Constraints on Lorentz invariance violation using HAWC observations above 100 TeV
H. Martínez-Huerta, S. Marinelli, J. T. Linnemann, J. Lundeen
CConstraints on Lorentz invariance violation usingHAWC observations above 100 TeV
H. Martínez-Huerta ∗ a , S. Marinelli b , J. T. Linnemann b and J. Lundeen b , c for the HAWC Collaboration † a Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, SP, Brasil b Department of Physics and Astronomy, Michigan State University, MI, USA c Physics Division, Los Alamos National Laboratory, Los Alamos, NM, USAE-mail: [email protected]
Due to the high energies and long distances involved, astrophysical observations provide a uniqueopportunity to test possible signatures of Lorentz Invariance Violation (LIV). Superluminal LIVenables the decay of photons at high energy over relatively short distances, giving astrophysicalspectra which have a hard cutoff above this energy. The High Altitude Water Cherenkov (HAWC)observatory is the most sensitive currently-operating gamma-ray observatory in the world above10 TeV. Together with the recent development of an energy-reconstruction algorithm for HAWCusing an artificial neural network, HAWC can make detailed measurements of gamma-ray ener-gies above 100 TeV. With these observations, HAWC can limit the LIV energy scale greaterthan 10 eV, over 800 times the Planck energy scale. This limit on LIV is over 60 times moreconstraining than the best previous value for E ( ) LIV . ∗ Speaker. † c (cid:13) Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/ a r X i v : . [ a s t r o - ph . H E ] A ug IV constraints with HAWC
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1. Introduction
The High Altitude Water Cherenkov Observatory (HAWC) is a wide-field of view array of 300tanks of 200,000 liters of water, each containing four photomultiplier tubes detectors. HAWC islocated at 4100 m above sea level at 19 o N near the Sierra Negra volcano, in Puebla, México andcovers an area of 22,000 m . Since 2015, HAWC has operated over 95% duty cycle and is the mostsensitive currently-operating gamma-ray observatory in the world above 10 TeV. In fact, HAWCrecently reported detailed measurements of gamma-ray energies above 100 TeV [1] with the recentdevelopment of advanced energy-reconstruction algorithms, including using an artificial neuralnetwork (see also Ref. [2] for the application to the Crab Nebula energy spectrum and Ref. [3] inthis Proceedings).Among the studies that this is generating, there is also the opportunity to test fundamentalphysics, such as the Lorentz invariance violation (LIV), through the precise measurement and re-construction of these unprecedented very-high-energy photons. Some effects of LIV are expectedto increase with energy and over very long distances due to cumulative processes in photon prop-agation. Therefore, astrophysical searches provide sensitive probes of LIV and its potential sig-natures, such as the energy-dependent time delay, photon splitting, vacuum Cherenkov radiation,photon decay, and many other phenomena [4–9].Previous studies of possible LIV constraints with HAWC have indicated its particle use inLIV searches. For instance, Ref. [10] analyzes the possibility to test energy-dependent time delaysthrough GRB and Pulsar measurements, which would result in strong sensitivity limits to LIV inthe photon sector. In Ref. [11], the potential of Lorentz invariant violating photons to decay toelectron-positron pairs was explored. Furthermore, preliminary results in this vein were presentedin Ref. [12] and will be considered in the present proceeding.Superluminal LIV enables the decay of photons at high energy over relatively short distancesand above the energy threshold of the process. Consequently, no high-energy photons should reachthe Earth from astrophysical distances above some photon energy [4]. Moreover, this suggestsa hard cutoff in astrophysical spectra [13]. In this work, seven sources are studied to determinewhether or not there is a hard cutoff compatible with the LIV photon decay in the observed spectraof each source. In the next section, we present the highlights of the LIV photon decay phenomena.In Section 3, we describe the developed analysis and present our preliminary results, and finally,we present our conclusions.
