Hints for leptonic CP violation or New Physics?

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by  David V. Forero

Hints for leptonic CP violation or New Physics?
David V. Forero∗ and Patrick Huber†
Center for Neutrino Physics, Virginia Tech, Blacksburg, VA 24061, USA
(Dated: January 18, 2016)
One of the major open questions in the neutrino sector is the issue of leptonic CP violation.
Current global oscillation data shows a mild preference for a large, potentially maximal value for
the Dirac CP phase in the neutrino mixing matrix. In this letter, we point out that New Physics
in the form of neutral-current like non-standard interactions with real couplings would likely yield
a similar conclusion even if CP in the neutrino sector were conserved. Therefore, the claim for a
discovery of leptonic CP violation will require a robust ability to test New Physics scenarios.
6 In2015aNobelprizeforthediscoveryofneutrinooscil- action are introduced above the electroweak symmetry
1 lation was given. The bulk of the existing data currently breakingscalehastoaddressthefactthatinvarianceun-
0 is very well described by the oscillation of three active der the weak SU(2) group will create a charged lepton
2
neutrinos, see for instance Ref. [1, 2]. There are poten- counter part of any neutrino-only operator. Given that

n tial indications for additional, sterile neutrinos, which at the electroweak scale is not very far from the scale at
a
this stage are not conclusive yet [3] and we therefore will whichtypicalneutrinoexperimentsareconducted,break-
J
neglect for the remainder of this letter. Lately, due to a ingoftheelectroweaksymmetrydoesnoterasethecorre-
4
tension between reactor and accelerator neutrino exper- spondencebetweenneutralandchargedleptonoperators,
1
iments, a preference for a value of the Dirac CP phase at best factors of a few are gained. The charged lepton

