Search

Study of the mechanism of heavy quarkonia production is a powerful tool for a better understanding of the dynamics of strong interactions and probably to search for new physics. It is well-known that the fragmentation mechanism is dominant for heavy quarkonia production and forms the nonperturbative aspect of hadron production. Since the main contribution of [Formula: see text] production in high energy processes results from the gluon fragmentation, through this work, we study the fragmentation mechanism of gluon into S-wave vector heavy charmonium [Formula: see text] at lowest order perturbative QCD and extend our work to the noncommutative standard model. To investigate the effects of space–time noncommutativity, we employ the Seiberg–Witten maps. Our results show that the noncommutative effects are considerable, specifically when the gluon transverse momentum is small; [Formula: see text][Formula: see text]GeV.

We study the scattering of electrons and positrons by argon and krypton atoms considering a generalized uncertainty principle (GUP). To proceed, we first prove the modified non-relativistic wave equation due to the minimal length in the GUP framework and then determine the wave function of incident particles applying a scattering potential including the static and the energy-dependent correlation–polarization contributions. Finally, we compute the transmission and reflection probabilities from potential barrier. It will be shown that some exotic phenomena occur in this framework which cannot be justified by the ordinary quantum mechanics.

Fragmentation is known as the dominant production mechanism of hadrons with large transverse momentum and forms the nonperturbative and little known aspect of hadroproduction process. In the present work, we calculate the fragmentation function of gluon into pseudoscalar heavy quarkonia to the leading order in $$\alpha _s$$ in the standard model as well as the noncommutative QCD framework. To study the noncommutative effects, we apply the Seiberg–Witten maps to the first order of the noncommutative parameter $$\theta ^{\mu \nu }$$ . Our study shows that for the large values of gluon transverse momentum, the noncommutative effects show up for $$\Lambda _{\mathrm{NC}}

Observing light or heavy charged Higgs bosons $$H^\pm $$ H ± , lighter or heavier than the top quark, would be instant evidence of physics beyond the Standard Model. For this reason, in recent years searches for charged Higgs bosons have been in the center of attention of current colliders such as the CERN Large Hadron Collider (LHC). In spite of all efforts, no signal has been yet observed. Especially, the results of CMS and ATLAS experiments have excluded a large region in the MSSM $$m_{H^+}-\tan \beta $$ m H + - tan β parameter space for $$m_{H^+}=80{-}160$$ m H + = 80 - 160 GeV corresponding to the entire range of $$\tan \beta $$ tan β up to 60. Therefore, it seems that one should concentrate on probing heavy charged Higgs bosons ($$m_{H^\pm }>m_t$$ m H ± > m t ) so in this context each new probing channel is welcomed. In this work, we intend to present our proposed channel to search for heavy charged Higgses through the study of scaled-energy distribution of bottom-flavored mesons (B) inclusively produced in charged Higgs decay, i.e., $$H^+\rightarrow t\bar{b}\rightarrow B+X$$ H + → t b ¯ → B + X . Our study is carried out within the framework of the generic two Higgs doublet model (2HDM) using the massless scheme where the zero mass parton approximation is adopted for bottom quark.

We study the impact of intrinsic strange (IS) component of nucleon sea on the global analysis of parton distribution functions (PDFs) considering a wide range of experimental data. To this aim, we consider two scenarios on the basis of BHPS model results for the IS distribution. In the first scenario, we apply the results presented through the BHPS model and in the second scenario we use its evolved distributions. For each scenarios, we present the limit of the IS probability $ {\cal P}_5^{s\bar{s}} $ for the standard tolerance criteria $ \Delta\chi^2=1 $ and $ 18.112 $ at $ 1\sigma $ and $ 4\sigma $ levels. Our results show that the experimental data can tolerate an IS component with a greater probability $ {\cal P}_5^{s\bar{s}} $ if one employs the second scenario. We obtain $ {\cal P}_5^{s\bar{s}}\approx 0.01 $ and $ {\cal P}_5^{s\bar{s}}\approx 0.025 $ for $ \Delta\chi^2=1 $ and $18.112$, respectively, at the $ 4\sigma $ level. We also calculate the ratio of strange-to-light sea-quark densities $r_s$ in the proton both including and excluding the IS component. Our results show that one can obtain a higher value for the ratio $r_s$ if the IS component is included., Comment: 12 pages, 5 figs , 2 tables

