Discovering CP violation in neutrino oscillation experiment using neutrino beam from electron capture

0.17 MB·English

by  Zini Rahman

Discovery limit of CP violating Phase δ in oscillation experiment using
neutrino beam from electron capture
Zini Rahman1,∗ and Rathin Adhikari1,†
1
Centre forTheoretical Physics, JamiaMilliaIslamia(Central University), JamiaNagar, New Delhi-110025, INDIA
Using the current value of θ13 obtained from Daya Bay experiment we discuss the discovery
reach of CP violating phase δ using a neutrino beam from electron capture process considering
two baselines- 250Km and 600 Km. We use Water Cherenkov detector. We find that even at 5σ
confidence level CP violation could be found for about 95% (90%) of the possible δ values for a
baselineof250km(600Km)forboththeneutrinomasshierarchiesincontrasttoabout45%ofthe
2 possible δ values for 130 Km baseline using superbeam as both neutrino and antineutrino sources.
1 It is also found that the precision of sensitivity of measurement of δ from electron capture process
0
arequitegood for certain truevaluesof δ - particularly for 250 Km baseline theprecision could be
2
asgoodas0.95%and3.26%forδ(true)=0◦ and90◦ respectivelyincontrasttoprecisionofabout
p
18.75%and18.36%forsuperbeamwithbothneutrinoandantineutrinosourcesat130KmCERN
e
S toFr´ejus baseline.

