Search

We present the characterization of a low background NaI(Tl) crystal for the SABRE North experiment. The crystal NaI-33, was studied in two different setups at Laboratori Nazionali del Gran Sasso, Italy. The Proof-of-Principle (PoP) detector was equipped with a liquid scintillator veto and collected data for about one month (90 kg$\times$days). The PoP-dry setup consisted of NaI-33 in a purely passive shielding and collected data for almost one year (891 kg$\times$days). The average background in the energy region of interest (1-6 keV) for dark matter search was 1.20 $\pm$ 0.05 and 1.39 $\pm$ 0.02 counts/day/kg/keV within the PoP and the PoP-dry setup, respectively. This result opens to a new shielding design for the physics phase of the SABRE North detector, that does not foresee the use of an organic liquid scintillator external veto., Comment: 5 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2205.13876

We present here a characterization of the low background NaI(Tl) crystal NaI-33 based on a period of almost one year of data taking (891 kgxdays exposure) in a detector configuration with no use of organic scintillator veto. This remarkably radio-pure crystal already showed a low background in the SABRE Proof-of-Principle (PoP) detector, in the low energy region of interest (1-6 keV) for the search of dark matter interaction via the annual modulation signature. As the vetoable background components, such as $^{40}$K, are here sub-dominant, we reassembled the PoP setup with a fully passive shielding. We upgraded the selection of events based on a Boosted Decision Tree algorithm that rejects most of the PMT-induced noise while retaining scintillation signals with > 90% efficiency in 1-6 keV. We find an average background of 1.39 $\pm$ 0.02 counts/day/kg/keV in the region of interest and a spectrum consistent with data previously acquired in the PoP setup, where the external veto background suppression was in place. Our background model indicates that the dominant background component is due to decays of $^{210}$Pb, only partly residing in the crystal itself. The other location of $^{210}$Pb is the reflector foil that wraps the crystal. We now proceed to design the experimental setup for the physics phase of the SABRE North detector, based on an array of similar crystals, using a low radioactivity PTFE reflector and further improving the passive shielding strategy, in compliance with the new safety and environmental requirements of Laboratori Nazionali del Gran Sasso., Comment: 8 pages, 9 figures

We present new results on the radiopurity of a 3.4-kg NaI(Tl) crystal scintillator operated in the SABRE proof-of-principle detector setup. The amount of potassium contamination, determined by the direct counting of radioactive $^{40}$K, is found to be $2.2\pm1.5$ ppb, lowest ever achieved for NaI(Tl) crystals. With the active veto, the average background rate in the crystal in the 1-6 keV energy region-of-interest (ROI) is $1.20\pm0.05$ counts/day/kg/keV, which is a breakthrough since the DAMA/LIBRA experiment. Our background model indicates that the rate is dominated by $^{210}$Pb and that about half of this contamination is located in the PTFE reflector. We discuss ongoing developments of the crystal manufacture aimed at the further reduction of the background, including data from purification by zone refining. A projected background rate lower than $\sim$0.2 counts/day/kg/keV in the ROI is within reach. These results represent a benchmark for the development of next-generation NaI(Tl) detector arrays for the direct detection of dark matter particles.

Ultra-pure NaI(Tl) crystals are the key element for a model-independent verification of the long standing DAMA result and a powerful means to search for the annual modulation signature of dark matter interactions. The SABRE collaboration has been developing cutting-edge techniques for the reduction of intrinsic backgrounds over several years. In this paper we report the first characterization of a 3.4 kg crystal, named NaI-33, performed in an underground passive shielding setup at LNGS. NaI-33 has a record low $^{39}$K contamination of 4.3$\pm$0.2 ppb as determined by mass spectrometry. We measured a light yield of 11.1$\pm$0.2 photoelectrons/keV and an energy resolution of 13.2% (FWHM/E) at 59.5 keV. We evaluated the activities of $^{226}$Ra and $^{228}$Th inside the crystal to be $5.9\pm0.6 \mu$Bq/kg and $1.6\pm0.3 \mu$Bq/kg, respectively, which would indicate a contamination from $^{238}$U and $^{232}$Th at part-per-trillion level. We measured an activity of 0.51$\pm$0.02 mBq/kg due to $^{210}$Pb out of equilibrium and a $\alpha$ quenching factor of 0.63$\pm$0.01 at 5304 keV. We illustrate the analyses techniques developed to reject electronic noise in the lower part of the energy spectrum. A cut-based strategy and a multivariate approach indicated a rate, attributed to the intrinsic radioactivity of the crystal, of $\sim$1 count/day/kg/keV in the [5-20] keV region.

