Probing Non-Standard Neutrino Physics at Neutrino Factory and T2KK
aa r X i v : . [ h e p - ph ] M a y PROBING NON-STANDARD NEUTRINO PHYSICS ATNEUTRINO FACTORY AND T2KK a HISAKAZU MINAKATA
Department of Physics, Tokyo Metropolitan University,1-1 Minami-Osawa, Hachioji, Tokyo 192-0397, Japan
E-mail: [email protected] discuss ways to explore non-standard interactions (NSI) which neutrinos maypossess by expressing them as effective four Fermi operators with coefficient ofthe order of ( M W /M NP ) ∼ − (10 − ) for energy scales of new physics as M NP ∼ L ∼ L ∼ θ − NSI confusion, and possibly also the two-phase confusion.The resultant sensitivities to off-diagonal NSI elements ε ’s are excellent, | ε eτ | ≃ a few × − and | ε eµ | ≃ a few × − . Our results suggest a new picture ofneutrino factory as a hunting machine for NSI while keeping its potential ofprecision measurement of lepton mixing parameters. Sensitivities to NSI byT2KK and the related settings are also discussed.
1. Introduction
This conference is sub-titled as “Ten Years after the Neutrino Oscillations”. Itrefers an unforgettable event which occurred in Neutrino 1998 conference in Takayama,Japan. The presentation by Kajita-san of atmospheric neutrino observation by Super-Kamiokande group 1 ) gave the first evidence for neutrino oscillation 2 ) , which receiveda long lasting ovation. But, as Koshiba-san pointed out in his presentation 3 ) , therewas a prehistory to that event. The Kamiokande II experiment b reported the deficitof muon-like events in its atmospheric neutrino observation in 1988 5 ) , the anomaly inratio of muon-type to electron-type neutrino events in 1992 6 ) , and then the anoma-lous zenith angle dependence of muon-type events in 1994 7 ) . In particular, the latteris strongly indicative of neutrino oscillation. The prehistory is reflected by the factthat the speaker in Neutrino 1998 represented not only Super-Kamiokande groupbut also Kamiokande II collaboration, as recollected in my slides in this conference8 ) . The anomaly was confirmed unambiguously by the high-statistics observation bySuper-Kamiokande experiment. In the context of three-flavor neutrino mixing, thisestablishes neutrino oscillation 9 ) in the 2-3 sector of the MNS matrix 10 ) . a Written version of a talk presented at the “Fourth International Workshop on Neutrino Oscil-lations in Venice” (NO-VE 2008), Venice, Italy, 15-18, April 2008. b In 1986 the Kamiokande detector started its phase II operation armed with lowered energythreshold to observe solar neutrinos, which soon blossomed as neutrino detection from SN1987A 4 ) . en years from Takayama declaration, as everybody knows, has been full of ex-citement. The solar neutrino experiment 11 ) , which was pioneered by Ray Davis 40years ago 12 ) , finally wrote its conclusion that the cause of the solar neutrino problemis not due to our ignorance of interior of the sun but to neutrino flavor transformation13 ) . The KamLAND reactor neutrino experiment 14 ) gave the first proof that neu-trino oscillation takes place also in the 1-2 sector of the MNS matrix with parametersappropriate for the solar neutrino deficit. By excluding various other mechanisms ofneutrino flavor transformation, it solved the solar neutrino problem. It is impressiveto see evidence for spectral distortion of reactor antineutrinos at more than 5 σ ) .The evidence for atmospheric neutrino oscillation was followed by confirmation bythe accelerator neutrino experiments, one in Japan 16 ) and the other in US 17 ) . Now,everybody agrees that neutrinos have masses and they oscillate.