We study the inclusive production of bottom-flavored hadrons from semileptonic decays of polarized top quarks at next-to-leading order in QCD using fragmentation functions recently determined from a global fit to $e^+e^-$ data. We provide the relevant differential decay widths at parton level in analytic form. These results fill an important gap in the theoretical interpretation of recent measurements of the top-quark polarization and the $t\bar{t}$ spin correlations using dilepton final states in proton-proton collisions at the CERN Large Hadron Collider. As an illustration, we study the distributions in the scaled bottom-hadron energy of the polarized-top-quark decay widths for different $W$-boson helicities., 16 pages, 6 figures; to appear in Physical Review D

During recent years, the study of exotic hadrons including tetraquarks and pentaquarks has attracted a lot of interests and more studies are in progress experimentally and theoretically. It is well-known that at sufficiently large transverse momentum the dominant production mechanism for standard heavy hadrons (mesons/baryons) is actually the fragmentation so that the same mechanism is also proposed for the production of heavy exotic hadrons. This work is the first attempt to study the direct fragmentation of a heavy quark into ground state heavy tetraquarks in leading order of perturbative QCD. In this regard, we will present an exact analytical expression for the fragmentation production of neutral hidden flavor tetraquarks $(Qq\bar{Q}\bar{q})$ which includes most of the kinematical and dynamical properties of the process., Comment: The manuscript includes 8 pages and 3 figures. Accepted to be published in Physical Review D (2022)

In this work, we study the properties of charm- and bottom-flavored baryons in the approximative quark-diquark modelin which the structure of baryons is considered as the bound states of quark-diquark pairs instead of the usual three equivalent quarks. To this aim, we use the Bethe-Salpeter equation including the Yukawa potential between the constituent quarks of baryons. Performing a fit procedure on the baryon masses in their ground state, we first determine the free parameters in the Yukawa potential and then compute the heavy baryons masses and energies in their excited states. We will also compute the magnetic moments of single heavy baryons as well as their semileptonic decay widths by evaluating the Isgur-Wise functions (IWF) for heavy baryons. Our results will be compared with available experimental data and other models so that the consistencies between them ensure the validity of IWF parameters extracted for the transitions of bottom baryons into charmed ones. Relying on the diquark model, we shall also predict the properties of some levels which have not yet observed.

At very high transverse momenta, the dominant mechanism for heavy hadron production is fragmentation. In this work, we first use the nonrelativistic quark model to compute the heavy baryon fragmentation functions at lowest order of perturbative QCD and then we apply the approximative quark-diquark model for the same fragmentation process. Diquark model enables one to analyze the two-stage fragmentation of a heavy quark into a heavy diquark followed by the fragmentation of produced diquark into outgoing heavy baryon. An acceptable agreement is found between the results obtained through both approaches. Relying on the diquark model, we extend our computation to next-to-leading order accuracy at perturbative QCD.

In this work, we calculate the fragmentation function (FF) of gluon splitting into the quarkonium bound state at next-to-leading order perturbative QCD. To this end, we apply the well-established Suzuki's model which is convenient to consider the polarization states of produced quarkonium. To be specific, we restrict ourselves to the fragmentation of gluon into the S-wave pseudoscalar mesons ηc and ηb. We will compare our results with the one computed at the leading-order (LO) to show the effects of higher order radiative corrections. Our results show that the NLO radiative corrections may improve the LO FFs up to 70%, so this shows the importance of NLO corrections.

Through data analysis, we present new sets of nonperturbative fragmentation functions (FFs) for Λc+ baryon both at leading and next-to-leading order and, for the first time, at next-to-next-to-leading order in the minimal subtraction factorization scheme with five massless quarks. The FFs are determined by fitting all available data of inclusive single Λc+ baryon production in e+e− annihilation taken by the OPAL Collaboration at CERN LEP1 and Belle Collaboration at KEKB. We also estimate the uncertainties in the Λc+ FFs as well as in the corresponding observables. In a completely different approach based on the Suzuki model, we will theoretically calculate the Λc+ FF from charm quark and present our results at leading order perturbative QCD framework. A comparison confirms a good consistency between both approaches. We will also apply the Λc+ FFs to make theoretical predictions for the energy distribution of Λc+ produced through the top quark decay, to be measured at the CERN LHC.

