Search

We study the non-leptonic puzzle of $B_{d(s)} \rightarrow K^{(\ast)}\bar{K}^{(\ast)}$ decay in the $R$-parity violating minimal supersymmetric standard model (RPV-MSSM) extended with the inverse seesaw mechanism. In this model, the chiral flip of sneutrinos can contribute to the observables $L_{K\bar{K}}$ and $L_{K^{\ast}\bar{K}^{\ast}}$, that is benefit for explaining the relevant puzzle. We also find that this unique effect can engage in the $B_s$-$\bar{B}_s$ mixing. We utilize the scenario of complex $\lambda^\prime$ couplings to fulfill the recent stringent constraint of $B_s$-$\bar{B}_s$ mixing, and examine other related bounds of $B,K$-meson decays, lepton decays, neutrino data, $Z$-pole results, CP violations (CPV), etc. Besides, inspired by the new measurement of ${\cal B}(B^+ \rightarrow K^+\nu\bar{\nu})$ by Belle II, which shows about $2.7\sigma$ higher than the Standard Model (SM) prediction, we investigate the NP enhancement to this observable and find this tension can also be explained in this model., Comment: 26 pages; 2 figures

We prove that the dimension of the $\mathbb{Q}$-linear span of $1,\zeta(3),\zeta(5),\ldots,\zeta(s-1)$ is at least $1.009 \cdot \log s/(1+\log 2)$ for any sufficiently large even integer $s$ and we claim that the constant $1.009$ can be improved further to $1.108$. This slightly refines a well-known result of Rivoal (2000) or Ball-Rivoal (2001). Quite unexpectedly, the proof only involves inserting the arithmetic observation of Zudilin (2001) into the original proof of Ball-Rivoal. Although our result is covered by a recent development of Fischler (2021+), our proof has the advantages of being simple and providing explicit non-vanishing small linear forms in $1$ and odd zeta values., Comment: 23 pages, 1 figure, 1 table

Local feature extractors are the cornerstone of many computer vision tasks. However, their vulnerability to adversarial attacks can significantly compromise their effectiveness. This paper discusses approaches to attack sophisticated local feature extraction algorithms and models to achieve two distinct goals: (1) forcing a match between originally non-matching image regions, and (2) preventing a match between originally matching regions. At the end of the paper, we discuss the performance and drawbacks of different patch generation methods.

We perform a comprehensive investigation of the PSF smoothing effect on the measurement of concentration-related parameters ($C$, Gini, $M_{20}$) of high redshift galaxies in the HST and JWST surveys. Our sample contains massive galaxies from the CANDELS/EGS survey (0 < z < 2), and the CEERS survey (1 < z < 3). The non-parametric concentration-related parameters ($C$, Gini, $M_{20}$) and the model-dependent parameters (n, Re) of these galaxies are derived from Statmorph and GALFIT, respectively. We try to evaluate the PSF smoothing effect by comparing the concentration-related parameters to the S\'{e}rsic index in both observations and mock images. We find that the concentration index is generally underestimated, especially for smaller galaxies with higher S\'{e}rsic index (eventually converging to the concentration index of the PSF). However, galaxies with lower S\'{e}rsic index ($n \leq 1$) or larger relative size are less affected by the PSF smoothing effect. The Gini coefficient and the absolute $M_{20}$ statistic also show similar behaviour as the concentration index. Caution should be taken for the possible correction of the concentration-related parameters, where both the relative size and the S\'{e}rsic index of the galaxy are important. Compared to the HST images, the PSF smoothing is much less severe for images in the CEERS survey due to the much higher spatial resolution. In fact, it is better to use the S\'{e}rsic index rather than the non-parametric morphology indicators to trace the light concentration for galaxies at high redshifts. From the single S\'{e}rsic modelling of the HST and JWST images, we also confirm that galaxies at higher redshift are more compact with smaller $R_e$. The lower mass galaxies are more disc-like ($n\sim1$) compared to the higher mass galaxies that are more spheroid dominated ($n\sim3$)., Comment: Accepted by A&A, 21 pages, 20 figures. Comments are welcome