2. A Bold Question
The important goal of the next generation accelerator 18 , ) and the reactor 20 , ) neutrino experiments is to measure θ . Fortunately, rich programs exist to serve forthis purpose. If θ is large enough we may be able to proceed to search for leptonicCP violation. If the experiments have sufficient sensitivities to the matter effect, theymay be able to determine the neutrino mass hierarchy.Suppose in some day all these goals are met and the MNS matrix elements aremeasured with precision comparable to those of CKM matrix 22 , ) . Then, one mightask; “Is this the final goal of neutrino experiments?” I argue that the answer is NO .Of course, my argument cannot be a solid one. Let me, however, mention it anyway. • Neutrinos are proved to be useful probe into physics beyond the StandardModel. Why should we believe that it is merely an accident? • Cosmological neutrinos will soon become one of our machineries for probingnature 24 ) . It is natural to suspect that they will bring us something entirelynew. • People already suspected several candidates; Non-standard interactions, quan-tum decoherence, Lorentz-invariance violation, etc.In this talk, I concentrate on non-standard interactions (NSI) 25 , , ) which mightbe possessed by neutrinos. c My presentation will be based on the two references30 , ) . There exist numerous references which devoted to this topics. Therefore, I c Of course, I do not say that the items above complete the all that should be in the list.For example, Majorana nature of neutrino must be demonstrated, so important to understandleptogenesis 28 ) , for example, as emphasized by Yoshimura-san in his talk 29 ) . ould like to apologize, before start, to those who are not mentioned in my reference.More bibliography is contained in these papers.
3. Non-Standard Interactions of Neutrinos
Suppose that there is a new physics at energy scale greater than ∼ M NP . Then, it is natural to expect that higher-dimentionaloperators would exist which gives rise to effective new interactions of neutrinos withmatter 32 , ) L NSIeff = − √ ε fPαβ G F ( ν α γ µ P L ν β ) ( f γ µ P f ) , (1)where G F is the Fermi constant, and f stands for the index running over fermionspecies in the earth, f = e, u, d , in which we follow 34 ) for notation. d P stands for aprojection operator and is either P L ≡ (1 − γ ) or P R ≡ (1 + γ ).To summarize its effects on neutrino propagation it is customary to introducethe ε parameters, which are defined as ε αβ ≡ P f,P n f n e ε fPαβ , where n f is the num-ber density of the fermion species f in matter. Approximately, the relation ε αβ ≃ P P (cid:16) ε ePαβ + 3 ε uPαβ + 3 ε dPαβ (cid:17) holds because of a factor of ≃ u and d quarks than electrons in iso-singlet matter. Using the ε parameters the neutrinoevolution equation which governs the neutrino propagation in matter is given as i ddt ν e ν µ ν τ = 12 E U m
00 0 ∆ m U † + a ε ee ε eµ ε eτ ε ∗ eµ ε µµ ε µτ ε ∗ eτ ε ∗ µτ ε ττ ν e ν µ ν τ (2)where U is the MNS matrix, and a ≡ √ G F n e E ) where E is the neutrino energyand n e denotes the electron number density along the neutrino trajectory in the earth.∆ m ij ≡ m i − m j with neutrino mass m i ( i = 1 − ε parameters mayprovide new sources of CP violation 36 ) .NSI comes in not only into neutrino propagation but also to neutrino productionand detection processes 32 ) . The current bounds on ε fPαβ are obtained at 90% CL 34 ) and at 95% CL 37 ) . When translated (in a bold way!) into the ε parameters definedabove they may read as follows 38 ) : − < ε ee < . | ε eµ | < . × − | ε eτ | < . − . < ε µµ < . | ε µτ | < . | ε ττ | < . . (3)I emphasize that it is important to constrain the NSI parameters by various ex-periments. The bound placed by the atmospheric 39 , , ) and the solar neutrino d There remains a serious question of whether effective dimension six operators like (1) which areconsistent with severe constraints on charged lepton counterpart which is related by SU(2) gaugerotation. This point which was first addressed in 33 ) is emphasized to me by Belen Gavela 35 ) . xperiments 42 ) are extensively discussed. It is also proposed that several low en-ergy neutrino experiments may be able to place equally severe constraints on NSI43 , , ) . The bounds from them are placed on the product of NSI at the source andthe detection.In this talk I concentrate on hunting NSI parameters during neutrino propaga-tion. It is the part that can be dealt with in a model-independent manner and freefrom the “unitarity violation”. By contrast, the way NSI comes in into productionand detection processes is model-dependent. e Therefore, categorizing the model pre-dictions is necessary before taking them into account. Moreover, I call the readers’attention to the fact that upon construction of the neutrino factory the near detectorsitting in front of the storage ring will give stringent bounds on NSI, possibly evenseverer ones than currently imagined 34 ) . Even in the case where the effects of NSI inthree different places are comparable in size, it is unlikely that the feature obtainedin our study with only propagation ε ’s are completely cancelled by the effects of ε ’sin production and detection processes.As a theorist the natural question for me to ask is: “What would be the magnitudeof ε αβ ?” On dimensional ground the operator in (1) is suppressed by M NP ) .Since we normalize the operator with Fermi constant G F , ε must be of the order of( M W /M NP ) ∼ M NP = 1(10) TeV. f Therefore, the apparatus has tohave sensitivity to the interactions with strength of 0.01% −
1% of weak interactionsto look for the effects of NSI. This is a highly demanding requirement.
