Exceptional Sensitivity to Neutrino Parameters with a Two Baseline Beta-Beam Set-up

Abstract

We examine the reach of a Beta-beam experiment with two detectors at carefully chosen baselines for exploring neutrino mass parameters. Locating the source at CERN, the two detectors and baselines are: (a) a 50 kton iron calorimeter (ICAL) at a baseline of around 7150 km which is roughly the magic baseline, e.g., ICAL@INO, and (b) a 50 kton Totally Active Scintillator Detector at a distance of 730 km, e.g., at Gran Sasso. We choose 8B/8Li source ions with a boost factor \gamma of 650 for the magic baseline while for the closer detector we consider 18Ne/6He ions with a range of Lorentz boosts. We find that the locations of the two detectors complement each other leading to an exceptional high sensitivity. With \gamma=650 for 8B/8Li and \gamma=575 for 18Ne/6He and total luminosity corresponding to 5\times (1.1 \times 10^{18}) and 5\times (2.9\times 10^{18}) useful ion decays in neutrino and antineutrino modes respectively, we find that our two detector set-up can probe maximal CP violation and establish the neutrino mass ordering if \sin^22\theta_{13} is 1.4\times 10^{-4} and 2.7\times 10^{-4}, respectively, or more. The sensitivity reach for \sin^22\theta_{13} itself is 5.5 \times 10^{-4}. With a factor of 10 higher luminosity, the corresponding \sin^22\theta_{13} reach of this set-up would be 1.8\times 10^{-5}, 4.6\times 10^{-5} and 5.3\times 10^{-5} respectively for the above three performance indicators. CP violation can be discovered for 64% of the possible \delta_{CP} values for \sin^22\theta_{13} \geq 10^{-3} (\geq 8\times 10^{-5}), for the standard luminosity (10 times enhanced luminosity). Comparable physics performance can be achieved in a set-up where data from CERN to INO@ICAL is combined with that from CERN to the Boulby mine in United Kingdom, a baseline of 1050 km.

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arXiv:0804.3007v2 [hep-ph] 28 Jul 2008
HRI-P-08-04-001
CU-PHYSICS/08-2008
HRI-RECAPP-08-04
Exceptional Sensitivity to Neutrino Parameters with a
Two-Baseline Beta-Beam Set-up
Sanjib Kumar Agarwalla⋆,†,a, Sandhya Choubey⋆,b, Amitava Raychaudhuri⋆,†,c
⋆Harish-Chandra Research Institute,
Chhatnag Road, Jhunsi, Allahabad 211019, India
†Department of Physics, University of Calcutta,
92 Acharya Prafulla Chandra Road, Kolkata 700009, India
ABSTRACT
We examine the reach of a Beta-beam experiment with two detectors at carefully chosen
baselines for exploring neutrino mass parameters. Locating the source at CERN, the two detectors
and baselines are: (a) a 50 kton iron calorimeter (ICAL) at a baseline of around 7150 km which
is roughly the magic baseline, e.g., ICAL@INO, and (b) a 50 kton Totally Active Scintillator
Detector at a distance of 730 km, e.g., at Gran Sasso. We choose8B and8Li source ions with a
boost factor γ of 650 for the magic baseline while for the closer detector we consider18Ne and6He
ions with a range of Lorentz boosts. We find that the locations of the two detectors complement
each other leading to an exceptional high sensitivity. With γ = 650 for8B/8Li and γ = 575 for
18Ne/6He and total luminosity corresponding to 5 × (1.1 × 1018) and 5 × (2.9 × 1018) useful ion
decays in neutrino and antineutrino modes respectively, we find that the two-detector set-up can
probe maximal CP violation and establish the neutrino mass ordering if sin22θ13is 1.4×10−4and
2.7 × 10−4, respectively, or more. The sensitivity reach for sin22θ13itself is 5.5 × 10−4. With a
factor of 10 higher luminosity, the corresponding sin22θ13reach of this set-up would be 1.8×10−5,
4.6×10−5and 5.3×10−5respectively for the above three performance indicators. CP violation can
be discovered for 64% of the possible δCPvalues for sin22θ13≥ 10−3(≥ 8×10−5), for the standard
luminosity (10 times enhanced luminosity). Comparable physics performance can be achieved in
a set-up where data from CERN to INO@ICAL is combined with that from CERN to the Boulby
mine in United Kingdom, a baseline of 1050 km.
aemail: sanjib@hri.res.in
bemail: sandhya@hri.res.in
cemail: raychaud@hri.res.in