In this work, using the Laplace transformation technique we present our results for non-singlet quark distributions as well as nucleon structure function $F_2(x,Q^2)$ in unpolarized case at next-to-next-to-leading order (NNLO) QCD accuracy. We shall particularly compare our results for the sets of valence-quark parton distribution functions with the contemporary collaborations like CT14, CT18, MMHT14, MKAM16 and NNPDF. To construct the nucleon structure function we employ the expansion of Jacobi polynomials which is a suitable transform to convert the results of non-singlet structure function from the Laplace $s$-space to Bjorken $x$-space. We shall also consider the contributions of target mass correction as well as the higher twist effects at large-$x$ region for the proton and deuteron structure functions. Our results for the unpolarized quark distribution functions and nucleon structure functions are in good agreement with recent theoretical models and available experimental data., Comment: 16 pages,6 figures, 5 table

The standard model (SM) of particle physics is a gauge-field theoretical model, produced of two non-abelian gauge groups and one abelian gauge group. This model has proved to be extremely successful during the past three decades. The Higgs boson which plays a unique role in the SM was the last part of the SM that was experimentally verified in 2012. In the SM, all observable particles are classified into three generations of matter, i.e., hadrons, leptons and gauge vector bosons. In this paper it is shown that the leptons and gauge bosons along with the interactions between their members construct a weak algebraic hyperstructure. Weak algebraic hyperstructures or $$H_v$$-structures introduced by Vougiouklis. The class of $$H_v$$-structures is larger than the well-known one originated from the hypergroup in the sense of Marty. This new sight to the elementary particles would make a new arrangement to the elementary particles.

The hadronization mechanism is described by the fragmentation functions (FFs) which are universal and process-independent quantities. They can be generally determined theoretically or phenomenologically. In the phenomenological approach which is based on the data analysis, we present the FFs of ${D}_{s}^{+}$ both at leading-order (LO) and next-to-leading order (NLO) and, for the first time, at next-to-next-to-leading order in the minimal subtraction factorization scheme with five massless quarks. These functions are determined by fitting all available experimental data of inclusive single ${D}_{s}^{+}$-meson production in electron-positron annihilation, from the OPAL Collaboration at CERN LEP1. We shall also estimate the uncertainties in these FFs as well as in the corresponding observables. In the theoretical approach, we apply the perturbative FFs formalism based on the Suzuki's model and present our analytical results at LO and NLO perturbative QCD framework. For the first time, a comparison between both approaches will be presented in this work. We also apply our new FFs to generate theoretical predictions for the energy distribution of ${D}_{s}^{+}$ mesons produced through the decay of unpolarized top quarks, to be measured at the CERN LHC.

In this work we introduce a new channel to indirect search for the light charged Higgs bosons, which are predicted in several extensions of the standard model (SM) such as the two-Higgs-doublet models (2HDMs). We calculate the O ( α s ) QCD radiative corrections to the energy distribution of bottom- and charmed-flavored hadrons ( B / D ) produced in the dominant decays of the polarized top quark in the 2HDM, i.e. t ( ↑ ) ⟶ b ( → B / D + jet ) + H + ( → τ + ν τ ) . Generally, the energy distribution of hadrons is governed by the unpolarized rate and the polar and the azimuthal correlation functions which are related to the density matrix elements of the decay t ( ↑ ) → b H + . In our proposed channel, any deviation of the B / D -meson energy spectrum from its corresponding SM predictions can be considered as a signal for the existence of charged Higgs at the LHC. We also calculate, for the first time, the azimuthal correlation rate Γ ϕ at next-to-leading order which vanishes at the Born level.

