Rm Exp Research Articles

Least-squares analysis of the moments of the charge distribution in the mean-field models

Abstract The nth moment, $R^{(n)}_c$, of the charge distribution is composed of not only the m(≤ n)th moments, $R^{(m)}_p$, of the point proton distribution, but also the m(≤ (n − 2))th ones, $R^{(m)}_n$, of the point neutron distribution. The experimental value of $R^{(n)}_c(R^{(n)}_{c,{\rm exp}})$ observed through electromagnetic interaction makes it possible to investigate the point proton and neutron distributions together on the same basis. In order to estimate $R^{(m)}_\tau (\tau =p,n)$ from $R^{(n)}_{c,{\rm exp}}$, however, nuclear models are required. The structure of the least-squares analysis (LSA) between $R^{(n)}_c$ and $R^{(m)}_\tau$ is investigated within the mean-field framework. The LSA reveals constraints inherent in the model framework through the least-squares lines (LSL) and determines the value of $R^{(m)}_\tau$ of $R^{(n)}_{c,{\rm exp}}$ uniquely as a result of the sum rule with respect to the coefficients of the LSL equations. The n-dependence of the values of $R^{(m)}_\tau$ in the LSA is examined numerically by using the moments calculated up to n = 6 for 40Ca, 48Ca, and 208Pb.

On improving a Schur-type theorem in shifted primes

We show that if $$N \geq {\rm exp}({\rm exp}({\rm exp} (k^{O(1)})))$$ , then any k-colouring of the primes that are less than N contains a monochromatic solution to $$p_1 - p_2 = p_3 -1$$ .

Ab initio low-energy effective Hamiltonians for the high-temperature superconducting cuprates Bi2Sr2CuO6, Bi2Sr2CaCu2O8, HgBa2CuO4, and CaCuO2

We derive $ab$ $initio$ low-energy effective Hamiltonians (LEH) for high-temperature superconducting (SC) copper oxides Bi$_2$Sr$_2$CuO$_6$ (Bi2201, $N_{\ell}=1$, $T_c^{\rm exp} \sim 10$ K), Bi$_2$Sr$_2$CaCu$_2$O$_8$ (Bi2212, $N_{\ell}=2$, $T_c^{\rm exp} \sim 84$ K), HgBa$_2$CuO$_4$ (Hg1201, $N_{\ell}=1$, $T_c^{\rm exp} \sim 90$ K) and CaCuO$_2$ (Ca11, $N_{\ell}=\infty$, $T_c^{\rm exp} \sim 110$ K), with different experimental optimal SC transition temperature $T_c^{\rm exp}$ and number $N_{\ell}$ of laminated CuO$_2$ planes between the two neighboring block layers. We apply the latest methodology of the multiscale $ab$ $initio$ scheme for correlated electron systems (MACE), and focus on the LEH consisting of one antibonding (AB) Cu$3d_{x^2-y^2}$/O$2p_{\sigma}$ orbital centered on each Cu atom. We discuss prominent features of this LEH: (1) The ratio $U/|t_1|$ between the onsite effective Coulomb repulsion (ECR) $U$ and amplitude of nearest neighbour hopping $t_1$ increases with $T^{\rm exp}_c$ and $N_{\ell}$, consistently with the expected increase in $d$-wave SC correlation function $P_{dd}$ with $U/|t_1|$. One possible cause of the increase of $U/|t_1|$ is the replacement of apical O atoms by Cu atoms from neighbouring CuO$_2$ planes when $N_{\ell}$ increases. Furthermore, we show that the increase in distance between Cu and apical O atoms decreases the effective screening (ES) by electrons outside of the LEH and increases $U/|t_1|$. (2) For Hg1201 and Ca11, we show that $U/|t_1|$ decreases when hole doping per AB orbital $\delta$ increases, which may partly account for the disappearance of SC when $\delta$ exceeds the optimal value in experiment. (3) For $N_{\ell} \geq 2$, off-site inter-CuO$_2$ plane ECR is comparable to off-site intra-CuO$_2$ plane ECR. We discuss contributions of inter-CuO$_2$ plane ECR to both $P_{dd}$ and the stability of the SC state.

