Energy-Dependent Neutrino Mixing Parameters at Oscillation Experiments

Energy-Dependent Neutrino Mixing Parameters at Oscillation Experiments

in collaboration with

K. S. Babu, Andr´e de Gouvˆea and Pedro A. N. Machado

Vedran Brdar

Energy-Dependent Neutrino Mixing Parameters at Oscillation Experiments TAUP 2021, IFIC, Valencia, Spain

Energy Dependence of the Standard Model Parameters

DELPHI 2004 SLD ALEPH OPAL DELPHI (B decays) DELPHI 1998

α_s(MZ)=0.1183±0.0027 → αs(mb)=0.224±0.010 m_b(m_b)=4.24±0.11 GeV/c²

400 500 600 700 800 900 1000

[GeV]

µ 0.85

0.9 0.95 1 1.05 )refµ(t) / mµ(tm

t σt NLO extraction from differential

µref Reference scale

) = 0.1191 (mZ αs = 5, One-loop RGE, nf

CMS 35.9 fb^-1 (13 TeV)

ABMP16_5_nlo PDF set = 476 GeV µref

µref = µ0

APV!Cs"

Qweak!first"

E158

SLAC LEP Ν"DIS

PVDIS

APV!Ra^#" Moller P2

Qweak SOLID

''Anticipated sensitivities''

"3 "2 "1 0 1 2 3

0.230 0.232 0.234 0.236 0.238 0.240 0.242

Log₁₀Q#GeV$

sin2ΘW!Q2"

I couplings and mass parameters in the Standard Model and Beyond are energy dependent

I while we know that from theoretical perspective (renormalization in QFT) it should be stressed that “running” of various parameters has actually been observed

DELPHI, EPJC 46 (2006) 569

PLB 803(2020)135263 Davoudiasl et al., arXiv:1507.00352

I What about neutrino sector?

Energy Dependence of the PMNS Matrix

Energy-Dependent Neutrino Mixing Parameters at Oscillation Experiments 3 / 14 TAUP 2021, IFIC, Valencia, Spain

να(Q²) =Uαi(Q²)νi α=e, µ, τ i,j= 1,2,3

Antusch et al. (JHEP 03 (2005) 024) Casas et al. (NPB 573 (2000)) Goswami et al. (PRD 80 (2009)) Balaji et al. (PLB 481 (2000))

I when higher-order quantum effects are included, doU_αi matrix elements change relative to one another?

I higher-order electroweak corrections lead to very minor effects but in neutrino mass modelsU_αi can change in a flavor-dependent way I this was already extensively studied for many models with heavy BSM

degrees of freedom, seee.g.

I we are however interested here in relatively light new physicswhere masses of new particles are comparable or lighter with respect to the neutrino energies at various experiments

Connection to Neutrino Experiments

M. Beuthe, arXiv:hep-ph/0109119 I.P. Volobuev, arXiv:1703.08070

QFT approach:

I amplitude: P

iU_αi^∗ e⁻ⁱ

m2 i−p2 2|~p| L

U_βi →P_αβ =P

j,kU_αj^∗ U_βjU_αkU_βk^∗ e⁻ⁱ

m2 j−m2

k 2|~p| L

I Energy dependence of oscillation parameters:

I propagatingneutrino is on shell (Q² =p_ν² =m²_ν ≈0)→mi in formula is the mass at√

Q²=m_i

I at production, contribution to the amplitude should be Lorentz invariant;

in the rest frame of decaying pionE =mπ →Uαi =Uαi(Q_p² =m²_π) I at detectionsite we takeUβi(Q_d²) whereQ_d² is Mandelstam t which has

no dependence onm_π²

Neutrino Oscillations in Vacuum

Energy-Dependent Neutrino Mixing Parameters at Oscillation Experiments 5 / 14 TAUP 2021, IFIC, Valencia, Spain

2 flavors:

U(Q²) =

cosθ(Q²) sinθ(Q²)

−sinθ(Q²) cosθ(Q²)

1 0

0 e^{iβ(Q˜ 2)}

θ(Q_p²)≡θp, θ(Q_d²)≡θd, and β(Q˜ _d²)−β(Q˜ _p²)≡β

P_µe = sin²(θ_p−θ_d) + sin 2θ_psin 2θ_dsin²

∆m²L 4E +^β₂

Grossman, PLB 359 (1995)

I β appears due to the CP-violating couplings in the new physics sector and has nothing to do with the nature of active neutrinos =⇒ it appears also in Dirac neutrino models

