Stringent constraint on CPT violation with the synergy of T2K-II NO A extension and JUNO T. V. Ngoc12S. Cao1 N. T. Hong Van3 and P. T. Quyen1

2025-05-02 0 0 574.91KB 10 页 10玖币

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Stringent constraint on CPT violation with the synergy of T2K-II, NOνA extension,

and JUNO

T. V. Ngoc1,2,∗S. Cao1, N. T. Hong Van3, and P. T. Quyen1

1Institute For Interdisciplinary Research in Science and Education,

ICISE, Quy Nhon, Vietnam.

2Graduate University of Science and Technology,

Vietnam Academy of Science and Technology, Hanoi, Vietnam.

3Institute of Physics,

Vietnam Academy of Science and Technology, Hanoi, Vietnam.

(Dated: December 29, 2022)

Neutrino oscillation experiments have measured precisely at few percent levels the mass-squared

diﬀerences (∆m2

21, ∆m2

31) of three neutrino mass eigenstates, and the three leptonic mixing angles

(θ12, θ13, θ23) by utilizing both neutrino and anti-neutrino oscillations. The possible CPT violation

may manifest itself in the diﬀerence of neutrino and anti-neutrino oscillation parameters, making

these experiments promising tools for testing CPT invariance at unprecedented precision. We in-

vestigate empirically the sensitivity of the CPT test via the diﬀerence in mass-squared splittings

(∆m2

31 −∆m2

31) and in leptonic mixing angles (sin2θ23 −sin2θ23) with the synergy of T2K-II, NOνA

extension, and JUNO experiments. If the CPT symmetry is found to be conserved, the joint analysis

of the three experiments will be able to establish limits of |∆m2

31 −∆m2

31|<5.3×10−3eV2and

|sin2θ23 −sin2θ23|<0.10 at 3σconﬁdence level (C. L.) on the possible CPT violation, extending

substantially the current bound of these parameters. We ﬁnd that with (∆m2

31 −∆m2

31), the de-

pendence of the statistical signiﬁcance on the relevant parameters to exclude the CPT conservation

is marginal, and that, if the diﬀerence in the best-ﬁt values of ∆m2

31 and ∆m2

31 measured by MI-

NOS(+) and NOνA persists as the true, the combined analysis will rule out the CPT conservation

at 4σC. L.. With the (sin2θ23 −sin2θ23), the statistical signiﬁcance to exclude CPT invariance

depends strongly on the true value of θ23 (θ23) mixing angle. In case of maximal mixing of θ23, as

indicated by the current T2K and NOνA measurements, the CPT conservation will be excluded at

3σC. L. or higher if the diﬀerence in the best-ﬁt values of θ23 and θ23 remains as the true.

I. CPT TEST WITH NEUTRINO

The CPT theorem, which connects three discrete sym-

metries: charge conjugation (C), parity (P), and time re-

versal (T), and has been theoretically proved in diﬀerent

ways [1–5], states that any Lorentz invariant local quan-

tum ﬁeld theory of point-particle must be CPT invariant.

If it is discovered that CPT symmetry is not conserved,

one of the three foundational assumptions (Lorentz in-

variance, Hamiltonian hermiticity, and locality) must be

sternly reconsidered. A consequence of the CPT invari-

ance is that the particle and its anti-particle must have

the same energy spectra. This important property opens

a possibility for direct testing CPT invariance by compar-

ing the mass spectra, or other properties such as lifetime

or magnetic moment of a particle and its anti-particle.