A new system to assign accurate timestamps to events recorded by experiments running underground has been designed, installed and tested at INFN Gran Sasso National Laboratory, Italy. This facility is based on a Master unit installed on surface and receiving time information from a GPS receiver, and Slave units placed underground which get data packet from the Master via optical fiber and assign the timestamps. The system is able to provide a time accuracy of 15 ns (1 $\sigma$) and precise reference frequencies to the experiments. It is now part of the infrastructure of the Laboratory for all the experimental activities which need accurate timestamps.

SABRE aims to directly measure the annual modulation of the dark matter interaction rate with NaI(Tl) crystals. A modulation compatible with the standard hypothesis in which our Galaxy is embedded in a dark matter halo has been measured by the DAMA experiment in the same target material. Other direct detection experiments, using different target materials, seem to exclude the interpretation of such modulation in the simplest scenario of WIMP-nucleon elastic scattering. The SABRE experiment aims to carry out an independent search with sufficient sensitivity to confirm or refute the DAMA claim. The SABRE concept and goal is to obtain a background rate of the order of 0.1 cpd/kg/keVee in the energy region of interest. This challenging goal is achievable by operating high-purity crystals inside a liquid scintillator veto for active background rejection. In addition, twin detectors will be located in the northern and southern hemispheres to identify possible contributions to the modulation from seasonal or site-related effects. The SABRE project includes an initial Proof-of-Principle phase at LNGS (Italy), to assess the radio-purity of the crystals and the efficiency of the liquid scintillator veto. This paper describes the general concept of SABRE and the expected sensitivity to WIMP annual modulation., Comment: 7 pages, 4 figures

SABRE (Sodium-iodide with Active Background REjection) is a direct dark matter search experiment based on an array of radio-pure NaI(Tl) crystals surrounded by a liquid scintillator veto. Twin SABRE experiments in the Northern and Southern Hemispheres will differentiate a dark matter signal from seasonal and local effects. The experiment is currently in a Proof-of-Principle (PoP) phase, whose goal is to demonstrate that the background rate is low enough to carry out an independent search for a dark matter signal, with sufficient sensitivity to confirm or refute the DAMA result during the following full-scale experimental phase. The impact of background radiation from the detector materials and the experimental site needs to be carefully investigated, including both intrinsic and cosmogenically activated radioactivity. Based on the best knowledge of the most relevant sources of background, we have performed a detailed Monte Carlo study evaluating the expected background in the dark matter search spectral region. The simulation model described in this paper guides the design of the full-scale experiment and will be fundamental for the interpretation of the measured background and hence for the extraction of a possible dark matter signal., Comment: 13 pages, 5 figures

Time modulations at per mil level have been reported to take place in the decay constant of several nuclei with period of one year (most cases) but also of about one month or one day. On the other hand, experiments with similar or better sensitivity have been unable to detect any modulation. In this letter we give the results of the activity study of two different sources: 40K and 226Ra. The two gamma spectrometry experiments have been performed underground at the Gran Sasso Laboratory, this way suppressing the time dependent cosmic ray background. Briefly, our measurements reached the sensitivity of 3.4 and 3.5 parts over 10^6 for 40K and 226Ra, respectively (1 sigma) and they do not show any statistically significant evidence of time dependence in the decay constant. We also give the results of the activity measurement at the time of the two strong X-class solar flares which took place in September 2017. Our data do not show any unexpected time dependence in the decay rate of 40K in correspondence with the two flares. To the best of our knowledge, these are the most precise and accurate results on the stability of the decay constant as function of time., Comment: Accepted for publication in Physics Letters B, 6 pages, 8 figures. arXiv admin note: text overlap with arXiv:1311.7043

We give the results of a study on the 222Rn decay we performed in the Gran Sasso Laboratory (LNGS) by detecting the gamma rays from the radon progeny. The motivation was to monitor the stability of radioactivity measuring several times per year the half-life of a short lifetime (days) source instead of measuring over a long period the activity of a long lifetime (tens or hundreds of years) source. In particular, we give a possible reason of the large periodical fluctuations in the count rate of the gamma rays due to radon inside a closed canister which has been described in literature and which has been attributed to a possible influence of a component in the solar irradiation affecting the nuclear decay rates. We then provide the result of four half-life measurements we performed underground at LNGS in the period from May 2014 to January 2015 with radon diffused into olive oil. Briefly, we did not measure any change of the 222Rn half-life with a 8*10^-5 precision. Finally, we provide the most precise value for the 222Rn half-life: 3.82146(16){stat}(4){syst} days., Comment: Accepted for publication in Physics Letters B, 6 pages, 6 figures

