Neutrino statistics and big bang nucleosynthesis

Neutrinos may possibly violate the spin-statistics theorem, and hence obey Bose statistics or mixed statistics despite having spin half. We find the generalized equilibrium distribution function of neutrinos which depends on a single fermi-bose parameter, \kappa, and interpolates continuously between the bosonic and fermionic distributions when \kappa changes from -1 to +1. We consider modification of the Big Bang Nucleosynthesis (BBN) in the presence of bosonic or partly bosonic neutrinos. For pure bosonic neutrinos the abundances change (in comparison with the usual Fermi-Dirac case) by -3.2% for 4He (which is equivalent to a decrease of the effective number of neutrinos by \Delta N_\nu = - 0.6), +2.6% for 2H and -7% for 7Li. These changes provide a better fit to the BBN data. Future BBN studies will be able to constrain the fermi-bose parameter to \kappa > 0.5, if no deviation from fermionic nature of neutrinos is found. We also evaluate the sensitivity of future CMB and LSS observations to the fermi-bose parameter.Comment: 11 pages, 3 figures, matches version in JCAP, discussion and references extended slightl

Measurement of double beta decay of 100Mo to excited states in the NEMO 3 experiment

The double beta decay of 100Mo to the 0^+_1 and 2^+_1 excited states of 100Ru is studied using the NEMO 3 data. After the analysis of 8024 h of data the half-life for the two-neutrino double beta decay of 100Mo to the excited 0^+_1 state is measured to be T^(2nu)_1/2 = [5.7^{+1.3}_{-0.9}(stat)+/-0.8(syst)]x 10^20 y. The signal-to-background ratio is equal to 3. Information about energy and angular distributions of emitted electrons is also obtained. No evidence for neutrinoless double beta decay to the excited 0^+_1 state has been found. The corresponding half-life limit is T^(0nu)_1/2(0^+ --> 0^+_1) > 8.9 x 10^22 y (at 90% C.L.). The search for the double beta decay to the 2^+_1 excited state has allowed the determination of limits on the half-life for the two neutrino mode T^(2nu)_1/2(0^+ --> 2^+_1) > 1.1 x 10^21 y (at 90% C.L.) and for the neutrinoless mode T^(0nu)_1/2(0^+ --> 2^+_1) > 1.6 x 10^23 y (at 90% C.L.).Comment: 23 pages, 7 figures, 4 tables, submitted to Nucl. Phy

Double beta decay: present status

The present status of double beta decay experiments (including the search for $2\beta^{+}$, EC$\beta^{+}$ and ECEC processes) are reviewed. The results of the most sensitive experiments are discussed. Average and recommended half-life values for two-neutrino double beta decay are presented. Conservative upper limits on effective Majorana neutrino mass and the coupling constant of the Majoron to the neutrino are established as $< 0.75$ eV and $<g_{ee} > < 1.9 \cdot 10^{-4}$, respectively. Proposals for future double beta decay experiments with a sensitivity for the $$ at the level of (0.01-0.1) eV are considered.Comment: 33 pages included 7 figures and 14 tables; an extended version of the invited talk at 13th Lomonosov Conference of Elementary Particle Physics, 23-29 August, 2007, Moscow, Russi

Collapse of topological texture

We study analytically the process of a topological texture collapse in the approximation of a scaling ansatz in the nonlinear sigma-model. In this approximation we show that in flat space-time topological texture eventually collapses while in the case of spatially flat expanding universe its fate depends on the rate of expansion. If the universe is inflationary, then there is a possibility that texture will expand eternally; in the case of exponential inflation the texture may also shrink or expand eternally to a finite limiting size, although this behavior is degenerate. In the case of power law noninflationary expansion topological texture eventually collapses. In a cold matter dominated universe we find that texture which is formed comoving with the universe expansion starts collapsing when its spatial size becomes comparable to the Hubble size, which result is in agreement with the previous considerations. In the nonlinear sigma-model approximation we consider also the final stage of the collapsing ellipsoidal topological texture. We show that during collapse of such a texture at least two of its principal dimensions shrink to zero in a similar way, so that their ratio remains finite. The third dimension may remain finite (collapse of cigar type), or it may also shrink to zero similar to the other two dimensions (collapse of scaling type), or shrink to zero similar to the product of the remaining two dimensions (collapse of pancake type).Comment: 23 pages, LaTeX, to be published in Phys. Rev.