Recently, the Belle and BABAR collaborations published the single-inclusive electron–positron annihilation data at the center of mass energies ([Formula: see text]) of 10.52 and 10.54 GeV, respectively. These new data offer one the possibility to determine the nonperturbative initial conditions of fragmentation functions (FFs) much more accurately. Here, we extract the FFs of π± and K± particles at next-to-leading order (NLO) including these new data, which are in the regions of larger scaled-energy z and lower [Formula: see text]. However, the π± and K± FFs were calculated previously, but our new analysis shows that adding these new data, for instance, changes the (u, s) → π+ FFs in the large-z region while the s → π+ FF is also changed at low z. These new data also change the u → K+ FF at low z (z < 0.2) more than at large z, but the d → K+ FF is affected at z > 0.07. The FF of g → K+ is decreased everywhere, for example, about 25% at z = 0.01. We also apply, for the first time, the extracted FFs to make our predictions for the scaled-energy distributions of π± and K± inclusively produced in top quark decays at NLO.

The main aim of this paper is to present new sets of non-perturbative fragmentation functions (FFs) for $D^0$ and $D^+$ mesons at next-to-leading (NLO) and, for the first time, at next-to-next-to-leading order (NNLO) in the $\overline{\mathrm{MS}}$ factorization scheme with five massless quark flavors. This new determination of FFs is based on the QCD fit to the {\tt OPAL} experimental data for hadron production in the electron-positron single-inclusive annihilation (SIA). We discuss in detail the novel aspects of the methodology used in our analysis and the validity of obtained FFs by comparing with previous works in literature which have been carried out up to NLO accuracy. We will also incorporate the effect of charmed meson mass corrections into our QCD analysis and discuss the improvements upon inclusion of these effects. The uncertainties in the extracted FFs as well as in the corresponding observables are estimated using the "Hessian" approach. For a typical application, we use our new FFs to make theoretical predictions for the energy distributions of charmed mesons inclusively produced through the decay of unpolarized top quarks, to be measured at the CERN LHC. As a result of this analysis, suggestions are discussed for possible future studies on the current topic to consider any theory improvements and other available experimental observables., 12 pages, 6 figures, 6 Tables, Accepted for Publication in European Physical Journal C

We present nonperturbative fragmentation functions (FFs) for bottom-flavored (B) hadrons both at next-to-leading (NLO) and, for the first time, at next-to-next-to-leading order in the ¯¯¯¯¯¯MS factorization scheme with five massless quark flavors. They are determined by fitting all available experimental data of inclusive single B-hadron production in e+e− annihilation, from the ALEPH, DELPHI, and OPAL collaborations at CERN LEP1 and the SLD collaboration at SLAC SLC. The uncertainties in these FFs as well as in the corresponding observables are estimated using the Hessian approach. We perform comparisons with available NLO sets of B-hadron FFs. We apply our new FFs to generate theoretical predictions for the energy distribution of B hadrons produced through the decay of unpolarized or polarized top quarks, to be measured at the CERN LHC.

Applying the narrow-width approximation, we first review the next-to-leading-order QCD predictions for the total decay rate of a top quark considering two unstable intermediate particles: the ${W}^{+}$ boson in the standard model of particle physics and the charged Higgs boson ${H}^{+}$ in the generic type-I and -II two-Higgs-doublet models, i.e., $t\ensuremath{\rightarrow}b+{W}^{+}/{H}^{+}(\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\nu}}_{\ensuremath{\tau}})$. We then estimate the errors that arise from this approximation at leading-order perturbation theory. Finally, we investigate the interference effects in the factorization of production and decay parts of intermediate particles. We will show that for nearly mass-degenerate states (${m}_{{H}^{+}}\ensuremath{\approx}{m}_{{W}^{+}}$) the correction due to the interference effect is considerable.

We analytically compute the process-independent fragmentation functions of heavy quarks to fragment into ground state triply heavy baryons considering the Fermi motion effect of their constituent quarks. The effect of Fermi motion is basically included in the baryon wave functions so in all previous studies, a delta function form was approximated for the baryon wave functions which corresponds to ignoring this effect. Here, we study for the first time the effect of nonperturbative dynamics of baryon bound state considering a typical wave function which is different from the delta function and is the nonrelativistic limit of the solution of Bethe-Salpeter equation with the QCD kernel. Our analytical results will be presented for the fragmentation processes $b\rightarrow\Omega_{bbc}$ and $c\rightarrow\Omega_{ccb}$ through a scalar bc diquark intermediated.

