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A partial width formula is proposed using the analytical extension of the wave function in momentum space. The distinction of the Riemann sheets is explained from the perspective of the Schrodinger equation. The analytical form in coordinate space and the partial width are derived subsequently. Then a coupled-channel analysis is performed to investigate the open-charm branching ratios of the $P_c$ states, involving the contact interactions and one-pion-exchange potential with the three-body effects. The low energy constants are fitted using the experimental masses and widths as input. The $P_c(4312)$ is found to decay mainly to $\Lambda_c\bar{D}^*$, while the branching ratios of the $P_c(4440)$ and $P_c(4457)$ in different channels are comparable. Under the reasonable assumption that the off-diagonal contact interactions are small, the $J^P$ quantum numbers of the $P_c(4440)$ and the $P_c(4457)$ prefer $\frac{1}{2}^-$ and $\frac{3}{2}^-$ respectively. Three additional $P_c$ states at 4380 MeV, 4504 MeV and 4516 MeV, together with their branching ratios, are predicted. A deduction of the revised one-pion-exchange potential involving the on-shell three-body intermediate states is performed., Comment: 16 pages, 5 figures

We investigate the $Z_b$, $Z_c$ and $Z_{cs}$ states within the chiral effective field theory framework and the $S$-wave single channel molecule picture. With the complex scaling method, we accurately solve the Schr\"odinger equation in momentum space. Our analysis reveals that the $Z_b(10610)$, $Z_b(10650)$, $Z_c(3900)$ and $Z_c(4020)$ states are the resonances composed of the $S-$wave $(B\bar{B}^{*}+B^{*}\bar{B})/\sqrt{2}$, $B^{*}\bar{B}^*$, $(D\bar{D}^{*}+D^{*}\bar{D})/\sqrt{2}$ and $D^{*}\bar{D}^*$, respectively. Furthermore, although the $Z_{cs}(3985)$ and $Z_{cs}(4000)$ states exhibit a significant difference in width, these two resonances may originate from the same channel, the $S-$wave $(D_{s}\bar{D}^{*}+D_{s}^{*}\bar{D})/\sqrt{2}$. Additionally, we find two resonances in the $S-$wave $D_s^*\bar{D}^*$ channel, corresponding to the $Z_{cs}(4123)$ and $Z_{cs}(4220)$ states that await experimental confirmation., Comment: 10 pages, 5 figures, 4 tables

We construct the effective potentials of the PψN and PψsΛ states based on the SU(3)f symmetry and heavy quark symmetry. Then we perform the coupled-channel analysis of the lowest-isospin PψN and PψsΛ systems. The coupled-channel effects play different roles in the PψN and PψsΛ systems. In the PψN systems, this effect gives minor corrections to the masses of the PψN states. In the PψsΛ system, the ΛcD¯s−ΞcD¯ coupling will shift the mass of the PψsΛ(4338)0 close to the ΞcD¯ threshold. The ΛcD¯s(*)−ΞcD¯(*) coupling will also produce extra PψsΛ states. We discuss the correspondence between the PψN and PψsΛ states. Our results prefer that the SU(3) partners of the observed PψN(4312)+, PψN(4440)+, and PψN(4457)+ in the PψsΛ system not have been found yet.

We use the leading order (LO) contact interactions and OPE potentials to investigate the newly observed double-charm state $T_{cc}^+$. The $DD\pi$ three-body effect is important in this system since the intermediate states can go on shell. We keep the dependence of the pion propagators on the center-of-mass energy, which results in a unitary cut of the OPE potential at the $DD\pi$ three-body threshold. By solving the complex scaled Schr\"odinger equation, we find a pole corresponding to the $T_{cc}^+$ on the physical Riemann sheet. Its width is around 80 keV and nearly independent of the choice of the cutoff. Assuming the $D\bar{D}\pi$ and $D\bar{D}^*$ channels as the main decay channels, we apply the similar calculations to the $X(3872)$, and find its width is even smaller. Besides, the isospin breaking effect is significant for the $X(3872)$ while its impact on the $T_{cc}^+$ is relatively small., Comment: 25 pages, 10 figures, 6 tables

We calculate the threshold T matrices of the light pseudoscalar meson and heavy meson scattering to fourth order in heavy meson chiral perturbation theory. We determine the low-energy constants by fitting to the lattice QCD data points through both the perturbative and iterated methods and obtain the physical scattering lengths in both formalisms. The values of the scattering lengths tend to be convergent at fourth order for most of the channels in the perturbative method. The value of the scattering length for the channel DK(I=0), which involves the bound state Ds0*(2317), is obtained correctly in the iterated method. Based on the heavy diquark-antiquark symmetry, we also estimate the meson and doubly charmed (bottom) baryon scattering lengths, and find that the bound states can be generated with high probability in the channels K¯Ξcc(I=0) and K¯Ξbb(I=0). We strongly urge the LHCb Collaboration to look for the very narrow K¯Ξcc state with IJP=012− through either the electromagnetic decay or the iso-spin violating strong decay Ωccπ.

