Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments Sabya Sachi Chatterjee sabya@iopb.res.in Institute of Physics, Bhubaneswar, India. XXI DAE-BRNS High Energy Physics Symposium 2014 8-12 December 2014, Indian Institute of Technology, Guwahati. Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 1 / 20
This work has been done in collaboration with My Supervisor, Prof. Sanjib Kumar Agarwalla (Institute of Physics, Bhubaneswar). Arnab Dasgupta (Center for Theoretical Physics, Jamia Millia Islamia, New Delhi). Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 1 / 20
Table of contents Concept of Long-range force. Numerical plots. Event spectrum with and without LRF. Bi-events plots. Mass-hierarchy sensitivity. Discovery reach of leptonic CP violation. Constraints of coupling strength. LRF at discovery level. Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 2 / 20
Concept of Long-range forces SM is invariant under four global symmetries corresponding to the baryon number and lepton numbers of the three lepton families which can t be gauged in anomally free way. But there exists global symmetries(u(1) X ) which can be gauged in anomally free way and that bring us beyond the SM. X= L e L µ, L e L τ and L µ L τ are the charge of the corresponding symmetries. Extra gauge boson Z µ comes into the picture due to an additional neutral current interactions. Minimally coupled interaction Lagrangian density L X = g x Ψγ µ Z µxψ. Now if these Z µ gauge bosons are massless or extremely light then the forces are long range. Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 3 / 20
Effective potential due to L e L µ global symmetry I The most important feature of this force is that, since this force is related to the charge X, it is flavour dependent. For example, the X-charge of electron flavour is opposite to that of muon flavour. As a result they will feel different potentials due to this force while propagating from one place to another. Since it is an additional neutral current interaction, the forward scattering amplitudes for different interactions depending on flavour are : Ω ( ν e e ν e e ) +g 2 /q 2 Ω ( ν µ e ν µ e ) g 2 /q 2 Ω ( ν τ e ν τ e ) = 0 Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 4 / 20
Effective potential due to L e L µ global symmetry II Flavour dependency of the effective Potential: V ee = +α d 3 r n e ( r)/r V eµ, V µµ = α d 3 r n e ( r)/r V eµ V ττ = 0 We know the potential due to large spherical electron sources is : Veµ = 4πα r eµ r 2 n e (r ) dr = α eµ r 0 r N e (1) Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 5 / 20
Potential due to the LRF Potential due to Sun Potential due to Earth V eβ = αn e R ES 1.3 10 11 ev ( αeβ 10 50 ) (2) V E eµ = M E M R ES R E V eµ (r ES ) 0.1V eµ (r ES ) (3) Potential due to Earth can be neglected. Potential due to Sun is almost constant across the earth. Potential in atmospheric or solar sector is basically m2 2E 10 12. So, even if α = 10 50 can effect neutrino oscillation significantly. Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 6 / 20
Numerical plots of Oscillation Amplitude 0.14 0.12 0.10 : Π to Π Le LΜ symmetry NH,SM IH,SM NH,Α 10 52 0.20 0.15 2300 km : Π to Π Le LΜ symmetry NH,SM IH,SM NH,Α 10 52 P ΝΜ Νe 0.08 0.06 IH,Α 10 52 P ΝΜ Νe 0.10 IH,Α 10 52 0.04 0.05 0.02 0.00 2 4 6 8 0.00 2 4 6 8 E GeV Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 7 / 20
Previous Bound from different Experiments : 1 The Super-K data of oscillation of multi-gev atmospheric neutrinos put an upper bound on coupling α eτ < 6.4 10 52 and α eµ < 5.5 10 52 at 90% CL. [Joshipura and Mohanty, Physics Letters B 584 (2004) 103 108]. 2 Solar neutrino and KamLAND data gives the 3σ limits α eµ < 3.4 10 53 and α eτ < 2.5 10 53. [Bandyopadhyay, Dighe and Joshipura, Physical Review D 75, 093005 (2007)]. 3 Conservative studies of these long-range forces with atmospheric neutrinos at ICAL considering only the muons of charge current interactions find stringent bounds on the couplings α eµ,eτ 1.65 10 53 at 3σ CL. Abhijit Samanta, JCAP 1109 (2011) 010]. Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 8 / 20
In this work, we want to check some important issues like : this new physics can spoil our standard expectations from three flavour neutrino oscillation framework like : (i) mass hierarchy sensitivity (ii) discovery reach of leptonic CP violation. Whether we can discover this new physics at certain confidence level. Long-Baseline Neutrino Oscillation Experiments like LBNF and LBNO are the best candidates to address these questions. LBNF will have 1300 km baseline from FNAL to Homestake and LBNO will be 2290 km baseline from CERN to Pyhasälmi. Both of them will use Neutrino Superbeam. Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 9 / 20
Event Spectrum Events per 0.125 GeV 1000 100 10 1 LRF Parameter, α=10-52 L e - L µ Symmetry LBNF35 Signal(ν µ -> ν e ) Int(ν e ) Mis-id (ν µ ) NC Signal(ν µ -> ν e ) with LRF Int(ν e ) with LRF Mis-id (ν µ ) with LRF NC with LRF 0.1 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Energy [GeV] Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 10 / 20
