Non-standard interactions versus planet-scale neutrino oscillations
NNon-standard interactions versus planet-scale neutrino oscillations
Wei-Jie Feng, ∗ Jian Tang, † Tse-Chun Wang, ‡ and Yi-Xing Zhou § School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
Abstract
The low-energy threshold and the large detector size of Precision IceCube Next Generation Upgrade (PINGU) can make thestudy on neutrino oscillations with a planet-scale baseline possible. In this task, we consider the configuration that neutrinosare produced at CERN and detected in the PINGU detector, as a benchmark. We discuss its sensitivity of measuring the sizeof non-standard interactions (NSIs) in matter, which can be described by the parameter (cid:15) αβ ( α and β are flavors of neutrinos).We find that the CERN-PINGU configuration improves ˜ (cid:15) µµ ≡ (cid:15) µµ − (cid:15) ττ and (cid:15) µτ significantly compared to the next-generationaccelerator neutrino experiments. Most of degeneracy problems in the precision measurements can be resolved, except theone for ˜ (cid:15) µµ ∼ − . . Moreover, we point out that this configuration can also be used to detect the CP violation brought byNSIs. Finally, we compare the physics potential in this configuration to that for DUNE, T2HK and P2O, and find that theCERN-PINGU configuration can significantly improve the sensitivity to NSIs. I. INTRODUCTION
Since confirming this phenomenon of neutrino oscilla-tions in [1], we nearly complete the knowledge of thisflavour-changing behaviour, which can be described bysix oscillation parameters including three mixing angles θ , θ and θ , two mass-square differences ∆ m and ∆ m , and one Dirac CP violating phase δ with solar,atmospheric, accelerator and reactor neutrino data [2–4].The rest of problems in neutrino oscillations are if θ islarger or smaller than ◦ , which the sign of ∆ m is, ifCP is violated and what its value δ is. These problemsare expected to be resolved in the next-generation neu-trino oscillation experiments, e.g. DUNE, T2HK, JUNO,etc. The neutrino oscillation reflects the fact that neu-trinos are massive, which conflicts with the massless-neutrino prediction in the standard model (SM). Thisphenomenon is obviously a key to the door of physics be-yond SM (BSM), and reveals that SM is not a completetheory.Far away in Antarctica, Precision IceCube Next Gen-eration Upgrade (PINGU), an extension of the IceCubeNeutrino Observatory, was proposed. In this proposal,the lower energy threshold and the -million-ton detec-tor are sketched [5]. Goals of PINGU are to detect at-mospheric neutrinos [6, 7], supernova neutrinos [8] andthe indirect signal of dark matter (by detecting the selfannihilation of WIMP-like dark matter [9]). Moreover,the configuration that PINGU receives neutrino beamsfrom accelerators in the northern hemisphere inspired byCERN to Frejus and J-PARC to HyperKamiokande hasbeen considered and discussed [10].As we believe that SM is not a complete theory, ef-fects from some exotic interactions are widely discussed,for example, non-standard interactions (NSIs) [11–15],neutrino decays [16–18], nonunitarity [19, 20]. NSIs are ∗ [email protected] † [email protected] ‡ [email protected] § [email protected] interactions evolving at least one neutrinos and other SMfermions by mediating BSM particles [21, 22]. NSIs maytake place in three different parts of neutrino oscillations:at the source, at the detector, and in matter (or NSI mat-ter effects). We describe the size of NSIs by the parame-ter (cid:15) ff (cid:48) αβ , which is the fraction of the strength of couplingfor the NSI to the Fermi constant ( ν α + f → ν β + f (cid:48) ). Forthose taking place in matter, we use the notation (cid:15) αβ ,as in these interactions f = f (cid:48) . In recent studies, theLarge-Mixing-Angle dark solution (LMA-Dark solution)for NSIs allows that NSI matter effects have a strongimpact on neutrino oscillations. This solution predicts (cid:15) ee (cid:39) − [12, 14]. One of upcoming long baseline acceler-ator neutrino experiments Deep Underground NeutrinoExperiment (DUNE) [23, 24] is expected to have somesensitivity to NSIs in matter. Impacts of NSI matter ef-fects on the precision measurement of oscillation param-eters and the expected constraints on NSI parameters forDUNE are widely studied [25–38]. The combined resultsfor sin θ and NSIs by Daya Bay and T2K experi-ments were given in Ref. [39]. The current global fits canprovide constraints at C.L. on NSI parameters withCOHERENT data [14]: − . (cid:54) ε uee (cid:54) . − . (cid:54) ε uµµ (cid:54) . − . (cid:54) ε uττ (cid:54) . − . (cid:54) ε ueµ (cid:54) . − . (cid:54) ε ueτ (cid:54) . − . (cid:54) ε uµτ (cid:54) . . Some possible theoretical models are also proposed torealize sizeable NSIs in matter [40–44].NSIs in matter can be detected by accelerator neu-trino oscillation experiments with non-negligible mattereffects. In this paper, we study the planet-scale neu-trino oscillations to measure the size of NSI matter ef-fects, by revisiting the configuration of sending a neu-trino beam from an accelerator facility in the northernhemisphere such as CERN to a detector in the southpole like PINGU. The CERN-PINGU configuration has1 a r X i v : . [ h e p - ph ] N ov baseline of km. The difference of this config-uration from observatories of atmospheric neutrinos isabout neutrino fluxes, which come from a specific di-rection with the well-controlled timing structure in theCERN-PINGU configuration. As a result, smaller sys-tematic errors and the higher ratio of signals over back-grounds are expected. This super long baseline has fouradvantages for (cid:15) αβ measurements as follows.1. The neutrino energy ( GeV - GeV) is higherthan current and future neutrino oscillation exper-iments. Therefore, larger matter effects are ex-pected, and the detection of ν τ and ¯ ν τ is achiev-able.2. As neutrinos propagate in a longer baseline, NSImatter effects are expected to be more important.With the help of this 11810 km baseline, the valueof NSI parameters can be measured with higheraccuracy.3. If neutrinos propagate through the core with alarger matter density, the effect of NSI in matterwill be greater. As a result, the matter density,which can reach g/cm , makes this configura-tion special and promising for the measurement of (cid:15) αβ .4. It is necessary to mention that though the statis-tics is lower as the baseline is much longer, thisdrawback can be compensated by the million-tondetector as PINGU.This paper is arranged as follows. We will firstlydemonstrate the neutrino oscillation probability with NSImatter effects, before presenting the simulation details.In the following, we will show the constraints on (cid:15) αβ andconstraint contours between any two of NSI parametersfor the CERN-PINGU configuration. Moreover, we willdiscuss how this configuration can exclude the CP con-served scenario once the phase of (cid:15) αβ is non-zero ( α (cid:54) = β ).Finally, we will summarize our results, and provide ourconclusion. II. NEUTRINO OSCILLATION PHYSICS WITHNSIS
