Measurement of the residual energy of muons in the Gran Sasso underground Laboratories

The MACRO detector was located in the Hall B of the Gran Sasso underground Laboratories under an average rock overburden of 3700 hg/cm^2. A transition radiation detector composed of three identical modules, covering a total horizontal area of 36 m^2, was installed inside the empty upper part of the detector in order to measure the residual energy of muons. This paper presents the measurement of the residual energy of single and double muons crossing the apparatus. Our data show that double muons are more energetic than single ones. This measurement is performed over a standard rock depth range from 3000 to 6500 hg/cm^2.Comment: 28 pages, 9 figure

Muon Energy Estimate Through Multiple Scattering with the Macro Detector

Muon energy measurement represents an important issue for any experiment addressing neutrino induced upgoing muon studies. Since the neutrino oscillation probability depends on the neutrino energy, a measurement of the muon energy adds an important piece of information concerning the neutrino system. We show in this paper how the MACRO limited streamer tube system can be operated in drift mode by using the TDC's included in the QTPs, an electronics designed for magnetic monopole search. An improvement of the space resolution is obtained, through an analysis of the multiple scattering of muon tracks as they pass through our detector. This information can be used further to obtain an estimate of the energy of muons crossing the detector. Here we present the results of two dedicated tests, performed at CERN PS-T9 and SPS-X7 beam lines, to provide a full check of the electronics and to exploit the feasibility of such a multiple scattering analysis. We show that by using a neural network approach, we are able to reconstruct the muon energy for $E_\mu<$40 GeV. The test beam data provide an absolute energy calibration, which allows us to apply this method to MACRO data.Comment: 25 pages, 11 figures, Submitted to Nucl. Instr. & Meth.

Low energy atmospheric muon neutrinos in MACRO

We present the measurement of two event samples induced by atmospheric $\nu_\mu$ of average energy $\bar {E}_\nu \sim 4 GeV$. In the first sample, the neutrino interacts inside the MACRO detector producing an upward-going muon leaving the apparatus. The ratio of the number of observed to expected events is $0.57 \pm0.05_{stat} \pm0.06_{syst} \pm0.14_{theor}$ with an angular distribution similar to that expected from the Bartol atmospheric neutrino flux. The second is a mixed sample of internally produced downward-going muons and externally produced upward-going muons stopping inside the detector. These two subsamples are selected by topological criteria; the lack of timing information makes it impossible to distinguish stopping from downgoing muons. The ratio of the number of observed to expected events is $0.71 \pm 0.05_{stat} \pm0.07_{syst} \pm0.18_{theor}$ . Using the ratio of the two subsamples (for which most theoretical uncertainties cancel) we can test the pathlength dependence of the oscillation hypothesis. The probability of agreement with the no-oscillation hypothesis is 5% . The deviations of our observations from the expectations has a preferred interpretation in terms of $\nu_\mu$ oscillations with maximal mixing and $\Delta m^2 \sim 10^{-3} \div 10^{-2} eV^2$. These parameters are in agreement with our results from upward throughgoing muons, induced by $\nu_\mu$ of much higher energies.Comment: 7 pages, 6 figures. Submitted to Phys. Lett.

Search for diffuse neutrino flux from astrophysical sources with MACRO

Many galactic and extragalactic astrophysical sources are currently considered promising candidates as high energy neutrino emitters. Astrophysical neutrinos can be detected as upward-going muons produced in charged-current interactions with the medium surrounding the detector. The expected neutrino fluxes from various models start to dominate on the atmospheric neutrino background at neutrino energies above some tens of TeV. We present the results of a search for an excess of high energy upward-going muons among the sample of data collected by MACRO during ~5.8 years of effective running time. No significant evidence for this signal was found. As a consequence, an upper limit on the flux of upward-going muons from high-energy neutrinos was set at the level of 1.7 10^(-14) cm^(-2) s^(-1) sr^(-1). The corresponding upper limit for the diffuse neutrino flux was evaluated assuming a neutrino power law spectrum. Our result was compared with theoretical predictions and upper limits from other experiments.Comment: 19 pages, 8 figures, 2 table