LRF at event level I 350 LBNF35 700 LBNO70 ν - e app. events 300 HO-IH+LRF L e -L µ symmetry 250 α = 10-52 HO-IH 200 150 LO-NH LO-IH+LRF LO-IH HO-NH 100 50 LO-NH+LRF HO-NH+LRF 0 0 100 200 300 400 500 600 700 800 900 ν e app. events ν - e app. events 600 500 400 300 200 LO-IH+LRF HO-IH LO-IH HO-IH+LRF LO-NH HO-NH 100 LO-NH+LRF HO-NH+LRF 0 0 200 400 600 800 1000 1200 1400 1600 1800 ν e app. events L e -L µ symmetry α = 10-52 Important points to note from these plots are : with the impact of LRF, we see that the area of ellipses under antineutrino events diminishes. Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 11 / 20
LRF at event level II But for only neutrino events, it is not possible to resolve the octant degeneracy in case of both LBNF and LBNO with SM and SM+LRF scenario and vice-versa for antineutrino events. So we should account both the neutrino and antineutrino events. Even if for α = 10 52, both the neutrino and antineutrino events are required to resolve the octant degeneracy problem. But for LBNO70, only neutrino events are sufficient to resolve hierarchy and octant degeneracy problem. So in overall view, LBNO70 is excellent. Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 12 / 20
Impact of LRF on Mass-hierarchy sensitivity Δ χ 2 10 5 10 4 10 3 L e -L µ symmetry (α, δ cp, θ 23 ) marginalized LBNF35 α(true) = 10-52, δ cp (true) = 0 SM, δ cp (true) = 0 α(true) = 10-52, δ cp (true) = 90 SM, δ cp (true) = 90 α(true) = 10-52, δ cp (true) = -90 SM, δ cp (true) = -90 α(true) = 10-52, δ cp (true) = 180 SM, δ cp (true) = 180 10 2 10 1 10-4 10-3 10-2 10-1 α 10-50 (test) We have considered NH be the true hierarchy and IH be the test hierarchy. We can exclude the IH to be the possible hierarchy at greater than 5σ level. Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 13 / 20
Impact of LRF on discovery reach of Leptonic CP Violation I Discovery reach of Leptonic CP Violation means identifying the δ CP (true) from all possible values of CP phases except two CP conserving phase 0 or 180 0. Δ χ 2 35 30 25 20 15 10 5 α, θ 23, δ cp marginalized L e -L µ symmetry LBNF35 0-180 -120-60 0 60 120 180 3σ 2σ δ cp (true)[degree] SM SM+LRF Δ χ 2 50 40 30 20 10 α, θ 23, δ cp marginalized L e -L µ symmetry LBNO70 0-180 -120-60 0 60 120 180 3σ 2σ δ cp (true)[degree] SM SM+LRF Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 14 / 20
Impact of LRF on discovery reach of Leptonic CP Violation II Expt LBNF35 LBNO70 SM 2σC.L. 67.1% 71.2% 3σC.L. 47.9% 54.7% SM+LRF 2σC.L. 63% 68.4% 3σC.L. 42.4% 53.4% Table : quantitative measurement of CPV favourable phases In the above figure, we have considered LRF in theory only. With the increase of detector mass, the chance of CP violation discovery increases. It spoils the discovery reach of CP violation upto a very few percentage. Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 15 / 20
Constraint on LRF parameter I LBNF35 LRF Sensitivity LBNF35 LRF Sensitivity 10 5 10 4 10 3 L e -L µ symmetry α(true) = 0, δ cp(true) = -90 0 θ 23(true) = 45 0 α,θ 23,δ cp marginalized 10 5 10 4 10 3 L e -L µ symmetry α(true) = 0, δ cp(true) = 90 0 θ 23(true) = 45 0 α,θ 23,δ cp marginalized Δ χ 2 10 2 10 1 3σ 90% C.L. 1.19 10-53 Δ χ 2 10 2 10 1 3σ 90% C.L. 1.05 10-53 10 0 3.0 10-53 10 0 2.52 10-53 10-1 10-4 10-3 10-2 10-1 α 10-50 (test) 10-1 10-4 10-3 10-2 10-1 α 10-50 (test) Important Points: We want to test, upto which value of coupling strength of LRF, our experiment is sensitive to the effect of LRF if we assume that there is no LRF in nature. Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 16 / 20
Constraint on LRF parameter II We have considered LRF with L e L µ global symmetry in theoretical model and no LRF in data. We have shown the upper bound of α in all plots for different setup and we have also done the same work for LBNO70 and we have seen that LBNO70 constraints the range more tightly than LBNF35. Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 17 / 20
Discovery of LRF parameter I LBNF35 LRF Discovery LBNF35 LRF Discovery 10 5 10 4 10 3 L e -L µ symmetry δ cp (true) = -90 0 θ 23 (true) = 45 0 θ 23,δ cp marginalized 10 5 10 4 10 3 L e -L µ symmetry δ cp (true) = 90 0 θ 23 (true) = 45 0 θ 23,δ cp marginalized Δ χ 2 10 2 2.0 10-53 Δ χ 2 10 2 1.9 10-53 10 1 10 0 90% C.L. 3σ 3.7 10-53 10 1 10 0 90% C.L. 3σ 6.4 10-53 10-1 10-4 10-3 10-2 10-1 α(true) 10-50 10-1 10-4 10-3 10-2 10-1 α(true) 10-50 Important Points: We have considered LRF with L e L µ global symmetry in observed value and no LRF in theoretical model. Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 18 / 20
Discovery of LRF parameter II The dotted lines in the plot indicates the value of coupling strength in 90% and 3σ C.L if LRF exists in nature. With the increase of detector mass, the value is more constraint as we have seen from LBNO70 case. Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 19 / 20
Conclusion We are so lucky! Even though the mass of the mediator of LRF is less than 10 20 ev, We can probe it through Neutrino oscillation. Even if it presents in nature, it does not spoil the discovery of mass-hierarchy sensitivity and discovery reach of leptonic CP violation. From Long-Baseline experiments like LBNF, we get the upper bound of α eµ 3 10 53. Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments 20 / 20