In this section, we briefly introduce how neutrino os-cillation probabilities are modified by NSIs in matter.These new interactions are neutral-current-like interac-tions ν α + f → ν β + f , and can be described by theoperator, [21, 45, 46],: L NSI = − √ G F ε fαβ ( ν α γ µ P L ν β ) (cid:0) f γ µ P C f (cid:48) (cid:1) (1)where G F is the Fermi constant. We note that the totalsize of NSI matter effects is the sum of those for NSIs withelectrons, neutrons and protons: (cid:15) αβ ≡ (cid:15) eαβ + (cid:15) nαβ + (cid:15) pαβ . Neutrino oscillations are governed by coherent evolu-tion of quantum statesi dd t ν e ν µ ν τ = H ν e ν µ ν τ . (2)Explicitly, the evolution of the neutrino flavor state isdetermined by the Hamiltonian: H ν = H vac + H mat for ν,H ¯ ν = [ H vac − H mat ] ∗ for ¯ ν, (3)where H vac is the Hamiltonian in vacuum. H mat corre-sponds to the matter, and is written by H mat = √ G F N e (cid:15) ee (cid:15) eµ (cid:15) eτ (cid:15) ∗ eµ (cid:15) µµ (cid:15) µτ (cid:15) ∗ eτ (cid:15) ∗ µτ (cid:15) ττ (4)where N e is the number density of electron. The constantterm √ G F N e in the ee component refers to the standardmatter effect [21]. It is obvious in Eqs. (2) and (4) thatone of the diagonal terms can be absorbed by an overallphase in neutrino states. Therefore, we define ˜ (cid:15) ee ≡ (cid:15) ee − (cid:15) ττ and ˜ (cid:15) µµ ≡ (cid:15) µµ − (cid:15) ττ without a loss of generality. A. Analytical approximation
The main probabilities for the CERN-PINGU configu-ration to measure the effect of NSIs are via P ( ν µ → ν µ ) and P ( ν µ → ν e ) and their CP-conjugate channels, be-cause of the difficulty of the ν τ and ¯ ν τ detection. Taking ∆ m ∆ m ∼ | (cid:15) αβ | ∼ s as the first order of perturbation ξ ,the approximation equations for the probability, P ( ν µ → ν µ ) = P ( ν µ → ν µ ) + δP NSI ( ν µ → ν µ )= P ( ν µ → ν µ ) − A(cid:15) µτ cos φ µτ × (cid:18) sin θ L E sin 2∆ +4 sin 2 θ cos θ m sin ∆ (cid:19) + A ˜ (cid:15) µµ c s (cid:0) c − s (cid:1) × (cid:18) LE sin 2∆ − m sin ∆ (cid:19) + O ( ξ ) , (5)2 ( ν µ → ν e ) = P ( ν µ → ν e ) + δP NSI ( ν µ → ν e )= P ( ν µ → ν e ) + 8 s | (cid:15) eµ | s ∆ m ∆ m − A sin ∆ A × (cid:18) s A ∆ m − A cos( δ + φ eµ ) sin ∆ A + c sin AL E cos( δ + φ eµ − ∆ ) (cid:19) + 8 s | (cid:15) eτ | c s ∆ m ∆ m − A sin ∆ A × (cid:18) A ∆ m − A cos( δ + φ eτ ) sin ∆ A − sin AL E cos( δ + φ eτ − ∆ ) (cid:19) + O ( ξ ) , (6)where P ( ν µ → ν µ ) and P ( ν µ → ν e ) are the probabilityfor ν µ → ν µ and ν µ → ν e channels without NSIs, respec-tively. And the notations ∆ and ∆ A are defined as ∆ ≡ ∆ m L E , and ∆ m A ≡ ∆ m − A E × L, (7)with A ≡ √ G F N e E . For antineutrino modes, the fac-tors A and δ are replaced by − A and − δ , respectively.These equations are consistent with Ref. [47, 48]. Theimpact of NSIs is proportional to A . As a result, theincrease of matter density enhances the measurement ca-pacity of NSIs. In the configuration of CERN-PINGU,the matter density can reach up to g/cm , which isroughly three-time larger than the average matte den-sity for DUNE ( ∼ g/cm ). Moreover, we notice that in P ( ν µ → ν µ ) , one term for (cid:15) µτ and ˜ (cid:15) µµ are proportional to L , of which for the CERN-PINGU configuration is aboutnine-time longer than the baseline for DUNE km.We can expect the larger improvement in the measure-ment for these two NSI parameters from DUNE by theCERN-PINGU configuration. The same dependence on L is also seen for (cid:15) eµ and (cid:15) eτ in the appearance channel.However, they are higher order terms than ˜ (cid:15) µµ and (cid:15) µτ .The impact of φ eµ or φ eτ on P ( ν µ → ν e ) depends onthe value of δ and ∆ . This dependence is not seen for φ µτ in P ( ν µ → ν µ ) . As a result, the impact of δ and ∆ m is larger in the measurement of φ eµ or φ eτ . Also, (cid:15) eµ and (cid:15) eτ are the higher order than (cid:15) µτ . Therefore, wecan expect it is easier to detect the CP violation by φ µτ ,and even measure its size.To sum up, we expect that the NSI measurement bythe CERN-PINGU configuration can be better than whatDUNE can achieve, because of the larger matter den-sity. Though the matter density for this configuration isnot