2
PACSnumbers:

]
h
p
-
p
e I. INTRODUCTION
h
[

Neutrino oscillation probability depends on various oscillation parameters present in the mixing matrix -
1
v the PMNS matrix [1] and the neutrino mass square differences. Two of the angles θ and θ have been
12 23
5 known with certain accuracy. Furthermore, recently sin22θ corresponding to the third mixing angle have
1 13
2 been predicted with 5σ accuracy by DAYA-BAY experiments[2]. This discovery of sin22θ13 has been the
0 inspirationtothiswork. Themasssquaredifferences- ∆m2 and∆m2 isknownbutthesignof∆m2 and
. | 31| 21 31
9 assuchthehierarchy(whetheritisnormal(NH)orinverted(IH))ofneutrinomassesisstillunknown. Also
0
the CP violating phase δ is still unknown. Hence the neutrino oscillation experiments focuses on finding
2
1 out the CP violating phase and in determining the hierarchy. Various neutrino oscillation experiments
: like superbeam, neutrino factory, beta beams and reactor experiments are focussing on determining these
v
i unknown parameters to complete the picture of neutrino oscillations.
X
r In order to determine these unknown parameters another option of using a neutrino beam with neutrinos
a
emitted from an electron capture is proposed in recent years [3–9]. Such beam can be produced using an
acceleratednuclei that decayby electroncapture . Electroncapture canbe defined as a process in whichan
electroniscapturedbyaprotonreleasinganeutronandanelectronneutrino. Intherestframeofthemother
nuclei the electron neutrino that is released from such process, has a definite energy Q. Since the idea of
using a neutrino beam emitted from an electron capture process is based on the acceleration and storage of
∗Electronicaddress: [email protected]
†Electronicaddress: [email protected]
2
radioactiveisotopes that decaysto daughter nuclei, one may get the suitable neutrino energy by acelerating
the mother nuclei with suitable Lorentz boost factor γ. One can control the neutrino energy by choosing
the appropriate Lorentz boost factor as the energy that has been boosted by an appropriate boost factor
towards the detector is given as E = 2γQ. Hence for certain mother nuclei to get the required neutrino
ν
energytheboostfactorhavetobe chosenappropriatelywithrespecttoQ.Usingsuchtypeofbeamsisquite
interesting in the sense that with one boost factor γ a large range of neutrino energy can be coveredand an
accurate neutrino energy can be determined simultanoeusly. Due to the nature of such beam it is expected
to have better precisionin finding variousneutrino oscillationparameters. In this work we use sucha flavor
pure electron neutrino beam emitted from electron capture process at high γ and target it towards a Water
Cherenkov detector and try to study the discovery limit of the CP violating phase.
InsectionIIwediscussthedetailsofthenucleiconsideredfortheelectroncaptureexperimentandapproach
of numerical simulation, the experimental setups that we have considered and the detector characteristics.
Next, using perturbation method we have shown the order of dependence of δ on ν ν oscillation
e µ
→
probability for 250 Km and 600 Km baselines. In section III we discuss the discovery reachof CP violation
andprecisionofmeasurementofδ(true)fortheabove-mentionedtwobaselines. Wesummarizeandconclude
in section IV.
II. EXPERIMENTAL SETUPS AND ν →ν OSCILLATION PROBABILITY
e µ
In doingthe analysisas done by earlierauthors[3], we considerthe isotope 110Sn. Inthe electroncapture
50
process of the above mentioned isotope, the produced neutrinos are monochromatic in nature and has an
energy of Q = 267 KeV in the rest frame. The boosted neutrino beam produced from such process hit the
detector at a baseline length of L at a radial distance R from the beam axis and the energy of this beam in
rest frame of the detector is given by:
−1
Q β 2γQ
E (R)= 1 (1)
ν γ(cid:20) − 1+(R/L)2(cid:21) ≈ 1+(γR/L)2
p
where R is the radius of the detector. From the above equation (1) the energy window considered for the
analysis which is constrained by the size of the detector is given by:
2γQ
E 2γQ (2)
1+(γR /L)2 ≤ ν ≤
max
While doing the analysis the radius of the detector is fixed at R =100 m. From equation (2) we cansee
max
that once the baseline length L and γ is fixed the energy window gets fixed.
In this work GLoBES[10] software has been used for doing the simulations. In order to use the software,
the radial binning is replaced by binning in energy and the bins are not equidistant. If we divide R2 into
max
k bins (k =100) the edges of the bins are given as:
R 2 =R2 (i 1)∆R2 (3)
i max− −
with
R2
∆R2 = max (4)
k
3
WeconsiderR2 >R2 sothatinGLoBEStherespectiveenergybinsareinthecorrectorderasgivenbelow
i i+1
E′(R2)<E′(R2 ) (5)
i i+1
where E′ is the neutrino energy in the lab frame and is given by:
−1
Q β
E′(R)= 1 (6)
γ(cid:20) − 1+(R/L)2(cid:21)
p
The mean value of each energy bin is considered as
E′(R2)+E′(R2 )
E = i i+1 (7)
i
2
In one energy bin the number of event is given by:
1 dn
N ǫ P(L,E ) (E′)σ(E′)N (8)
i ≃ i i νe→νµL2dΩ′ i i nuc,i
where ǫ is the signal efficiency in the respective bin, P(L,E ) is the neutrino oscillation probability,
i i νe→νµ
σ(E′) is the charged current cross section per nucleon, N is the number of target nucleons in the
i nuc,i
geometrical size of the i-th bin and dn(E′) is the angular neutrino flux and is given as:
dΩ′ i
dn N E′ 2
= decays i (9)
dΩ′ 4π (cid:18)Q(cid:19)
i
The detailed derivation of these expressions can be found in [3].
Following the perturbation method [12] and by considering the standard model matter effect A α for