Optical and spectral observations and hydrodynamic modelling of type IIb supernova 2017gpn

ABSTRACTIn this work we present the photometric and spectroscopic observations of type IIb supernova 2017gpn. This supernova was discovered in the error-box of the LIGO/Virgo G299232 gravitational-wave event. We obtained the light curves in the B and R passbands and modelled them numerically using the one-dimensional radiation hydrocode stella. The best-fitting model has the following parameters: the pre-SN star mass and the radius are M ≈ 3.5 M⊙ and R ≈ 50 R⊙, respectively; the explosion energy is $E_{\rm exp} \approx 1.2\times 10^{51}$ erg; the mass of radioactive nickel is $M_{\rm ^{56}Ni} \approx 0.11$ M⊙, which is completely mixed throughout the ejecta; and the mass of the hydrogen envelope $M_{\rm H\_{env}}$ ≈ 0.06 M⊙. Moreover, SN 2017gpn is a confirmed SN IIb that is located at the farthest distance from the centre of its host galaxy NGC 1343 (i.e. the projected distance is ∼21 kpc). This challenges the scenario of the origin of type IIb supernovae from massive stars.

A Markov process for an infinite interacting particle system in the continuum

An infinite system of point particles placed in $\mathds{R}^d$ is studied. Its constituents perform random jumps with mutual repulsion described by a translation-invariant jump kernel and interaction potential, respectively. The pure states of the system are locally finite subsets of $\mathds{R}^d$, which can also be interpreted as locally finite Radon measures. The set of all such measures $\Gamma$ is equipped with the vague topology and the corresponding Borel $\sigma$-field. For a special class $\mathcal{P}_{\rm exp}$ of (sub-Poissonian) probability measures on $\Gamma$, we prove the existence of a unique family $\{P_{t,\mu}: t\geq 0, \ \mu \in \mathcal{P}_{\rm exp}\}$ of probability measures on the space of cadlag paths with values in $\Gamma$ that solves a restricted initial-value martingale problem for the mentioned system. Thereby, a Markov process with cadlag paths is specified which describes the stochastic dynamics of this particle system.

CONSERVATION LAWS, EXACT SOLUTIONS OF TIME-SPACE FRACTIONAL GENERALIZED GINZBURG-LANDAU EQUATION FOR SHALLOW WAKE FLOWS

<abstract> In this study, starting from the rigid-lid shallow water equations, an amplitude evolution equation is derived by using the multi-scale and perturbation analysis method. The resulting equation has complex coefficients and is called (2+1)-dimensional generalized Ginzburg-Landau(gGL) equation. Then, the (2+1)-dimensional time-space fractional gGL equation is obtained by using the semi-inverse method and fractional variational principle in the first time. Finally, the conservation laws and exact solutions of the fractional gGL equation are discussed on the basis of Lie symmetry analysis and $ {\rm exp}(-\phi(\zeta)) $-expansion method. By analyzing these solutions, we conclude that there are solitary waves and rogue waves in shallow wake flows. </abstract>