overwhelmingly larger than that for DUNE. But thenine-time longer baseline can largely improve the mea-surement for (cid:15) eτ and ˜ (cid:15) µµ by the disappearance channels. B. Probabilities by numerical calculations / E [ km / GeV ] P ( ν μ -> ν e ) / E [ km / GeV ] P ( ν μ -> ν e ) Std. Osc. ϵ ee = | ϵ e μ |= | ϵ e τ |= ϵ μμ = | ϵ μτ |= / E [ km / GeV ] P ( ν μ -> ν μ ) / E [ km / GeV ] P ( ν μ -> ν μ ) / E [ km / GeV ] P ( ν μ -> ν τ ) / E [ km / GeV ] P ( ν μ -> ν τ ) Figure 1. The neutrino oscillation probabilities P ( ν µ → ν e ) (upper-left), P (¯ ν µ → ¯ ν e ) (upper-right), P ( ν µ → ν µ ) (central-left), P (¯ ν µ → ¯ ν µ ) (central-right), P ( ν µ → ν τ ) (lower-left),and P (¯ ν µ → ¯ ν τ ) (lower-right) in the case with standard mat-ter effects and in the case with nonzeoro (cid:15) αβ . The probabili-ties are shown as functions of L/E [km/GeV] in the range of < E/ GeV < with the baseline of km. The valuesare used according to the σ uncertainty of the current globalfit result [14]. All phases are set to be . Fig. 1 shows probabilities in each of channels in thecase only including standard matter effects, and for thosewith a non-zero (cid:15) αβ , of which the value is used accordingto the σ bound of the current global fit result [14]. Theseprobabilities are shown as functions of L/E [km/GeV] inthe range of neutrino energy ( GeV - GeV) with thebaseline of km. We obtain that the behavior ofprobabilities for non-zero ˜ (cid:15) µµ or | (cid:15) µτ | in some channelsis very different from that without NSI matter effects.For example, when L/E = 2700 [km / GeV], P ( ν µ → ν e ) is about . in the case with non-zero | (cid:15) µτ | , while it isaround . for the standard case. We also see that theprobability of the ¯ ν µ disappearance channel approachesthe maximum at L/E = 2500 [km / GeV] in the non-zerocase of ˜ (cid:15) µµ , while this probability is around zero in theframework of standard neutrino oscillations.The probabilities with possible values of φ αβ are shownin Fig. 2. We vary each phase φ αβ from − ◦ to ◦ ,and fix the value of | (cid:15) αβ | at . . Two probabilities P ( ν µ → ν e ) and P ( ν µ → ν µ ) are shown, because eventsin the other channels are less than these two. We findthe variation of the probability is the most dramatic for φ µτ . What follows is that for φ eτ , while the smallest oneis for φ eµ . We see the same result in the other channels.3
00 1000 1500 2000 2500 3000 3500 40000.00.20.40.60.81.0 L / E [ km / GeV ] P ( ν μ -> ν e ) Std. Osc. ϕ em Band 500 1000 1500 2000 2500 3000 3500 40000.00.20.40.60.81.0 L / E [ km / GeV ] P ( ν μ -> ν μ ) Std. Osc. ϕ em Band500 1000 1500 2000 2500 3000 3500 40000.00.20.40.60.81.0 L / E [ km / GeV ] P ( ν μ -> ν e ) Std. Osc. ϕ e τ Band 500 1000 1500 2000 2500 3000 3500 40000.00.20.40.60.81.0 L / E [ km / GeV ] P ( ν μ -> ν μ ) Std. Osc. ϕ e τ Band500 1000 1500 2000 2500 3000 3500 40000.00.20.40.60.81.0 L / E [ km / GeV ] P ( ν μ -> ν e ) Std. Osc. ϕ μτ Band 500 1000 1500 2000 2500 3000 3500 40000.00.20.40.60.81.0 L / E [ km / GeV ] P ( ν μ -> ν μ ) Std. Osc. ϕ μτ Band
Figure 2. The neutrino oscillation probabilities P ( ν µ → ν e ) (left panels), P ( ν µ → ν µ ) (right panels) for phases φ eµ (pink), φ eτ (light blue) and φ µτ (light-magenta) varying over ( − ◦ , ◦ ] . For the band with non-zero φ αβ , the absolutevalue | (cid:15) αβ | is fixed at . . The probabilities are shown asfunctions of L/E [km/GeV] in the range of < E/ GeV < with the baseline of km. C. The θ - ˜ (cid:15) µµ degeneracy There is a degeneracy between θ and ˜ (cid:15) µµ . This de-generacy can be easier to be understood by further taking δθ ≡ θ − ◦ as a perturbation at the first order O ( ξ ) .For the disappearance channel, P ( ν µ → ν µ ) = P ( ν µ → ν µ ) − | (cid:15) µτ | cos φ µτ AL E sin 2∆ − δθ ˜ (cid:15) µµ A × (cid:18) LE sin 2∆ − m sin ∆ (cid:19) + O ( ξ ) (8)This is obvious that there is a degeneracy between δθ and ˜ (cid:15) µµ . In our work, δθ ∼ . for the true value θ = 49 . ◦ . This degeneracy has also been studied inRef. [25, 48–51].The degeneracy between ˜ (cid:15) ee and (cid:15) ττ that is from thehigher order terms has been also studied in Ref. [25, 52]. III. SIMULATION DETAILS