] close to −π/2 was first reported in Ref. [4]. The ques- bounds involving the first and second family are very
h
tion of CP violation in the leptonic sector is a priority of stringent. InRef.[13]asystematicanalysisofdimension
p
the future neutrino program and the main effort is dedi- 6 and 8 operators is performed and it is found that for
-
p catedtotheDUNEexperiment[5]. Apartfromanumber dimension 8 operators it is possible to arrange for can-
e
of experimental challenges and the need to understand cellations, provided a suitable particle content is chosen,
h
[ neutrino-nucleus interactions, sub-leading effects of the- suchthatlargeNSIintheneutrinosectorcanberealized
oretical origin can also affect the determination of the withoutcreatingsizableeffectsinthechargedleptonsec-
1
DiracCPphase. Inthisletterwefocus onso-callednon- tor. This requires fine tuning and no actual models have
v
standard interactions (NSI), which have been speculated been put forward. It is worth noting that even with-
6
3 aboutevenbeforethediscoveryofneutrinooscillation[6] out fine tuning, third family NSI in the τ sector can be
7 and fora recentreview seeRef.[7]. NSIprovidea model potentially large of order 0.1G , see e.g. [14], since the
F
3 independent, effective field theory framework to include correspondingchargedleptonboundsthemselvesarevery
0
new physics effects in the standard neutrino description, weak.
.
1 see e.g. Ref. [8]. The situation is quite different if we consider models
0
NSI are parameterized by dimensionless couplings, ε, where NSI is generated below the scale of electroweak
6
which are measured relative to G . From neutrino data symmetry breaking, since by construction there will be
1 F
: alone large magnitudes for the dimensionless couplings no correspondence between neutral and charged lepton
v |εf=u,d| (cid:46) 0.14 at 90% [9] are allowed, which for Earth operators. An early example of a low-scale neutrino
i eτ
X matter densities translates into |ε | ∼ O(1). Generally, massmodel(withoutNSI)isgiveninRef.[15],wherethe
eτ
r NSI can provide new phases that can potentially be new breakingofadiscretegaugesymmetryatascaleaslowas
a
sourcesofCPviolation. Inthecontextofflavorchanging afewkeVisresponsibleforsmallDiracneutrinomasses.
NSIinthesourceandthedetectionofneutrinosadiscus- Itwouldbestraightforwardtoaugmentthismodelbyad-
sionofnewsourcesofCPviolationappearedinRef.[10]. ditional flavor changing neutral currents to create large
In the case of neutral current NSI a discussion of this NSI. The general idea is to invoke new light degrees of
issueappearedinRef.[11]. InthecontextofNOvA,and freedom which preferentially couple to neutrinos and/or
motivated by large NSI allowed by solar neutrino data, darkmatterparticles,e.g.[16,17]. Thesemodelstendto
one example of the potential NSI and standard oscilla- introduce new self-interactions in the dark matter sector
tion confusion was analyzed at the probability level in and need to observe the relevant astrophysical bounds
Ref. [12]. from structure formation. Also, in some of these models
Directboundsderivedfromtheneutrinosectoraretyp- thereareconnectionstothesterileneutrinosector,which
ically of the order 0.1-1 in units of G , that is, New inturncanhelptoaccommodatesterileneutrinosincos-
F
Physics contributions of about the same size as the lead- mology[18]. Thus, weseethatthereisampleroomfrom
ing Standard Model (SM) contribution are still allowed. bothanexperimentalandtheoreticalperspectiveforrela-
On the other hand, any model where these new inter- tivelylargeNSI.TheresultingdegeneraciesbetweenNew
2
35 35
T2K NOvA
SM,δCP=free
30 |ε|=0.3,ϕ=free,δCP=π 30
|ε|=0.3,ϕ=free,δCP=0
25 25
e e
at at
r r
o 20 o 20
n n
ri ri
ut ut
e 15 e 15
n n
nti nti
A A
10 10
SM,δCP=free
5 5
|ε|=0.3,ϕ=free,δCP=π
GLoBES2016 GLoBES2016 |ε|=0.3,ϕ=free,δCP=0
0 0
20 40 60 80 100 120 20 40 60 80 100 120
Neutrino rate Neutrino rate
FIG. 1. Bi-rate plots. The full line curve corresponds to the SM for all Dirac CP phase values. The dashed and dotted curves
correspond to a fixed NSI magnitude |ε| = 0.3 and for all NSI phase φ values but for different values of the Standard CP
phase. The cross for the SM point δ = −π/2 shows the statistical uncertainty. The left (right) panel corresponds to our
CP
implementation of the T2K (NOvA) experiment. All parameters not labeled in the plot were fixed to their best fit values, see
text for details.
Physics and oscillation physics recently have been stud- In the particular case of the (anti)neutrino appearance
ied in Ref. [19] in a more general setting. Here, we will channel, only the two NSI complex parameters ε and
eµ
studyspecificallytheimpactneutralcurrent-likeNSIcan ε play a role [20]. Instead of an exhaustive analysis to
eτ
have on the analysis of Daya Bay, T2K and NOvA data quantifytheinterplayofalltheNSIparameterswiththe
sets and point out that the current hint for maximal CP SM ones, we will consider ε =0 and ε ≡|ε|exp(iφ)
eµ eτ
violationmaybeinfactbecausedbyCPconserving New which is enough for our discussion. Throughout this let-
Physics. ter, ourresultswillcorrespondonlytothenormalorder-
The standard neutrino oscillations in vacuum are de- ing for the neutrino spectrum.
scribed by the Hamiltonian:
We have implemented a GLoBES [21, 22] simulation
H = 1 (cid:2)Udiag(cid:0)0,∆m2 ,∆m2 (cid:1) U†(cid:3) (1) of a 295km baseline neutrino beam experiment with the
0 2E 21 31 characteristicsofT2Kbutscalingitsexposurebyafactor
5 relative to the current data [23]. In addition, we have
where U is the lepton mixing matrix parameterized by
also implemented a simulation of NOvA running 3 years
three mixing angles θ and a CP violating phase δ .
ij CP in neutrino mode plus 3 years in antineutrino mode [24].
∆m2 in Eq. (1) denotes the two known mass square
k1 The set of oscillation parameters used along this work
differences and E the neutrino energy.
corresponds to the best fit values in Ref. [1] except for
Since we will consider long-baseline neutrino oscilla-
the reactor mixing angle that was fixed to the Daya Bay
tions, the neutrino forward scattering interactions in
best fit value in Ref. [25].
matter, can be effectively parameterized in the presence
The interplay of the Dirac CP phase and the NSI pa-
of NSI by the following Hamiltonian:
rameters in each of the two considered facilities is shown
 