2. Lorentz invariance violation
The introduction of a Lorentz violating term in the standard model Lagrangian or spontaneousLorentz symmetry breaking can induce modifications to the particle dispersion relation, comparedto the standard energy-momentum relationship in special relativity [6, 14, 15]. Although there areseveral forms of modified dispersion relation (MDR) for different particles and underlying LIV-theories, some of them may lead to similar phenomenology, which can be useful for LIV tests inextreme environments such as astroparticle scenarios. Phenomenologically, the LIV effects can begeneralized as a function of energy and momentum. In this way, a family of effective MDRs can1
IV constraints with HAWC
H. Martínez-Huerta (a) (b)
Figure 1:
Left (a). True spectrum with LIV hard cutoff at some energy E c and the expected observerspectrum due to the detector energy resolution [13]. Right (b). Likelihood curve as a function of the LIVEnergy cutoff in the Crab analysis; the lower point (green) shows the lower limit at 95% CL. be addressed by the following expression , E a − p a = m a ± | α a , n | A n + a , (2.1)where a stands for the particle type. A can take the form of E or p. α a , n is the LIV parameter and n is the leading order of the correction from the underlying theory. In some effective field theories, α a , n = ε ( n ) / M , where ε ( n ) are LIV coefficients and M is the energy scale of the new physics, suchas the Plank energy scale (E Pl ≈ . × ) or some Quantum Gravity energy scale (E QG ).The phenomenology derived from Eq. (2.1) can demonstrate superluminal phenomena pre-dicted in some LIV scenarios, such as photon decay and vacuum Cherenkov radiation [4]. In thephoton decay scenario, the resulting decay rates into electron-positron are very fast and effectiveat energies where the process is allowed [16]. This creates a hard cutoff in the gamma-ray spec-trum with no high-energy photons reaching the Earth from cosmological distances above a giventhreshold. The derived general threshold for any order n from Eq. (2.1), is given by α n ≥ m e E n γ ( E γ − m e ) , (2.2)where E γ is the photon energy and m e stands for the electron mass.
3. Analysis and Lorentz violation limits
To test LIV photon decay, the precise measurement of the most energetic gamma-ray eventsis crucial. HAWC is capable of detecting very high energy gamma-rays by studying astrophysicalsources such as the Crab Nebula and other TeV sources. HAWC is also especially sensitive tosources with spatially-extended emission because of its large instantaneous field of view (2 sr). Hereafter, natural units are used, c = ¯ h = IV constraints with HAWC
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Furthermore, a recent Neural-Net-based (NN) energy estimation technique has improved the energyresolution of the instrument [1].A study of high-energy HAWC sources has been performed which uses a selection of sevensources with significant high energy emission above 56 TeV in reconstructed energy. They are theCrab Nebula, modeled as a point source with a log-parabola spectrum, and six sources within 2degrees of the Galactic plane, with spectra are shaped as a power-law with an exponential cut-off.These six sources are spatially extended and modeled by a Gaussian morphology with radius fixedat best-fit values found during the construction of HAWC’s high-energy catalog [17].To test the LIV photon decay signature, we assume a LIV hard cutoff at some energy E c inthe true spectrum, which is expected to be softened in the observed spectra due to the effects ofthe detector energy resolution (Fig. 1 (a)). A profile log-likelihood is performed to find the best-fitspectrum model for each source, including a energy cutoff, ˆE c , as a free parameter. The LI scenariois recovered when ˆE c → ∞ . The test-statistic between the best-fit LIV and LI is given by D = (cid:18) L ( ˆE c ) L ( ˆE c → ∞ ) (cid:19) . (3.1)To determine whether or not the data is compatible with a hard cutoff at some energy scale, wecalculate a p-value of observing D , where the null hypothesis is the LI limit. The resulting p-valuefor each of the seven sources is shown in Tab. 1. As can be seen, the p-values are large enoughthat the null hypothesis cannot be rejected; therefore, none of the sources favor a spectrum with anLIV hard cutoff. Instead, we consider limits to how high in energy the presence of photons can beverified with HAWC. In this analysis, it is found that the lower limit to E c at 95% CL occurs where2 ln L ( E c ) changes by 2 .
71 units from the best fit. An example is given in Fig. 1 (b), which showsthe likelihood curve as a function of the energy cutoff for the Crab source. The top point (orange)shows the best-fit value and the lower point (green) is the lower limit at 95% CL. The lower limitresults for E c at 95% for all sources are presented in Tab 1. Then, by using Eq. (2.2), the 95% CLthe limits are reinterpreted as limits on LIV parameters in Tab. 1. In this way, HAWC can excludethe energy scale of the new LIV physics, E ( ) LIV , to greater than 10 eV, over 800 times the Planckenergy scale and 60 times more constraining than the best previous value. Previous strong limitstesting photon decay using very-high energy photons from HEGRA telescope [4], Tevatron [5], andHESS [7] are given for comparison in Tab. 2 . Limits due to LIV energy-dependent time delaysearches with the Fermi -LAT are also shown [8], as well as the limits due to superluminal photonsplitting [9].