The dominant mechanism to produce hadronic bound states with large transverse momentum is fragmentation. The hadronization processes are described by the fragmentation functions (FFs) which are universal and process-independent functions. In this paper, we study for the first time the noncommutative effects to the FF of a heavy quark to fragment into heavy mesons to leading order in the QCD coupling constant. As an example, we focus on the FF of a charm quark to split into the S-wave D-meson and compare our analytical results with both the experimental data and a well-known phenomenological model. Here, we compute the corrections of FFs induced by noncommutativity and find a bound on the energy scale where the noncommutative effects of the space-time will be relevant.

In this work, we calculate the fragmentation function (FF) of pseudoscalar S -wave heavy quarkonia from gluon splitting. We also study, for the first time, the Fermi motion effect of constituent quarks on the fragmentation production of the $ \eta_c(1S)$ and $ \eta_b(1S)$ states. In all previous studies of heavy quarkonium FFs, by ignoring the Fermi motion of constituents a Dirac-delta functional form was approximated for the wave function of bound state. Here, to study the Fermi motion of quarkonium constituents we consider a typical wave function which is different from the delta form and is the nonrelativistic limit of the solution of the Bethe-Salpeter equation with the QCD kernel. We shall present our results for the fragmentation of $ g\rightarrow (\eta_c, \eta_b)$ and show how the Fermi motion effect changes the results.

In this paper, we present {\tt SMKA18} analysis which is a first attempt to extract the set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach. Using the Laplace transformations, we present an analytical solution for the spin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NNLO approximation. The results are extracted using a wide range of proton $g_1^{p}(x, Q^2)$, neutron $g_1^{n}(x, Q^2)$ and deuteron $g_1^{d}(x, Q^2)$ spin-dependent structure functions dataset including the most recent high-precision measurements from {\tt COMPASS16} experiments at CERN which are playing an increasingly important role in global spin-dependent fits. The careful estimations of uncertainties have been done using the standard 'Hessian error' propagation. We will compare our results with the available spin-dependent inclusive deep inelastic scattering dataset and other results for the spin-dependent PDFs in literature. The results obtained for the spin-dependent PDFs as well as spin-dependent structure functions are clearly explained both in the small and large values of $x$., Comment: 30 Pages,5 figures,3 Table

We present, for the first time, a set of next-to-next-to-leading order (NNLO) fragmentation functions (FFs) describing the production of charmed-meson ${D}^{*}$ from partons. Exploiting the universality and scaling violations of FFs, we extract the NLO and NNLO FFs through a global fit to all relevant data sets from single-inclusive ${e}^{+}{e}^{\ensuremath{-}}$ annihilation. The uncertainties for the resulting FFs as well as the corresponding observables are estimated using the Hessian approach. We evaluate the quality of the SKM18 FFs determined in this analysis by comparing with the recent results in literature and show how they describe the available data for single-inclusive ${D}^{*\ifmmode\pm\else\textpm\fi{}}$-meson production in electron-positron annihilation. As a practical application, we apply the extracted FFs to make our theoretical predictions for the scaled-energy distributions of ${D}^{*\ifmmode\pm\else\textpm\fi{}}$-mesons inclusively produced in top quark decays. We explore the implications of SKM18 for LHC phenomenology and show that our findings of this study can be introduced as a channel to indirect search for top-quark properties.

Fragmentation is the dominant mechanism for heavy quarkonia production with large transverse momentum. The study of heavy quarkonium production is a powerful tool to understand the dynamics of strong interactions. In this work, we study the effect of Fermi motion of constituents on the direct fragmentation of the $ J/\psi$ and $ \Upsilon$ states from the gluon using a light-cone wave function. Following this study, we compute the process-independent fragmentation functions (FFs) for a gluon to fragment into these bound states. Consistent with such a wave function we set up the kinematics of a gluon fragmenting into a quarkonium such that the Fermi motion of the constituents splits into longitudinal as well as transverse direction. In all previous calculations of heavy quarkonia FFs, by ignoring the Fermi motion of constituents, a delta function form was approximated for the meson wave function. Here, we present our numerical results for the $ g\rightarrow J/\psi$ and $ g\rightarrow \Upsilon$ FFs and show how the proposed meson wave function improves the previous results.

