Eta Production Research Articles

Replicable functions arising from code-lattice VOAs fixed by automorphisms

We ascertain properties of the algebraic structures in towers of codes, lattices, and vertex operator algebras (VOAs) by studying the associated subobjects fixed by lifts of code automorphisms. In the case of sublattices fixed by subgroups of code automorphisms, we identify replicable functions that occur as quotients of the associated theta functions by suitable eta products. We show that these lattice theta quotients can produce replicable functions not associated to any individual automorphisms. Moreover, we show that the structure of the fixed subcode can induce certain replicable lattice theta quotients and we provide a general code theoretic characterization of order doubling for lifts of code automorphisms to the lattice-VOA. Finally, we prove results on the decompositions of characters of fixed subVOAs.

Evaluation of water productivity of smallholder irrigation along a Sand River, in the Maigobo watershed of northern Ethiopia

Sand dams are a type of rainwater harvesting technology that can increase groundwater recharge in dry land environments. They are constructed across seasonal sandy rivers and trap sand and water during floods. The sand acts as a natural filter and storage medium for the water, which can be extracted by the local communities through wells, pumps, or scoop holes. This research aims to evaluate agricultural water productivity based on water consumption (ETa) and biomass production of smallholder irrigation schemes along a sand river with a sand dam in the riverbeds of northern Ethiopia. Remotely sensed satellite data, WaPOR (Water Productivity through Open access of Remotely sensed derived data) database was used to estimate water productivity in the arid and semi-arid area. Following the installation of the sand dam at the irrigated parts of the Mai Gobo watershed, both the annual and seasonal values increased over a number of years, according to the spatial analysis of ETa and biomass production. For instance, the maximum seasonal ETa before the dam was about 70 mm/season, whereas after the dam the spatially analysed ETa reached 174 mm/season. Likewise, maximum seasonal biomass production of 1117 kg/ha and 4433 kg/ha were obtained before and after the construction of the sand dam, respectively. Agricultural water productivity at the irrigated plots of the Mai Gobo watershed was also improved from 1.4 kg/m3 to 2.9 kg/m3 before and after the sand dam respectively. Generally, the output of the study can be used as an input for the concerned stakeholder to take measures against the water scarcity problem in the study area. The study also contributes to the scientific knowledge and understanding of the hydrological and agronomical impacts of the sand dam in the arid and semi-arid regions.

BCOV cusp forms of lattice polarized K3 surfaces

We introduce the BCOV formula for the lattice polarized K3 surfaces. We find that it yields cusp forms expressed by certain eta products for many families of rank 19 lattice polarized K3 surfaces over P1. Moreover, for Clingher-Doran's family of U⊕E8(−1)⊕E7(−1)-polarized K3 surfaces, we obtain the Igusa cusp forms χ10 and χ12 from the formula. Inspired by the arithmetic properties of mirror maps studied by Lian-Yau, we also derive the K3 differential operators for all the genus zero groups of type Γ0(n)+.

Construction of Eicosatetraenoic Acid Producing Cell Factory by Genetic Engineering of Mucor circinelloides

Eicosatetraenoic acid (ETA, 20:4, ω-3) is the desaturation product of dihomo-gamma linolenic acid (DGLA, 20:3, ω-6) catalyzed by delta-17 desaturase, which is considered as a healthy product that helps to lower risk of heart diseases. The oleaginous filamentous fungus, Mucor circinelloides, has been used for a long time as a model micro-organism for GLA production at industrial scales. However, M. circinelloides lacks the key enzymes to synthesize C20 polyunsaturated fatty acids (PUFAs). M. circinelloides could produce DGLA by overexpressing the D6E(GLELO) gene, which could be a useful tool to produce ETA due to the availability of established genetic manipulation tools. Therefore, in this study, delta-17 desaturase (PpD17 and PaD17) genes from Phytophthora parasitica and Pythium aphanidermatum, respectively, were introduced into M. circinelloides to construct an ETA-producing cell factory. Our results showed that the PaD17 and PpD17 overexpression strains’ biomass increased by 25.98 and 23.34 g/L (39.98 and 25.75%), respectively, compared with the control strain. Meanwhile, the lipid contents of the recombinant strains also increased and reached up to 28.88% in Mc-PaD17 and 30.95% in Mc-PpD17, respectively, compared with the control strain (23.38% in Mc-2076). The RT-qPCR results showed that overexpression of delta-17 desaturase genes promoted the expression of cme2, fas2, and D6E, thereby contributing to lipid biosynthesis in M. circinelloides. Meanwhile, the content of ETA reached up to 1.95%, and the yield of ETA was up to 114.69 mg/L in PpD17 overexpression mutants at 96 h. This study provided the first report on the construction of an ETA-producing cell factory by heterologous overexpression of the PpD17 gene in M. circinelloides, which established a new scope for further research in the production of ETA in oleaginous fungi.