Measurement of the atmospheric neutrino-induced upgoing muon flux using MACRO

We present a measurement of the flux of neutrino-induced upgoing muons (~100 GeV) using the MACRO detector. The ratio of the number of observed to expected events integrated over all zenith angles is 0.74 +/- 0.036 (stat) +/- 0.046(systematic) +/- 0.13 (theoretical). The observed zenith distribution for -1.0 < cos(theta) < -0.1 does not fit well with the no oscillation expectation, giving a maximum probability for chi^2 of 0.1%. The acceptance of the detector has been extensively studied using downgoing muons, independent analyses and Monte-Carlo simulations. The other systematic uncertainties cannot be the source of the discrepancies between the data and expectations. We have investigated whether the observed number of events and the shape of the zenith distribution can be explained by a neutrino oscillation hypothesis. Fitting either the flux or zenith distribution independently yields mixing parameters of sin^2 (2theta)=1.0 and delta m^2 of a few times 10^-3 eV^2. However, the observed zenith distribution does not fit well with any expectations giving a maximum probability for chi^2 of 5% for the best oscillation hypothesis, and the combined probability for the shape and number of events is 17%. We conclude that these data favor a neutrino oscillation hypothesis, but with unexplained structure in the zenith distribution not easily explained by either the statistics or systematics of the experiment.Comment: 7 pages (two-column) with 4 figure

The primary cosmic ray composition between 10**15 and 10**16 eV from Extensive Air Showers electromagnetic and TeV muon data

The cosmic ray primary composition in the energy range between 10**15 and 10**16 eV, i.e., around the "knee" of the primary spectrum, has been studied through the combined measurements of the EAS-TOP air shower array (2005 m a.s.l., 10**5 m**2 collecting area) and the MACRO underground detector (963 m a.s.l., 3100 m w.e. of minimum rock overburden, 920 m**2 effective area) at the National Gran Sasso Laboratories. The used observables are the air shower size (Ne) measured by EAS-TOP and the muon number (Nmu) recorded by MACRO. The two detectors are separated on average by 1200 m of rock, and located at a respective zenith angle of about 30 degrees. The energy threshold at the surface for muons reaching the MACRO depth is approximately 1.3 TeV. Such muons are produced in the early stages of the shower development and in a kinematic region quite different from the one relevant for the usual Nmu-Ne studies. The measurement leads to a primary composition becoming heavier at the knee of the primary spectrum, the knee itself resulting from the steepening of the spectrum of a primary light component (p, He). The result confirms the ones reported from the observation of the low energy muons at the surface (typically in the GeV energy range), showing that the conclusions do not depend on the production region kinematics. Thus, the hadronic interaction model used (CORSIKA/QGSJET) provides consistent composition results from data related to secondaries produced in a rapidity region exceeding the central one. Such an evolution of the composition in the knee region supports the "standard" galactic acceleration/propagation models that imply rigidity dependent breaks of the different components, and therefore breaks occurring at lower energies in the spectra of the light nuclei.Comment: Submitted to Astroparticle Physic

When Homomorphism Becomes a Liability

We show that an encryption scheme cannot have a simple decryption circuit and be homomorphic at the same time. Specifically, if a scheme can homomorphically evaluate the majority function, then its decryption circuit cannot be a linear function of the secret key (or even a succinct polynomial), even if decryption error is allowed. An immediate corollary is that known schemes that are based on the hardness of decoding in the presence of noise with low hamming weight cannot be fully homomorphic. This applies to known schemes such as LPN-based symmetric or public key encryption. An additional corollary is that the recent candidate fully homomorphic encryption, suggested by Bogdanov and Lee (ePrint ’11, henceforth BL), is insecure. In fact, we show two attacks on the BL scheme: One by applying the aforementioned general statement, and another by directly attacking one of the components of the scheme. An encryption scheme is called homomorphic if there is an efficient transformation that given Enc(m) for some message m, and a function f, produces Enc(f(m)) using only public information