We investigate numerically the spectral flow introduced by Adams for the staggered Dirac operator on realistic (quenched) gauge configurations. We obtain clear numerical evidence that the definition works as expected: there is a clear separation between crossings near and far away from the origin, and the topological charge defined through the crossings near the origin agrees, for most configurations, with the one defined through the near-zero modes of large taste-singlet chirality of the staggered Dirac operator. The crossings are much closer to the origin if we improve the Dirac operator used in the definition, and they move towards the origin as we decrease the lattice spacing., Comment: References added. Slight changes to the text

Time modulations at per mil level have been reported to take place in the decay constant of about 15 nuclei with period of one year (most cases) but also of about one month or one day. In this paper we give the results of the activity measurement of a 40K source and a 232Th one. The two experiments have been done at the Gran Sasso Laboratory during a period of about 500 days, above ground (40K) and underground (232Th) with a target sensitivity of a few parts over 10^5. We also give the results of the activity measurement at the time of the X-class solar flares which took place in May 2013. Briefly, our measurements do not show any evidence of unexpected time dependence in the decay rate of 40K and 232Th., Comment: version accepted for publication (Astroparticle Physics)

We analyze the vacuum structure of a generalized lattice Nambu--Jona-Lasinio model with two flavors of Wilson fermions, such that its continuum action is the most general four-fermion action with 'trivial' color interactions, and having a $SU(2)_V x SU(2)_A$ symmetry in the chiral limit. The phase structure of this model in the space of the two four-fermion couplings shows, in addition to the standard Aoki phases, new phases with $<\bar\psi \gamma_5\psi> != 0$, in close analogy to similar results recently suggested by some of us for lattice QCD with two degenerate Wilson fermions. This result shows how the phase structure of an effective model for low energy QCD cannot be entirely understood from Wilson Chiral Perturbation Theory, based on the standard QCD chiral effective Lagrangian approach., Comment: 24 pages, 3 figures, sent to Nuclear Physics B

The deacay rate of three different radioactive sources 40K, 137Cs and natTh has been measured with NaI and Ge detectors. Data have been analyzed to search for possible variations in coincidence with the two strongest solar flares of the years 2011 and 2012. No significant deviations from standard expectation have been observed, with a few 10-4 sensitivity. As a consequence, we could not find any effect like that recently reported by Jenkins and Fischbach: a few per mil decrease in the decay rate of 54Mn during solar flares in December 2006., Comment: 5 pages, 3 figures

Starting from June 2011, the activity of a 137Cs source has been measured by means of a HPGe detector installed deep underground in the Gran Sasso Laboratory. In total about 5100 energy spectra, one hour measuring time each, have been collected. These data allowed the search for time variations of the decay constant with periods from a few hours to 1 year. No signal with amplitude larger than 9.6{\cdot}10-5 at 95% C.L. has been detected. These limits are more than one order of magnitude lower than the values on the oscillation amplitude reported in literature. In particular, for 1 year period an oscillation amplitude larger than 8.5{\cdot}10-5 has been excluded at 95% C.L., independently of the phase. The same data give a value of 29.96{\pm}0.08 years for the 137Cs half life, in good agreement with the world mean value of 30.05{\pm}0.08 years., Comment: 5 pages, 4 figures

We investigate numerically the spectral flow introduced by Adams for the staggered Dirac operator on realistic gauge configurations. We study both the unimproved and the HISQ Dirac operators. We compare the spectral flow index with the index obtained by identifying low-lying modes of large chirality., Comment: Talk presented at The XXIX International Conference on Lattice Field Theory - Lattice 2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, California