We adopt General Long Baseline Experiment Simula-tor [53, 54] with the PINGU simulation package.For the production, we assume µ decays driving the Table I. Disappearance and appearance channels consideredin this experiment.Disappearance channels appearance channels ν µ → ν µ ν µ → ν e ¯ ν µ → ¯ ν e ¯ ν µ → ¯ ν µ ν µ → ν τ ¯ ν µ → ¯ ν τ production of neutrinos: π − → µ − + ν µ , (9) π + → µ + + ¯ ν µ . (10)We set the run time of years for neutrino and antineu-trino modes (total run time is years) with 1 × pro-tons on target (POTs) per year. The energy of protonsis assumed 120 GeV and the power is 708 kW.To include NSI matter effects, we adopt the GLoBESextension package mentioned in Refs. [55–58]. We adoptthe PREM onion shell model of the earth for the matterdensity profile [59, 60], which is shown in Appendix A.The matter density can reach 11 g / cm .All oscillation channels are listed in Table I. We con-sider the intrinsic ν e and ¯ ν e backgrounds in the beamand the atmospheric neutrino backgrounds. We note thatWater Cherenkov neutrino detector cannot make a dis-tinction between neutrinos and antineutrinos. Therefore,for the electron-flavor channels, we analyse the combina-tion of ν e and ¯ ν e spectra. Because of the difficulty of ν τ and ¯ ν τ detection, we adopt a relative conserved assump-tion for detection efficiency for ν τ and ¯ ν τ .The expected spectra are shown in Fig. 3. We comparethe case with standard matter effects to that in vacuum,for demonstrating the advantage of the CERN-PINGUconfiguration to collect matter effects through such a longbaseline km. Assumed the normal mass ordering,events are much less in the ¯ ν mode. We see that mattereffects make great impacts on the spectra in the ν e ap-pearance and ν µ and ¯ ν µ disappearance channels for thelower neutrino energy.Values used for oscillation and NSI parameters throughthis paper are listed in Table II. These values are takenfrom current global-fit results [2, 14]. The normal massordering is assumed. We neglect NSIs at the source anddetector, and marginalise over all parameters, includingstandard oscillation parameters, the matter density andeight parameters for NSIs in matter ( (cid:15) ττ is subtractedby an overall phase of neutrino states) unless we showedthem in the plot. IV. RESULTS
In this section, our simulation results will be presented.In Sec. IV A, we will firstly show the expected constraintson (cid:15) αβ for the CERN-PINGU configuration. In the fol-lowing section, we will discuss the sensitivity of CPV in4 td. Matter EffectsVaccum Osc. / GeV N ( ν μ -> ν e ) Std. Matter EffectsVaccum Osc. / GeV N ( ν μ -> ν e ) Std. Matter EffectsVaccum Osc. / GeV N ( ν μ -> ν μ ) Std. Matter EffectsVaccum Osc. / GeV N ( ν μ -> ν μ ) Std. Matter EffectsVaccum Osc. / GeV N ( ν μ -> ν τ ) Std. Matter EffectsVaccum Osc. / GeV N ( ν μ -> ν τ ) Figure 3. The spectra for P ( ν µ → ν e ) (upper-left), P (¯ ν µ → ¯ ν e ) (upper-right), P ( ν µ → ν µ ) (central-left), P (¯ ν µ → ¯ ν µ ) (central-right), P ( ν µ → ν τ ) (lower-left), and P (¯ ν µ → ¯ ν τ ) (lower-right) with (purple) and without (orange) the stan-dard matter effects. The ν τ and ¯ ν τ spectra shown here areoptimistic without considering the detection difficulty.Table II. The central value and the width of the prior for stan-dard neutrino oscillation and NSI parameters used throughoutour simulation. We note that the central values are as sameas the true values, except for the case in which the true val-ues are specified. These values are used according to currentglobal fit results [2, 14].parameter true/central value 1 σ width θ / ◦ θ / ◦ θ / ◦ ∆ m / − eV ∆ m / − eV δ CP / ◦