Charged current neutrino and antineutrino induced eta production off the nucleon

The charged current (anti)neutrino induced eta production from the nucleons is studied in a model based on the effective Lagrangians to evaluate the contribution from the nonresonant and resonant diagrams. The contribution from the nonresonant background terms has been obtained using a microscopic model based on the SU(3) chiral Lagrangians. The contribution from the resonant diagrams due to the low lying ${S}_{11}(1535)$, ${S}_{11}(1650)$, and ${P}_{11}(1710)$ resonances has been evaluated using an effective phenomenological Lagrangian with its parameters determined from the experimental values of their branching ratios and decay widths to the $N\ensuremath{\eta}$ channel. The model is first used to reproduce satisfactorily the experimental data from the MAINZ and JLab on the total cross sections for the photo- and electro- production of $\ensuremath{\eta}$ mesons, which fixes the model parameters in the vector current interaction. The partially conserved axial vector current (PCAC) hypothesis and generalized Goldberger-Treiman relation are used to fix the parameters of the axial vector current interaction. The model is then applied to study the weak production of eta mesons induced by the neutrinos and antineutrinos, and predicts the numerical values for the ${Q}^{2}$-distribution, $\ensuremath{\eta}$-momentum distribution, and the total cross section for the reactions ${\ensuremath{\nu}}_{\ensuremath{\mu}}+n\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}+p+\ensuremath{\eta}$ and ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}+p\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}+n+\ensuremath{\eta}$ in the energy region up to 2 GeV. It is found that the photo, electro, and (anti)neutrino induced production of eta mesons is dominated by the contribution from the ${S}_{11}(1535)$ resonance. The results discussed in this work are relevant for the present and future accelerator experiments like MicroBooNE, T2K, NOvA, MINERvA, T2-HyperK, and DUNE as well as for the atmospheric neutrino experiments.

$G$-fixed Hilbert schemes on $K3$ surfaces, modular forms, and eta products

Let $X$ be a complex $K3$ surface with an effective action of a group $G$ which preserves the holomorphic symplectic form. Let $$ Z_{X,G}(q) = \sum_{n=0}^{\infty} e\left(\operatorname{Hilb}^{n}(X)^{G} \right)\, q^{n-1} $$ be the generating function for the Euler characteristics of the Hilbert schemes of $G$-invariant length $n$ subschemes. We show that its reciprocal, $Z_{X,G}(q)^{-1}$ is the Fourier expansion of a modular cusp form of weight $\frac{1}{2} e(X/G)$ for the congruence subgroup $\Gamma_{0}(|G|)$. We give an explicit formula for $Z_{X,G}$ in terms of the Dedekind eta function for all 82 possible $(X,G)$. The key intermediate result we prove is of independent interest: it establishes an eta product identity for a certain shifted theta function of the root lattice of a simply laced root system. We extend our results to various refinements of the Euler characteristic, namely the Elliptic genus, the Chi-$y$ genus, and the motivic class.

G-invariant Hilbert schemes on Abelian surfaces and enumerative geometry of the orbifold Kummer surface

For an Abelian surface A with a symplectic action by a finite group G, one can define the partition function for G-invariant Hilbert schemes $$\begin{aligned} Z_{A, G}(q) = \sum _{d=0}^{\infty } e(\text {Hilb}^{d}(A)^{G})q^{d}. \end{aligned}$$We prove the reciprocal \(Z_{A,G}^{-1}\) is a modular form of weight \(\frac{1}{2}e(A/G)\) for the congruence subgroup \(\Gamma _{0}(|G|)\) and give explicit expressions in terms of eta products. Refined formulas for the \(\chi _{y}\)-genera of \(\text {Hilb}(A)^{G}\) are also given. For the group generated by the standard involution \(\tau : A \rightarrow A\), our formulas arise from the enumerative geometry of the orbifold Kummer surface \([A/\tau ]\). We prove that a virtual count of curves in the stack is governed by \(\chi _{y}(\text {Hilb}(A)^{\tau })\). Moreover, the coefficients of \(Z_{A, \tau }\) are true (weighted) counts of rational curves, consistent with hyperelliptic counts of Bryan, Oberdieck, Pandharipande, and Yin.