Muon g−2 and Δα connection

The discrepancy between the Standard Model theory and experimental measurement of the muon magnetic moment anomaly, $a_{\mu}=\left(g_{\mu}-2\right)/2$, is connected to precision electroweak (EW) predictions via their common dependence on hadronic vacuum polarization effects. The same data for the total $e^+e^- \rightarrow \text{hadrons}$ cross section, $\sigma_{\rm had}(s)$, are used as input into dispersion relations to estimate the hadronic vacuum polarization contributions, $a_{\mu}^{\rm had,\,VP}$, as well as the five-flavor hadronic contribution to the running QED coupling at the $Z$-pole, $\Delta\alpha_{\rm had}^{(5)}(M_{Z}^2)$, which enters natural relations and global EW fits. The EW fit prediction of $\Delta\alpha_{\rm had}^{(5)}(M_{Z}^2) = 0.02722(41)$ agrees well with $\Delta\alpha_{\rm had}^{(5)}(M_{Z}^2) = 0.02761(11)$ obtained from the dispersion relation approach, but exhibits a smaller central value suggestive of a larger discrepancy $\Delta a_{\mu}=a_{\mu}^{\rm exp} - a_{\mu}^{\rm SM}$ than currently expected. Postulating that the $\Delta a_{\mu}$ difference may be due to missing $\sigma_{\rm had}(s)$ contributions, implications for $M_W$, $\sin^2 \! \theta^{\rm lep}_{\rm eff}$ and $M_H$ obtained from global EW fits are investigated. Shifts in $\sigma_{\rm had}(s)$ needed to bridge $\Delta a_{\mu}$ are found to be excluded above $\sqrt{s} \gtrsim 0.7$ GeV at the 95\%CL. Moreover, prospects for $\Delta a_{\mu}$ originating below that energy are deemed improbable given the required increases in the cross section. Such hypothetical changes to the hadronic data are also found to affect other related observables, such as the electron anomaly, $a_e^{\rm SM}$, the ratio $R_{e/\mu} = (m_\mu/m_e)^2 (a_{e}^{\rm had,\,LO\,VP}/a_{\mu}^{\rm had,\,LO\,VP})$ and the running of the weak mixing angle at low energies, although the consequences of these are currently less constraining.

Search for the correction term to Fermi’s golden rule in positron annihilation

Abstract In the positron–electron annihilation process, finite deviations from the standard calculation based on Fermi’s golden rule are suggested in recent theoretical work. This paper describes an experimental test of the predictions of this theoretical work by searching for events with two photons from positron annihilation of energy larger than the electron rest mass ($511\,{\rm keV}$). The positrons came from a ${\rm {}^{22}Na}$ source, tagging the third photon from the spontaneous emission of ${\rm {}^{22}{Ne}^*}$ de-exitation to suppress backgrounds. Using the collected sample of $1.06\times 10^{7}$ positron–electron annihilations, triple coincidence photon events in the signal-enhanced energy regions are examined. The observed number of events in two signal regions, $N^{\rm SR1}_{\rm obs}=0$ and $N^{\rm SR2}_{\rm obs}=0$, are, within the current precision, consistent with the expected number of events, $N^{\rm SR1}_{\rm exp}=0.86\pm0.08({\rm stat.})^{+1.85}_{-0.81}({\rm syst.})$ and $N^{\rm SR2}_{\rm exp}=0.37\pm 0.05({\rm stat.})^{+0.80}_{-0.29}({\rm syst.})$ from Fermi’s golden rule, respectively. Based on the $P^{(d)}$ modeling, a 90% CL lower limit on the photon wave packet size is obtained.

Cosmic microwave background dipole asymmetry could be explained by axion monodromy cosmic strings

Observations by the Wilkinson Microwave Anisotropy Probe and the Planck mission suggest a hemispherical power amplitude asymmetry in the cosmic microwave background, with a correlation length on the order of the size of the observable Universe. We find that this anomaly can be naturally explained by an axion-like particle (ALP) cosmic string formed near our visible Universe. The field variation associated to this cosmic string creates particle density fluctuations after inflation, which consequently decay into radiation before the Big Bang Nucleosynthesis (BBN) era and resulted in the observed power asymmetry. We find in this scenario that the hemispherical power amplitude asymmetry is strongly scale dependent: $A(k)\propto {\rm exp}(-kl)/k$. Admittedly, typical inflation models predict a relic number density of topological defects of order one per observable Universe and so in our model the cosmic string must be tuned to have an impact factor of order $1/H_0$. Interestingly, the constraints based on purely cosmological considerations also give rise to a Peccei-Quinn scale $F_a$ of order $10^3$ larger then the Hubble scale of inflation $H_I$. Assuming $H_I\sim 10^{13}$GeV, we then have an ALP with $F_a\sim 10^{16}$GeV, which coincides with the presumed scale of grand unification. As we require ALP decays occur before the BBN era, which implies a relatively heavy mass or strong self-coupling, and considering that the associated potential should break the shift symmetry softly in order to protect the system from radiative corrections, we also conclude that the required ALP potential should be monodromic in nature.