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1Introduction
Long baseline experiments with powerful neutrino beams [1, 2, 3, 4] from upgraded accelera-
tor facilities are the next frontier in neutrino oscillation physics. Set-ups with intense neutrino
beam sources and smart detector technologies are being planned to fathom the hitherto uncharted
regimes of the neutrino mass matrix. In particular, the long baseline experiments are being de-
signed to measure the third mixing angle θ13, CP phase δCP and sgn(∆m2
mass hierarchy1. The most promising avenue for this purpose is the νe→ νµoscillation channel
Peµ(or its T-conjugate Pµe), often referred to in the literature as the “golden channel” [5]. It was
realized that while this channel can be used in the most cost-effective way to measure all three
neutrino oscillation parameters listed above, it is also rife with the so-called problem of “parameter
degeneracies”. These are identified as the (θ13,δCP) intrinsic degeneracy [6], the (sgn(∆m2
degeneracy [7], and the (θ23,π/2 − θ23) degeneracy [8]. Together they could result in as many as
eight-fold degenerate solutions [9], of which, obviously, only one is true. This is evidently a very
undesirable situation and a large body of existing literature is devoted to finding ways of combat-
ing this menace [6, 10, 11, 12, 13, 14, 15, 16, 17]. A particularly attractive way of killing the clone
solutions from the δCPdependent degeneracies is to perform the experiment at the “magic base-
line” [18, 19, 20]. At this baseline all δCPdependent terms drop out, providing an ideal bedrock
for measuring θ13and sgn(∆m2
In [21, 22, 23] we expounded the sensitivity reach of a magic baseline experimental set-up
where the neutrino source is a Beta-beam [24] at CERN and the detector is a large magnetized
iron calorimeter (ICAL) at the India-based Neutrino Observatory2(INO) [25]. Using a 50 kton
fiducial mass and 80% detector efficiency3for ICAL@INO, and considering a Beta-beam using
8B and8Li as ion source [26, 27], with a Lorentz boost γ = 650 and assuming 5 × (1.1 × 1018)
and 5×(2.9×1018) useful ion decays in neutrino and antineutrino modes respectively, we showed
that this set-up could unambiguously probe sgn(∆m2
find a signal for θ13at the same level of significance if sin22θ13(true) > 5.1 × 10−4, independent
of the true neutrino mass hierarchy and δCP(true). The θ13and hierarchy sensitivity reach of this
“magical” set-up is therefore superior to that of most other rival proposals involving Beta-beams
[16, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39], and is almost comparable to that possible with
a Neutrino Factory [40] at the magic baseline. This tremendous sensitivity of the CERN-INO
Beta-beam project to θ13 and hierarchy comes from a combination of being close to the magic
baseline as well as from being sensitive to near-maximal matter effects.
The main drawback of the CERN-INO Beta-beam set-up is its inability to determine δCP, since
being almost at the magic baseline it is insensitive to the CP phase. Note that this is also true for
the Neutrino Factory experiment at the magic baseline. This is why the optimal Neutrino Factory
set-up demands a combination of two baselines, one magic and the other around L = 4000 km,
where one has the best sensitivity to δCP [40]. For Beta-beams, one has to optimize not only
31) aka, the neutrino
31),δCP)
31).
31) at 3σ if4sin22θ13(true) > 5.6×10−4and
1In this paper we define ∆m2
0 is called “normal hierarchy”(NH) while sgn(∆m2
arguments are valid for both hierarchical as well as quasi-degenerate neutrino mass spectra.
2The CERN to INO distance is 7152 km, which is tantalizingly close to the magic baseline.
3We give details about the detector configuration in section 3.
4These are the values of the parameters chosen by Nature, to be distinguished from the fitted values. Throughout
this paper we denote the true value of a parameter by putting “(true)” after the symbol for the parameter.
ij= m2
i−m2
jand refer to sgn(∆m2
31) < 0 is called “inverted hierarchy”(IH). We stress that the
31) as the neutrino mass hierarchy – sgn(∆m2
31) >
2