217 10% (cid:101) (cid:15) ee (cid:101) (cid:15) µµ | (cid:15) eµ | | (cid:15) eτ | | (cid:15) µτ | φ eµ φ eτ φ µτ NSIs. In more details, what will be studied further is howmuch the hypothesis φ αβ = 0 and π can be excluded bythis configuration, once CP is violated because of non-zero of φ αβ . A. Constraints on NSI parameters * ϵ ee ϵ μμ - - ϵ αα Δ χ ϵ αβ Δ χ ϵ e τ ϵ e μ ϵ μτ Figure 4. ∆ χ value against ˜ (cid:15) αα (left) and | (cid:15) αβ | (right). Thethree dashed lines represent the values at 68%, 90% and 95%C.L. The central values and priors of neutrino mixing param-eters are taken from Table II. The ∆ χ values against to each NSI parameter areshown in Fig. 4. The size of the σ uncertainty for ˜ (cid:15) ee is about . . For the µµ component, the σ error isabout − . < (cid:15) µµ < . . We find out a degeneracyaround ˜ (cid:15) µµ = − . with ∆ χ (cid:38) . For the off-diagonalterms, bounds at σ C.L. are at | (cid:15) eµ | ∼ . , | (cid:15) eτ | ∼ . ,and | (cid:15) µτ | ∼ . , respectively. We reach the conclusionthat constraints on ˜ (cid:15) µµ and | (cid:15) µτ | are better than the oth-ers, which is consistent with the conclusion of Secs. II Aand II B. We review the σ uncertainties in the currentglobal fit result, which are shown in Table II. We seethe weak constraint at σ C.L. on the diagonal terms ˜ (cid:15) ee and ˜ (cid:15) µµ , whose sizes are almost O (1) . As for theoff-diagonal terms, we have better understandings in theglobal fit. The size of σ uncertainty is smaller than . ,especially the σ uncertainty for (cid:15) µτ is . . We findthat the CERN-PINGU configuration can improve sensi-tivities of NSIs at σ C.L. by at least of the currentglobal fit result. As the uncertainty for (cid:101) (cid:15) ee is greatly im-proved, we have the interest on the exclusion ability ofthe LMA-dark solution. Though the result is not shownhere, we have checked that the LMA-dark solution canbe excluded by more than σ C.L., without any prior for θ and (cid:15) ee .In Fig. 5, we show the allowed region at , , confidence level (C.L.) on the projected plan spanned bytwo of NSI parameters. Though we do not see strong cor-relations in these results, a degeneracy for ˜ (cid:15) µµ ∼ − . can be seen for contours of and C.L. As men-tioned in Sec. II C, this degeneracy is caused with themixing angle θ . Mentioned in Ref. [25], this degener-acy can be removed by including T2HK data. Obviously,the degeneracy between ˜ (cid:15) ee and (cid:15) τe and the one around ˜ (cid:15) µµ = 0 . for DUNE, are excluded.In Fig. 6, we present allowed regions on the planespanned by the absolute value | (cid:15) αβ | and the phase φ αβ for off-diagonal elements (cid:15) eµ , (cid:15) eτ , and (cid:15) µτ at , and C.L.. We see a strong correlation between theabsolute value and the phase in these three panels. Forthe hypothesis with φ αβ near ± ◦ , the bound on theabsolute value | (cid:15) αβ | is the worst. This behavior also ap-plies to all off-diagonal elements. (cid:15) αβ will be improved5 igure 5. The allowed regions on the plane spanned by two of NSI parameters. The central values and priors are taken fromTable II. All parameters are marginalized except those shown in each panel. - - - | ϵ e μ | ϕ e μ / ° C u rr en t B ounda t % C . L . - - - | ϵ e τ | ϕ e τ / ° C u rr en t B ounda t % C . L . - - - | ϵ μτ | ϕ μ τ / ° C u rr en t B ounda t % C . L . % C.L.90 % C.L.95 % C.L.