Ref. [6] provides the latest results on Lorentz and CPT

violation searches in the context of Standard Model Ex-

tension. A summary of the model-independent CPT test-

ing based on diﬀerent properties of the diﬀerent systems

of particle and anti-particle can be found in Ref. [7]. In

terms of relative precision, the most stringent constraint

on the CPT test was achieved on the neutral kaon system

∗Corresponding Author tranngocapc06@iﬁrse.icise.vn

[8]



m(K◦)−m(K◦)



<6×10−19 at 90% C. L. (1)

As pointed out in Ref. [9], when expressed in terms of

the mass-squared diﬀerence, the bound on the K◦−K◦

mass diﬀerence does not appear to be formidable. From

Eq.(1), one can get

|m2(K◦)−m2(K◦)|<0.3 eV2.(2)

Comparing this to the two mass-squared diﬀerences of

the three neutrino mass eigenstates [8], m2

ν2−m2

ν1≈

7.4×10−5eV2and |m2

ν3−m2

ν2| ≈ 2.45 ×10−3eV2,

it becomes clear that neutrino measurements, rather

than neutral kaons, provide the best constraint on the

CPT test in terms of the mass-squared diﬀerence [9,10].

The aforementioned neutrino mass-squared diﬀerences

come from measuring the neutrino oscillation, which is

a macroscopic quantum phenomenon establishing that

neutrinos are massive and thus beyond the Standard

Model’s description. It is worth noting that the neu-

trino mass spectrum cannot be calculated solely from

neutrino oscillations, but must be combined with cosmo-

logical constraints and beta decay, as recently discussed

in Ref. [11]. Neutrinos, unlike neutral B and K mesons,

arXiv:2210.13044v2 [hep-ph] 27 Dec 2022

are neutral elementary particles, and it is intriguing that

this particle could be a Majorana particle, where neu-

trino and anti-neutrino are indistinguishable in the con-

ventional sense of the CPT invariant paradigm. The neu-

trino nature under the CPT-violating scenario has been

explored in Ref. [12]. Here we focus on the phenomeno-

logical consequence of the CPT violation in the observ-

able neutrino oscillation.

In context of three-ﬂavor PMNS framework [13,14], for

a given propagation distance Land matter density ρ, the

probabilities (Pνα→νβ, Pνα→νβ) for a neutrino and anti-

neutrino at a speciﬁc energy (Eν, Eν) oscillating from one

ﬂavor (να, να) to another ﬂavor (νβ, νβ) are completely

and commonly described with six oscillation parameters

including three leptonic mixing angles (θ12, θ13 , θ23),

one Dirac CP-violating phase δCP , and two mass-squared

diﬀerences (∆m2

21,∆m2

31). Under CPT symmetry, the

neutrino and anti-neutrino oscillation probabilities are

well connected as follows:

Pνα→νβ

CPT

−−−→Pνβ→να=Pνα→νβ

=f(θ12, θ13, θ23, δCP,∆m2

21,∆m2

31).

If the CPT is violated in neutrino sector, the under-

lying sets of oscillation parameters in neutrino and anti-

neutrino may diﬀer. Empirically, we assume

Pνα→νβ=f(θ12, θ13, θ23, δCP,∆m2

21,∆m2

31),(3)

for describing the neutrino oscillations, and

Pνβ→να=f(θ12, θ13, θ23, δCP ,∆m2

21,∆m2

31),(4)

for anti-neutrino oscillations.

If there are observable diﬀerences in the parameters

of the two sets, it may indicate a CPT violation in the

lepton sector. Since the discovery of neutrino oscilla-

tions [15,16] at the end of the twentieth century, neu-

trino oscillation experiments [8] using both natural and

man-made neutrino sources have transitioned into the

precision measurement phase of three mixing angles and

two mass-squared diﬀerences, and being explored three

remained known unknowns including the neutrino mass

ordering, whether CP is violated, and whether the mix-

ing angle θ23 is maximal (θ23 = 45◦) or belong to a

lower (θ23 <45◦) or higher (θ23 >45◦) octant. Each

experiment is typically sensitive to a subset of the os-

cillation parameters but not the entire set. The ex-

periments with solar neutrinos provide the most con-

straints on the (θ12,∆m2

21) parameters while the reactor-

based long-baseline neutrino (R-LBL) experiments can

measure precisely the (θ12,∆m2

21) parameters. The

reactor-based short-baseline (order of 1 km) neutrino (R-

SBL) experiments play a central role in measuring the

(θ13,∆m2

31) parameters. The under-developing reactor-

based medium-baseline neutrino (R-MBL) experiment

JUNO, which will be discussed later, takes advantage of

interference of oscillations at diﬀerent wavelengths, huge

statistics, and good energy resolution to achieve sub-

percent precision in measuring the (θ12,∆m2

21,∆m2

31)

parameters. Experiments with the atmospheric neu-

trino and accelerator-based neutrino sources can pre-

cisely measure the (θ23, θ23,∆m2

31,∆m2

31) parameters.