On the number of weakly prime-additive numbers

A positive integer n is called weakly prime-additive if n has at least two distinct prime divisors and there exist distinct prime divisors $$p_{1},\ldots, p_{t}$$ of n and positive integers $$\alpha_{1}, \ldots , \alpha_{t}$$ such that $$n = p_{1}^{\alpha_{1}}+ \cdots + p_{t}^{\alpha_{t}}$$. Erdős and Hegyvari [2] proved that, for any prime p, there exists a weakly prime-additive number which is divisible by p. Recently, Fang and Chen [3] proved that for any given positive integer m, there are infinitely many weakly prime-additive numbers which are divisible bym with t = 3 if and only if $$8 \nmid m$$. In this paper, we prove that for any given positive integer m, the number of weakly prime-additive numbers which are divisible by m and less than x is larger than $${\rm exp}(c({\rm log log} x)^{2}/ {\rm log log log} x)$$ for all sufficiently large x, where c is a positive absolute constant. The constant c depends on the result on the least prime number in an arithmetic progression.

Emergence of cosmological scaling behavior in the asymptotic regime

In this paper we consider a scalar field system with a class of potentials given by the expression, $V(\phi)\propto \phi^m {\rm exp}({-\lambda \phi^n/{M^n_{Pl}}})$; $m\geqslant 0, n>1$ for which $\Gamma=V_{\phi \phi}V/V^2_{\phi}\to 1 $ as $|\phi|\to \infty$. We carry out dynamical analysis for the underlying system choosing a suitable set of autonomous variables and find all the fixed points. In particular, we show that the scaling solution is an attractor of the system in the asymptotic regime. We indicate the application of the solution to models of quintessential inflation.

The Function ${\rm exp}\,{[-p\&gt;{\rm Trace}\,\sqrt {2A}]}$ as a Laplace Transform on Symmetric Matrices

The Function ${\rm exp}\,{[-p\&gt;{\rm Trace}\,\sqrt {2A}]}$ as a Laplace Transform on Symmetric Matrices

Resolving the Λ Hypernuclear Overbinding Problem in Pionless Effective Field Theory.

We address the Λ hypernuclear "overbinding problem" in light hypernuclei which stands for a 1-3MeV excessive Λ separation energy calculated in _{Λ}^{5}He. This problem arises in most few-body calculations that reproduce ground-state Λ separation energies in the lighter Λ hypernuclei within various hyperon-nucleon interaction models. Recent pionless effective field theory (πEFT) nuclear few-body calculations are extended in this work to Λ hypernuclei. At leading order, the ΛN low-energy constants are associated with ΛN scattering lengths, and the ΛNN low-energy constants are fitted to Λ separation energies (B_{Λ}^{exp}) for A≤4. The resulting πEFT interaction reproduces in few-body stochastic variational method calculations the reported value B_{Λ}^{exp}(_{Λ}^{5}He)=3.12±0.02 MeV within a fraction of MeV over a broad range of πEFT cutoff parameters. Possible consequences and extensions to heavier hypernuclei and to neutron-star matter are discussed.