The regional contribution to the geo-neutrino signal at Gran Sasso National Laboratory (LNGS) was determined based on a detailed geological, geochemical and geophysical study of the region. U and Th abundances of more than 50 samples representative of the main lithotypes belonging to the Mesozoic and Cenozoic sedimentary cover were analyzed. Sedimentary rocks were grouped into four main "Reservoirs" based on similar paleogeographic conditions and mineralogy. Basement rocks do not outcrop in the area. Thus U and Th in the Upper and Lower Crust of Valsugana and Ivrea-Verbano areas were analyzed. Based on geological and geophysical properties, relative abundances of the various reservoirs were calculated and used to obtain the weighted U and Th abundances for each of the three geological layers (Sedimentary Cover, Upper and Lower Crust). Using the available seismic profile as well as the stratigraphic records from a number of exploration wells, a 3D modelling was developed over an area of 2^{\circ}x2^{\circ} down to the Moho depth, for a total volume of about 1.2x10^6 km^3. This model allowed us to determine the volume of the various geological layers and eventually integrate the Th and U contents of the whole crust beneath LNGS. On this base the local contribution to the geo-neutrino flux (S) was calculated and added to the contribution given by the rest of the world, yielding a Refined Reference Model prediction for the geo-neutrino signal in the Borexino detector at LNGS: S(U) = (28.7 \pm 3.9) TNU and S(Th) = (7.5 \pm 1.0) TNU. An excess over the total flux of about 4 TNU was previously obtained by Mantovani et al. (2004) who calculated, based on general worldwide assumptions, a signal of 40.5 TNU. The considerable thickness of the sedimentary rocks, almost predominantly represented by U- and Th- poor carbonatic rocks in the area near LNGS, is responsible for this difference., Comment: 45 pages, 5 figures, 12 tables; accepted for publication in GCA

In order to elucidate the vacuum structure of the Aoki phase, we carried out a numerical investigation of QCD with two flavours of Wilson fermions, within the p.d.f. framework and in the absence of external sources. The simulations performed at V = 44 suggest a rich vacuum structure, where the observable $i\bar\psi\gamma_5\psi$ is allowed to take non-zero values of the same order of magnitude than the order parameter of the Aoki phase $i\bar\psi\gamma_5\tau_3\psi$. However, the simulation at higher volumes V = 6^4 suffers from large statistical errors., Comment: 7 pages, talk given at the XXVIII International Symposium on Lattice Field Theory, June 14-19, 2010, Villasimius, Italy. v2 corrects agreements

The Vafa-Witten arguments on the realization of parity and flavour symmetries in the QCD vacuum do not apply to two lattice regularizations of QCD which are able to reproduce the chiral anomaly: Wilson fermions and Ginsparg-Wilson fermions. We show here how using the last regularization one can get, from first principles, that the more standard order parameters for these symmetries take a vanishing vacuum expectation value for any number of flavours, if quarks have a non-vanishing mass., Comment: 14 pages. References added

The vacuum structure of QCD with two degenerated flavours of Wilson fermions is discussed by means of the p.d.f. (probability distribution function) formalism. Under certain assumptions, either new phases related to Aoki's appear, characterized by a non-vanishing expectation value of the condensate $i\bar\psi_u\gamma_5\psi_u + i\bar\psi_d\gamma_5\psi_d$, enriching the standard picture of the QCD vacuum structure with Wilson fermions; or the eigenvalues of the Dirac-Wilson operator must comply with a non-trivial, infinite set of sum rules, enforcing the currently accepted structure of the Aoki vacuum. The same scenario is analyzed using the Ginsparg-Wilson regularization. In this case, the absence of any parity and/or flavour breaking phase is proved for a non-zero value of the fermion mass., Comment: 7 pages, no figures, to be published in PoS(Lattice'09)

We discuss the vacuum structure of QCD with two flavors of Wilson fermions. We derive two possible scenarios: (i) If the spectral density $\rho_U(\lambda,\kappa)$ of the overlap hamiltonian in a fixed background gauge field is not symmetric in $\lambda$, Hermiticity is violated and Hermiticity violation effects could influence numerical determinations of the $\eta$ meson mass if we are not near enough to the continuum limit, where Hermiticity should be recovered; (ii) otherwise we argue that, under certain assumptions, new phases appear beside the Aoki phase, which can be characterized by a nonvanishing vacuum expectation value of $i\bar\psi_u\gamma_5\psi_u+i\bar\psi_d\gamma_5\psi_d$, and with vacuum states that cannot be connected with the Aoki vacua by parity-flavor symmetry transformations. Quenched numerical simulations suggest that the second scenario is more likely realized., Comment: 9 pages, 6 figures, to be published in Physical Review D1

