of the experiment in the neutrino channel and for NH true.We next calculated the corresponding events for the antineutrinos using fluxes obtained from the P2O collaboration, using the same simulation parameters as for the neutrino channel.We assumed a total run time of 6 years for the experiment and varied the neutrino vs antineutrino run time ratio for mass hierarchy, CP violation and octant of θ 23 .We showed that for mass hierarchy measurement, the sensitivity of P2O is always very high for both hierarchies.While the sensitivity does change with neutrino-antineutrino fraction, systematics and backgrounds, especially for NH true.The significance with which mass hierarchy can be measured remains high for both NH and IH true.
The situation with CP violation and octant of θ 23 determination is more complicated for P2O.We found that the significance of CP violation measurement for the baseline design of the experiment is not as high as that for DUNE and T2HK.For the current best-fit of δ CP = −90 • and θ 23 (true)= 42 • , it can be measured at 2σ for 5+1 years of running of the experiment with 20% mis-id background.We showed that this could be increased to 3σ if the background is reduced to to 5% and run time increased to 8+2 years.For octant the reach of P2O baseline design is expected to be 2σ at θ 23 (true)= 42 • and δ CP = −90 • with a background of 20%.We showed that if the mis-id is controlled within 5%, then octant can be measured with χ 2 = 6 for 8+2 year run of the experiment.Finally, we made a comparative study of P2O along with DUNE, T2HK and T2HKK and showed that P2O is expected to give the best sensitivity to neutrino mass hierarchy owing to its long baseline which is close to being bi-magic.In terms of CP violation and octant of θ 23 discovery, even though P2O baseline configuration appears to have a weaker sensitivity compared to DUNE, T2HK and T2HKK, we showed what is needed in order for P2O to be competitive with other long-baseline proposals.
In conclusion, P2O has the best sensitivity to neutrino mass hierarchy.For octant of θ 23 and CP violation discovery it can be competitive if the experimental collaboration is able to control mis-id and systematics, and run the experiment for 8+2 years in neutrino and antineutrino mode.where 'sg' is signal and 'bg' is background.Now, as the mis-id background depends on the survival probability of ν µ , it is a function of the oscillation parameters.Therefore, unlike oscillation independent backgrounds like the neutral current background, the cancellation of the mis-id background does not happen in the numerator.As in this case the mis-id background has octant sensitivity coming from large matter effect, this sensitivity can add up with the signal sensitivity giving a higher octant sensitivity.We have checked that this does not happen for hierarchy or δ CP sensitivity.

Fig. 2
Fig. 2 Hierarchy sensitivity in NH for different combinations of neutrino and antineutrino ratio.

Fig. 3
Fig. 3 Effect of background and systematics in hierarchy sensitivity for NH.

Fig. 4 Fig. 5
Fig. 4 Octant sensitivity in NH for different combinations of neutrino and antineutrino

Fig. 6
Fig.6CPV discovery sensitivity vs δ CP (true) for different combinations for neutrino and antineutrino in NH.

Fig. 7
Fig. 7 Effect of background and systematics for CPV discovery in NH.

Fig. 9
Fig. 9 Hierarchy sensitivity for different combinations for neutrino and antineutrino in IH is shown in the left panel.The right panel shows the impact of systematics and backgrounds on the hierarchy sensitivity in IH.

Fig. 10
Fig. 10 The left panel shows the CPV sensitivity as a function of δ CP (true) in IH.The right panel shows the impact of systematics and backgrounds on the CPV sensitivity in IH.

Fig. 11
Fig. 11 CP resolution sensitivity in IH at a function of δ CP (true).