Besides, this type of experiment is also sensitive to the

(θ13,θ13) parameters, but the precision of these param-

eters is much lower in comparison to the R-SBL experi-

ment due to the statistical limit and their strong correla-

tion with two known unknowns, CP-violating phase and

neutrino mass ordering. Although there is some hint [17]

of non-zero CP-violating phase δCP , precise measure-

ment on this parameter is not possible until the next gen-

eration of the accelerator-based long-baseline (A-LBL)

experiments. It is provided in Ref. [18] the most recent

update at 3σconﬁdence level (C. L.) on the bounds of

CPT violation on each individual parameter with global

neutrino data.

|δνν (∆m2

21)|<4.7×10−5eV2,

|δνν (∆m2

31)|<2.5×10−4eV2,

|δνν (sin2θ12)|<0.14,

|δνν (sin2θ13)|<0.029,

|δνν (sin2θ23)|<0.19,(5)

where δνν (X) = X−Xfor the X neutrino oscillation

parameter and the Xanti-neutrino oscillation param-

eter. In this study, we focus on the synergy between

two on-going A-LBL experiments (T2K and NOνA) and

one under-developing R-MBL experiment (JUNO) to ex-

plore the potential sensitivity to the measurement of

δνν (∆m2

31) and δνν (sin2θ23 ) parameters. The A-LBL

experiments utilize the highly intense beam of the al-

most pure muon neutrinos νµand muon anti-neutrinos

νµfor measuring the four transitions categorized into two

channels, appearance channels (νµ→νe, νµ→νe), and

disappearance channels (νµ→νµ, νµ→νµ). While the

appearance channels are sensitive to a wider subset of pa-

rameters and being explored for searching the CP viola-

tion in the lepton sector, measuring (νµ→νe, νµ→νe)

is not suﬃcient to test CPT directly since the corre-

sponding CPT-mirrored processes are missing. The dis-

appearance channels, on the other hand, are well-suited

for testing CPT since they are two CPT-mirrored pro-

cesses. We characterize the diﬀerence in the probabili-

ties of the muon neutrino disappearance and muon anti-

neutrino disappearance,ACPT

µµ =Pνµ→νµ−Pνµ→νµas an

observable measure of the CPT-violating eﬀect.

The observable asymmetry ACPT

µµ may consist of two

parts: intrinsic CPT asymmetry and extrinsic CPT

asymmetry caused by diﬀerences in interactions between

neutrinos and anti-neutrinos with the matter of the prop-

agation medium [19–23]. Fig. 1illustrates the CPT

asymmetries ACPT

µµ calculated in vacuum and in the mat-

ter presence at baselines of the T2K experiment (L =

295 km) and of the NOνA experiment (L = 810 km).

Here we take the best-ﬁt values of the mainly involved

(∆m2

31,∆m2

31, θ23, θ23) parameters from the recent T2K

results [24] and of the others from the global data anal-

ysis [25], which are summarized in Table I. It is wor-

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StringentconstraintonCPTviolationwiththesynergyofT2K-II,NOAextension,andJUNOT.V.Ngoc1;2,S.Cao1,N.T.HongVan3,andP.T.Quyen11InstituteForInterdisciplinaryResearchinScienceandEducation,ICISE,QuyNhon,Vietnam.2GraduateUniversityofScienceandTechnology,VietnamAcademyofScienceandTechnology,Hanoi,Vietnam.3I...

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Stringent constraint on CPT violation with the synergy of T2K-II NO A extension and JUNO T. V. Ngoc12S. Cao1 N. T. Hong Van3 and P. T. Quyen1

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