4. Conclusions
The HAWC observatory measurements of the highest-energy photons can be used as a test toprobe fundamental physics such as Lorentz violation. In this work, we set preliminary LIV limitsby testing the LIV photon decay through the study of seven sources with significant high energyemission, including the Crab Nebula. It was found that none of them favor a spectrum with a where α n = E ( − n ) LIV ≈ E ( − n ) QG , and in the framework of the Standard Model Extension [15], α ≈ − (cid:101) κ tr and α = − c ( )( I ) , / √ π . IV constraints with HAWC
H. Martínez-HuertaSource E c TeV | α | − | α | − eV − | α | − eV − E ( ) LIV eV E ( ) LIV eV pvalue2HWC J1825-134 253 1.63 0.64 0.26 15.5 6.26 12HWC J1908+063 213 2.30 1.08 0.51 9.25 4.44 0.99Crab (HAWC) 152 4.52 2.97 1.96 3.4 2.26 12HWC J2031+415 144 5.04 3.5 2.43 2.9 2.02 0.7142HWC J2019+367 121 7.13 5.6 4.87 1.7 1.43 0.828J1839-057 79 16.74 21.1 26.8 0.47 0.61 0.3572HWC J1844-032 77 17.62 22.9 29.7 0.44 0.58 0.294 Table 1: The HAWC Sources used in this analysis and the derived 95% CL lower limits on E c andits different LIV coefficients (Prel.). Source E γ TeV | α | − | α | − eV − | α | − eV − E ( ) LIV eV E ( ) LIV eV Ref.Crab (HEGRA) 2017 ∼
56 - 66.7 128 0.15 0.28 [4]Tevatron 2016 0.442 6 × - - - - [5]RX J1713.7–3946 (HESS) 2008 30 180 - - - - [7]Coleman & Glashow (1997) 20 100 - - - - [6]GRB09510 ( Fermi ) 2013 v > c - - - - 0.134 0.009 [8]GRB09510 ( Fermi ) 2013 v < c - - - - 0.093 0.013 [8]Crab (HEGRA) 2019 75 - - 0.059 - 13 [9] Table 2: Previous strong constraints to LIV photon decay are shown as well as the best limits basedon energy-dependent time delay and superluminal photon splitting at bottom.hard cutoff. However, the dedicated search of such signature in the spectra increases the energyto which the existence of the most energetic photons can be confirmed, which leads to new andstringent limits to LIV. A study including detailed systematic uncertainties in the source spectraand HAWC detector response will be addressed in a future publication.
Acknowledgments
We acknowledge the support from: the US National Science Foundation (NSF); the US Department of En-ergy Office of High-Energy Physics; the Laboratory Directed Research and Development (LDRD) program of LosAlamos National Laboratory; Consejo Nacional de Ciencia y Tecnología (CONACyT), México (grants 271051, 232656,260378, 179588, 239762, 254964, 271737, 258865, 243290, 132197), Laboratorio Nacional HAWC de rayos gamma;L’OREAL Fellowship for Women in Science 2014; Red HAWC, México; DGAPA-UNAM (grants IG100317, IN111315,IN111716-3, IA102715, 109916, IA102917); VIEP-BUAP; PIFI 2012, 2013, PROFOCIE 2014, 2015;the University ofWisconsin Alumni Research Foundation; the Institute of Geophysics, Planetary Physics, and Signatures at Los AlamosNational Laboratory; Polish Science Centre grant DEC-2014/13/B/ST9/945; Coordinación de la Investigación Científicade la Universidad Michoacana. Thanks to Luciano Díaz and Eduardo Murrieta for technical support. HMH acknowl-edges FAPESP support No. 2015/15897-1 and 2017/03680-3 and the National Laboratory for Scientific Computing(LNCC/MCTI, Brazil) for providing HPC resources of the SDumont supercomputer (sdumont.lncc.br). IV constraints with HAWC
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