∼
neutrino energy E around 1 GeV where α = ∆m2 /∆m2 and A = 2√2G n E and n is the electron
12 13 F e e
number density in matter; we present below the probability of oscillation P for 250 Km
νe→νµ
L2α2∆m4 cos2[θ ]sin2[2θ ] sin2[θ ]sin2[θ ] L∆m2 L∆m2
P = 31 23 12 + 13 23 sin 31 2AL∆m2 cos 31
νe→νµ 16E2 E (cid:20) 4E (cid:21)(cid:18)− 31 (cid:20) 4E (cid:21)
L∆m2
+ 2E(1+4A+cos[2θ ])sin 31
13
(cid:20) 4E (cid:21)(cid:19)
Lα∆m2 L∆m2 L∆m2
+ 31 sin[θ ]sin[θ ] cos δ 31 cos[θ ]sin 31 sin[2θ ]
13 23 23 12
E (cid:18) (cid:20) − 4E (cid:21) (cid:20) 4E (cid:21)
L∆m2
sin 31 sin2[θ ]sin[θ ]sin[θ ] (10)
12 13 23
− (cid:20) 2E (cid:21) (cid:19)
Similarly, considering A √α we present below the probability of oscillation for 600 Km as given below:
∼
L2α2∆m4 cos2[θ ]cos2[θ ]sin2[θ ]
P = 31 12 23 12
νe→νµ 4E2
1 L∆m2
+ 4 1+4A+6A2 E2+A2L2∆m4 cos 31 +4E(E(1+4A+6A2
4E2 (cid:18) − 31 (cid:20) 2E (cid:21)
(cid:0) (cid:0) (cid:1) (cid:1)
L∆m2 L∆m2
+ 2cos[2θ ]sin2 31 ) A(1+2A)L∆m2 sin 31 ) sin2[θ ]sin2[θ ]
13 (cid:20) 4E (cid:21) − 31 (cid:20) 2E (cid:21) (cid:19) 13 23
Lα∆m2 L∆m2 L∆m2
+ 31 sin[θ ]sin[θ ]sin[θ ] cos δ 31 cos[θ ]cos[θ ] AL∆m2 cos 31
2E2 12 13 23 (cid:18) (cid:20) − 4E (cid:21) 12 23 (cid:18)− 31 (cid:20) 4E (cid:21)
L∆m2 L∆m2
+ 4(1+A)Esin 31 2Esin 31 sin[θ ]sin[θ ]sin[θ ] (11)
12 13 23
(cid:20) 4E (cid:21)(cid:19)− (cid:20) 2E (cid:21) (cid:19)
4
One may note that in both the baselines the leading contribution to probability which is coming from the
second term is independent of δ. Based on recent Daya Bay result considering sinθ √α the leading
13
∼
term in both the expressions are of order α. However, the third term in both the expressions shows that
P depends on δ which is of order α3/2. So the precision measurement of δ is relatively difficult in
νe→νµ
comparisonto other neutrino mixing parameters. We have plotted the probability P(ν ν ) with respect
e µ
→
to energy for the two different setups in figure 1 for three different values of δ as mentioned in the figures.
The length of the baseline is also mentioned in the figures. The shaded band in the figures show somewhat
suitable energy windows for the different setups. For illustration, we have considered only normal hierarchy
in plotting figure 1.
0.14 L=250Km 0.14 L=600Km
∆=0 ∆=0
0.12 0.12
∆=Π(cid:144)2 ∆=Π(cid:144)2
∆=-Π(cid:144)2 ∆=-Π(cid:144)2
0.1 0.1
L Γ=2000 L Γ=2500
Μ Μ
Ν Ν
® 0.08 ® 0.08
e e
Ν 0.06 Ν 0.06
H H
P P
0.04 0.04
0.02 0.02
0. 0.
0.2 0.5 1 1.5 2 0.2 0.5 1 1.5 2
E HGeVL E HGeVL
Ν Ν
FIG. 1: Probability P(νe→νµ) vsneutrino energy Eν for two different setups.
We consider a Water Cherenkov detector of fiducial mass 500 kt. The signal efficiency is consideredto be
0.55, background rejection factor to be 10−4, signal error of 2.5% and background error to be 5%. Energy
resolution is taken to be 0.15E. We assume 1018 electron capture decays per year and the datas are taken
over a period of 5 years. Further for doing the analysis we choose two different setups:
Setup(a): The length of the baseline is taken to be 250 Km and the boost factor γ to be 2000.
Setup(b): The length of the baseline is taken to be 600 Km and the boost factor γ to be 2500.
We have compared discovery potentials of CP violation obtained using monoenergetic neutrino beam to
that using neutrino superbeam (SPL) facility at CERN. For that we have considered third setup as follows:
Setup(c): The length of the baseline is taken to be 130 Km corresponding to CERN-Fr´ejus baseline. For
this wehaveconsideredwaterCherenkovdetectorwithfiducialmassof500kt,runningtime (ν+ν¯)for5+5
yrs. We have considered beam intensity 4 MW and systemetics on signal and background as 2%. For the
simulation we have used the setup as provided by GLoBES [11] based on reference [13].
In doing the simulations we have considered the following parameter values as the true values [14]:
∆m2 = 2.45 10−3, ∆m2 = 7.64 10−5, sin22θ = 45◦, sin22θ = 34.2◦, sin22θ = 9◦. Also
| 31| × 21 × 23 12 13
we haveconsideredpriors of 3% for θ , 2.5%for ∆m2 , 8% for θ , 4% for ∆m2 and 0.005for sin22θ . A
12 21 23 31 13
2% uncertainty is considered on the matter density.
5
III. RESULTS
103
103
102
2∆χ 5 σ 2∆χ 102
5 σ
101 3 σ
Setup (b) 101 3 σ
Setup (a) Setup (b)
Setup (c) Setup (a)
Setup (c)
100 100
-180 -90 0 90 180 -180 -90 0 90 180
δ(true) δ(true)
FIG. 2: Discovery of CP violating phase δ for two setups and for both thehierachies.
In figure 2 we have shown the discovery of the CP violating phase δ at 5σ confidence levels for three
different setups-setup(a), setup(b) and setup(c) for both the hierarchies (NH and IH). We find that the
discoveryofCP violationforsetup(a)isremarkableevenat5σ andthatofsetup(b)isalsogood. Ingeneral,
thediscoveryreachforCP violationconsideringsuperbeamasconsideredinsetup(c)for130Kmbaselineis
expected to be quite goodwith highbeam poweraround4 MW andthis cancompensate the reducedcross-
section coming due to low neutrino energy. Furthermore, there is negligible matter effect which otherwise
could mimic strongly the CP violation. However, as seen from the figures 2 for the setup (a) and (b) the
discovery reach is significantly better than setup (c). This is because of high energy resolution and also
better statistics with large number of events in using monoenergetic neutrino beam. We find that even at
5σ confidence level CP violation could be found for about 95% (90%) of the possible δ values for a baseline
of250km(600Km)forboththe neutrino masshierarchiesincontrasttoabout45%ofthe possible δ values
for 130 Km baseline using superbeam as neutrino source.
6
180 180

