Extricating New Physics Scenarios at DUNE with High Energy Beams

TL;DR

This paper proposes a novel strategy for the DUNE experiment to distinguish non-standard neutrino interactions from standard oscillations by optimizing beam configurations and analyzing energy-dependent effects.

Contribution

It introduces a new theoretical metric and experimental approach to separate NSI effects from standard neutrino oscillations at DUNE, enhancing sensitivity to new physics.

Findings

Optimized beam tune combinations for NSI detection

New metric for separating NSI from standard oscillations

Enhanced ability to identify new physics scenarios

Abstract

The proposed Deep Underground Neutrino Experiment (DUNE) utilizes a wide-band on-axis tunable muon-(anti)neutrino beam with a baseline of 1300 km to search for CP violation with high precision. Given the long baseline, DUNE is also sensitive to effects due to non-standard neutrino interactions (NSI) which can interfere with the standard 3-flavor oscillation paradigm. In this Letter, we exploit the tunability of the DUNE neutrino beam over a wide-range of energies and utilize a new theoretical metric to devise an experimental strategy for separating oscillation effects due to NSI from the standard 3-flavor oscillation scenario. Using our metric, we obtain an optimal combination of beam tunes and distribution of run times in neutrino and anti-neutrino modes that would enable DUNE to isolate new physics scenarios from the standard. To the best of our knowledge, our strategy is entirely new and has not been reported elsewhere.

Figures

Tables

Table 1. Table 1: Beamline parameters assumed for the different design fluxes used in our sensitivity calculations  Adams  et al. ( 2013 ); Alion  et al. ( 2016 ) . The target is a thin Be cylinder 2 interaction lengths long. The target location is given with respect to the upstream face of Horn 1.

Parameter	LE	ME	HE
Proton Beam	$E_{p^{+}}=120$ GeV, 1.2 - 2.4 MW
Focusing	2 NuMI horns, 230kA, 6.6 m apart
Target location	-25cm	-1.0m	-2.5m
Decay pipe length	250 m	250 m	250 m
Decay pipe diameter	4 m	4 m	4m

Equations

$${\mathcal{H}}_{\mathrm{f}}$$

$$+$$

$$\lambda \equiv \frac{\delta m_{31}^2}{2E};r_{\lambda }\equiv \frac{\delta m_{21}^2}{\delta m_{31}^2};r_A\equiv \frac{A(x)}{\delta m_{31}^2}.$$

$${\chi }^2({\delta }_{tr})$$

Full text

I Introduction

Neutrino oscillations among the three flavours have been firmly established and the experimental confirmation of neutrino oscillations vindicates that the Standard Model (SM) of particle physics is incomplete Kajita and McDonald . The minimal extension of SM invokes a mechanism to generate tiny neutrino masses while retaining the interactions as predicted in the SM. We refer to this minimal model as Standard Interactions (SI).

Most of the parameters responsible for standard 3-flavor neutrino oscillations have been measured with fairly good precision except for a few Bergstrom et al. (2015). Some of the yet unresolved questions in neutrino physics include whether CP is violated, if the neutrino mass hierarchy is normal or inverted and what the correct octant of $\theta_{23}$ is. Detecting CP violation is one of the most challenging goals in particle physics. An attractive possibility to measure the neutrino CP phase is via long-baseline accelerator experiments such as the Deep Underground Neutrino Experiment (DUNE) Bass et al. (2015). DUNE and the facility that will support it, the Long-Baseline Neutrino Facility (LBNF), will be an internationally designed, coordinated and funded program, hosted at the Fermi National Accelerator Laboratory (Fermilab) in Batavia, Illinois Acciarri et al. (2015).

In the presence of new physics effects, clean extraction of the CP violating phase becomes a formidable task Nunokawa et al. (2008); Rout et al. (2017). In fact, a given measured value of CP phase could be a hint of new physics Forero and Huber (2016); Miranda et al. (2016). In our earlier work, we have pointed out that there are degeneracies within the large parameter space in the presence of non-standard interactions (NSI) Ohlsson (2013); Masud et al. (2016); de Gouvêa and Kelly (2016); Coloma (2016); Liao et al. (2016); Masud and Mehta (2016a, b) and the need to devise ways to distinguish between the standard paradigm and new physics scenarios has been extensively discussed (for new physics scenarios with extra sterile neutrinos see Gandhi et al. (2015); Dutta et al. (2016); Agarwalla et al. (2017) and for non-unitarity see Dutta and Ghoshal (2016); Escrihuela et al. (2016)).