We reconsider in this paper the old aim of trying to understand if the observed realization of discrete symmetries as Parity or CP in the QCD vacuum can be satisfied from first principles. We show how under the appropriate assumptions implicitely done by Vafa and Witten in their old paper on parity realization in vector-like theories, all parity and CP odd operators constructed from fermion bilinears of the form $\bar\psi\tilde O\psi$ should take a vanishing vacuum expectation value in a vector-like theory with N degenerate flavours (N>1). In our analysis the Vafa-Witten theorem on the impossibility to break spontaneously the flavour symmetry in a vector-like theory plays a fundamental role., Comment: 12 pages, no figures To be published in JHEP

Using an approach to analyze the theta dependence of systems with a theta-term we recently proposed, the critical behavior of CP^1 at theta=pi is studied. We find a region outside the strong coupling regime where Haldane's conjecture is verified. The critical line however does not belong to the universality class of the Wess-Zumino-Novikov-Witten model at topological coupling k=1 since it shows continuously varying critical exponents., Comment: 4 pages, 5 figures

A new approach for non zero chemical potential simulations is tested in the Gross-Neveu model for infinite flavor number, where the critical line is reconstructed in a large $\mu/T$ interval. A comparison with results from standard imaginary chemical potential approach as well as first results for $N_f=4$ QCD are presented., Comment: Talk presented at Lattice2004(non-zero), Fermilab, June 21-26, 2004, 3 pages, 4 figures

We proposed two different methods for simulating theta-vacuum systems. Both can be affected by systematic effects but these errors can be controlled by comparing the results of the two unrelated methods. This has been done for some analytically soluble models and here the same procedure is successfully applied to the interesting case of CP^9 in the scaling region., Comment: Lattice2003(topology); 3 pages, 3 figures

The possibility of diquark condensation at sufficiently large baryon chemical potential and zero temperature is analyzed in QCD at strong coupling. In agreement with other strong coupling analysis, it is found that a first order phase transition separates a low density phase with chiral symmetry spontaneously broken from a high density phase where chiral symmetry is restored. In none of the phases diquark condensation takes place as an equilibrium state, but, for any value of the chemical potential, there is a metastable state characterized by a non-vanishing diquark condensate. The energy difference between this metastable state and the equilibrium state decreases with the chemical potential and is minimum in the high density phase. The results indicate that there is attraction in the quark-quark sector also at strong coupling, and that the attraction is more effective at high baryon density, but for infinite coupling it is not enough to produce diquark condensation. It is argued that the absence of diquark condensation is not a peculiarity of the strong coupling limit, but persists at sufficiently large finite couplings., Comment: 10 pages, 2 figures. An important discussion concerning the extension of the results to finite couplings added

We apply to the $CP^9$ model two recently proposed numerical techniques for simulation of systems with a theta term. The algorithms, successfully tested in the strong coupling limit, are applied to the weak coupling region. The results agree and errors have been evaluated and are at % level. The results scale well with the renormalization group equation and show that, for $CP^9$ in presence of a theta term, CP symmetry is spontaneously broken at $\theta=\pi$ in the continuum limit., Comment: 4 pages, 4 figures

Inspired by the results of the Ising model within an imaginary external magnetic field, we introduce a transformation in quantum systems with a theta-vacuum term that amounts to a rescaling of z=cos(theta/2). Making use of this transformation we are able to determine the order parameter as a function of theta. The approach is successfully tested in models with both broken and unbroken CP symmetry at theta=pi., Comment: 14 pages, 6 figures; To appear in Phys. Lett. B

We consider diquark condensation in finite density lattice SU(2). We first present an extension of Vafa-Witten result, on spontaneous breaking of vector-like global symmetries, that allows us to formulate a no-go theorem for diquark condensation in a region of the chemical potential-mass parameter space. We then describe a new technique to calculate diquark condensation at any number of flavours directly at zero external source without using any potentially dangerous extrapolation procedure. We apply it to the strong coupling limit and find compelling evidences for a second order phase transition, where a diquark condensate appears, as well as quantitative agreement between lattice results and low-energy effective Lagrangian calculations., Comment: 21 pages, 7 figures

We study unquenched lattice SU(2) at nonzero chemical potential at strong coupling and with eight flavours of Kogut-Susskind fermions. Introducing a diquark source term we analyze the behaviour of different types of fermion condensates. Using a non standard approach we can obtain results at zero external source without extrapolations. We find strong evidences for a (high density) second order phase transition where a diquark condensate appears. The corresponding critical chemical potential is in good agreement with half the pion mass., Comment: 18 pages, 5 figures, to appear on Phys. Lett. B

