Constraining the nonstandard interaction parameters in long baseline neutrino experiments Katri Huitu, Timo J. K¨arkk¨ainen, Jukka Maalampi and Sampsa Vihonen University of Helsinki and University of Jyv¨ askyl¨ a, Finland
[email protected]
28 August 2017
Phys. Rev. D 93, 053016 (2016), arXiv: 1601.07730. Second article in preparation
Introduction > Model > Simulations > Results
Introduction: Current status of physics of neutrino oscillations Corrections to neutrino flavor transition by NSI Numerical simulations and analysis: how to take into account varying baseline? Correlation between CP angle and matter NSI parameters
Neutrinos – the invisible schizophrenic particles An elementary particle, predicted by Wolfgang Pauli and detected by Clyde Cowan and Frederick Reines. weakly interacting light:
P
mν . 0,2 eV
stable ultrarelativistic electrically neutral three flavours: νe , νµ , ντ spin- 12 fermion
3 / 34
Neutrinos – the invisible schizophrenic particles An elementary particle, predicted by Wolfgang Pauli and detected by Clyde Cowan and Frederick Reines. weakly interacting light:
P
mν . 0,2 eV
stable ultrarelativistic
Fact #1 Neutrinos are massless in Standard Model
electrically neutral three flavours: νe , νµ , ντ spin- 12 fermion
4 / 34
Neutrinos – the invisible schizophrenic particles An elementary particle, predicted by Wolfgang Pauli and detected by Clyde Cowan and Frederick Reines. weakly interacting light:
P
mν . 0,2 eV
stable ultrarelativistic electrically neutral three flavours: νe , νµ , ντ spin- 12 fermion
Fact #1 Neutrinos are massless in Standard Model Fact #2 Neutrino oscillations ⇒ mν > 0
5 / 34
Neutrinos – the invisible schizophrenic particles An elementary particle, predicted by Wolfgang Pauli and detected by Clyde Cowan and Frederick Reines. weakly interacting light:
P
mν . 0,2 eV
stable ultrarelativistic electrically neutral three flavours: νe , νµ , ντ spin- 12 fermion
Fact #1 Neutrinos are massless in Standard Model Fact #2 Neutrino oscillations ⇒ mν > 0
Neutrino oscillation indicates physics beyond the SM! Nobel prize to T. Kajita and A. B. McDonald for its discovery in 2015. 6 / 34
Current status of physics of neutrino oscillations Entering precision era of ν oscillation physics! Oscillations are described by mixing matrix UPMNS (θ12 , θ13 , θ23 , δCP ), analogous to quark mixing matrix VCKM .
7 / 34
Current status of physics of neutrino oscillations Entering precision era of ν oscillation physics! Oscillations are described by mixing matrix UPMNS (θ12 , θ13 , θ23 , δCP ), analogous to quark mixing matrix VCKM .
8 / 34
Current status of physics of neutrino oscillations Entering precision era of ν oscillation physics! Oscillations are described by mixing matrix UPMNS (θ12 , θ13 , θ23 , δCP ), analogous to quark mixing matrix VCKM .
9 / 34
Current status of physics of neutrino oscillations Entering precision era of ν oscillation physics! Oscillations are described by mixing matrix UPMNS (θ12 , θ13 , θ23 , δCP ), analogous to quark mixing matrix VCKM . Neutrino mass ordering still unknown; 2 ≈ 7.5 · 10−5 eV2 , ∆m12 2 | ≈ 2.5 · 10−3 eV2 |∆m31
10 / 34
Current status of physics of neutrino oscillations Entering precision era of ν oscillation physics! Oscillations are described by mixing matrix UPMNS (θ12 , θ13 , θ23 , δCP ), analogous to quark mixing matrix VCKM . Neutrino mass ordering still unknown; 2 ≈ 7.5 · 10−5 eV2 , ∆m12 2 | ≈ 2.5 · 10−3 eV2 |∆m31 CP violating angle 6= 0, π with 2σ C.L., best fit near maximal violation −π/2.
11 / 34
Current status of physics of neutrino oscillations Entering precision era of ν oscillation physics! Oscillations are described by mixing matrix UPMNS (θ12 , θ13 , θ23 , δCP ), analogous to quark mixing matrix VCKM . Neutrino mass ordering still unknown; 2 ≈ 7.5 · 10−5 eV2 , ∆m12 2 | ≈ 2.5 · 10−3 eV2 |∆m31 CP violating angle 6= 0, π with 2σ C.L., best fit near maximal violation −π/2. Octant degeneracy of θ23 persists.