Double Beta Decay: Historical Review of 75 Years of Research

Main achievements during 75 years of research on double beta decay have been reviewed. The existing experimental data have been presented and the capabilities of the next-generation detectors have been demonstrated.Comment: 25 pages, typos adde

Limits on different Majoron decay modes of 100^{100}Mo and 82^{82}Se for neutrinoless double beta decays in the NEMO-3 experiment

The NEMO-3 tracking detector is located in the Fr\'ejus Underground Laboratory. It was designed to study double beta decay in a number of different isotopes. Presented here are the experimental half-life limits on the double beta decay process for the isotopes $^{100}$Mo and $^{82}$Se for different Majoron emission modes and limits on the effective neutrino-Majoron coupling constants. In particular, new limits on "ordinary" Majoron (spectral index 1) decay of $^{100}$Mo ($T_{1/2} > 2.7\cdot10^{22}$ y) and $^{82}$Se ($T_{1/2} > 1.5\cdot10^{22}$ y) have been obtained. Corresponding bounds on the Majoron-neutrino coupling constant are $< (0.4-1.9) \cdot 10^{-4}$ and $< (0.66-1.7) \cdot 10^{-4}$.Comment: 23 pages includind 4 figures, to be published in Nuclear Physics

Study of 2b-decay of Mo-100 and Se-82 using the NEMO3 detector

After analysis of 5797 h of data from the detector NEMO3, new limits on neutrinoless double beta decay of Mo-100 (T_{1/2} > 3.1 10^{23} y, 90% CL) and Se-82 (T_{1/2} > 1.4 10^{23} y, 90% CL) have been obtained. The corresponding limits on the effective majorana neutrino mass are: m < (0.8-1.2) eV and m < (1.5-3.1) eV, respectively. Also the limits on double-beta decay with Majoron emission are: T_{1/2} > 1.4 10^{22} y (90% CL) for Mo-100 and T_{1/2}> 1.2 10^{22} y (90%CL) for Se-82. Corresponding bounds on the Majoron-neutrino coupling constant are g < (0.5-0.9) 10^{-4} and < (0.7-1.6) 10^{-4}. Two-neutrino 2b-decay half-lives have been measured with a high accuracy, T_{1/2} Mo-100 = [7.68 +- 0.02(stat) +- 0.54(syst) ] 10^{18} y and T_{1/2} Se-82 = [10.3 +- 0.3(stat) +- 0.7(syst) ] 10^{19} y.Comment: 5 pages, 4 figure

Possible background reductions in double beta decay experiments

The background induced by radioactive impurities of $^{208}\rm Tl$ and $^{214}\rm Bi$ in the source of the double beta experiment NEMO-3 has been investigated. New methods of data analysis which decrease the background from the above mentioned contamination are identified. The techniques can also be applied to other double beta decay experiments capable of measuring independently the energies of the two electrons.Comment: 15 pages, 13 figures, accepted in the Nuclear Instruments and Methods

Algorithm for selecting the winning strategies in the processes of managing the state of the system "supplier - consumer" in the presence of aggressive competitor