Unquenched lattice SU(2) is studied at nonzero chemical potential in the strong coupling limit. The topic of diquark condensation is addressed analyzing the probability distribution function of the diquark condensate. We present results at zero external source without using any potentially dangerous extrapolation procedure. We find strong evidences for a (high density) second order phase transition where a diquark condensate appears, and show quantitative agreement of lattice calculations with low-energy effective Lagrangian calculations., Comment: 9 pages, 6 figures, to be published in the proceedings of the ``International Workshop on Non-Perturbative Methods and Lattice QCD'', Guangzhou, China, 15-21 May 2000

Simulations in finite density, beta=0 lattice QCD by means of the Monomer-Dimer-Polymer algorithm show a signal of first order transition at finite temporal size. This behaviour agrees with predictions of the mean field approximation, but is difficult to reconcile with infinite mass analytical solution. The MDP simulations are considered in detail and severe convergence problems are found for the SU(3) gauge group, in a wide region of chemical potential. Simulations of SU(2) model show discrepancies with MDP results as well., Comment: 18 pages, 9 figures, to appear in Nucl. Phys. B

The analytical results obtained in the infinite mass and strong coupling limits of QCD are difficult to reconcile with the predictions of the Monomer Dimer Polymer algorithm. We have reconsidered in detail the results obtained with this simulation scheme and evidences of severe convergence problems are presented for the SU(3) and SU(2) gauge group., Comment: LATTICE99(Finite Temperature and Density), 3 pages, 3 postscript figures

Lattice formulation of Finite Baryon Density QCD is problematic from computer simulation point of view; it is well known that for light quark masses the reconstructed partition function fails to be positive in a wide region of parameter space. For large bare quark masses, instead, it is possible to obtain more sensible results; problems are still present but restricted to a small region. We present evidence for a saturation transition independent from the gauge coupling $\beta$ and for a transition line that, starting from the temperature critical point at $\mu=0$, moves towards smaller $\beta$ with increasing $\mu$ as expected from simplified phenomenological arguments., Comment: 14 pages, 10 figures

QCD at finite chemical potential is analytically investigated in the region of large bare fermion masses. We show that, contrary to the general wisdom, the phase of the fermion determinant is irrelevant at zero temperature. However if the system is put at finite temperature, the contribution of the phase is finite. We also discuss on the quenched approximation and suggest that the origin of the failure of this approximation in finite density QCD could relay on the fundamental role that Pauli exclusion principle plays in this case., Comment: 16 pages, 5 figures

In the large fermion mass limit of QCD at finite density the structure of the partition function greatly simplifies and can be studied analytically. We show that, contrary to general wisdom, the phase of the Dirac determinant is relevant only at finite temperature and can be neglected for zero temperature fields., Comment: LATTICE98(hightemp), 3 pages, 3 figures

The Grand Canonical formalism is generally used in numerical simulations of finite density QCD since it allows free mobility in the chemical potential $\mu$. We show that special care has to be used in extracting numerical results to avoid dramatic rounding effects and spurious transition signals. If we analyze data correctly, with reasonable statistics, no signal of first order phase transition is present and results using the Glasgow prescription are practically coincident with the ones obtained using the modulus of the fermionic determinant., Comment: 6 pages, 5 ps figs. To appear in Proceedings of "QCD at Finite Baryon Density" workshop, Bielefeld, 27-30 April 1998

We present a detailed analysis of the QCD partition function in the Grand Canonical formalism. Using the fugacity expansion we find evidence for numerical instabilities in the standard evaluation of its coefficients. We discuss the origin of this problem and propose an issue to it. The correct analysis shows no evidence for a discontinuity in the baryonic density in the strong coupling limit. The moderate optimism that was inspired by the Grand Canonical Partition Function calculations in the last years has to be considered ill-founded., Comment: 9 pages, 6 Postscript figures; some comments added

We introduce a lattice model with local U(1) gauge symmetry which incorporates explicit frustration in d >2. The form of the action is inspired from the loop expansion of the fermionic determinant in standard lattice QED. We study through numerical simulations the phase diagram of the model, revealing the existence of a frustrated (antiferromagnetic) phase for d=3 and d=4, once an appropriate order parameter is identified., Comment: 7 pages, 7 figures