The physics potential of low-performance and high-performance neutrino
factories is briefly reviewed..Comment: Talk presented at NUFACT02, London, 1-6 July, 2002. 8 pages, 5
  figure

Ahmad Q R

Barger V

Fukuda Y

Geer S

Huber P

Lindner M

Steve Geer

English

arXiv

The physics potential of low-performance and high-performance neutrino factories is briefly reviewed

Geer, Steve

UNT Digital Library

Fermilab FERMILAB-Conf-02/394  December 2003arXiv:hep-ph/0210113 v1   7 Oct 2002Neutrino Factories: Physics PotentialSteve Geery xy Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510, USAAbstract. The physics potential of low-performance and high-performance neutrinofactories is briey reviewed.1. IntroductionThe recent evidence for neutrino oscillations [1] opens a new and exciting era in neutrinophysics. We now know that neutrinos of one avor can transform themselves intoneutrinos of a dierent avor. The atmospheric{ and solar{neutrino results from theSuper-Kamiokande (Super-K) and Sudbury Neutrino Observatory (SNO) experimentssuggest that all three known avors participate in neutrino oscillations. Within theframework of three-avor mixing, the oscillation probabilities are determined by threemixing angles (12; 23, 13), one complex phase (Æ), and two mass splittings (m232and m221 where m2ij  m2i - m2j, the dierence between the squares of the massesof the neutrino mass eigenstates). The Super-K and SNO data suggest that (i)jm232j  2  10 3 eV2, (ii) sin2223  1, and if the LMA MSW solution is conrmed,(iii) m221  5  10 5 eV2, and (iv) sin2212  0:87. In addition, the CHOOZ reactore disappearance search result implies (v) sin2213 < O(0:1). However, there is a lot wedon't know: Does three-avor mixing provide the right framework, or are there also contributionsfrom additional sterile neutrinos, neutrino decay, CPT-violation ... ? Is sin2213 small, tiny, or zero ? Is Æ non-zero ? Is there CP-violation in the lepton sector, and does it contributesignicantly to baryogenesis via leptogenesis ? What is the sign of m232 (which determines the neutrino mass hierarchy) ? Is sin2223 maximal (= 1) ?The answers to these questions may lead us towards an understanding of the originof avor. However, getting the answers will require the right tools, and a neutrinofactory [2] appears to be the tool that we will ultimately require.x sgeer@fnal.gov. Presented at NUFACT02, London, 1-6 July 200222. Beam propertiesIn a neutrino factory muons are stored in a ring with long straight sections. Muondecays generate a neutrino beam downstream of each straight section. If + are stored+ ! e+e decays generate a beam consisting of 50% e and 50% . If   are storedthe beam consists of 50%  and 50% e. Design studies [3] suggest that neutrinofactories can provide O(1020) useful muon decays per year. Since the kinematics ofmuon decay is well known, we expect minimal systematic uncertainties on the neutrinoux and spectrum. Hence, compared to conventional neutrino beams made using a decay channel, neutrino factories provide e and e beams in addition to  and beams, with small systematic uncertainties on the beam ux and spectrum.2.1.  beam propertiesAt a high performance 20 GeV neutrino factory providing 21020 useful muon decays/yrthe  beam ux is about an order of magnitude larger than the anticipated futureNuMI beam ux at Fermilab. Eventually superbeams (very high intensity conventionalneutrino beams driven by MW-scale primary proton beams) may also be able to achievebeam uxes that are about a factor of 10 greater than the NuMI ux. However, withhigher energy neutrino factories the event rate at a distant detector increases like E3,rapidly exceeding any corresponding rate we can imagine at a superbeam. This isnot the whole story. The beam energy distributions are also dierent. The neutrinofactory beam has a sharp cut-o at the energy of the stored muons. In a conventionalneutrino beam there is an annoying high-energy tail which gives rise to backgroundsfrom neutral current (NC) events in which a leading 0 is misinterpreted as an electron,faking a  ! e signal. This background source is absent at a neutrino factory.2.2. e beam propertiesAlthough the  beam properties are interesting, the main reason for wanting a neutrinofactory is that it would also provide e and e beams, enabling very sensitive searchesfor e !  