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on γ, the baseline L, and the luminosity, but also on the choice of the source ions. A detailed
optimization study has revealed that for intermediate values of γ, one would preferentially use
8B and8Li at the magic baseline for the mass hierarchy,18Ne and6He at an intermediate baseline
of L = 600 − 900 km for CP violation, and either18Ne and6He at the intermediate baseline or
8B and8Li at the magic baseline for the sin22θ13discovery [41].
In this paper we consider a two-baseline Beta-beam set-up, one with L = 7152 km, the CERN-
INO baseline, and another with L = 730 km which is the CERN-Gran Sasso (LNGS) distance.
For the CERN-INO case8B and8Li are the preferred source ions and we take γ = 650. For the
CERN-LNGS set-up, on the other hand, we choose the18Ne and6He ions and allow their γ to
vary between 250-6505in order to examine the dependence of the sensitivity on the value of the
boost factor. Since the8B and8Li ions would produce multi-GeV neutrino beams for γ = 650,
we use a 50 kton iron calorimeter (ICAL) for the longer baseline at INO and call this set-up
CERN-ICAL@INO. For the intermediate baseline option, since we are interested in the lower
energy18Ne and6He ions, we assume a 50 kton Totally Active Scintillator Detector (TASD) in
order to harness the low energy events required for better CP sensitivity. We present results for
5×(1.1×1018) and 5×(2.9×1018) useful ion decays in neutrino and antineutrino modes respectively
for both baseline set-ups. We also show the projected sensitivity if one achieves statistics that are
larger by a factor of 10. Since the statistics depend on the product of the size of the detector, the
exposure time, detector efficiency and the number of useful ion decays, this one order of magnitude
increase could come from a combination of enhanced performance in any of the factors mentioned
above. In particular, it might be possible to have 10 times larger useful ion decays per year in the
storage ring [43]. ICAL@INO could also be upgraded to 100 kton.
Note that while most of our figures and discussion in the text would explicitly be for the
CERN-LNGS intermediate baseline set-up, we also present results for the case where a18Ne and
6He Beta-beam is shot from CERN to the Boulby mine in the United Kingdom (see [38] and
references therein). The CERN-Boulby distance is 1050 km, and one can check from Fig. 5 of
[41] that the CP sensitivity for this baseline is only marginally weaker than that for L = 730
km. Therefore, when combined with the CERN-INO data, we expect similar performance for this
baseline option as well.
In some sense this work is a part of an ongoing international exercise in sharpening the full
capability of long baseline Beta-beam experiments to explore neutrino properties. In addition
to the work discussed earlier in the Introduction, some of the milestones on this route can be
identified as the CERN-MEMPHYS proposal [16, 28, 29], its variants with higher γ [32, 33], using
a cocktail of sources [37], detector options, etc.
While the best CP violation sensitivity comes with18Ne and6He as source at our chosen
intermediate baseline, it might be more convenient and less demanding to use the same set of
ions at both the baselines. The optimal baseline for CP studies with8B and8Li was seen to be
around 1000-2000 km in [41]. In [31], the authors proposed a set-up with this scenario where they
5With the existing facilities at CERN, one will be able to accelarate6He to only about γ = 150. This corresponds
to a boost factor of about 250 for18Ne and 280 for8B, due to the different charge to mass ratios for these ions.
However, with the “Super-SPS”, an upgraded version of the SPS with super-conducting magnets [33, 30] it should
be possible to accelarate6He to γ = 350, which corresponds to γ = 575 for18Ne and γ = 650 for8B. The Tevatron
at Fermilab could produce a Beta-beam with similar boost factors. Higher acceleration at CERN would require
the use of the LHC itself, with γ > 1000 possible [42].
3