We construct the effective potentials of the $P_c$ and $P_{cs}$ states based on the SU(3)$_{\text{f}}$ symmetry and heavy quark symmetry. Then we perform the coupled-channel analysis of the lowest isospin $P_c$ and $P_{cs}$ systems. The coupled-channel effects play different roles in the $P_c$ and $P_{cs}$ systems. In the $P_c$ systems, this effect gives minor corrections to the masses of the $P_c$ states. In the $P_{cs}$ system, the $\Lambda_c\bar{D}_s-\Xi_c\bar{D}$ coupling will shift the mass of the $P_{cs}(4338)$ close to the $\Xi_c\bar{D}$ threshold. The $\Lambda_c\bar{D}^{(*)}_s-\Xi_c\bar{D}^{(*)}$ coupling will also produce extra $P_{cs}$ states. We discuss the correspondence between the $P_c$ and $P_{cs}$ states. Our results prefer that the SU(3) partners of the observed $P_{c}(4312)$, $P_{c}(4440)$, and $P_{c}(4457)$ in the $P_{cs}$ system have not been found yet., Comment: 10 Pages, 3 figures, and 6 Tables

We calculate the threshold $T$ matrices of the light pseudoscalar meson and heavy meson scattering to fourth order in heavy meson chiral perturbation theory. We determine the low-energy constants by fitting to the lattice QCD data points through both the perturbative and iterated methods and obtain the physical scattering lengths in both formalisms. The values of the scattering lengths tend to be convergent at fourth order for most of the channels in the perturbative method. The value of the scattering length for the channel $DK (I=0)$, which involves the bound state $D_{s0}^{*}(2317)$, is obtained correctly in the iterated method. Based on the heavy diquark-antiquark symmetry, we also estimate the meson and doubly charmed (bottom) baryon scattering lengths, and find that the bound states can be generated with high probability in the channels $\bar{K}\Xi_{cc}(I=0)$ and $\bar{K}\Xi_{bb}(I=0)$. We strongly urge the LHCb Collaboration to look for the very narrow $\bar{K}\Xi_{cc}$ state with $IJ^P=0{1\over 2}^-$ through either the electromagnetic decay or the iso-spin violating strong decay $\Omega_{cc} \pi$., Comment: 21 pages, 3 figures, 12 tables

Two-photon excitation fluorescence (2PEF) and coherent anti-Stokes Raman scattering (CARS) are both third-order nonlinear optical processes, but for a long time, the true relationship and differences between them are not clearly understood. For decades, the second harmonic generation has been studied in conjunction with two-photon excitation fluorescence, so it was thought that the latter was a second-order nonlinear optical process. In order to make the two nonlinear interaction processes clear enough, the two nonlinear interaction processes are worthy to study at the same time. In this paper, firstly, we give the relationships between the 2PEF, CARS signal and their third-order nonlinear susceptibility, respectively; secondly, we use our own near infrared super-continuum CARS microscopy system to study both processes. In doing so, we describe the relationship between their third-order nonlinear susceptibility and the signal. The reconstructed images derived from CARS and those derived from 2PEF differ significantly when imaging the same 1.01 $\muup$m fluorescence polystyrene beads. If the lateral spatial resolution of the CARS imaging system is larger than the fluorescence polystyrene beads, the measured size cannot be used to calculate the real spatial resolution of the CARS system. However, the resolution of the 2PEF microscopy system can be obtained through the de-convolution of the 2PEF image, which is approximately equivalent to the current resolution of the CARS imaging system, which is measured using 280 nm polystyrene beads. The images of 280 nm polystyrene beads and 190 nm fluorescent polystyrene beads also exhibit differences between the two samples and the environment around them, respectively. This means that although CARS and 2PEF are both third-order nonlinear optical processes, they have their own properties. In particular, CARS is a third-order nonlinear optical oscillation process which is caused by the phasing match condition, but 2PEF is not influenced by the phasing match condition. The phase matching condition is responsible for the differences around the sample in the images of the 280 nm pure polystyrene beads, but not for the 190 nm fluorescent polystyrene beads. The de-convolution results for the 1.01 $\muup$m fluorescence polystyrene beads and the 280 nm pure polystyrene beads are very similar, so we can use the de-convolution results for 2PEF by the 1.01 $\muup$m fluorescence polystyrene beads to approximate the current measure condition and the resolution of the CARS imaging system. If we want to gain a more accurate resolution from the CARS imaging system, the spherical sample should be smaller than the lateral spatial resolution of this system.