4. Which Apparatus?
Let us consider which apparatus may be required to meet the condition of searchfor new interactions 100 − θ is comparable to that of ε . I expect, very roughly, that sensitivity to sin θ is up to ∼ .
01 in conventionalmuon neutrino superbeam experiments 47 ) , which can be translated into ε sensitivityof ∼ .
05. Thus, most probably, superbeam is not the right apparatus as a machineto hunt NSI. (We will however comments on its sensitivity later.)As is well known, the alternative apparatus which is capable for looking intoeffects of smaller θ is either neutrino factory 48 ) or beta beam 49 ) . Then, theyare the good candidates for apparatus for hunting NSI. In my talk I concentrate onneutrino factory, leaving beta beam capability a subject of future studies by experts.For earlier analyses of NSI effects in neutrino factory, see e.g., 50 , , , , , ) . We e It appears to me that the main difference between our and the “unitarity violation” approach46 ) exists in that the latter chooses to specify a model (or a class of models) to allow them to relatethe propagation ε ’s to the production and the detector ε ’s. f If we have to go to dimension eight operators their effective strength would be at most( M W /M NP ) ∼ − even for M NP = 1 TeV. ill see that the sensitivity to NSI by neutrino factory is fantastic.
5. Problems in Neutrino Factory Search for NSI
Unfortunately, it is known that one has to encounter inherent troubles in doingneutrino factory search for NSI. There exist two types of confusion problem: • θ − NSI confusion 51 , ) ; The effects of non-vanishing θ can be mimicked bysome of the NSI elements ε ’s. • Two-phase confusion 54 ) ; The effects of leptonic Kobayashi-Maskawa (KM)phase δ can be imitated by the phases of the NSI elements ε αβ , which will bedenoted as φ αβ .The former confusion is fatal for precision θ measurement, while the latter oneserious for identifying nature of CP violation even if it were observed.It is not difficult to understand the causes of the two types of confusion. In Fig. 1presented are the bi-probability plots in P ( ν e → ν µ ) − P (¯ ν e → ¯ ν µ ) space 56 ) . Theneutrino energy is taken to be E = 30 GeV and the baseline L = 3000 km. The blueand the red ellipses correspond to the case of positive and negative ε αβ . Except forthe case with ε eµ these two are barely distinguishable. The orange ellipses are the bi-probability diagrams without NSI. There are so many of them because they are resultsof varying θ . The point is that, apart from the case with ε eµ , the blue and the redellipses are completely “absorbed” into the background of orange ellipses. Namely,the system with NSI can be mimicked by adjusting θ , the θ − NSI confusion.The two-phase confusion is also easy to understand. Let us ignore the solar∆ m assuming that it gives relatively small effect. The system is then reduced toan effective two generation problem. In such a system CP violating phase must beunique if a single type of off diagonal NSI element is introduced, because effects ofthe KM type phase must be (effectively) absent. Therefore, the two phases δ and φ αβ must come together, the reasoning spelled out in 30 ) . It was shown in pertubativecomputation 54 ) that it is via the form δ + φ αβ . This is nothing but the cause of thetwo-phase confusion.