The absence of semitauonic decays of charmed hadrons makes the decay processes mediated by the quark-level $c\to d \tau^+ \nu_{\tau}$ transition inadequate for probing a generic new physics (NP) with all kinds of Dirac structures. To fill in this gap, we consider in this paper the quasielastic neutrino scattering process $\nu_{\tau}+n\to \tau^-+\Lambda_c$, and propose searching for NP through the polarizations of the $\tau$ lepton and the $\Lambda_c$ baryon. In the framework of a general low-energy effective Lagrangian, we perform a comprehensive analysis of the (differential) cross sections and polarization vectors of the process both within the Standard Model and in various NP scenarios, and scrutinize possible NP signals. We also explore the influence on our findings due to the uncertainties and the different parametrizations of the $\Lambda_c \to N$ transition form factors, and show that they have become one of the major challenges to further constrain possible NP through the quasielastic scattering process., Comment: 31 pages, 17 figures, and 3 tables. Comments are welcome

For any prime $p$ and $\varepsilon>0$ we prove that for any sufficiently large positive odd integer $s$ at least $(c_p-\varepsilon) \sqrt{\frac{s}{\log s}}$ of the $p$-adic zeta values $\zeta_p(3),\zeta_p(5),\dots,\zeta_p(s)$ are irrational. The constant $c_p$ is positive and does only depend on $p$. This result establishes a $p$-adic version of the elimination technique used by Fischler--Sprang--Zudilin and Lai--Yu to prove a similar result on classical zeta values. The main difficulty consists in proving the non-vanishing of the resulting linear forms. We overcome this problem by using a new irrationality criterion., Comment: 35 pages

Let $\zeta_2(\cdot)$ be the Kubota-Leopoldt $2$-adic zeta function. We prove that, for every nonnegative integer $s$, there exists an odd integer $j$ in the interval $[s+3,3s+5]$ such that $\zeta_2(j)$ is irrational. In particular, at least one of $\zeta_2(7),\zeta_2(9),\zeta_2(11),\zeta_2(13)$ is irrational. Our approach is inspired by the recent work of Sprang. We construct explicit rational functions. The Volkenborn integrals of these rational functions' (higher-order) derivatives produce good linear combinations of $1$ and $2$-adic Hurwitz zeta values. The most difficult step is proving that certain Volkenborn integrals are nonzero, which is resolved by carefully manipulating the binomial coefficients., Comment: 21 pages

In this paper, we shall prove two conjectures of Z.-W. Sun concerning Ap\'ery-like series. One of the series is alternating whereas the other one is not. Our main strategy is to convert the series (resp.~the alternating series) to log-sine-cosine (resp.~log-sinh-cosh) integrals. Then we express all these integrals in terms of single-valued Bloch-Wigner-Ramakrishnan-Wojtkowiak-Zagier polylogarithms. The conjectures then follow from a few highly non-trivial functional equations of the polylogarithms of weight $3$ and $4$., Comment: 19 pages

We investigate the potential for searching and identifying the leptoquark (LQ) effects in the charm sector through the low-energy polarized scattering processes $\vec{e}^{\,-}p\to e^-\Lambda_c$, $e^-\vec{p}\to e^-\Lambda_c$, and $\vec{e}^{\,-}\vec{p}\to e^-\Lambda_c$. Considering only the longitudinally polarized processes, we show that the different LQ models can be disentangled from each other by measuring the four spin asymmetries, $A_{L}^e$, $A_{L}^p$, $A_{L3}^{ep}$, and $A_{L6}^{ep}$, constructed in terms of the polarized cross sections. Although it is challenging to accomplish the same goal with transversely polarized processes, we find that investing them in future experiments is especially beneficial, since they can directly probe into the imaginary part of the Wilson coefficients in the general low-energy effective Lagrangian. With our properly designed experimental setups, it is also demonstrated that promising event rates can be expected for all these processes and, even in the worst-case scenario -- no LQ signals are observed at all, they can still provide a competitive potential for constraining the new physics, compared with those from the conventional charmed-hadron weak decays and the high-$p_T$ dilepton invariant mass tails at high-energy colliders., Comment: 24 pages, 11 tables, and 7 figures; more discussions and references added, final version published in the journal