The experimental data taken from both Drell-Yan and deep-inelastic scattering experiments suggest a sign change in $\overline{d}(x)\ensuremath{-}\overline{u}(x)$ flavor asymmetry in the proton at large values of momentum fraction $x$. In this work, we present a phenomenological study of $\overline{d}(x)\ensuremath{-}\overline{u}(x)$ flavor asymmetry. First, we extract the $\overline{d}(x)\ensuremath{-}\overline{u}(x)$ distribution using the more recent data from the BONuS experiment at Jefferson Lab on the ratio of neutron to proton structure functions, ${F}_{2}^{n}/{F}_{2}^{p}$, and show that it undergoes a sign change and becomes negative at large values of momentum fraction $x$, as expected. The stability and reliability of our obtained results are examined by including target mass corrections as well as higher twist terms which are particularly important in the large-$x$ region at low ${Q}^{2}$. Then, we calculate the $\overline{d}(x)\ensuremath{-}\overline{u}(x)$ distribution using the Brodsky-Hoyer-Peterson-Sakai model and show that if one chooses a mass for the down quark smaller than the one for the up quark it leads to a better description for the Fermilab E866 data. To prove this claim, we determine the masses of down and up sea quarks by fitting to the available and up-to-date experimental data for the $\overline{d}(x)\ensuremath{-}\overline{u}(x)$ distribution. In this respect, unlike the previous theoretical studies, we have shown that this distribution has a sign change at $xg0.3$ after evolution to the scale of available experimental data.

Using a quark-diquark model of baryons and by working in the framework of perturbative quantum chromodynamics we present, for the first time, the next-to-leading-order (NLO) corrections to the fragmentation process of a heavy quark into a ground state triply heavy baryon. For a complete analysis, we also study the effect of nonperturbative dynamic of baryon bound state on the extracted fragmentation functions considering a typical wave function which is different from the Dirac-delta function that was applied in all previous works. Our results show that the NLO corrections are significant, while the effect of the baryonic wave function is of minor importance.

At sufficiently large transverse momentum, the dominant production mechanism for heavy baryons is actually the fragmentation. In this work, we first study the direct fragmentation of a heavy quark into the unpolarized triply heavy baryons in the leading order of perturbative QCD. In a completely different approach, we also analyze the two-stage fragmentation of a heavy quark into a scalar diquark followed by the fragmentation of such a scalar diquark into a triply heavy baryon: quark-diquark model of baryons. The results of this model are in acceptable agreement with those obtained through a full perturbative regime. Relying on the quark-diquark model and considering two different scenarios we determine the spin-dependent fragmentation functions of polarized heavy baryons in such a way that a vector or a pseudoscalar heavy diquark is an intermediate particle between the initial heavy quark and the final state baryon.

Light and heavy charged Higgs bosons are predicted by many models with an extended Higgs sector such as the two-Higgs-doublet model (2HDM). Searches for the charged Higgs bosons have been done by the ATLAS and the CMS experiments at the Large Hadron Collider (LHC) in proton-proton collision. However, a definitive search is a program that still has to be carried out so this belongs to the LHC experiments. The experimental observation of charged Higgs bosons would indicate physics beyond the Standard Model. In the present work we study the ${\cal O}(\alpha_s)$ correction to the energy spectrum of the inclusive bottom-flavored mesons $(X_b)$ in polarized top quark decays into a light charged Higgs boson ($m_{H^+}, Comment: arXiv admin note: text overlap with arXiv:1610.03811

Performing a fit procedure on the hyperon masses, we first determine the free parameters in the Cornell-like hypercentral potential between the constituent quarks of hyperons in their ground state. To this end, using the variational principle, we apply the hyperspherical Hamiltonian including the Cornell-like hypercentral potential and the perturbation potentials due to the spin–spin, spin–isospin and isospin–isospin interactions between constituent quarks. In the following, we compute the hyperon magnetic moments as well as radiative decay widths of spin-3/2 hyperons using the spin-flavor wave function of hyperons. Our analysis shows acceptable consistencies between theoretical results and available experimental data. This leads to reliable wave functions for hyperons at their ground state.