In a novel approach, we use experimental handles that could prove useful to differentiate between the standard scenario (with only one source of CP violation) and new physics scenarios (which inevitably bring in more parameters including new sources of CP violating phases). Recent studies have explored the sensitivities to SI paramaters and the synergies between experiments (DUNE and T2HK) using different baselines and neutrino beam energies Ballett et al. (2016). In this study, for the first time, we explore sensitivities to both SI and NSI effects at a fixed baseline over a large range of $L/E$ using DUNE’s unique broad-band tunable beam. Different wide-band fluxes can be experimentally achieved using the DUNE NuMI-style reference beam design Acciarri et al. (2015) by simply varying the target and horn placement Adamson et al. (2016). We propose a new theoretical metric that allows us to optimize experimental strategies and beam tunes for clean inference of the leptonic CP phase in the presence of new physics.

II Non-Standard $\nu$ Interaction Model

The effective Hamiltonian in the flavour basis entering the Schr$\ddot{\rm o}$dinger equation for neutrino propagation is given by

[TABLE]

where

[TABLE]

and $A(x)=2\sqrt{2}EG_{F}n_{e}(x)$ where $n_{e}$ is the electron number density. The three terms in Eq. 7 are due to vacuum, matter with standard interaction (SI) and matter with NSI respectively. For the NSI case, the ${\varepsilon}_{\alpha\beta}\,(\equiv|\varepsilon_{\alpha\beta}|\,e^{i\varphi_{\alpha\beta}})$ are complex parameters which appear in ${\cal H}_{NSI}$. As a result of the hermiticity of the Hamiltonian, we have nine additional parameters (three phases and six amplitudes appearing ${\cal H}_{NSI}$). Thus, there are new genuine sources of CP violation as well as new fake sources of CP violation (aka matter effects) that can change the asymmetries even further. For more details, see Masud et al. (2016); Masud and Mehta (2016a, b) and references therein.

To quantify the separation of physics scenarios (SI-NSI separation), we define111The definition of the $\chi^{2}$ in Eq. 13 includes only statistical effects and facilitates our understanding. The systematic effects are taken into account in the numerical results. the (statistical) $\chi^{2}$ as follows in order to interpret results -

[TABLE]

where, we have marginalised over the standard CP phase $\delta$ in the test dataset. This $\chi^{2}$ was calculated using a set of conservative values of the non-zero NSI parameters ($|\varepsilon_{e\mu}|$ = 0.04, $|\varepsilon_{e\tau}|$ = 0.04 $\varepsilon_{ee}$ = 0.4) Biggio et al. (2009); Davidson et al. (2003).

III Neutrino Beam Tunes

For this study, we considered three wide-band beam tunes obtained from a full Geant4 simulation Agostinelli et al. (2003); Allison et al. (2006) of a neutrino beamline using NuMI-style focusing. The tunes considered are: low energy (LE); medium energy (ME); and high energy (HE) as shown in Fig. 1. These tunes are consistent with what could be achieved by the LBNF facility. The energy range considered is $E=0.5-20$ GeV. The beamline parameters assumed for the different design fluxes used in our sensitivity calculations are given in Table 1 (see Adams et al. (2013); Alion et al. (2016)).

IV Results and Discussion

We have implemented a GLoBES Huber et al. (2005, 2007) simulation of a $1300\,\text{km}$ baseline neutrino beam experiment using a parameterization of the DUNE far detector response as described in  Alion et al. (2016). We assume normal hierarchy (NH) in all the plots. We show the variation in the $\nu_{e}$ event spectrum in Fig. 2 for the LE, ME and HE beam tunes under SI-only and SI+NSI scenarios. In all beams, the red and magenta dashed lines (for $\delta\sim\pm\pi/2$ with NSI) lie almost completely within the cyan band (SI for $\delta\in[-\pi,\pi]$) and that makes the separation between the two considered scenarios more difficult. The black dashed lines (for $\delta\sim 0$ with NSI) lie farthest apart from the cyan band (SI). This particular feature results in better separability between the two considered scenarios at values of $\delta\sim 0$ (or $\pm\pi$). In addition, better separation is obtained at higher energies in the ME and HE beams.

In Fig. 3, we show the ability of DUNE to separate SI from NSI using different combinations of beam tunes and running times at the $\chi^{2}$ level. The first panel is for an equal distribution of run time among neutrino and anti-neutrino modes while the second panel corresponds to running in neutrino-only mode with the same total run time. For this analysis, we consider the energy range $E\in 0.5-20$ GeV. A CP conserving NSI scenario is assumed in this plot222We assume $\varphi_{e\mu}=\varphi_{e\tau}=0$.. We have considered a combination of appearance ($\nu_{\mu}\to\nu_{e}$) and disappearance ($\nu_{\mu}\to\nu_{\mu}$) channels. The solid and dashed lines assume a beam power of 1.2 MW for both LE and ME. The dotted black line corresponds to an ME option upgraded to 2.4 MW which is planned for later stages of DUNE. We note that the dominant channel contributing to the distinction of different physics scenarios is the $\nu_{\mu}\to\nu_{e}$ channel irrespective of our choice of beam tune. The $\nu_{\mu}\to\nu_{\mu}$ channel adds somewhat to the total sensitivity but the $\nu_{\mu}\to\nu_{\tau}$ contribution is negligible.