6. Two-Detector Setting in Neutrino Factory
We ask questions: What is the way to look for effects of NSI with highest possiblesensitivities? What is the way to resolve the two confusion problems? I argue thatthe two-detector setting, one at baseline ∼ ∼ , ) . Nonetheless, we will observe that thesynergy between the two detectors in the present case is far more spectacular thanthe other cases. .00.51.01.52.0 ε > 0ε < 0δ=0δ=π/2δ=πδ=3π/2 Bi-Probability plot for the baseline L=3000km, E=30 GeV for sin θ = 0.0005, 0.001 and 0.0015 P( ν e ν µ ) [ x10 -4 ] P ( ν e ν µ ) [ x10 - ] | ε ee | = 0.02 | ε e µ |=0.001 | ε µτ |=0.02 | ε e τ | = 0.001 | ε µµ |=0.02 | ε ττ |=0.05 No NSI
Figure 1: Bi-probability plots in P ( ν e → ν µ ) − P (¯ ν e → ¯ ν µ ) space at L = 3000 km, for E = 30 GeV,computed numerically using the constant matter density ρ = 3 . with the electron numberdensity per nucleon equals to 0.5. The both axes is labeled in units of 10 − . In each panel onlythe indicated particular ε αβ is turned on. The upper (lower) panels, from left to right, correspondto the case of non-vanishing ε ee , ε eµ , and ε eτ ( ε µτ , ε µµ , ε ττ ), respectively. The red and the blueellipses are for positive and negative signs of ε , respectively, for the cases with (from left to right)sin θ = 0 . ε overlap almost completely and each individual curveis not visible. The green ellipses which correspond to the same three values of sin θ but withoutNSI are clearly visible. You may ask “why a detector at ∼ ∼ ) as the magic baseline, aL E = π : • It was shown in a previous study 60 ) that the baseline comparable to the magicbaseline gives the best sensitivity to measurement of the earth matter density.The relevant figure drawn by Uchinami-kun for his Mr. thesis is pasted in myprevious Venice report 61 ) as Fig. 1. (For a related work, see 62 ) .) Measuringthe matter density is equivalent to determine ε ee in our present language. Then,it is natural to suspect that a detector at the magic baseline can be a sensitivetool for detecting the effects of diagonal ε ’s. • The magic baseline is characterized as the baseline where the solar oscillationamplitude vanishes 63 ) , and hence the effect of CP phase δ is absent. Thankso this property a detector at L ∼ ε ’s. ε > 0ε < 0 Bi-Probability plot for the Magic Baseline L=7200km, E=30 GeV for sin θ = 0.0005, 0.001 and 0.0015 P( ν e ν µ ) [ x10 -4 ] δ = 0δ = π/2δ = πδ = 3π/2 P ( ν e ν µ ) [ x10 - ] | ε ee | = 0.02 | ε e µ |=0.001 | ε µτ |=0.02 | ε e τ | = 0.001 | ε µµ |=0.02 | ε ττ |=0.05 No NSI
Figure 2: The same as in Fig. 1 but for the baseline L = 7200 km, the magic baseline, with thematter density ρ = 4 . . The same values of ε are used in each panel. Because of the latter property it has been proposed 64 , ) that a second detectorat the magic baseline is a powerful tool for resolving the conventional parameterdegeneracy 64 , , ) , in particular its intrinsic part. In fact, it allows us to have evenhigher sensitivity to off-diagonal ε αβ . This is demonstrated in Fig. 2, in which thebi-probability plots in P ( ν e → ν µ ) − P (¯ ν e → ¯ ν µ ) space at L = 7200 km are presented.As is clear in Fig. 2 the ellipses without NSI shrink into points because of the absenceof δ dependence, giving orange strips when θ is varied. On the other hand, theellipses with NSI stand out. This property is nothing but the secret behind extremelyhigh sensitivity to NSI which we will discover later.In fact, we observe a prominent feature in systems with ε eµ and ε eτ that (1) theellipses shrink to lines, and (2) they look identical. These features are easy to un-derstand if one derives the approximate analytic formulas of oscillation probabilities.See 30 ) for details. The one with ε eτ is given as P ( ν e → ν µ ; ε eτ ) = 4 (∆ m ) ( a − ∆ m ) s s sin ∆ m L E ! + 4 ac s ( a − ∆ m ) h m s | ε eτ | cos( δ + φ eτ ) + c a | ε eτ | i sin ∆ m L E ! . (4)he corresponding formula for anti-neutrinos can be obtained by making the replace-ment a → − a , δ → − δ , and φ eτ → − φ eτ . The formula with ε eµ can be obtainedby replacing c ε eτ by s ε eµ in the second line of Eq. (4), which explains the feature(2) above. The property (1), shrunk ellipse, is also evident by looking into (4); Sincethere is only cos( δ + φ eτ ) dependence the ellipse must shrink into a line. Notice thatat magic baseline the solar ∆ m effect is absent and hence the two phase has to cometogether, as we have argued before and as indicated in (4).