Pi ^-prightarrow eta ^{(prime )}, pi ^- p in the double-Regge region

The production of eta ^{(prime )}pi pairs constitutes one of the golden channels to search for hybrid exotics, with explicit gluonic degrees of freedom. Understanding the dynamics and backgrounds associated to eta ^{(prime )}pi production above the resonance region is required to impose additional constraints to the resonance extraction. We consider the reaction pi ^-prightarrow eta ^{(prime )} pi ^- ,p measured by COMPASS. We show that the data in 2.4< m_{eta ^{(prime )}pi } < 3.0{mathrm {,GeV}} can be described by amplitudes based on double-Regge exchanges. The angular distribution of the meson pairs, in particular in the eta ' pi channel, can be attributed to flavor singlet exchanges, suggesting the presence of a large gluon content that couples strongly to the produced mesons.

Theoretical study of the D^0 rightarrow K^- pi ^+ eta reaction

We develop a model to study the D^0 rightarrow K^- pi ^+ eta weak decay, starting with the color favored external emission and Cabibbo favored mode at the quark level. A less favored internal emission decay mode is also studied as a source of small corrections. Some pairs of quarks are allowed to hadronize producing two pseudoscalar mesons, which posteriorly are allowed to interact to finally provide the K^- pi ^+ eta state. The chiral unitary approach is used to take into account the final state interaction of pairs of mesons, which has as a consequence the production of the kappa (K^*_0(700)) and the a_0(980) resonances, well visible in the invariant mass distributions. We also introduce the bar{K}^{*0} eta production in a phenomenological way and show that the s-wave pseudoscalar interaction together with this vector excitation mode are sufficient to provide a fair reproduction of the experimental data. The model provides the relative weight of the a_0(980) to the kappa excitation, and their strength is clearly visible in the low energy part of the K pi spectrum.

Prompt eta _c meson production at the LHC in the NRQCD with k_T-factorization

In the framework of the k_T-factorization approach, the prompt production of eta _c mesons at the LHC conditions is studied. Our consideration is based on the off-shell amplitudes for hard partonic subprocesses and on the nonrelativistic QCD (NRQCD) formalism for the formation of bound states. We try two latest parametrizations for noncollinear, or transverse momentum dependent (TMD) gluon densities derived from the Catani–Ciafaloni–Fiorani–Marchesini (CCFM) equation. We use the values of the nonperturbative matrix elements obtained from a combined fit of the eta _c and J/psi differential cross sections. Finally, we show an universal set of parameters that provides a reasonable simultaneous description for all of the available data on the prompt J/psi and eta _c production at the LHC.

Complementary‐Relationship‐Based Modeling of Terrestrial Evapotranspiration Across China During 1982–2012: Validations and Spatiotemporal Analyses

AbstractHaving recognized the limitations in spatial representativeness and/or temporal coverage of (i) current ground ETa observations and (ii) land surface model‐ and remote sensing‐based ETa estimates due to uncertainties in soil and vegetation parameters, a calibration‐free nonlinear complementary relationship (CR) model is employed with inputs of air and dew‐point temperature, wind speed, and net radiation to estimate 0.1°, monthly ETa over China during 1982–2012. The modeled ETa rates were first validated against 13 eddy‐covariance measurements, producing Nash‐Sutcliffe efficiency values in the range of 0.72–0.94. On the basin scale, the modeled ETa values yielded a relative bias of 6%, and a Nash‐Sutcliffe efficiency value of 0.80 in comparison with water‐balance‐derived evapotranspiration rates across 10 major river basins in China, indicating the CR‐simulated ETa rates reliable over China. Further evaluations suggest that the CR‐based ETa product is more accurate than seven other mainstream ETa products. The 31‐year mean annual ETa value decreases from the southeast to the northwest in China, resulting in a country average of 406 ± 15 mm/year. The country‐representative annual ETa rates slightly decreased with a rate of −0.5 mm/year (p = 0.86) during 1982–2012. Annual ETa increased significantly over most parts of western and northeastern China but decreased significantly in many regions of the North China Plain as well as in the eastern and southern coastal regions. The present CR‐based method, with its calibration‐free nature and minimal data requirement, could help future calibrations/verifications of the more complex and more data‐intensive land surface model‐ and remote sensing‐based models.