oscillations. The resulting  component can interact in the far detectorvia the charged current (CC) interaction to produce a muon with a charge of oppositesign to that of the muons stored in the neutrino factory. The experimental signatureis therefore the appearance of a wrong-sign muon, for which backgrounds are expectedto be at the 10 4 level or lower. In contrast to this, the equivalent  ! e oscillationsearch using a superbeam suers from background levels that are at about the 10 2level. To compare signal and background rates it is useful to consider some explicitexamples [4] corresponding to entry-level and high-performance neutrino facilities: Entry-Level Superbeam (JHF ! Super-K). Running period = 5 years, detectormass = 22.5 kt, proton beam power = 0.75 MW. High-Performance Superbeam (Super-JHF! Hyper-K). Running period = 8 years,detector mass = 1000 kt, proton beam power = 4 MW.3Table 1. Superbeam and neutrino factory event rates from ref. [4]. The event numberscorrespond to the scenarios described in the text, with jm232j = 3  10 3 eV2,m221 = 3:7 10 5 eV2 sin2223 = 1, sin2212 = 0:8, sin2213 = 0:1, and Æ = 0.JHF-SK JHF-HK NUFACT I NUFACT IISignal 140 13000 1500 65000Background 23 2200 4.2 180S/B 6 6 360 360 Entry-Level Neutrino Factory (NUFACT I): 1 1019 useful muon decays / year at50 GeV. Running period = 5 years, detector mass = 100 kt. High-Performance Neutrino Factory (NUFACT II): 2:6  1020 useful muon decays/ year at 50 GeV. Running period = 8 years, detector mass = 100 kt.For these four examples, the signal and background rates are compared in Table 1.Based on the signal to background (S/B) ratios we might expect that the sensitivityat a neutrino factory will ultimately be about two orders of magnitude better thanat a high-performance superbeam. More detailed studies [4] suggest that this naiveconclusion is not far from the truth although the full story is much more complicated.3. Physics reachNeutrino factory data can be separated into 6 subsamples with events tagged by theappearance of (i) a right-sign muon, (ii) a wrong-sign muon, (iii) an e+ or e , (iv) a +,(v) a  , or (vi) the absence of a lepton. Measurements can be made with + and thenwith   stored in the ring. Hence there are 12 event energy distributions that can besimultaneously t to obtain the oscillation parameters. Since neutrino factories provideintense high energy beams, oscillation baselines can be long, or very long (thousandsof km). With multiple experiments, measurements can be checked with a wide rangeof baselines. Recent studies have suggested that this wealth of information will benecessary to pin down the oscillation parameters and provide suÆcient redundancy toensure we have the right oscillation framework. To better understand this it is instructiveto expand the expressions for the oscillation probabilities in terms of small quantities,keeping just the leading order terms. We already know that sin2 213 is small. We canconstruct a second small quantity   m221=m231. Dening   m231L=(4E ), toleading order in sin2 213 and , the oscillation probabilities in vacuum are given by:P = 1   cos2 13 sin2 223 sin2+ 2 cos2 13 cos2 12 sin2 223cosPe = sin2 213 sin2 23 sin2+ 2 cos2 23 sin2 212 sin2  sin2 213 sin Æ cos 13 sin 212 sin 223 sin3   sin2 213 cos Æ cos 13 sin 212 sin 223 cos sin24Figure 1. Minimum value of sin2 213 for which a e $  would be observed, shownas a function of m221 for superbeam and neutrino factory experiments. Figure basedon calculations described in ref. 6.where the  sign in the expression for Pe corresponds to neutrino/antineutrinooscillations. Examining the leading order oscillation expressions we note that:i) We can replace m231 with  m231 without changing Pe since vacuum oscillationsdo not depend upon the sign of . For suÆciently long (neutrino factory) baselineswithin the Earth this degeneracy is broken by matter eects.ii) For non-maximal mixing we can replace 23 with =2   23 and compensate thechange in the predicted oscillation probabilities by changing sin2 213.iii) We expect a strong correlation between the tted values for Æ and sin2 213. Inmany cases the best t combination (Æ; 13) is accompanied by another pair (Æ0; 013)that yields the same predicted leading order oscillation probabilities.Hence, we can expect strong correlations between the values of the oscillation parametersextracted from ts to the data. In addition we can expect degenerate solutions(alternative regions in parameter space that are consistent with the data). Tounderstand the physics capabilities of neutrino factories (or superbeams) we must takeinto account the impact of these correlations and degeneracies.3.1. sin2 213Consider rst the smallest value of sin2 213 that will yield a  $ e signal. We willbegin by ignoring eects of the all important