12 / 34
Effective theory: Non-Standard interactions (NSI) Grossman (1995) arXiv:hep-ph/9507344 et al.
New physics responsible for neutrino masses and mixing may change the effects of matter on propagating neutrinos, and also neutrino production at the source and detection process at detector: NSI
13 / 34
Effective theory: Non-Standard interactions (NSI) Grossman (1995) arXiv:hep-ph/9507344 et al.
New physics responsible for neutrino masses and mixing may change the effects of matter on propagating neutrinos, and also neutrino production at the source and detection process at detector: NSI In low energy regime consider nonrenormalizable and not gauge invariant dimension-6 operators √ ff 0 C µ µ 0 0 LCC NSI = −2 2GF εαβ (ν α γ PL νβ )(f γ PC f ), f 6= f √ fC µ µ LNC NSI = −2 2GF εαβ (ν α γ PL νβ )(f γ PC f ). |ε| describes the strength of the NSI with respect to Fermi interaction.
14 / 34
Effective theory: Non-Standard interactions (NSI) Grossman (1995) arXiv:hep-ph/9507344 et al.
New physics responsible for neutrino masses and mixing may change the effects of matter on propagating neutrinos, and also neutrino production at the source and detection process at detector: NSI In low energy regime consider nonrenormalizable and not gauge invariant dimension-6 operators √ ff 0 C µ µ 0 0 LCC NSI = −2 2GF εαβ (ν α γ PL νβ )(f γ PC f ), f 6= f √ fC µ µ LNC NSI = −2 2GF εαβ (ν α γ PL νβ )(f γ PC f ). |ε| describes the strength of the NSI with respect to Fermi 2 , interaction. As GF ∼ 1/MW |ε| ∼
MW , Λ
where Λ is the scale new physics. (Maybe at TeV scale?) 15 / 34
Standard neutrino oscillations in matter Wolfenstein (1978), Mikheyev and Smirnov (1985)
Description of neutrino oscillation in matter is depicted with Schr¨odinger equation, with Standard Interaction (SI) Hamiltonian HSI = Hmass + Hmatter VCC + VNC 1 0 Udiag(m12 , m22 , m32 )U † + = 2Eν
0
where VCC =
√
0 0 VNC 0 , 0 VNC
√
2GF Eν Ne and VNC = −
2 2 GF Eν Nn .
16 / 34
Standard neutrino oscillations in matter Wolfenstein (1978), Mikheyev and Smirnov (1985)
Description of neutrino oscillation in matter is depicted with Schr¨odinger equation, with Standard Interaction (SI) Hamiltonian HSI = Hmass + Hmatter VCC + VNC 1 0 Udiag(m12 , m22 , m32 )U † + = 2Eν
0
0 0 VNC 0 , 0 VNC
√ √ where VCC = 2GF Eν Ne and VNC = − 22 GF Eν Nn . Oscillation probability is then
2
Pαβ ≡ P(να → νβ ) = hνβ |e −iHSI L |να i . and with L = 0 we have P(να → νβ ) = δαβ . 17 / 34
Non-standard neutrino oscillations in matter Matter NSI matrix elements are obtained by summing over chirality and fermion states, εm αβ =
X f ,C
εfC αβ
Nf . Ne
18 / 34
Non-standard neutrino oscillations in matter Matter NSI matrix elements are obtained by summing over chirality and fermion states, εm αβ =
X f ,C
εfC αβ
Nf . Ne
Oscillation probability is calculated with NSI Hamiltonian:
P(να → νβ ) = hνβd |e −i(HSI +VCC ε
m /2E )L ν
2
|ναs i .
19 / 34
Non-standard neutrino oscillations in matter Matter NSI matrix elements are obtained by summing over chirality and fermion states, εm αβ =
X f ,C
εfC αβ
Nf . Ne
Oscillation probability is calculated with NSI Hamiltonian:
P(να → νβ ) = hνβd |e −i(HSI +VCC ε
m /2E )L ν
2
|ναs i .
In general case we would also change the state vectors accordingly: |ναs i = |να i + εsαβ |νβ i,
hνβd | = hνβ | + εdαβ hνα |,
where εsαβ = εd∗ βα , resulting in zero-distance flavor transition.
20 / 34
Non-standard neutrino oscillations in matter Matter NSI matrix elements are obtained by summing over chirality and fermion states, εm αβ =
X f ,C
εfC αβ
Nf . Ne
Oscillation probability is calculated with NSI Hamiltonian:
P(να → νβ ) = hνβd |e −i(HSI +VCC ε
m /2E )L ν
2
|ναs i .
