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We analyze the ground state pentaquark structures with a single heavy quark ($qqqq\Bar{Q}$) using various phenomenological models. The recent observations of singly heavy tetraquark structures at LHCb serve as a significant motivation for this investigation. We studied the symmetric 15-plet configuration of SU(3) flavor representation with the spin-parity assignment of $5/2^-$, representing the symmetric spin state for the pentaquark systems. We employed an extended Gursey-Radicati mass formula and an effective mass scheme to compute the mass spectra of pentaquark states. Additionally, the methodology of the screened charge scheme is introduced to calculate the magnetic moment assignments, specifically for configurations involving both charm and bottom quarks. We also proposed the potential production modes originating from the weak decay of heavy baryons. We identified the strong decay channels where pentaquark transitions into a light baryon and a heavy meson. Our analysis of mass spectra, magnetic moments, and possible strong decay channels helps us to explore the inner structure of pentaquarks and their underlying quark dynamics. This work not only augments the theoretical frameworks used to describe such systems but is also helpful for future experimental pursuits at facilities like LHCb, fostering further experimental validations and discoveries in heavy quark spectroscopy.

This work investigates the use of a fiber piano in controlling spatial modes in few mode fibers. It has been found that together with sub-optimal coupling into SMF-28 fibre and half and quarter waveplates, the fiber piano is capable of producing and reproducing desired spatial modes up to $LP_{11}$ when using 808 nm light and up to $LP_{21}$ when using 632.8 nm light. The control of spatial mode profile extends down to the single photon level. This is demonstrated with the help of correlated photon pairs generated via spontaneous parametric down conversion., Comment: 7 pages, 7 figures

We carried out the systematic analysis of the $s$-wave triply heavy pentaquarks with possible configurations like $q\Bar{q}QQQ$ and $qqQQ\Bar{Q}$, ($q = u, d, s$ and $Q = c, b$ quarks). Special unitary representations are utilized to study the classification scheme for triply heavy configurations like $q\Bar{q}QQQ$ and $qqQQ\Bar{Q}$. We classified the $q\Bar{q}QQQ$-type pentaquarks into an octet and $qqQQ\Bar{Q}$-type pentaquarks into sextet configurations with the help of SU(3) flavor representation. Also, with the help of SU(2) spin representation, we studied the possible spin assignments ($\frac{1}{2}^-$, $\frac{3}{2}^-$, and $\frac{5}{2}^-$) for ground state triply heavy pentaquarks. Furthermore, we used the formalism of the extended Gursey-Radicati mass formula and effective mass scheme to estimate the masses of triply heavy pentaquarks. Additionally, we calculated the magnetic moment assignments using the effective mass and screened charge schemes. The predicted outcomes align well with the existing theoretical data and benefit future studies. Our work provides a comprehensive framework that combines the theoretical aspects of SU(3) and SU(2) symmetries with practical predictions for observables, offering a strong foundation for experimental verification. This integrated approach enhances our understanding of the complex interactions within triply heavy pentaquarks and underscores their potential role in probing deeper into the dynamics of the strong force. These findings are crucial for designing future high-energy experiments that directly observe these exotic states and confirm their properties, paving the way for new insights into quantum chromodynamics.

Large Language Models (LLMs) have demonstrated remarkable reasoning abilities, prompting interest in their application as black-box optimizers. This paper asserts that LLMs possess the capability for zero-shot optimization across diverse scenarios, including multi-objective and high-dimensional problems. We introduce a novel population-based method for numerical optimization using LLMs called Language-Model-Based Evolutionary Optimizer (LEO). Our hypothesis is supported through numerical examples, spanning benchmark and industrial engineering problems such as supersonic nozzle shape optimization, heat transfer, and windfarm layout optimization. We compare our method to several gradient-based and gradient-free optimization approaches. While LLMs yield comparable results to state-of-the-art methods, their imaginative nature and propensity to hallucinate demand careful handling. We provide practical guidelines for obtaining reliable answers from LLMs and discuss method limitations and potential research directions.