correlations and degeneracies. The valueof sin2 213 that will yield a signicant appearance signal is shown as a function of m221in Fig. 1 for the JHF ! Super-K superbeam and for neutrino factories with energiesbetween 20 GeV and 50 GeV. Superbeams can probe values of sin2 213 an order of510-6 10-5 10-4 10-3 10-2 10-1sin22Θ13Sensitivity to sin22Θ13SystematicCorrelationDegeneracyJHF-SKNuMIJHF-HKNuFact-INuFact-IIFigure 2. Impact of systematics, correlations, and degeneracies on the minimumvalue of sin2 213 probed by superbeam experiments (as indicated) and neutrino factoryexperiments with L = 3000 km. Figure from ref. 4.10-6 10-5 10-4 10-3 10-2 10-1sin22Θ13Sensitivity to sin22Θ13 for NuFact-II3000 km8100 kmFigure 3. Impact of systematics, correlations, and degeneracies on the minimumvalue of sin2 213 probed by neutrino factory experiments with baselines of 3000 kmand 8100 km. Figure from ref. 4magnitude below the present limit. If m221 is very small, so that the sub-leadingscale does not contribute to the appearance signal, a high-performance neutrino factorywould improve on the superbeam sensitivity by more than another order of magnitude.If m221 is in the upper half of the presently allowed region (spanned by the gure) thenneutrino factory experiments will measure an appearance signal even if sin2 213 = 0,enabling oscillations generated by the sub-leading scale to be directly measured.We must now consider the impact of correlations and degeneracies. The calculatedsin2 213 sensitivities (90% CL) from ref. [4] are shown in Fig. 2 for the superbeam andneutrino factory scenarios listed in Section 2.2. The leftmost end of the bars indicate thesensitivities in the absence of correlations, degeneracies, and systematic uncertainties.The impact of each of these eects on the sensitivity is indicated by the shaded sub-bars. Systematic uncertainties degrade the sensitivity by a modest amount. With6!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC2000 4000 6000 80001001010.10.01Baseline   (km)N(νe −> νµ) / N(νe −> νµ)sin 2 2θ13 = 0.004|∆m232| = 0.0035 eV 2∆m232 < 0∆m232 > 0|∆m221| = 5 x 10−5 eV 2Figure 4. Predicted ratios of wrong-sign muon event rates when + and   are storedin a 20 GeV neutrino factory, shown versus baseline. The two bands correspond tothe two signs of m232. The widths of the bands show the variation as the CP phaseÆ changes from  =2 to +=2. The thick lines are for Æ = 0. The statistical errorscorrespond to a neutrino factory providing 1021 muon decays with a 50 kt detector.The gure is from ref. 6.Figure 5. Impact of systematics, correlations, and degeneracies on the minimumvalue of sin2 213 for which the sign of m232 could be determined by superbeam andneutrino factory experiments. Figure from ref. 4.a baseline of 3000 km, the impact of correlations and degeneracies limits the high-performance neutrino factory sin2 213 sensitivity to O(10 3). We can ght correlationsand degeneracies by using a longer baseline, or multiple baselines. In fact with a baselineof  8000 km the sensitivity is expected to have improved to a few 10 5 (Fig. 3).3.2. CP Violation and the neutrino mass hierarchyIf present, CP violation (CPV) and matter eects will modify the measured e $ oscillation probabilities. These modications are dierent for neutrinos and7antineutrinos. The predicted ratio of events N(e ! )=N(e ! ) at a neutrinofactory experiment with equal + and   running is shown as a function of baselinein Fig. 4. With no CPV and no matter eects (L = 0) the ratio is 0.5, reecting thedierent neutrino and antineutrino cross-sections. As L increases the ratio is enhanced(suppressed) by matter eects if the sign of m232 is negative (positive). At suÆcientlylong baselines the matter eects are much larger than eects due to possible CPV(indicated by the bands in the gure). The sign of m232 and the CP phase Æ cantherefore be determined by precise measurements of N(e ! ) and N(e ! ).However, in this simple picture we have xed the values of jm232j, m221, and sin2 213.If we now allow all of these parameters to vary in our t to the data we must dealwill the resulting correlations and ambiguities. The impact of these complicationson the sensitivities of neutrino factory and superbeam experiments can be seen inFig. 