7. How Does the Two-Detector Setting Solve θ − NSI Confusion?
Before we discuss the sensitivity to NSI, let us first address the question of how theproblem of θ − NSI confusion can be solved by the two detector setting at L = 3000and 7000 km. Unless we are able to solve this problem it is not practical to speakabout neutrino factory as a hunting tool for NSI. It should be noticed that if NSIexists at the magnitude we anticipate in the present discussion and the effects of θ is comparable to that we inevitably have such the confusion. Therefore, this is notthe problem only for neutrino factory, but for any other apparatuses which exploresuch region of mixing parameters.The results presented in this articles are based on 30 ) . Therefore, the readers areadvised to consult the reference whenever more detailed informations are necessary.In short our analysis assumed: The number of muons decays per year is 10 , theexposure considered is 4 (4) years for neutrino (anti-neutrino), and each detector massis assumed to be 50 kton. The efficiency is assumed to be 100% and the backgroundis ignored. g In Fig. 3 and Fig. 4, presented are the allowed regions projected into the plane ofsin θ - δ corresponding to the cases with various combinations of NSI parameterswhich are turned on. The input parameters are taken as sin θ = 0 . δ = 3 π/ ε αβ = 0. In the top panels (which show the constraint placed by the detectorat L = 3000km) the θ − NSI confusion is clearly visible in most cases except for thepanels involving ε eµ . Despite the vanishing input of NSI parameters, the freedom ofadjusting them to nonvanishing values during the fit creates the θ − NSI confusion.An exceptional situation occurs in the systems with ε eµ ; The θ − NSI confusion ismuch milder than that in other systems. This is, of course, expected from the behaviorof ellipses in Fig. 1.We notice that the extent of the confusion depend on many things, e.g., on whichcombination of NSI parameters are turned on. In particular, the confusion is muchseverer for smaller θ as shown in Fig. 5 in which sin θ = 0 . ε eµ and for dependence on δ , see Figs. 14 andFigs. 7-10, respectively, in 30 ) . g Alternatively, one may regard this setting as 5+5 years running with 80% efficiency, which maynot be so far from the reality. ε ee and ε e τ marginalized δ δ -4 -3 δ σ σ σ ε ττ and ε e τ marginalized Input: δ = 3 π /2 sin θ = 0.001 ε ee = ε e τ = ε ττ = 010 -4 -3 sin θ ε ee and ε ττ marginalized k m k m -4 -3 -2 C o m b i n e d Figure 3: Allowed regions projected into the plane of sin θ - δ corresponding to the case wherethe input parameters are sin θ = 0 .
001 and δ = 3 π/ ε ’s are zero), for E µ = 50 GeV and the baseline of L = 3000 km (upper panels), 7000 km(middle horizontal panels) and combination (lower panels). The fit was performed by varying freely4 parameters, θ , δ and 2 ε ’s where ε ee and ε eτ are marginalized (left panels), ε ττ and ε eτ aremarginalized (middle panels) and ε ee and ε ττ are marginalized (right panels). We observe in the bottom panels in Fig. 3, Fig. 4, and Fig. 5 that the confusion isresolved by adding the informations gained by the detector at L = 7000km which areshown in the middle panels. The far detector has little sensitivity to δ , as expected,but it has a good sensitivity to θ , and hence has potential of resolving the θ − NSIconfusion. This is analogous to the role played by the far detector at the magicbaseline which helps resolving the conventional neutrino parameter degeneracy.