On the Density of the Odd Values of the Partition Function

The purpose of this note is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely, the conjecture that the partition function p(n) is equidistributed modulo 2. Our main result will relate the densities, say, $${\delta_t}$$ , of the odd values of the t-multipartition functions $${p_t(n)}$$ , for several integers t. In particular, we will show that if $${\delta_t > 0}$$ for some $${t \in \{5, 7, 11, 13, 17, 19, 23, 25\}}$$ , then (assuming it exists) $${\delta_1 > 0}$$ ; that is, p(n) itself is odd with positive density. Notice that, currently, the best unconditional result does not even imply that p(n) is odd for $${\sqrt{x}}$$ values of $${n \leq x}$$ . In general, we conjecture that $${\delta_t = 1/2}$$ for all t odd, i.e., that similarly to the case of p(n), all multipartition functions are in fact equidistributed modulo 2. Our arguments will employ a number of algebraic and analytic methods, ranging from an investigation modulo 2 of some classical Ramanujan identities and several other eta product results, to a unified approach that studies the parity of the Fourier coefficients of a broad class of modular form identities recently introduced by Radu.

Systematic few-body analysis of ηd, ηHe3 , and ηHe4 interaction at low energies

The Alt-Grassberger-Sandhas N-body theory is used to study interaction of eta-mesons with d, 3He, and 4He. Separable expansion of the subamplitudes is adopted to convert the integral equations into the quasi-two-body form. The resulting formalism is applied to fit the existing data for low-energy eta production on few-nucleon targets. On the basis of this fitting procedure the scattering lengths a_{eta d}, a_{eta 3He}, a_{eta 4He} as well as the subthreshold behaviour of the elementary eta-N scattering amplitude are obtained.

Pi ^{0} and eta meson production in proton-proton collisions at sqrt{s}=8 TeV

An invariant differential cross section measurement of inclusive pi ^{0} and eta meson production at mid-rapidity in pp collisions at sqrt{s}=8 TeV was carried out by the ALICE experiment at the LHC. The spectra of pi ^{0} and eta mesons were measured in transverse momentum ranges of 0.3<p_{ text{ T }} <35 text{ GeV/c } and 0.5<p_{ text{ T }} <35 text{ GeV/c }, respectively. Next-to-leading order perturbative QCD calculations using fragmentation functions DSS14 for the pi ^{0} and AESSS for the eta overestimate the cross sections of both neutral mesons, although such calculations agree with the measured eta /pi ^0 ratio within uncertainties. The results were also compared with PYTHIA 8.2 predictions for which the Monash 2013 tune yields the best agreement with the measured neutral meson spectra. The measurements confirm a universal behavior of the eta /pi ^0 ratio seen for NA27, PHENIX and ALICE data for pp collisions from sqrt{s}=27.5 GeV to sqrt{s}=8 TeV within experimental uncertainties. A relation between the pi ^{0} and eta production cross sections for pp collisions at sqrt{s}=8 TeV is given by m_{ text{ T }} scaling for p_{ text{ T }} >3.5 text{ GeV/c }. However, a deviation from this empirical scaling rule is observed for transverse momenta below p_{ text{ T }} <3.5 text{ GeV/c } in the eta /pi ^0 ratio with a significance of 6.2sigma .

Eta products of weight one, and decomposition of primes in non-abelian extensions

This article is a slightly extended and revised version of a conference talk at “Arithmetik an der A7” in Wurzburg, June 23rd, 2017. We present a conjecture on the coincidence of Hecke theta series of weight 1 on three distinct quadratic fields. Then we discuss a special instance of the Deligne–Serre Theorem, implying that the decomposition of prime numbers in a certain extension of the rationals is governed by the coefficients of the eta product $$\eta^{2}(z)$$ .