I β “shifts” the oscillation phase: ∆m²L/2E →∆m²L/2E+β In the small new physics effect,θ=θd−θp1and β1:

Pµe=²_θ+O(⁴θ) +

sin²2θd−sin 4θdθ+O(²θ)h sin²

∆m²L 4E

+₂^βsin

∆m²L 2E

+O(²β)i

I In the zero-baseline limit,L→0, the new-physics effects areO(²_θ, ²_β) I for a finite baseline, instead, the new-physics effects areO(_θ, _β)

Neutrino Oscillations in Vacuum

3 flavors:

I more CP-odd phases when compared to 2-flavor case: β,α,δ(Q_p²),δ(Q_d²) I expressions for 3 flavor oscillation probabilities are lengthy but looking at

Pαβ−P_α¯β¯ gives simple and useful results:

P_µe−P_µ¯¯e ' −8J∆₂₁sin²

∆31

2

h 1 +

2_{sin 2θ}¹²

12 +_α^c_s^δ

δ

_cot(∆

31/2)

∆21

i

ij≡θij(Q_d²)−θij(Q_p²),δ=δ(Q_d²)−δ(Q_p²),α=α,β=β ∆_ij ≡∆m²_ijL/2E

I in the δ→0 limit, in which there is no standard CP violation in the lepton sector, new RG induced CP violation is stillpresent and nonzero

Pee−Pe¯e¯'(β−δ) sin²2θ13sin ∆31−α s₁₂² sin²2θ13sin ∆31−sin²2θ12sin ∆21

I apparent violation of CPT symmetry but CPT invariance, P(να(Q_p²)→να(Q_d²)) =P(¯να(Q_d²)→ν¯α(Q_p²)), is satisfied I for T2K and NOvA matter effects are included in our analysis

Model

Energy-Dependent Neutrino Mixing Parameters at Oscillation Experiments 7 / 14 TAUP 2021, IFIC, Valencia, Spain

I We consider scotogenic-like model withU(1) and Z₂ symmetry

−L⁽¹⁾_ν =LYνH˜1N_R +ϕN_R^cY_NN_R+h.c.

forM_Nⁱ =Y_Nⁱv_ϕ/√

2M_H,A, M_ν ' ^vϕ

16√

2π²Y_νY_NY_ν^Tln^M_M^H22 A

I 16π²β(YN)≡16π²_d^dY_ln|Q|^N = 4YN

Y_N²+ ¹₂Tr(Y_N²)

=⇒ obtainYN and henceM_ν at q

Q_p² and q

Q_d²;Y_N hasO(1) entries to maximize RG effect I Y_ν is obtained using Casas-Ibarra parametrization

RGE Effect

I we take parameters at Q_p² in accord with NuFIT, evolve mass matrix between Q_p² and Q_d² and extract oscillation parameters at the latter scale I RG effect is largest for quasidegenerate masses

Constraints from Short Baseline Experiments

Energy-Dependent Neutrino Mixing Parameters at Oscillation Experiments 9 / 14 TAUP 2021, IFIC, Valencia, Spain

I RG running leads to zero baseline effects since U(Q_p²)U^†(Q_d²)6=1

I experiments with high average neutrino energy are especially sensitive due to thelarger difference between Q_p² =m_π² andQ_d²

I while we found successful explanations or LSND and MiniBooNE, constraints from short baseline experiments rule out such possibilities

Constraints from Short Baseline Experiments

I short baseline constraints remove parameter points with strongest RG running

Oscillation Probabilities

Energy-Dependent Neutrino Mixing Parameters at Oscillation Experiments 11 / 14 TAUP 2021, IFIC, Valencia, Spain

0.02 0.04 0.06 0.08 0.10 0.12 0.14

P(νμ->νe)orP(νμ->νe)

NO m1=^{0.05 eV} BP1(^solid) standard(^dashed) P(νμ->νe)NOvA P(νμ->νe)NOvA

NOvA

1 2 3 4 5

-0.2 -0.1 0.0 0.1 0.2

E[^GeV]

(PBSM-PSM)/PSM

0.02 0.04 0.06 0.08 0.10 0.12 0.14

P(νμ->νe)orP(νμ->νe)

NO m1=^{0.05 eV} BP2(^solid) standard(^dashed)

P(νμ->νe)NOvA P(νμ->νe)NOvA

NOvA

1 2 3 4 5

0 2 4 6 8 10

E[^GeV]