By taking into light the discovery of pentaquark structures like $P_{\psi s}^\Lambda(4338)^0$, $P_c(4380)$ and $P_c(4450)$, we performed the spectroscopy of hidden-bottom pentaquarks. By utilizing special unitary representations, we systematically classified the hidden bottom pentaquarks into two distinct configurations within the SU(3) flavor representation: the octet and decuplet. In this study, we employed an extended version of the GR mass formula along with the effective mass scheme to provide estimations of the masses associated with hidden-bottom pentaquarks. Furthermore, we extend our analysis to estimate the magnetic moments using the effective mass scheme and screened charge scheme. Moreover, by employing the effective Lagrangian, we computed the partial widths for the octet configuration. This comprehensive analysis offers crucial insights into the decay mechanisms and lifetimes of these exotic particles, enhancing our understanding of their fundamental properties. Our findings, which include calculations of masses and magnetic moments, demonstrate reasonable agreement with existing theoretical predictions., Comment: arXiv admin note: text overlap with arXiv:2401.02146

Motivated by the recent discovery of single heavy tetraquark structures, $T_{c\bar{s}0}^a (2900)^{++}$ and $T_{c\bar{s}0}^a(2900)^0$ by the LHCb collaboration, masses and magnetic moments of singly heavy pentaquark states are estimated in this work. To classify the singly heavy pentaquark structures, we employ the special unitary representation. By using the SU(3) flavor representation, we placed singly heavy pentaquark states into the allowed flavor multiples. Also, by using the extension of the Gursey-Radicati mass formula and the effective mass scheme, we estimated the masses of singly heavy pentaquark states. Further, magnetic moments of these states have been calculated using the effective mass and the screened charge techniques. A thorough comparison of our results shows reasonable agreement with the available theoretical data and may be helpful for future experimental studies.

In this work, the multiquark approach is used to analyze the spectroscopy of hidden-charm pentaquark states, motivated by recent discoveries at the LHCb collaboration. Using the SU(3) flavor representation, pentaquarks having $J^P = 5/2^-$ are arranged into 10 (decuplet) of the SU(3) flavor multiplets. The masses of pentaquarks are calculated using the extension of the Gursey-Radicati mass formula and the effective mass scheme. Also, we calculated the magnetic moments of the hidden-charm pentaquarks using the effective mass and shielded charge technique. Further, we suggested the possible production modes for $J^P = 5/2^-$ pentaquarks from the decay of bottom baryons, which consist of pentaquark states as intermediate states. Our results for masses demonstrate reasonable agreement with the available data and our analysis for both masses and magnetic moments may be useful for future experimental studies.

Tetraquark states are classified using the $SU(6)_{sf}$ spin-flavor symmetry and Young tableau technique. Further, by using the extension of Gursey-Radicati mass formula, masses of tetraquark states are predicted upto good level of accuracy. Also, Decay channels and decay widths of tetraquark states are calculated and found to be in good agreement with the experimental and available theoretical data., Comment: 12 pages , 4 figures

Quantum random number generators are becoming mandatory in a demanding technology world of high performing learning algorithms and security guidelines. Our implementation based on principles of quantum mechanics enable us to achieve the required randomness. We have generated high-quality quantum random numbers from a weak coherent source at telecommunication wavelength. The entropy is based on time of arrival of quantum states within a predefined time interval. The detection of photons by the InGaAs single-photon detectors and high precision time measurement of 5 ps enables us to generate 16 random bits per arrival time which is the highest reported to date. We have presented the theoretical analysis and experimental verification of the random number generation methodology. The method eliminates the requirement of any randomness extractor to be applied thereby, leveraging the principles of quantum physics to generate random numbers. The output data rate is on an average of 2.4 Mbps. The raw quantum random numbers are compared with NIST prescribed Blum-Blum-Shub pseudo random number generator and an in-house built hardware random number generator from FPGA, on the ENT and NIST Platform., Comment: 8 pages, 4 figures, 3 Tables, RevTex