In general case we would also change the state vectors accordingly: |ναs i = |να i + εsαβ |νβ i,
hνβd | = hνβ | + εdαβ hνα |,
where εsαβ = εd∗ βα , resulting in zero-distance flavor transition. Pαβ (L = 0) = δαβ (1 + O(ε)) + O(ε2 ) 21 / 34
Setting up oscillation simulations How the future neutrino oscillation experiments would constrain matter NSI parameters?
Huber, Lindner, Winter et al., arXiv:hep-ph/0407333, arXiv:hep-ph/0701187
22 / 34
Setting up oscillation simulations How the future neutrino oscillation experiments would constrain matter NSI parameters? What is the optimal baseline for L ∈ [100, 5000] km?
Huber, Lindner, Winter et al., arXiv:hep-ph/0407333, arXiv:hep-ph/0701187
23 / 34
Setting up oscillation simulations How the future neutrino oscillation experiments would constrain matter NSI parameters? What is the optimal baseline for L ∈ [100, 5000] km? We set δCP and mass ordering free, θ23 to higher octant and assume εm is real with only one non-zero element. Huber, Lindner, Winter et al., arXiv:hep-ph/0407333, arXiv:hep-ph/0701187
Our benchmarks are LBNO/DUNE 20/40 kt doublephase LAr setup. 24 / 34
Problem: flux is optimized to a certain baseline!
25 / 34
Problem: flux is optimized to a certain baseline! Instead of recalculating the neutrino flux for every baseline, we take the flux optimized to 2288 km baseline and shift it assuming L/E = constant (≈ 4π/∆m2 ). Lnew Eold , φnew (Enew ) = φold (Eold ) Enew = Lold
26 / 34
Problem: flux is optimized to a certain baseline! Instead of recalculating the neutrino flux for every baseline, we take the flux optimized to 2288 km baseline and shift it assuming L/E = constant (≈ 4π/∆m2 ). Lnew Eold , φnew (Enew ) = φold (Eold ) Enew = Lold
27 / 34
90 % CL. discovery reach for εm eµ with SPS/LBNO and DUNE
Strong correlation found between some NSI parameters and CP angle. Discovery potential reaches maximum at ∼ 3000 km with SPS/LBNO. 28 / 34
90 % CL. discovery reach for εm τ τ with SPS/LBNO and DUNE
However weak or nonexistent correlation found between some other NSI parameters and CP angle. Discovery potential reduced at small distances, as expected. 29 / 34
Why are the correlations so different? We investigate analytically the correlation between the CP angle δ and the various NSI parameters εm ``0 within the first power in m sin(θ13 ) and ε``0 (both fixed). A(ν` → ν`0 ) = δ``0 −
3 X
L U`j Hjk (U † )k`0 + O(ε2 , sin2 θ13 ) 2E ν j,k=1
Two examples (for ε = 10−3 ): Peµ ∝ 1.56 − 1.22 cos δ Pτ τ ∝ 3.200 + 0.120 cos δ + 0.001 cos2 δ Hence the transition probability Pτ τ has significantly smaller dependence on the CP angle than Peµ . This is seen in the discovery reach plot, where the CP variation band is narrower than the corresponding band in the case of νe → νµ transition. How to quantify this? 30 / 34
Relative variation sheds light on δCP interference
R``0 ≡
max − P min P`` 0 ``0 min P`` 0
31 / 34
Conclusions
Physics of neutrino oscillations is entering precision era.
32 / 34
Conclusions
Physics of neutrino oscillations is entering precision era. Strong correlation between some matter NSI parameters and CP angle.
33 / 34
Conclusions
Physics of neutrino oscillations is entering precision era. Strong correlation between some matter NSI parameters and CP angle. Optimal baseline for matter NSI studies at & 3000 km.
34 / 34
References
Huitu, K¨arkk¨ainen, Maalampi and Vihonen: Constraining the nonstandard interaction parameters in long baseline neutrino experiments, Phys. Rev. D 93, 053016 (2016), arXiv: 1601.07730. Y. Grossman, Phys. Lett. B359, 141 (1995), arXiv:hep-ph/9507344. NuFit 3.0 (as of November 2016), JHEP 11 (2014) 052 arXiv:1409.5439 Huber et al., Comput. Phys. Commun. 177, 432 (2007) and Int. J. Mod. Phys. C 19 (2008).
35 / 34