The magnetic moments of [Formula: see text]-hypernuclei are the most interesting observables which provide a highly sensitive probe of lambda in the hypernuclei structure and also supply direct information on hyperon–nucleon interactions. In this work, in a relativistic approach we analytically determine the magnetic moment of several [Formula: see text]-hypernuclei such as [Formula: see text], [Formula: see text] and [Formula: see text] in their ground and excited states, i.e., the [Formula: see text], [Formula: see text] and [Formula: see text] states. For our analysis, we consider the central potential of Wood–Saxon and the spin-orbital potential and determine the wave function of hypernuclei. Then, we compute the Dirac, the anomalous and the total magnetic moments of the ground and excited states of [Formula: see text]-hypernuclei.

In recent years, the physics of hypernuclei has been in progress dramatically both in experiments and theories. In this regard, there have been considerable interests in the study of [Formula: see text]-particle 1s state in hypernuclei using relativistic quantum mechanics. Many theoretical results have been obtained numerically in the relativistic frameworks. In this work, using the relativistic Dirac equation, we study the properties of [Formula: see text]-particle in the hypernuclei analytically and, specifically, we determine its binding energies of ground state in a single [Formula: see text]-hypernuclei. The [Formula: see text]-N potential is considered as a spin-dependent term and the radial dependence of potential is approximated by a Gaussian function. For a more complete analysis, we will also compute the hypernuclei mass, its wave function and the root mean square (RMS) radii of [Formula: see text] orbits in [Formula: see text]-hypernuclear system.

In this paper, our main aim is to obtain the transmission (T) and the reflection (R) coefficients for one-dimensional scattering state of the spin-[Formula: see text] particles in an interaction with a special nuclear potential. For this reason, at first, we consider Dirac equation and then obtain the Milne’s nonlinear differential equation due to minimal length from Schrödinger-like equation and then calculate the T- and R-coefficients using one-dimensional Woods–Saxon potential on the basis of the generalized uncertainty principle. Finally, we will check the validity and the correctness of our results.

We present a detailed QCD analysis of nucleon structure functions $xF_3 (x, Q^2)$, based on Laplace transforms and Jacobi polynomials approach. The analysis corresponds to the next-to-leading order and next-to-next-to-leading order approximation of perturbative QCD. The Laplace transform technique, as an exact analytical solution, is used for the solution of nonsinglet Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at low- and large-$x$ values. The extracted results are used as input to obtain the $x$ and Q$^2$ evolution of $xF_3(x, Q^2)$ structure functions using the Jacobi polynomials approach. In our work, the values of the typical QCD scale $\Lambda_{\overline{\rm MS}}^{(n_f)}$ and the strong coupling constant $\alpha_s(M_Z^2)$ are determined for four quark flavors ($n_f=4$) as well. A careful estimation of the uncertainties shall be performed using the Hessian method for the valence-quark distributions, originating from the experimental errors. We compare our valence-quark parton distribution functions sets with those of other collaborations; in particular with the {\tt BBG}, {\tt CT14}, {\tt MMHT14} and {\tt NNPDF} sets, which are contemporary with the present analysis. The obtained results from the analysis are in good agreement with those from the literature., Comment: 14 Pages, 8 Figures, 4 Tables

It is well-known that the dominant mechanism to produce hadronic bound states with large transverse momentum is fragmentation. This mechanism is described by the fragmentation functions (FFs) which are the universal and process-independent functions. Here, we review the perturbative FFs formalism as an appropriate tool for studying these hadronization processes and detail the extension of this formalism at next-to-leading order (NLO). Using the Suzuki's model, we calculate the perturbative QCD FF for a heavy quark to fragment into a S-wave heavy meson at NLO. As an example, we study the LO and NLO FFs for a charm quark to split into the S-wave $D$-meson and compare our analytic results both with experimental data and well-known phenomenological models.

We calculate the process-independent fragmentation functions (FFs) for a heavy quark to fragment into heavy mesons considering the effects of meson wave function. In all previous works, where the FFs of heavy mesons or heavy baryons were calculated, a delta function form was approximated for the wave function of hadrons. Here, for the first time, we consider a typical mesonic wave function which is different from the delta function and is the nonrelativistic limit of the solution of Bethe-Salpeter equation with the QCD kernel. We shall present our numerical results for the heavy FFs and show how the proposed wave function improves the previous results. As an example, we focus on the fragmentation function for c -quark to split into S -wave $ D^0$ -meson and compare our results with experimental data from BELLE and CLEO.