In this paper, we give elementary proofs of Zagier's formula for multiple zeta values involving Hoffman element and its odd variant due to Murakami. Zagier's formula was a key ingredient in the proof of Hoffman's conjecture. Moreover, using the same approach, we prove Murakami's formula for multiple $t$-values. This formula is essential in proving a Brown type result which asserts that each multiple zeta value is a $\mathbb{Q}$-linear combination of multiple $t$-values of the same weight involving $2$'s and $3$'s., Comment: 15 pages, new version

We investigate the potential for discovering new physics through the low-energy scattering processes $e^-p\to e^-(\mu^-)\Lambda_c$, which could be accessible in the forthcoming $ep$ scattering experiments once adapted to our proposed setups. In the framework of a general low-energy effective Lagrangian, we demonstrate that, compared with the conventional flavor-changing neutral-current weak decays of charmed hadrons and the dilepton productions at high-energy colliders, the low-energy scattering processes can provide more competitive potentials for hunting the underlying new physics. In some specific leptoquark models, we also show that promising event rates can be expected for both the scattering processes, and point out a possible way to distinguish the experimental signals due to the scalar leptoquarks from those of the vector ones., Comment: 18 pages, 4 figures, and 6 tables; details of the amplitudes squared and further discussions added, final version to be published in PRD

For an integer $m >1$, we denote by $P(m)$ the largest prime divisor of $m$. We prove that $\limsup_{n \rightarrow +\infty} P(n!+1)/n \geqslant 1+9\log 2>7.238$, which improves a result of Stewart. More generally, for any nonzero polynomial $f(X)$ with integer coefficients, we show that $\limsup_{n \rightarrow +\infty} P(n!+f(n))/n \geqslant 1+9\log2$. This improves a result of Luca and Shparlinski. These improvements come from an additional combinatoric idea to the works mentioned above., Comment: 11 pages

Let $\zeta(s)$ be the Riemann zeta function. We prove the statement in the title, which improves a recent result of Rivoal and Zudilin by lowering $69$ to $35$. We also prove that at least one of $\beta(2),\beta(4),\ldots,\beta(10)$ is irrational, where $\beta(s) = L(s,\chi_4)$ and $\chi_4$ is the Dirichlet character with conductor $4$., Comment: 14 pages. A better collection of parameters for Thm. 6.1 (motivated by one referee). Some minor corrections according to referee reports

We prove a perturbative result concerning the uniqueness of Kerr-Newman family of black holes: given an asymptotically flat space-time with bifurcate horizons, if it agrees with a non-extremal Kerr-Newman space-time asymptotically flat at infinity and it is sufficiently close to the Kerr-Newman family, then the space-time must be one of the Kerr-Newman solutions. The closeness to the Kerr-Newman family is measured by the smallness of a pair of Mars-Simon type tensors, which were introduced by Wong in \cite{Wong_09} to detect the Kerr-Newmann family., Comment: 36 pages, 4 figures

It is proved that, for all odd integer $s \geqslant s_0(\varepsilon)$, there are at least $\big( c_0 - \varepsilon \big) \frac{s^{1/2}}{(\log s)^{1/2}} $ many irrational numbers among the following odd zeta values: $\zeta(3),\zeta(5),\zeta(7),\cdots,\zeta(s)$. The constant $c_0 = 1.192507\ldots$ can be expressed in closed form. The work is based on the previous work of Fischler, Sprang and Zudilin [FSZ19], improves the lower bound $2^{(1-\varepsilon)\frac{\log s}{\log\log s}}$ therein. The main new ingredient is an optimal design for the zeros of the auxiliary rational functions, which relates to the inverse of Euler totient funtion., Comment: 15 pages, corrected typos, improved the constant 1/10 to about 1.19