Theory of energy spectra in superfluid He4 counterflow turbulence

In the thermally driven superfluid He-4 turbulence, the counterflow velocity $U_{\rm ns}$ partially decouples the normal and superfluid turbulent velocities. Recently we suggested [J. Low Temp. Phys. 187, 497 (2017)] that this decoupling should tremendously increase the turbulent energy dissipation by mutual friction and significantly suppress the energy spectra. Comprehensive measurements of the apparent scaling exponent nexp of the 2nd-order normal fluid velocity structure function $S_2(r)\propto r^{n_{\rm exp}}$ in the counterflow turbulence [Phys.Rev.B 96, 094511 (2017)] confirmed our scenario of gradual dependence of the turbulence statistics on the flow parameters. We develop an analytical theory of the counterflow turbulence, accounting for a twofold mechanism of this phenomenon: i) a scale-dependent competition between the turbulent velocity coupling by the mutual friction and the $U_{\rm ns}$-induced turbulent velocity decoupling and ii) the turbulent energy dissipation by the mutual friction enhanced by the velocity decoupling. The suggested theory predicts the energy spectra for a wide range of flow parameters. The mean exponents of the normal fluid energy spectra $\langle m_n\rangle_{10}$, found without fitting parameters, qualitatively agree with the observed $n_{\rm exp} + 1$ for $T\gtrsim 1.85$K

Halo histories versus galaxy properties at z = 0 – III. The properties of star-forming galaxies

We measure how the properties of star-forming central galaxies correlate with large-scale environment, $\delta$, measured on $10$Mpc/h scales. We use group catalogs to isolate a robust sample of central galaxies with high purity and completeness. The properties we investigate are star formation rate (SFR), exponential disk scale length $R_{\rm exp}$, and Sersic index of the light profile, $n$. We find that, at all stellar masses, there is an inverse correlation between SFR and $\delta$, meaning that above-average star forming centrals live in underdense regions. For $n$ and $R_{\rm exp}$, there is no correlation with $\delta$ at $M_{\rm star}\lesssim 10^{10.5}$ $M_\odot$, but at higher masses there are positive correlations; a weak correlation with $R_{\rm exp}$ and a strong correlation with $n$. These data are evidence of assembly bias within the star-forming population. The results for SFR are consistent with a model in which SFR correlates with present-day halo accretion rate, $\dot{M}_h$. In this model, galaxies are assigned to halos using the abundance matching ansatz, which maps galaxy stellar mass onto halo mass. At fixed halo mass, SFR is assigned to galaxies using the same approach,but $\dot{M}_h$ is used to map onto SFR. The best-fit model requires some scatter in the $\dot{M}_h$-SFR relation. The $R_{\rm exp}$ and $n$ measurements are consistent with a model in which these quantities are correlated with the spin parameter of the halo, $\lambda$. Halo spin does not correlate with $\delta$ at low halo masses, but for higher mass halos, high-spin halos live in higher density environments at fixed $M_h$. Put together with the earlier installments of this series, these data demonstrate that quenching processes have limited correlation with halo formation history, but the growth of active galaxies, as well as other detailed properties, are influenced by the details of halo assembly.

Efimov effect in D spatial dimensions in AAB systems

The existence of the Efimov effect is drastically affected by the dimensionality of the space in which the system is embedded. The effective spatial dimension containing an atomic cloud can be continuously modified by compressing it in one or two directions. In the present article we determine for a general $AAB$ system formed by two identical bosons $A$ and a third particle $B$ in the two-body unitary limit, the dimensionsality $D$ for which the Efimov effect can exist for different values of the mass ratio $\mathpzc{A}=m_B/m_A$. In addition, we provide a prediction for the Efimov discrete scaling factor, ${\rm exp}\,(\pi/s)$, as a function of a wide range of values of $\mathpzc{A}$ and $D$, which can be tested in experiments that can be realized with currently available technology.