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considered a two-baseline combination with a longer L ≃ 7000 km and a shorter L ≃ 2000 km. A
γ = 350 Beta-beam produced by8B and8Li as source ions feeds both detectors and they consider
up to 5 × (10 × 1018) total useful ion decays in both neutrino and antineutrino modes. They
consider 50 kton of magnetized iron as the end detector for both baselines. In this set-up the mass
hierarchy can be discovered if sin22θ13(true) > 3 × 10−4and CP violation can be established for
70% of the possible δCP(true) values if sin22θ13(true) > 10−3. Signal for the mixing angle itself
could be observed for sin22θ13(true) > 1 × 10−4. For 5 × (2 × 1018) total useful decays, which is
comparable to our standard luminosity, the corresponding reaches are sin22θ13(true)∼>10−3for
the mass hierarchy, and sin22θ13(true)∼>8 × 10−4for discovering θ13. CP violation sensitivity
gets severely restricted and deteriorates, especially for δCP(true) = 270◦. The poor CP reach
for lower luminosity comes due to the choice of8B and8Li as source ions (see [41] for a detailed
discussion). Since much better CP sensitivity for plausible luminosity and γ can be achieved with
the18Ne and6He combination, we will exclusively use them for our intermediate baseline option
of CERN to LNGS. Since our chosen γ is larger, we also achieve sensitivity to mass hierarchy and
θ13which is better by at least an order of magnitude for the same number of useful ions decays.
The paper is organized as follows. In the next section we briefly discuss the oscillation proba-
bility for the golden channel and highlight the magic baseline behavior. The experimental set-up
which we consider is outlined in the subsequent section. In the following section we explore the
prospects of the TASD@LNGS detector, in a stand-alone mode, for exploring CP violation. This
is to set the stage for the next section where the results of a combined two-baseline analysis are
presented with emphasis on the sensitivities to CP violation, θ13, and the neutrino mass hierar-
chy. We end by summarizing the results for our combined CERN-INO and CERN-LNGS set-ups
and make a comparative discussion of this set-up vis-a-vis the combined CERN-INO and CERN-
Boulby set-up. We also compare our set-up against the one studied in [31] and discuss the pros
and cons of the two proposals. Some remarks about the beam related as well as atmospheric
neutrino backgrounds are collected in the Appendix.
2 Golden channel oscillations
For the results presented in this paper we have calculated the neutrino oscillation probability in
matter exactly, using the PREM profile for the Earth matter density [44]. However, for elucidating
the behavior of neutrino oscillations as a function of baseline and/or neutrino energy, it is useful
to exploit the approximate analytic formula for the golden channel probability Peµin matter [45,
46, 47], keeping terms only up to second order in the small quantities θ13and α ≡ ∆m2
[5, 48]
21/∆m2
31
Peµ ≃ sin2θ23sin22θ13sin2[(1 −ˆA)∆]
± αsin2θ13sin2θ12sin2θ23sinδCPsin(∆)sin(ˆA∆)
+ αsin2θ13sin2θ12sin2θ23cosδCPcos(∆)sin(ˆA∆)
(1 −ˆA)2
ˆA
sin[(1 −ˆA)∆]
(1 −ˆA)
sin[(1 −ˆA)∆]
(1 −ˆA)
ˆA
4

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+ α2cos2θ23sin22θ12sin2(ˆA∆)
ˆA2
, (1)
where
∆ ≡∆m2
31L
4E
,
ˆA ≡
A
∆m2
31
, A = ±2√2GFNeE.(2)
Above, A is the matter potential, expressed in terms of the electron density Neand the (anti)neutrino
energy E; the ‘+’ sign refers to neutrinos while the ‘−’ to antineutrinos.
From Eq. (1) it is apparent that at a baseline for which
sin(ˆA∆) ≃ 0, (3)
the oscillation probability is insensitive to δCP. This defines the “magic baseline”. As noted, the
CERN-INO distance closely matches this baseline and it has been shown in earlier work [21, 22, 23]
that this ensures a high sensitivity at the same time to the determination of θ13and the extraction
of the neutrino mass hierarchy. In this work, we examine the benefits which accrue from combining
two Beta-beam experiments both with the source at CERN, one with the detector at INO and the
other located at an appropriate distance where the impact of CP violation is prominent. Taking a
cue from an optimization analysis of such Beta-beam set-ups [41], this second detector is assumed
to be at Gran Sasso.
We will refer to Eqs. (1) and (2) from time to time to identify the physics underlying the
results which we present later.
3 The Experimental Set-up
The number of (anti)muon events in the ith energy bin in the detector is given by
Ni=T nnfIDǫ
4πL2
?Emax
0
dE
?Emax
Emin
Ai
Ai
dEAφ(E)σνµ(E)R(E,EA)Peµ(E), (4)
where T is the total running time, nnis the number of target nucleons in the detector, fIDis the
charge identification efficiency (meaningful only for the magnetized iron detector), ǫ is the detector
efficiency and R(E,EA) is the energy resolution function of the detector, which we assume is a
Gaussian. For muon (antimuon) events, σνµis the neutrino (antineutrino) interaction cross-section.
The quantities E and EAare the true and reconstructed (anti)neutrino energies respectively. The
quantity φ(E) is the (anti)neutrino Beta-beam flux produced at the source, with Lorentz boost γ
and L is the baseline.
3.1The Source Ions
The technological challenge for producing the Beta-beam involves creating, bunching, accelerating
and storing beta unstable radioactive ions [49, 50]. A pure and intense νe and/or ¯ νe beam is
produced when these highly accelerated ions decay along the straight sections of the storage ring.
5