Measuring the vibration dephasing time in molecular vibration is the free-mark method for detecting molecules harmlessly. Since molecular vibration refund processes are associated with molecular environment change, molecular vibration dephasing time also may reflect the substance's molecular environment change, which can be used to study the interaction between a certain molecule and its neighboring molecules. The molecular vibration spectrum and vibration dephasing time are obtained from the time-resolved coherent anti-stokes Raman scattering (CARS) simultaneously. Benzonitrile and methanol are used as samples for studying, the vibration dephasing time changes for the main vibration spectra when the environment changes. With benzonitrile mixed with anhydrous alcohol, its vibration dephasing time changes with environment are measured in three typical benzonitrile molecular vibrations 1017 cm-1, 2247 cm-1 and 3085 cm-1. For adjoining methanol molecular vibrations 2851 cm-1, and 2960 cm-1, vibration dephasing time changes are measured under environmental conditions. Results show that significant changes of molecular vibration dephasing time will take place in different environments. For a unidirectional molecular environment change, the molecular vibration dephasing time of benzonitrile is a one-way change, while the methanol molecule is of non-unidirectional vibration dephasing time change. But methanol molecules with vibration intensity ratios between two unidirectional changes with environment for I2851/I2960 are of a one-way change. By experimental measurement the vibration dephasing time of the main vibration mode of benzonitrile and methanol molecules varies with the changes in the environment, further understanding of differences on vibration dephasing time of molecular vibration spectra of adjacent and non-adjacent variations can explain the variation of vibration dephasing time of benzonitrile molecules. This method has the ability of detecting molecular environment change and molecular interactions, and has an important application prospect in the field of life science, molecular biology, and material science etc..

In order to exactly distinguish and quantitatively analyze the different or unknown components in a mixture, the global molecular CARS spectra information should be obtained simultaneously with a broad-band coherent anti-Stokes Raman scattering (CARS) spectroscopy in supercontinuum. In a broad-band CARS spectroscopy, two-and three-color CARS processes are generated due to different functions of effective spectroscopic components in supercontinuum. Firstly, we theoretically analyzed the generation conditions of CARS signals and the relationships between their intensity and power of excitation lights in the two types of CARS process with the broad-band excitation. On this basis, the two types of CARS process are achieved with a home-built broad-band CARS spectroscopic system, respectively. Using the functional fitting analysis of the obtained CARS spectral signals of benzonitrile, the relationships between CARS signals and excitation lights are experimentally verified in two different kinds of CARS process. Further optimizations of broad-band time-resolved CARS spectroscopic and microscopic systems, for simultaneously obtaining the global CARS spectral signals of samples, can be achieved under the guidance of theoretical and experimental results.

In a coherent anti-Stokes Raman scattering (CARS) microscope, when samples with different shapes and dimensions are excitated by collinearly introduced and tightly focused Gaussian beams, the microscopic structure will be determined by the spatial distributions of generated CARS signals. Therefore, we build a theoretical model for CARS signals from spherical sample under the tightly focused condition. The intensity and phase distributions of tightly focused linear polarization Gaussian beams are analyzed with vector wave equations. The vector wave equation of CARS signals is derived from Green's function. The far-field CARS radiation patterns of spherical scatters with different diameters are simulatively calculated. Theoretical analysis and simulative calculation results show that the intensities of forward and backward CARS signals from the small spherical sampler are similar. The images with high contrast can be obtained by backward detection method from an objective with a high numerical aperture. For big spherical samplers, intensities of CARS signals are greatly increased. The emission direction is mainly concentrated in a spatial angle. The forward CARS signals can be effectively collected by an objective with low numerical aperture.