(PBSM-PSM)/PSM

I BP1best fits T2K and NOvA data and BP2is strongly disfavoured by both short and long baseline experiments

RG Evolution of the Mixing Parameters

0.5 1.0 1.5 2.0 2.5

0.4 0.6 0.8 1.0 1.2

Q²[^GeV] X/X(Qp

2 )

NO m1=0.05 eV BP1(solid) BP2(dashed)

θ12

θ13

θ23

δ

α

β

T2K NOvA

I the strongest effects are in running of θ12

I variation of θ12 relative to the other mixing angles θ13 andθ23is enhanced by|∆θ₁₂/∆θ₁₃|,

|∆θ₁₂/∆θ23| ∝ |∆m²₃₁/∆m₂₁² |

0.5 1.0 1.5 2.0 2.5

0 20 40 60 80

Q²[GeV]

mixingparameter[°]

NO m1=0.05 eV BP1(solid) BP2(dashed)

θ12

θ13

θ23

δ/10

α/10 β

/10

T2K NOvA

Ultra-High Energy Neutrinos - Flavor Ratios

Energy-Dependent Neutrino Mixing Parameters at Oscillation Experiments 13 / 14 TAUP 2021, IFIC, Valencia, Spain

I we postulate thatQp²is above the detection scale in accelerator- based experiments;Q_d²is fixed to (1000 GeV)²

I detected neutrinos are incoherent superposition of mass eigenstates

Pαβ= P3 j=1

Uαj(Qp²)

2

Uβj(Q_d²)

2

Conclusion

I we considered the effects of scale-dependent lepton mixing parameters at neutrino oscillation experiments

I mismatch betweenU(Q_p²) andU(Q_d²) leads to novel phenomenology I signatures include difference between mixing angle measurementsat

various experiments,zero-baseline flavor transition,new sources of CP violationandapparent but not actual violation of CPT

I all of this can be induced bylight new physics sectorthat does not need to be produced at experiments - such light particles can remain undiscovered and onlyimpact neutrino experiments through quantum corrections that induce non-trivial energy depedence ofU(Q²) I we showed that the renormalization group evolution of the mixing

parameters can induce observable effects at T2KandNOvA and in the flavor compositionof ultra-high energy neutrinos

Energy-Dependent Neutrino Mixing Parameters at Oscillation Experiments 14 / 14 TAUP 2021, IFIC, Valencia, Spain

BACKUP SLIDES

Inverted Ordering

I for fixed lightest neutrino mass, RG running in the inverted ordering is stronger than in the normal one

Bi-probabilities Plots

Energy-Dependent Neutrino Mixing Parameters at Oscillation Experiments 14 / 14 TAUP 2021, IFIC, Valencia, Spain

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.01

0.02 0.03 0.04 0.05 0.06 0.07 0.08

P(ν_μ→νe) P(νμ→νe)

T2K NO(solid), IO(dashed)

sin²θ23=0.55,Δm₃₁²=2.56×10^-3eV²,δ=-π/2 sin²θ23=0.55,Δm₃₁²=2.56×10^-3eV²,δ=0 sin²θ23=0.55,Δm₃₁²=-2.46×10^-3eV²,δ=π/2

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.01

0.02 0.03 0.04 0.05 0.06 0.07 0.08

P(ν_μ→νe) P(νμ→νe)

NOvA NO(solid), IO(dashed)

sin²θ23=0.58,Δm₃₁²=2.52×10^-3eV²,δ=-π/2 sin²θ23=0.58,Δm₃₁²=2.52×10^-3eV²,δ=0 sin²θ23=0.57,Δm₃₁²=-2.41×10^-3eV²,δ=π/2

Oscillation Probabilities - T2K

0.02 0.04 0.06 0.08 0.10 0.12 0.14

P(νμ->νe)orP(νμ->νe)

NO m₁=^{0.05 eV} BP1(^solid) standard(^dashed) P(νμ->νe)T2K P(νμ->νe)T2K

T2K

1 2 3 4 5

-0.4 -0.2 0.0 0.2 0.4 0.6

E[^GeV]

(PBSM-PSM)/PSM

0.02 0.04 0.06 0.08 0.10 0.12 0.14

P(νμ->νe)orP(νμ->νe)

NO m₁=^{0.05 eV} BP2(^solid) standard(^dashed) P(νμ->νe)T2K P(νμ->νe)T2K

T2K

1 2 3 4 5

0 5 10 15 20 25

E[^GeV]

(PBSM-PSM)/PSM