8. Synergy of Two Detectors and Sensitivity to NSI
Now, we turn to our original problem, the sensitivity to NSI possessed by the two-detector setting. The power of the synergy by the two-detector setting is enormous;Let us see it in Fig. 6 and Fig. 7; Seeing is believing! ε ee and ε e µ marginalized δ Input: δ = 3 π /2 sin θ = 0.001 ε ee = ε e µ = 0246 δ -4 -3 δ σ σ σ ε ττ and ε e µ marginalized Input: δ = 3 π /2 sin θ = 0.001 ε ττ = ε e µ = 010 -4 -3 sin θ ε e τ and ε e µ marginalized k m Input: δ = 3 π /2 sin θ = 0.001 ε e τ = ε e µ = 0 k m -4 -3 -2 C o m b i n e d Figure 4: The same as in Fig. 3 but for different combination of 2 ε ’s to which the fit to sin θ and δ is marginalized; ε ee - ε eµ (left panels), ε ττ - ε eµ (middle panels) and ε eµ - ε eτ (right panels). In Fig. 6 and Fig. 7 presented are the allowed regions in space spanned by two ofthe NSI parameters ε αβ which are turned on in these particular simulations. The top,the middle, and the bottom panels are for the detector at L = 3000 km, L = 7000km, and the two detector combined, respectively.In Fig. 6, we notice a remarkable synergy by the near (3000 km) and the far(7000 km) detectors. Normally, one does not expect that such a tiny allowed regionemerges in the bottom panel by combing the ones in the top and the middle panels.The secret behind the extreme synergy is in the CP phase δ ; The region of apparentoverlap between regions in the top and the middle panels differs in the fit value of δ , and therefore disappear when two detectors are combined. It implies that keepingthe solar ∆ m is crucial to make the synergy active. Though it may sound trivial, Inote that this effect is dropped off in many of the earlier treatment of NSI.We have concluded as follows in our paper 30 ) : “The sensitivities to off-diagonal ε ’s are excellent, | ε eτ | ≃ a few × − and | ε eµ | ≃ a few × − , while the ones forthe diagonal ε ’s are acceptable, | ε ee | ( | ε ττ | ) ≃ . .
2) at 3 σ CL and 2 DOF. These ε ee and ε e τ marginalized δ δ -4 -3 δ σ σ σ ε ττ and ε e τ marginalized Input: δ = 3 π /2 sin θ = 0.0001 ε ee = ε e τ = ε ττ = 010 -4 -3 sin θ ε ee and ε ττ marginalized k m k m -4 -3 -2 C o m b i n e d Figure 5: The same as in Fig. 3 but with sin θ = 0 . sensitivities remain more or less independent of θ down to extremely small valuessuch as sin θ = 10 − . They seem also very robust in the sense that they are notvery disturbed by the presence of another non-zero NSI contribution. The abovecharacteristics of the sensitivities to NSI suggest that in our setting the off-diagonal ε ’s are likely the best place to discover NSI.” This last point was confirmed by arecent calculation 66 ) .
9. Two-Phase Confusion
Our treatment in 30 ) does not contain full treatment of the two-phase confusion,but a partial one. We allowed negative values of ε αβ , which can be interpreted asallowing two discrete values of phase φ αβ = 0 and π . Therefore, we can in principleaddress the question of the two-phase confusion, its discrete version, in our treatment.In Fig. 8 we show the similar allowed regions but obtained in analysis with nonzeroinput values of NSI. In the middle panels in Fig. 8, which correspond to constraintsimposed by the far detector, there are two discrete solutions of ε eτ . It is nothing but ε e τ -0.02-0.0100.01 ε e τ -0.02-0.0100.01-0.2 -0.1 0 0.1 0.2 ε ee ε e τ σ σ σ -0.02-0.0100.010.02 ε e τ sin θ and δ marginalized Input: δ = π /4 sin θ = 0.001 ε ee = ε e τ = ε ττ = 0 -0.02-0.0100.01 ε e τ -0.02-0.0100.01 -0.4 -0.2 0 0.2 0.4 ε ττ ε e τ -0.4-0.200.20.4 ε ττ k m -0.4-0.200.20.4 ε ττ k m -0.4-0.200.20.4-0.2 -0.1 0 0.1 0.2 ε ee ε ττ C o m b i n e d Figure 6: Allowed regions projected into the plane of 2 NSI parameters, ε ee - ε eτ (left panels), ε ττ - ε eτ (middle panels) and ε ee - ε ττ (right panels) corresponding to the case where the input parameters aresin θ = 0 .