1+ε ε ε inthebi-rateplotsofFig.1. Forthechosenvaluesofthe
ee eµ eτ
Hint =V  ε∗eµ εµµ εµτ  (2) NSI parameters, and considering the errors in both NSI
ε∗ ε∗ ε andSMrates,anoverlapintheSMpointδ =−π/2is
eτ µτ ττ CP
clearly shown in both panels for T2K and NOvA. How-
√
with V = 2G N , where G is the Fermi constant ever, noticethatinthecaseoftheT2Krates(leftpanel)
F e F
and N is the electron density on Earth. Notice that the there is a tension between the considered NSI cases and
e
Hamiltonian in Eq. (2) has 8 new physical parameters in the the SM point δ = −π/2. Thus, in combination
CP
addition to the standard oscillation ones. However, only withNOvAthe‘confusion’willbesignificantfortheNSI
fewofthemarepresentinanspecificoscillationchannel. case with δ =π.
CP
3
GLoBES2016 δCTrPue=π,|ε|=0.3 SM GLoBES2016 δCTrPue=π,|ε|=0.3 SM
0.15
ϕ=-π/2 0.08 ϕ=-π/2
ϕ=0 ϕ=0
ϕ=π/2 ϕ=π/2
y ϕ=π y ϕ=π
c c
n n 0.06
e e
u 0.10 u
q q
e e
r r
f f
e e
v v 0.04
ati ati
el el
R 0.05 R
0.02
0.00 0.00
-1.0 -0.5 0.0 0.5 1.0 20 40 60 80 100
δ /π χ2
CP min
FIG. 2. Results assuming δTrue =π. In the left panel, the Dirac CP phase best fit distributions for Standard Model (SM) and
CP
NSIinteractionsareshown. TheNSImagnitudewasfixedtothevalue|ε|=0.3forthedifferentNSIphaseφvaluesshowedin
the plot. In the right panel appears the minimum χ2 distributions from the fit to the SM Dirac CP phase for each of the SM
and NSI cases showed in the left panel. All not shown parameters were marginalized over, see text for details of the analysis.
By assuming CP conserving values, in the presence of ters but δ were included in the analysis.
CP
NSI, the freedom in |ε| and φ can be used to ‘mimic’ Our main result is presented in Fig. 2. The distribu-
the SM point δ = −π/2. Basically, the value of |ε| tion of the Dirac CP phase best fit values for SM and
CP
sets the opening of the NSI ellipse while the phase φ can NSI interactions are shown in the left panel. In all cases
be tuned to coincide with the SM and NSI intersection δtrue =π. In the case of the SM, the δ has values dis-
CP CP
point. Noticethat,forT2K(leftpanel),alargervaluefor tributedaroundCPconservingvaluesincludingzerobut
|ε| is needed to exactly pick the SM point δ = −π/2 it is mainly distributed around δ = ±π as expected.
CP CP
whileforNOvA(rightpanel)asmallerεwouldinsteadbe When NSI are considered, two general features appear:
required. This is mainly due to the different baseline of InthecaseofcomplexNSI,φ=−π/2andφ=π/2, δ
CP
bothexperimentssincethesensitivitytotheNSIdepends is distributed with a higher probabilities respect to the
ontheSMandNSIinterferenceofvacuumandmatteros- SM case around values that are close to zero and π, re-
cillations(seeEq.(33)ofRef.[20]). Thus,acombination spectively; and the distributions are very peaked around
of experiments with different baselines limits the param- their mean value. However, when φ = 0 (real NSI) the
eter tuning we are discussing, which in the future may distributionofδ isbroaderandextendsforhalfofthe
CP
allow to disentangle these effects if both high-statistic parameter space in the positive region. In this case, the
data sets from DUNE and T2HK are available [26–28]. mean value is located near δ = π with a probability
CP
However, our philosophy here is quite different: Given closer to the one of the SM case. In the remaining case
a particular set of NSI parameters (allowed by current of real NSI φ = π also the distribution is broader but
bounds) we want to quantified the level of ‘confusion’ if the main feature is that its mean value is centered at
the currently preferred value for the δ turned out to δ =−π/2almostwiththesameprobabilityoftheSM
CP CP
be correct. case. InbothcaseswithrealNSIthereisanon-negligible
ToquantifythesensitivitytotheSMDiracCPphasein probabilitytofindδ violatingvalueseventhoughδTrue
CP CP
the presence of NSI we have adopted the usual χ2 analy- hasassumedtobeCPconserving. Thisresultisremark-
siswheren =n ((cid:126)λtrue,εtrue)andµ =µ ((cid:126)λ)corresponds able,inparticularwhenφ=π,inthelightofthecurrent
i i i i
to the simulated and test events, respectively. The set of preference for the Dirac CP phase value.
standardoscillationparameters,mixingangles,DiracCP The corresponding distribution of the χ2-minima, for
phase and the solar and atmospheric splittings, are rep- each case of the right hand panel, are shown in the left
resented by (cid:126)λ. To test SM oscillations rates µ against hand panel of Fig. 2. Due to the random statistical fluc-
i
the ones with NSI, we implemented random statistical tuations the χ2 for the SM case is centered at χ2 (cid:39)40
min
fluctuations (Poisson distributed) on the ‘true’ rates n . corresponding the number of bins minus the number of
i
Gaussian priors for all the standard oscillation parame- fitted parameters. However, the main feature is that all
4
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