5, which shows the minimum values of sin2 213 for which the sign of m232, andhence the neutrino mass hierarchy, can be determined. With a single experiment atone baseline, correlations and degeneracies can degrade the expected sensitivities byorders of magnitude. It is believed that at a high-performance neutrino factory, withtwo experiments having very dierent baselines, the sign can probably be determinedprovided sin2 213 exceeds O(10 4) or perhaps a few 10 5. Further study is needed tounderstand this better, and to understand how the picture is improved by combiningsuperbeam and neutrino factory measurements. The sensitivity to CPV has also beenstudied and found to be very dependent on m221. If m221  4  10 5 eV2, in thecenter of the presently favored LMA parameter space, maximal CPV would be observedat a high performance neutrino factory if sin2 213 exceeds a few 10 4. In the next fewyears KamLAND is expected to improve our knowledge of m221, allowing us to sharpenour understanding of the CPV capabilities of superbeams and neutrino factories.3.3. If LSND is conrmedIf the LSND oscillation result is conrmed, the simple three-avor mixing frameworkwill need to be modied to include, for example, additional light neutrinos that aresterile and/or CPT violation. We will already have some knowledge of  $ e and !  oscillations. It seems likely that there will be a premium on searching forand measuring e !  oscillations, a program unique to neutrino factories. It hasbeen shown [5] that there are viable regions of four-neutrino mixing parameter space inwhich both CPV and thousands of e !  events could be seen at a neutrino factorydelivering only O(1018) decays/yr. Hence, if the LSND result is conrmed, a very lowintensity neutrino factory might provide a well motivated rst (fast and cheap ?) steptowards the high-performance facility we will ultimately want.3.4. Non-oscillation physicsFinally, we must not forget the extensive non-oscillation physics program at a neutrinofactory facility. A high-performance 50 GeV neutrino factory can provide 106  8107 neutrino events per kg per year, enabling highly instrumented detectors to obtaindata samples of unprecedented magnitude. Experiments that might benet from theseintense beams include (i) precise neutrino cross-section measurements, (ii) structurefunction measurements (with no nuclear corrections), in which individual quark-avorparton distributions can be extracted, (iii) precise S measurements from non-singletstructure functions, (iv) studies of nuclear eects (e.g. shadowing) separately for valenceand sea quarks, (v) spin structure functions, (vi) tagged single charm meson and baryonproduction ( a 1 ton detector could yield 108 avor-tagged charm hadrons / yr), (vii)electroweak tests (sin2 W and (   e)), (viii) exotic interaction searches, (ix) neutralheavy lepton searches, and (x) searches for anomalous neutrino interactions in EM elds.This is only a representative list, to which would be added the possible physics programsthat exploit very intense cold muon beams and the very intense primary proton beamsthat would also be available at a neutrino factory complex.4. SummaryNeutrino factories seem to oer a way to probe sin2 13 and determine the sign ofm232 provided sin2 13 exceeds a few 10 5. Neutrino factories would also enablee !  oscillation searches. No other candidate future facility has these capabilities.Should the LMA solar neutrino solution be conrmed, sensitive CPV searches wouldalso be possible. This would either extend the reach that would already have beenobtained at superbeams, or possibly follow up an initial indication of CPV with aprecise measurement of the phase Æ. In addition, an extensive non-oscillation physicsprogram would enable neutrino factories to serve a broad community.AcknowledgementsOur understanding of the physics capabilities of neutrino factories is based on the workof many groups over several years. This brief summary is indebted to all those thathave contributed. I am particularly indebted to M. Lindner for Figs. 2,3, and 5.References[1] Y. Fukuda et al., Phys. Lett. B433, 9 (1998); Phys. Lett. B436 33 (1998); Phys. Rev. Lett.81, 1562 (1998); Phys. Rev. Lett. 82, 2644 (1999); Q.R. Ahmad et al., nucl-ex/0204008; nucl-ex/0204009; Phys. Rev. Lett. 87, 071301 (2001).[2] S. Geer, Phys. Rev. D57, 6989(1998).[3] Design study reports: FERMILAB-Pub-00/108-E, April 2000; BNL-52623, June 2001.[4] P. Huber, M. Lindner, W. Winter, hep-ph/0204352; M. Lindner, hep-ph/0209083[5] V. Barger, S. Geer, R. Raja, K. Whisnant, hep-ph/0007181, Phys. Rev. D63 (2001) 033002.[6] V. Barger, S. Geer, R. Raja, K. Whisnant, hep-ph/0003184, Phys. Rev. D62 (2000) 073002.

Neutrino factories: Physics potential

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Neutrino factories: physics potential

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