In-medium and isospin effects on eta production in heavy-ion collisions near threshold energies

The dynamics of $ \eta$ meson produced in heavy-ion collisions has been investigated within the Lanzhou quantum molecular dynamics model (LQMD). The in-medium corrections have been considered in the model, in which an attractive $ \eta$ -nucleon potential is implemented. The impacts of the $ \eta$ optical potential and the nuclear symmetry energy on the $ \eta$ dynamics are investigated. It is found that the total yields are slightly influenced by the potential and weakly depend on the symmetry energy. However, the structure of the kinetic spectra is related to the optical potential and the stiffness of symmetry energy. The attractive potential leads to the reduction of high-momentum (kinetic energy) $ \eta$ production, i.e., the spectra of momentum and transverse mass distributions, increasing the reabsorption process by surrounding nucleons, and favoring the in-plane eta emissions. The reabsorption process in $ \eta$ -nucleon collisions plays a significant role on the $ \eta$ dynamics.

Pion and eta production in elementary and heavy-ion collisions at SIS energies

A main emphasis of the HADES program is on the dielectron signal from the early phase of heavy-ion collisions. We discuss the data with respect to the emission of charged hadrons, specifically the production of π + and π − mesons, which are related to neutral pions representing a dominant contribution to the dielectron yield. In addition, inclusive pion production obtained with the photon-conversion method is disscused. Preliminary results from Au+Au at 1.23 AGeV are presented.

Upper Limits for the Production of the $\eta $-mesic Helium in the $dd\rightarrow ^{3}$He$n\pi ^0$ and $dd\rightarrow ^3$He$p\pi ^-$ Reactions

We performed a search for 4He-eta bound state in dd -> 3Henpi0 and dd -> 3Heppi- reactions with the WASA-at-COSY facility using a ramped beam technique. The measurement was carried out with high statistics and high acceptance. The signature of eta-mesic nuclei was searched for by the measurement of the excitation functions in the vicinity of the eta production threshold for each of the considered channels. We did not observe the narrow structure which could be interpreted as a bound state. The preliminary upper limits of the total cross sections for the bound state production and decay varies from 21 nb to 36 nb for the dd -> 3Henpi0 channel, and from 5 nb to 9 nb for the dd -> 3Heppi- channel for the bound state width ranging from 5 to 50 MeV.

In-medium and isospin effects on particle production near threshold energies in heavy-ion collisions

Dynamics of pseudoscalar mesons ($\pi$, $\eta$, $K$ and $\overline{K}$ ) and hyperons ($\Lambda$ and $\Sigma$) produced in heavy-ion collisions near threshold energies has been investigated within the Lanzhou quantum molecular dynamics (LQMD) transport model. The in-medium modifications on particle production in dense nuclear matter are implemented in the model through corrections on the elementary cross sections and by inclusion of the meson (hyperon)-nucleon potentials, in which the isospin effects are considered. It is found that the transportation of particles are influenced with the in-medium corrections. The total number of pions is reduced with an isospin, density and momentum dependent pion-nucleon potential. However, the ratios of charged pions is enhanced with inclusion of the potential. The production of eta in the domain of mid-rapidities and high momenta is sensitive to the $\eta$-nucleon potential, but weakly depends on symmetry energy. The attractive antikaon-nucleon potential enhances the subthreshold $\overline{K}$ production and also influences the structure of phase-space distributions. Dynamics of etas, kaons, antikaons and hyperons is also influenced by the pion potential because of collisions between pions and nucleons (resonances). The impacts of mean-field potentials on particle dynamics are investigated, such as the phase-space distributions from rapidity and transverse momentum spectra, inclusive invariant spectra, collective flows etc.

Lepton-pair production in ultraperipheral collisions at AFTER@LHC

We investigate the potentialities offered by the study of lepton-pair production in ultraperipheral collisions at a fixed-target experiment using the proton and ion LHC beams. In these collisions, exclusive or semi-exclusive lepton-pair production can be used as luminosity monitor as well as a check of the equivalent-photon approximation, via the measurement of the Bethe-Heitler cross section. It can also serve as a probe of the inner hadron structure via the measurement of the lepton-pair azimuthal asymmetry which is sensitive to the timelike virtual Compton scattering. We also briefly discuss the possibility offered by the study of eta(c) production. Finally, we outline the possibilities for lepton-pair production by Pomeron-Odderon fusion in exclusive pp and pA collisions.