Figure 6. The allowed region on the plane spanned by the absolute value | (cid:15) αβ | and the phase φ αβ for off-diagonal elements (cid:15) eµ (left), (cid:15) eτ (middle), and (cid:15) µτ (right) at 68% (red), (blue) and (green) C.L.. All parameters are marginalized overexcept those shown in each panel. by more than an order of magnitude. Compared with sensitivities of NSIs at DUNE, our proposal will improve6esults by at least a factor of three. Of course, the phaseof NSI parameters will play an important role here. B. CP violations of NSI
We further discuss how the CERN-PINGU configura-tion can exclude the CP-conserved scenario where φ αβ isneither nor ◦ . We study the CPV sensitivity, whichis defined ∆ χ CP ( φ trueαβ ) ≡ min { ∆ χ ( φ αβ = 0) , ∆ χ ( φ αβ = π ) } , (11)where φ trueαβ is the true value for φ αβ , and ∆ χ ( φ αβ = 0) and ∆ χ ( φ αβ = 180 ◦ ) are the ∆ χ value for the hypothe-sis φ αβ = 0 and ◦ respectively. This definition is sameas how we study the sensitivity of CP violation where δ CP is not or ◦ . - - -
50 0 50 100 150012345 ϕ αβ /° Δ χ C P ϕ e μ ϕ e τ ϕ μτ | ϵ αβ |= | ϵ αβ |= Figure 7. The ∆ χ CP value against to the phase for the eµ (purple), eτ (green), and µτ (orange) components. For thestudied component, the true absolute value is . (solid) and . (dashed), while the other NSIs are switched off. In Fig. 7, we study the value of ∆ χ CP for three phases: φ eµ , φ eτ and φ µτ in the range between − ◦ and ◦ .For ∆ χ CP ( φ αβ ) , we fix the absolute value of the othertwo off-diagonal terms at , as we focus on the CP vio-lation by one specific φ αβ . Studying ∆ χ CP ( φ αβ ) values,we set the true value of | (cid:15) αβ | to be . (solid) and . (dashed). We focus on the case with the absolute valuefixed at . . We see that the CPV sensitivity for φ µτ is the best. In about of possible φ µτ this configu-ration can exclude the CP-conserved scenario with thesignificance better than C.L.. ∆ χ CP ( φ eτ ) is slightlybetter than ∆ χ CP ( φ eµ ) . For ∆ χ CP ( φ eτ ) ( ∆ χ CP ( φ eµ ) )larger than the value for C.L., it covers ( )of all possible phases. With the absolute value of . ,the sensitivity is worse, especially for φ eµ and φ eτ , ofwhich ∆ χ CP is smaller than . . For (cid:15) µτ , phases withthe sensitivity larger than C.L. cover about ofall possible phases. We note that the result shown inFig. 7 is consistent with what we see in Fig. 2. Our sim-ulation result is based on the assumption that we focuson one specific off-diagonal element. Though not shownhere, we find that once we also marginalize over absolutevalues and phases of the other off-diagonal terms, thesensitivity is much worse.