90 90

st) st)
δ (te 0 δ (te 0

-90 -90
Setup (b) Setup (b)
Setup (a) Setup (a)
Setup (c) Setup (c)
-180 -180
-180 -90 0 90 180 -180 -90 0 90 180
δ (true) δ (true)
FIG. 3: δ (true) vs δ (test) at 5σ confidence level for two different setups and for both NH and IH as mentioned in
thefigures.
Infigure3wehaveshownthecontourforδ(true)vsδ(test)forthethreesetupsandboththehierarchiesat
5σ confidence level. From the figures one may find out the precision(P ) of sensitivity of measurement
δ(true)
for any true value of δ using the following expression for it:
δ(test)(max) δ(test)(min)
P = − (12)
δ(true) 2π+δ(test)(max) δ(test)(min)
−
whereδ(test)(max)andδ(test)(min)arethemaximumandminimumδ(test)valuesrespectivelycorrespond-
ing to certain true values as shown in figure 3. As for example, for setup (a) the precisions of measurement
of δ(true) for 0◦ and 90◦ are about 0.95 % and 3.26% respectively; for setup (b) those are about 1.8 % and
12.5% respectively whereas for superbeam (setup (c)) those are about 18.75 % and 18.36 % respectively.
IV. CONCLUSION
In this work for comparative study we have considered two different type of neutrino sources to find the
discovery reach of the CP violating phase δ. One type of source is only ν from electron capture decays of
e
110Sn isotopes (setup (a) and setup (b) ) directed towards water Cherenkov detector and the other type is
50
bothneutrinoandantineutrinofromsuperbeam(setup(c)). Asseenfromfigure2forthefirsttypeofsource
CP violation could be observed for almost 95 % of the possible δ(true) values for 250 Km baseline which
couldbe atbest about45% for the secondtype ofsourcefor 130Kmbaseline. Fromfigure3 corresponding
toδ(true)thepresionofmeasurementcouldbeasgoodas0.95%forfirsttypeofsourceincontrasttoabout
18.75 % for superbeam. The overall excellent discovery reach for the first type of source has been found.
This is primarily due to the scope of precise resolution of neutrino energy reconstruction and also for the
presence of purely one type of neutrino flavor (ν ) in the beam [3]. After the discovery of neutrino vacuum
e
mixing angle θ by Daya Bay experiment [2] it is now very important to know precisely the value of CP
13
violating phase δ. For this it seems that considering the neutrino source from electron capture decays could
be quite worthwhile in future.
7
Acknowledgment: ZRlikestothankUniversityGrantsCommission,Govt. ofIndiaforprovidingresearch
fellowship.
[1] ParticleDataGroup,K.Hagiwaraetal.,Phys.Rev.D66,010001(2002);B.PontecorvoSov.Phys.JETP26:984
(1968).
[2] Daya-Bay collaboration, Phys.Rev.Lett.108 171803 (2012), arXiv:1203.1669.
[3] M. Rolinec, J. Sato, JHEP 0708:079 (2007), hep-ph/0612148.
[4] J. Bernabeu, J. Burguet-Castell and C. Espinoza, JHEP, 0512:014, (2005).
[5] Joe Sato, Phys.Rev.Lett 95, 131804 (2005); Christopher Orme,arXiv:0901.4287.
[6] J. Bernabeu, J. Burguet-Castell, C. Espinoza, and M. Lindroos, Nucl.Phys.Proc.Suppl.155,222-224 (2006),
hep-ph/0510278 .
[7] Joe Sato, Phys.Rev.Lett.95, 131804 (2005), hep-ph/0503144.
[8] Christopher Orme, JHEP 1007:049 (2010).
[9] M.E. EstevezAguado et al., Phys.Rev.C84,034304 (2011).
[10] P. Huber,M. Lindnerand W. Winter, Comput. Phys.Commun.167, 195 (2005), hep-ph/0407333; P. Huber,J.
Kopp,M. Lind- ner, M. Rolinec and W. Winter,Comput. Phys. Com- mun.177, 432 (2007),hep-ph/0701187.
[11] P.Huber, M. Lindnerand W. Winter, Comput. Phys. Commun.167, 195 (2005).
[hep-ph/0407333]., http://www.mpi-hd.mpg.de/lin/globes/
[12] Rathin Adhikari,Sabyasachi Chakraborty,Arnab Dasgupta, Sourov Roy,arXiv:1201.3047
[13] J. -E. Campagne, M. Maltoni, M. Mezzetto and T. Schwetz, JHEP 0704, 003 (2007) [hep-ph/0603172].
[14] P.Coloma, E. Fernandez-Martinezand L. Labarga, arXiv:1206.0475.