Algorithm for selecting the winning strategies in the processes of managing the state of the system "supplier - consumer" in the presence of aggressive competitor / O. Domina, D. Lunin, O. Barabash, O. Balynska, Y. Paida, L. Mikhailova, O. Niskhodovska // Eastern-European Journal of Enterprise Technologies. – 2018. – № 6 (3-96). – Р. 48-61. – DOI: https://doi.org/10.15587/1729-4061.2018.152793 Domina, O., Lunin, D., Barabash, O., Balynska, O., Paida, Y., Mikhailova, L., & Niskhodovska, O. (2018). Algorithm for selecting the winning strategies in the processes of managing the state of the system &quot;supplier – consumer&quot; in the presence of aggressive competitor. Eastern-European Journal of Enterprise Technologies, 6(3 (96), 48–61. https://doi.org/10.15587/1729-4061.2018.152793Розглянуто проблему, пов'язану з пошуком оптимальної стратегiї цiноутворення компанiєю-постачальником у разi появи у неї конкурента, що пропонує нижчу цiну продукцiї. Виникнення такої проблеми породжує необхiднiсть пошуку оптимального шляху зниження своєї вiдпускної цiни, з метою не програти в агресивному конкурентному середовищi, що формується новими гравцями, що заходять на ринок зi свiдомо кращими пропозицiями. Для вирiшення цiєї проблеми розроблено алгоритм вибору виграшних стратегiй на основi оцiнювання стратегiчних можливостей конкурента в умовах невизначеностi. Запропоновано для оцiнки вартостi товару в системi «постачальник - споживач» використовувати поняття масштабу l-го рiвня. Показано, що при такому поданнi стає можливою безрозмiрна оцiнка цiноутворення товару, незалежно вiд його виду або натурального грошового вираження. Для формалiзованого опису вiдносин компанiї-постачальника i компанiї-конкурента запропоновано використання теорiї стратегiчних iгор, матриця гри в якiй формується на основi унiверсальних рiвнянь регресiї. Особливiстю запропонованих рiшень є те, що значення виграшу в матрицi гри визначається рiшенням оптимiзацiйної задачi на основi рiвняння регресiї, що описує вплив транспортних витрат, прибутку та податку на додану вартiсть (VAT) на цiну гри. Встановлено, що при такому описi має мiсце гра з сiдловою точкою i чистої цiною гри z=-0,5. На пiдставi математичного моделювання встановлено, що вибiр компанiї-постачальника обмежується стратегiями, в якiй власний прибуток має знаходитися поблизу середнього або мiнiмально можливого значення. Розроблено прогнозна модель стратегiчних можливостей конкурента в системi «постчальник - споживач», що представляє собою унiверсальне рiвняння регресiї. На пiдставi нього може бути зроблено коригування чисельних показникiв компонентiв цiноутворення товару. Показано, що таке коригування допускає наявнiсть декiлькох альтернатив, якi зводять до нуля переваги конкурента. Обґрунтовано обмеження на одержуванi рiшення, пов'язанi з двома обставинами: припущенні про точнiсть визначення компонентiв цiноутворення у конкурента i наявнiстю особливостей оподаткування в мiжнародних вантажоперевезеннях. The issue examined in this work relates to the search for an optimal pricing strategy by an enterprise-supplier in case it faces a new competitor that offers products at a lower price. The emergence of such a problem necessitates looking for a rational way to reduce its selling price, in order to prevent losing in an aggressive competitive environment, formed by new players entering the market with proposals that are obviously better. To resolve this problem, we have developed an algorithm for selecting the winning strategies based on the estimation of strategic capabilities of a competitor under conditions of uncertainty. It has been proposed, in order to assess the cost of a product in the system "supplier-consumer", to apply the concept of the l- level scale. It is shown that, given such a representation, it becomes possible to employ a dimensionless estimation of product pricing, regardless of its type or natural cash value. For a formalized description of relations between an enterprise- supplier and a competing company, it is proposed to use the theory of strategic games, in which a game matrix is built based on universal regression equations. A feature of the proposed solutions is that the value of winning in the game matrix is defined by solving an optimization problem based on the regression equation that describes the impact of transportation costs, profit, and a value-added tax (VAT) on the price of the game. It has been established that, given such a description, the game that is played has a saddle point with the net price of the game z=-0.5. Based on mathematical modelling, it was established that the selection of a supplier company is limited by strategies at which own profit must be close to the average or the minimally possible value. We have constructed a predictive model for strategic opportunities of a competitor in the system "supplier-consumer", representing a universal regression equation. Based on it, an adjustment of numerical indicators for the components in product pricing can be made. It is shown that such an adjustment allows the existence of multiple alternatives, neutralizing competitor's advantages. We have substantiated constraints for the solutions derived, related to two factors: an assumption about the accuracy of determining the pricing components of a competitor, and the presence of taxation specificity in international cargo transportation. Рассмотрена проблема, связанная с поиском оптимальной стратегии ценообразования компанией-поставщиком при появлении у нее конкурента, предлагающего более низкую цену продукции. Возникновение такой проблемы порождает необходимость поиска оптимального пути снижения своей отпускной цены, с целью не проиграть в агрессивной конкурентной среде, формируемой новыми игроками, которые заходят на рынок со заведомо лучшими предложениями. Для решения этой проблемы разработан алгоритм выбора выигрышных стратегий на основе оценки стратегических возможностей конкурента в условиях неопределенности. Предложено для оценки стоимости товара в системе «поставщик - потребитель» использовать понятие масштаба l-го уровня. Показано, что при таком представлении становится возможным безразмерная оценка ценообразования товара, независимо от его вида или натурального денежного выражения. Для формализованного описания отношений компании-поставщика и компании-конкурента предложено использование теории стратегических игр, матрица игры в которой формируется на основе универсальных уравнений регрессии. Особенностью предложенных решений является то, что значение выигрыша в матрице игры определяется решением оптимизационной задачи на основе уравнения регрессии, описывающей влияние транспортных расходов, прибыли и налога на добавленную стоимость (VAT) на цену игры. Установлено, что при таком описании имеет место игра с седельной точкой и чистой ценой игры z=-0,5. На основании математического моделирования установлено, что выбор компании-поставщика ограничивается стратегиями, в которых собственная прибыль должна находиться вблизи от среднего или минимально возможного значения. Разработана прогнозная модель стратегических возможностей конкурента в системе «поставщик – потребитель», представляющая собой универсальное уравнение регрессии. На основании него может быть произведена корректировка численных показателей компонентов ценообразования товара. Показано, что такая корректировка допускает наличие нескольких альтернатив, сводящих к нулю преимущества конкурента. Обоснованы ограничения на получаемые решения, связанные с двумя обстоятельствами: предположение о точности определения компонентов ценообразования у конкурента и наличие особенностей налогообложения в международных грузоперевозках

Technical design and performance of the NEMO3 detector

The development of the NEMO3 detector, which is now running in the Frejus Underground Laboratory (L.S.M. Laboratoire Souterrain de Modane), was begun more than ten years ago. The NEMO3 detector uses a tracking-calorimeter technique in order to investigate double beta decay processes for several isotopes. The technical description of the detector is followed by the presentation of its performance.Comment: Preprint submitted to Nucl. Instrum. Methods A Corresponding author: Corinne Augier ([email protected]