In this paper, we present the development and experimental results of a time-resolved coherent anti-Stokes Raman scattering (CARS) experiment setup that is based on supercontinuum excitation and precise time-delay control. The output of a Ti-sapphire femtosecond laser is divided into two parts. One part is used to pump a photonic crystal fiber (PCF) to generate supercontinuum spectrum which is used as pump and stokes beams. The other part of the femtosecond laser is used as the probe light. Dimethyl sulfoxid, a sample with broad range of Raman spectrum was tested. Experimental results show that this system can inhibit the non-resonant background noise effectively and obtain CARS spectrum of dimethyl sulfoxide in the frequency range of 690—3200 cm-1 in one measurement, which means that spectrum range of the acquired CARS spectrum of dimethyl sulfoxide is 2500 cm-1. We also present experimental results of supercontinuum generation using a PCF.

The magnetic-field-Induced reorientation of a planar alignment nematic liquid crystal (5CB) doped with different paramagnetic dopants has been studied in this paper. It was observed that compared with the pure 5CB, 5CB doped with five-coordinated [Cu(o-xyTQ)H2O](NO3)2 dramatically decreased the critical magnetic field strength for the reorientation, while 5CB doped with six-coordinated [Cu(DETQ)](ClO4)2 revealed no such effect. Although the two paramagnetic dopants possess the same magnetic property, they have different intermolecular couplings with host 5CB, which produce the different results. This phenomenon is very useful to study the magneto-optical component of liquid crystal.

Microscopical imaging method of five-dimensional simultaneity fluorescence information is a new technology for acquiring fluorescence information, which makes use of two-photon array excitation to acquire information of fluorescence position, fluorescence spectrum and fluorescence lifetime for each array element. It removes the limitation on existing fluorescence detection technology in which different functional informations are not obtained simultaneously. In this paper, the methods for deriving geometrical intensity image, different spectral intensity images and different spectral life-time images from the complex information of the new technology are presented. Because of array excitation, there is asymmetry in the array excitation intensity, which influences the excited fluorescence intensity. A method based on the excitation fluorescence intensity correction coefficient matrix is put forward, which eliminates effectively the influence of the asymmetry of array excitation intensity. Data collection and processing for actual samples are made and imaging results are got. The experimental results show the validity of the processing methods and some unsolved problems in the processing methods are discussed.

The optical phase retardation method is used in this paper. Based on the experiments on magnetic-field-induced Freedericksz transition of planar nematic liquid crystal, doped with trace bulin, fibre protein and double-azo etc, the trace adulteration effects on the transition of planar nematic liquid crystal are discussed; experimental curves and numerical calculation curves are given. Numerical calculation results are in agreement with measured results. It is shown that different impurities whose magnetic property, molecule shape and size are different, lead to different magnetic-field-induced Freedericksz transition, which is ulteriorly illuminated with the experiment on magnetic-field-induced Freedericksz transition of planar nematic liquid crystal doped with 2-benzothiazolethiol-linked porphyrinatozinc(Ⅱ).

The optical phase retardation method was employed to observe the transient twist reorientation effect of a plane-aligned nematic liquid crystal induced by ultra-short laser pulses. The experimental result indicated that, although the electric field intensity of laser pulses is much higher than that needed for twist deformation, it does not ensure the twist reorientation under the laser pulse. This is because the width of laser pulse is very short and the response time for the twist reorientation is very long. To overcome this barrier an optimum angle (45°)between the polarization of the laser pulse and the director orientation in substrates is found by analysis.Using this initial angle, we observed a plane-aligned nematic liquid crystal cell doped with a few o-(D-Thr)N-C2-(TPP) to possess memory effect after the laser pulse pump, which was important in optical data storage and memory display.

By means of the optical phase retardation method the YAG laser was used to observe the transient heating behavior in planar nematic liquid crystals. According to the experimental results, heating effect may induce molecular reorientation in liquid crystals. Azo-dye and photoisomerized-dye in planar nematic liquid crystals have little effect on heating behavior, but the liquid crystal doped with chiral molecules shows temporary memory effect.

In this paper,numerical calculations of magnetically induced twist effeet in planar nematic liquid crystal are presented.The transmission of polarized light passing through magnetically induced twist distribution in planar nematic liquid crystal is calculated with “4*4”matrix algorithm.On the ex-perimental side,the optical phase retardation method is used to detect the magnetically induced twist effect in planar nematic liquid crystal 5CB(4′-n-penty1-4-cyanobiphenyl) at 27℃.Theoretical cal-culation and experimental results illustrate that polarized light can be used to study the twist effect in thin sample of planar nematic liquid crystal.