As noted earlier, we find that the ability to separate between the two scenarios tends to increase at CP conserving values of $\delta$ i.e. $\delta\sim 0,\pm\pi$. The dips seen near $\delta\sim\pm\pi/2$ (true) in Fig. 3 for all the LE and ME options imply the inability of DUNE to distinguish between the scenarios at those values. If the standard beam power is assumed, one gets the best optimization for LE (2+2) + ME(3+3) (dashed black line). In fact, in general the different beam tunes and run time combinations other than LE only (solid red line) yield better results. From the right panel, we can see that the best sensitivity at $\delta\sim 0$ is reached for LE (4+0) + ME (6+0) (dashed black line). An upgrade of beam power in ME (dotted black line) to 2.4 MW significantly improves the outcome.

Another important factor driving the sensitivity to SI-NSI separation is the fraction of values of CP phase for which the sensitivity is more than $3\sigma$ or $5\sigma$. This quantity is plotted in Fig. 4 for the fraction lying above $3\sigma$ (magenta) and $5\sigma$ (blue) as a function of the run time for a combination of LE and ME (or HE) tuned beams. Both the panels are for a total run time of 10 years : the left one showing the case of 5 years of $\nu$ and 5 years of $\bar{\nu}$ run time while the right panel depicting the scenario of 10 years of $\nu$ run time alone. In the left panel, the 5+5 years of run time are distributed among the LE and ME (HE) beams for the solid (dashed) lines in the following manner: $(x+x)$ years of LE beam +\big{(}(5-x)+(5-x)\big{)} years of ME or HE runtime with the run-time in one mode, $x$, in years along the x-axis. Similarly, the runtime in the right panel has been distributed as $(x+0)$ years of LE beam +\big{(}(10-x)+0\big{)} years of ME or HE run time. We note as long as the distribution of runtime among the two different beams is evenly distributed (approximately) in the LE and ME or HE options, the fraction is close to its maximum value and remains almost flat. However as we go to the extreme cases (ME or LE taken in isolation for e.g.), the fraction sees a drop (this is more significant for LE only towards the right edge). So, this observation implies that one must consider ME (HE) or both LE and ME (HE) beam tunes in order to obtain the discrimination of new physics from standard at some given level of significance. We wish to stress that the fraction curves in Fig. 4 only show what portion of the sensitivity curve lies above $3\sigma$ (or $5\sigma$), and not necessarily the absolute value of the sensitivities. The estimate of the fraction of $\delta$ values thus depends on the points of intersection of the sensitivity curve with the $3\sigma$ (or $5\sigma$) horizontal lines in Fig. 3.

In Fig. 5, we go beyond the CP conserving NSI scenario considered so far and generalize Fig. 3 by considering non-zero NSI phases. We show the ability to discriminate between SI-NSI using oscillograms. The projection of the $\chi^{2}$ values at $\varphi_{e\mu}=0$ in Fig. 5 corresponds to Fig. 3. For CP violating NSI scenarios, the peak position in the sensitivity plot shifts left or right (with respect to $\delta_{tr}=0$) as shown in Fig. 5. The separation between scenarios in Fig. 5 is consistent with Fig. 3 as the darker patches are around $\delta\sim 0,\pm\pi$ while the lighter patches are around $\delta\sim\pm\pi/2$.

V Summary

It is crucial to separate different physics scenarios at DUNE to be able to infer the parameters cleanly. The key point of the study reported in this Letter is to demonstrate the feasibility of using DUNE’s experimental flexibility to expand the physics reach beyond the neutrino standard model. We have demonstrated that it is plausible to have better separation of SI from NSI if we consider different combinations of beam tunes and run times. For the CP conserving NSI scenario, a mix of LE (4+0) + ME (6+0) is close to optimal with neutrino only mode. The results also show that LE+HE beam combinations give slightly better results than LE+ME combinations with more LE than HE in the mix. For the CP violating NSI scenario, the peak position in the sensitivity plot shifts left or right (with respect to $\delta_{tr}=0$) as can be seen from Fig. 5. We are currently expanding the study to include more new physics scenarios.

Acknowledgements.

It is a pleasure to thank Raj Gandhi for useful discussions and critical comments on the manuscript. This material is based upon work supported by the Spanish grants FPA2014- 58183-P, SEV-2014-0398 (MINECO) and PROMETEOII/ 2014/084 (Generalitat Valenciana); the U.S. Department of Energy, Office of Science, Office of High Energy Physics under contract number DE-SC0012704; the Indian funding from University Grants Commission under the second phase of University with Potential of Excellence (UPE II) and DST-PURSE at JNU; and the European Union’s Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant No 674896. PM acknowledges support and kind hospitality from the particle physics group at BNL during the finishing stages of this work.