001 and δ = π/ ε ’s are zero), for E µ =50 GeV and the baseline of L = 3000 km (upper panels), 7000 km (middle horizontal panels) andcombination (lower panels). The thin dashed lines are to indicate the input values of ε αβ . The fitwas performed by varying freely 4 parameters, θ , δ and 2 ε ’s with θ and δ being marginalized. remnant of the two-phase confusion. Notice that there is no chance of resolving theconfusion only by the detector at the magic baseline, as indicated in the expressionof the oscillation probability in (4).Again the synergy of the near and the far detectors makes it possible to resolvethe discrete version of the two-phase confusion, as indicated in the bottom panels inFig. 8. Though our treatment in 30 ) did not allow us to fully address the issue, weexpect that the two-phase confusion will be resolved by the two detector setting.
10. Sensitivity to NSI by T2KK and the Related Settings
So far we have confined ourselves into neutrino factory, and apparently there islittle room for superbeam experiments as commented earlier. But, it is not completely ε e µ -0.004-0.00200.002 ε e µ -0.004-0.00200.002-0.2 -0.1 0 0.1 0.2 ε ee ε e µ σ σ σ -0.004-0.00200.0020.004 ε e µ sin θ and δ marginalized Input: δ = π /4 sin θ = 0.001 ε ee = ε e τ = ε e µ = ε ττ = 0 -0.004-0.00200.0020.004 ε e µ -0.004-0.00200.002 -0.4 -0.2 0 0.2 0.4 ε ττ ε e µ -0.004-0.00200.0020.004 ε e µ k m -0.004-0.00200.002 ε e µ k m -0.004-0.00200.002-0.02 -0.01 0 0.01 0.02 ε e τ ε e µ C o m b i n e d Figure 7: The same as in Fig. 6 but for a different combination of 2 ε ’s, ε ee - ε eµ (left panels), ε ττ - ε eµ (middle panels) and ε eµ - ε eτ (right panels). true. As far as (2-3) (or µ − τ ) sector of the MNS matrix is concerned superbeamexperiments with tuned beam energy to the one corresponding to the oscillationmaximum is competitive to neutrino factory 18 , , ) .Therefore, I briefly discuss NSI sensitivity achievable by some of the superbeamexperiments. For brevity I treat only three options with an upgraded beam of 4 MWfrom J-PARC: • Kamioka-Korea setting: Two identical detectors one at Kamioka and the otherin Korea each 0.27 Mton fiducial mass • Kamioka-only setting: A single 0.54 Mton detector at Kamioka • Korea-only setting: A single 0.54 Mton detector at somewhere in Korea.The second option is nothing but the one described in LOI of T2K experiment as itssecond phase 18 ) , which I call T2K II. The first one is sometimes dubbed as T2KK ε e τ -0.02-0.0100.01 ε e τ -0.02-0.0100.01-0.2 -0.1 0 0.1 0.2 ε ee ε e τ σ σ σ -0.02-0.0100.010.02 ε e τ sin θ and δ marginalized Input: δ = 3 π /2 sin θ = 0.001 ε ee = 0.1 ε e τ = 0.01 ε ττ = 0.2 -0.02-0.0100.01 ε e τ -0.02-0.0100.01 -0.4 -0.2 0 0.2 0.4 ε ττ ε e τ -0.4-0.200.20.4 ε ττ k m -0.4-0.200.20.4 ε ττ k m -0.4-0.200.20.4-0.2 -0.1 0 0.1 0.2 ε ee ε ττ C o m b i n e d Figure 8: These figures are similar to those presented in Fig. 6 but for non-vanishing input valuesof ε ; ε ee = 0 . ε eτ = 0 .
01 and ε ττ = 0 .
2. We note that only the input values of 2 ε ’s are set to benon-zero at the same time. The thin dashed lines indicate the corresponding non-zero values of ε αβ for each panel. (abbreviation of Tokai-to-Kamioka-Korea), h a modified version of T2K II by dividingthe detector into 2 and bring one of them to Korea 58 ) .In Fig. 9 presented are the sensitivities to NSI elements ε µτ and ε ττ achievableby, from top to bottom, T2K II, the Korea-only setting, and by T2KK. They are theresults obtained by a truncated treatment of the µ − τ sector done in 31 ) . Though notspectacular the both T2K II and T2KK have reasonable sensitivities to NSI; The sensi-tivities of three experimental setups at 2 σ CL can be read off from Fig. 9. The approx-imate 2 σ CL sensitivities of the Kamioka-Korea setup for sin θ = 0 .