C. Comparison with the other experiments
In Table III, we compare the CERN-PINGU configura-tion with the other future accelerator neutrino oscillationexperiments, DUNE, T2HK, and the Protvino-ORCA ex-periment (P2O), with the simulation details about theseconfiguration. For all of them, we use the PREM onionshell model of the earth for the matter density [59, 60],and include the prior that presents the constraint withthe global and COHERENCE [14]. Taking the samefluxes, effective masses, our ν -mode simulation for P2Oreproduces the event spectra in [62, 63]. However, be-cause the spectra for ¯ ν are not shown in this reference, weuse the same detection efficiency for ¯ ν same as those for ν . The other assumption for detection is used the sameas what we use for PINGU. We find that the CERN-PINGU configuration performs the best among all, andthat T2HK is the worst one to measure NSI parame-ters. The constraints of the CERN-PINGU configura-tion is smaller than DUNE by at least a factor of . .We need to point it out that for this result, DUNE re-quests0 more POTs than that for the CERN-PINGU con-figuration, by a factor of ∼ . The physics capability ofP2O to measure NSI parameters, is the closet one to theCERN-PINGU configuration. The measurements of | (cid:15) eµ | and | (cid:15) eτ | for the CERN-PINGU configuration are slightlybetter than those for P2O. The constraint of | (cid:15) µτ | by theCERN-PINGU configuration can be of the result byP2O. Finally, the measurement of the diagonal terms forthe CERN-PINGU configuration can be improved by oneorder of magnitude, than that for P2O. V. CONCLUSION
With the interest on the planet-scale neutrino oscil-lations, we have considered the configuration that neu-trinos are generated at CERN, and detected in thePINGU detector (CERN-PINGU), as an extended studyof Ref. [10]. We have analyzed how such a configurationcan measure the size of non-standard interactions (NSIs)in matter. Three advantages of this configuration areas follows: (1) the energy range GeV- GeV enhanc-ing effects of NSIs, (2) the -km baseline cumulatingthese effects, and (3) the high matter density g/cm making the impact of NSIs on neutrino oscillations moresignificant.We have adopted the GLoBES library with an exten-sion package to simulate the CERN-PINGU configura-tion for the neutrino oscillation with NSI matter effects.We have studied the predicted uncertainty of NSI param-eters (cid:15) αβ . We have found that this configuration mea-sures ˜ (cid:15) µµ ≡ (cid:15) µµ − (cid:15) ττ and | (cid:15) µτ | better than the others.Most of degeneracy problems for DUNE on (cid:15) αβ measure-ments are resolved, except the one around ˜ (cid:15) µµ ∼ − . .We have investigated strong correlations between the ab-solute value and the phase for all off-diagonal terms,which can also be seen in the recent work with regards to7 able III. The σ allowed range of ˜ (cid:15) ee , ˜ (cid:15) µµ , | (cid:15) eµ | , | (cid:15) eτ | , and | (cid:15) µτ | for the CERN-PINGU configuration, DUNE, T2HK and P2Oexperiments. We also present the simulation details for each experiments.parameter CERN-PINGU DUNE [23] T2HK [61] P2O [62, 63] (cid:101) (cid:15) ee [ − . , . − . , . − . , . − . , . (cid:101) (cid:15) µµ [ − . , . − . , . − . , . − . , . | (cid:15) eµ | [0 , . , . . , . | (cid:15) eτ | [0 , . , . , . , . | (cid:15) µτ | [0 , . , . , . , . POTs × . × . × . × Energy range [GeV] -
20 0 . - . - . - Baseline [km]
Target material ice liquid argon pure water sea waterDetector size [kton] O (10 ) 40 186 O (10 ) NSI-parameter measurements for DUNE. As phases φ αβ play important roles, we have extended our study on thesensitivity of CP violation in NSIs. We have found thatwith the absolute value of . the sensitivity can be bet-ter than C.L. in the CERN - PINGU configuration,which shows this configuration can be used to measurethe CP violation caused by NSIs. Compared to other ex-periments, DUNE, T2HK, and P2O, we find that theCERN-PINGU configuration can significantly improvethe constraints of NSI parameters, except the measure-ments of (cid:15) eµ and (cid:15) eτ , for which the CERN-PINGU con-figuration performs slightly better than P2O.This study should not be limited at the CERN-PINGUconfiguration. Our conclusion on the improvement of (cid:15) αβ measurements could be applied for any experimentswith the neutrino source or detector that satisfies threerequirements: the proper energy range, a planet-scalebaseline, and the high matter density. As PINGU is un-der consideration, we can put more focus on looking forpossible sources, such as accelerator neutrinos producedby future proton drivers as super proton-proton collider(SPPC) [64], and the point source of astrophysical neu-trinos [65]. ACKNOWLEDGMENTS
This work is supported in part by the grant Na-tional Natural Science Fundation of China under GrantNo. 11505301 and No. 1188124024. JT appreciateICTP’s hospitality and discussions during the workshop PANE2018. Wei-Jie Feng and Yi-Xing Zhou are sup-ported in part by Innovation Training Program for bach-elor students at School of Physics in SYSU.
Appendix A: The matter density profile for CERN-PINGU
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