Pseudogap Regime of a Two-dimensional Uniform Fermi Gas

We investigate pseudogap phenomena in a two-dimensional Fermi gas. Including pairing fluctuations within a self-consistent $T$-matrix approximation, we determine the pseudogap temperature $T^*$ below which a dip appears in the density of states $\rho(\omega)$ around the Fermi level. Evaluating $T^*$, we identify the pseudogap region in the phase diagram of this system. We find that, while the observed BKT (Berezinskii-Kosterlitz-Thouless) transition temperature $T^{\rm exp}_{\rm BKT}$ in a $^6$Li Fermi gas is in the pseudogap regime, the detailed pseudogap structure in $\rho(\omega)$ at $T^{\rm exp}_{\rm BKT}$ still differs from a fully-gapped one, indicating the importance of amplitude fluctuations in the Cooper channel there. Since the observed $T^{\rm exp}_{\rm BKT}$ in the weak-coupling regime cannot be explained by the recent BKT theory which only includes phase fluctuations, our results may provide a hint about how to improve this BKT theory. Although $\rho(\omega)$ has not been measured in this system, we show that the assessment of our results is still possible by using the observable Tan's contact.

The Muon $g-2$ in Progress

Two next generation muon $g-2$ experiments at Fermilab in the US and at J-PARC in Japan have been designed to reach a four times better precision from 0.54 ppm to 0.14 ppm and the challenge for the theory side is to keep up in precision as far as possible. This has triggered a lot of new research activities. The main motivation is the persisting 3 to 4 $\sigma$ deviation between standard theory and experiment. As Standard Model predictions almost without exception match perfectly all other experimental information, the deviation in one of the most precisely measured quantities in particle physics remains a mystery and inspires the imagination of model builders. Plenty of speculations are aiming to explain what beyond the Standard Model effects could fill what seems to be missing. Here very high precision experiments are competing with searches for new physics at the high energy frontier lead by the Large Hadron Collider at CERN. Actually, the tension is increasing steadily as no new states are found which could accommodate the $g_\mu-2$ discrepancy. With the new muon $g-2$ experiments this discrepancy would go up at least to 6 $\sigma$, in case the central values do not move, up to 10 $\sigma$ could be reached if the present theory error could be reduced by a factor of two. Interestingly, the new $\alpha$ from Berkeley by R. H. Parker et al. Science 360, 191 (2018): $\alpha^{-1}({\rm Cs18})=137.035999046(27)$ gives an $a_e$ prediction $a_e=0.00115965218157(23)$ such that $a_e^{\rm exp}-a_e^{\rm the}=(-84\pm36)\times 10^{-14}$ shows a $- 2.3~ \sigma$ deviation now.

Adaptive Filtering Under a Variable Kernel Width Maximum Correntropy Criterion

The maximum correntropy criterion (MCC) algorithm with constant kernel width leads to a tradeoff problem in terms of convergence rate and steady-state misalignment. Thus, this brief proposes a variable kernel width (VKW) MCC algorithm to overcome this problem. The optimal kernel width of the proposed VKW-MCC algorithm is calculated at each iteration by maximizing ${{\rm exp}(-e_{k}^{2}/2\sigma _{k}^{2})}$ with respect to the kernel width ${ \sigma _{k}}$ , wherein the kernel width is a function of the error, to make the error with greatest attenuation along the direction of the gradient ascent. Simulations in the contexts of system identification and echo cancellation have demonstrated that the proposed VKW-MCC algorithm yields a superior performance.

Optimal elliptic regularity: A comparison between local and nonlocal equations

Given $L≥1$ , we discuss the problem of determining the highest $α=α(L)$ such that any solution to a homogeneous elliptic equation in divergence form with ellipticity ratio bounded by $L$ is in $C^α_{\rm loc}$ . This problem can be formulated both in the classical and non-local framework. In the classical case it is known that $α(L)≳ {\rm exp}(-CL^β)$ , for some $C, β≥q$ depending on the dimension $N≥q$ . We show that in the non-local case, $α(L)≳ L^{-1-δ}$ for all $δ&gt;0$ .