45 (sin θ = 0 . | ε µτ | < .
03 (0 . , | ε ττ − ε µµ | < . . . (5) h As I repeatedly emphasize, it is no more than a temporary name for idea of such apparatus.Even in the case people prefer one which succeeds to T2K, the last letter is naturally be the nameof place (P if Pohang, for example) where Korean detector is placed. ε ττ -2-1.5-1-0.500.511.52-0.3 -0.2 -0.1 0 0.1 0.2 0.3 ε µτ -0.2 -0.1 0 0.1 0.2 0.3 ε µτ Figure 9: The allowed regions in ε µτ − ε ττ space for 4 years neutrino and 4 years anti-neutrinorunning. The upper, the middle, and the bottom three panels are for the Kamioka-only setting, theKorea-only setting, and the Kamioka-Korea setting, respectively. The left and the right panels arefor cases with sin θ ≡ sin θ = 0 .
45 and 0.5, respectively. The red, the yellow, and the blue linesindicate the allowed regions at 1 σ , 2 σ , and 3 σ CL, respectively, for 2 degrees of freedom. The inputvalue of ∆ m is taken as 2 . × − eV . Here, we neglected a barely allowed region near | ε ττ | = 2 .
3, which is already excludedby the current data. The bound on | ε µτ | above modestly improves the current boundobtained by analyzing atmospheric neutrino data of Super-Kamiokande and MACRO40 ) .The sensitivity to NSI by T2K II is slightly better than that of T2KK. I note,however, that if we examine wider class of new physics such as quantum decoherence,Lorentz violation, etc., the over-all performance of T2KK is the best among the abovethree settings, always remaining as the next best if not the best 31 ) .
11. Bounds from Ongoing and Near Future Experiments
It is a legitimate question to ask to what extent the ongoing and the near futureexperiments are powerful. Sensitivities to NSI by the MINOS experiments are ex-mined in 69 , , ) . The sensitivities to ε parameters are of order unity. Possiblecontribution by OPERA experiment is also examined 72 , , ) which however doesnot alter the situation. Combination of superbeam experiments with reactor is alsoconsidered 75 ) which entailed the sensitivities ε eµ ∼ .
12. Conclusion
I have raised a question of whether a successful precision measurement of neu-trino masses and the lepton mixing parameters is the last word for future neutrinoexperiments. As a possible candidate for “the answer is No” options, I examinedthe possibility that non-standard neutrino interactions outside the Standard Modelcan be uncovered by neutrino factory experiments. It, however, raises two seriousissues, the θ − NSI confusion and the two-phase confusion, which we proposed to beresolved by the near (3000 km) - far (7000 km) two detector setting. I would liketo emphasize that the results obtained in our analysis is strongly indicative of thefeature that neutrino factory can be used as a discovery machine for NSI while keep-ing its primary function of performing precision measurement of the lepton mixingparameters. I also touched upon the sensitivity to NSI search by some superbeamtype experiments which utilizes neutrino beam from J-PARC.
13. Acknowledgements
It was my fifth visit to Venice (as a scientist), but it was the most memorableone for me for many reasons. In particular, it was the first chance for me to breatheair outside Japan after my disease. I deeply thank Milla for her invaluable kindhelp offered to me in transportation from/to the airport, curing my limited abilityto walk, without which my participation would not be possible. I am grateful to allof my collaborators, Hiroshi Nunokawa, Takaaki Kajita, Renata Zukanovich Funchal,Nei Cipriano Ribeiro, Pyungwon Ko, Shoei Nakayama, and Shoichi Uchinami, forfruitful collaborations. I was benefited by conversations with Osamu Yasuda andNoriaki Kitazawa. This work was supported in part by KAKENHI, Grant-in-Aid forScientific Research, No 19340062, Japan Society for the Promotion of Science.
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