We compute leading-power fragmentation corrections to $J/\ensuremath{\psi}$ production at the Tevatron and LHC. find that, when these are combined with perturbative through next-to-leading order in strong coupling constant ${\ensuremath{\alpha}}_{s}$, we obtain a good fit high-${p}_{T}$ cross section data from CDF CMS Collaborations. The fitted long-distance matrix elements lead predictions of near-zero polarization helicity frame large ${p}_{T}$.

We compute fragmentation corrections to hadroproduction of the quarkonium states $J/\psi$, $\chi_{cJ}$, and $\psi(2S)$ at leading power in $m_c^2/p_T^2$, where $m_c$ is charm-quark mass $p_T$ transverse momentum. The computation carried out framework nonrelativistic QCD. include parton-production cross sections through next-to-leading order strong coupling $\alpha_s$ functions second $\alpha_s$. also sum logarithms $p_T^2/m_c^2$ all orders perturbation theory. find that, when we combine...

We resum threshold double logarithms in inclusive production of heavy quarkonium that arise from singularities near the boundary phase space. This resolves catastrophic failure conventional approach based on fixed-order perturbation theory calculations nonrelativistic QCD, where cross sections at large transverse momentum can turn negative. identify root cause this negative section problem as appearance radiative corrections, and them to all orders leading logarithmic level. find resummation...

We resum threshold double logarithms that appear in inclusive production of heavy quarkonium. This resolves the catastrophic failure fixed-order perturbation theory where quarkonium cross sections at large transverse momentum can turn negative due to radiative corrections. find resummation is imperative for describing measured prompt rates J/ψ momentum.

A bstract We study two types of models involving a scalar dark matter multiplet global O ( N ) symmetry. These are distinguished by the absence (Type I) or presence II) mediator with Z 2 derive allowed regions for mass and new couplings based on constraints from Higgs invisible decay, relic abundance matter, spin-independent matter-nucleon scattering cross section. Within parameter space, we also discuss vacuum stability potential perturbativity in both models. find that Type I model cannot...

Abstract We present an interesting application of the solution to simple harmonic oscillator (SHO) that can serve as a computation $$\pi$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> . begin with review compact teaching strategy for solving its equation motion through integration in general physics course, where many students face difficulties conventional methods differential equations. This approach leads arcsine function, inverse sine...

We compute fragmentation functions for a quark to fragment quarkonium through an $S$-wave spin-triplet heavy quark-antiquark pair. consider both color-singlet and color-octet ($Q\bar Q$) pairs. give results the case in which fragmenting that is constituent of have different flavors these quarks same flavors. Our sum over all spin polarizations $Q\bar Q$ pairs confirm previous results. longitudinally polarized agree with calculations flavor cases correct error calculation different-flavor case.

We illustrate a rigorous approach to express the totally symmetric isotropic tensors of arbitrary rank in n-dimensional Euclidean space as linear combination products Kronecker deltas. By making full use symmetries, one can greatly reduce efforts compute cumbersome angular integrals into straightforward combinatoric counts. This method is generalised cases which such symmetries are present subspaces. further demonstrate mechanism tensor-integral reduction that widely used various physics...

A bstract We consider the exclusive pseudoscalar heavy-quarkonium ( η b , c ) production in association with a photon at future lepton colliders where collider energies of O (10 2 GeV are far greater than quarkonium mass. At these energies, logarithm mass to collision energy becomes increasingly large hence its resummation particularly important. By making use light-cone-distribution factorization formula, we resum logarithms up next-to-leading-logarithmic accuracy (NLL) that corresponds...

Within the nonrelativistic quantum chromodynamics (NRQCD) factorization formalism, we compute relativistic corrections to exclusive decays of bottomonia with even charge conjugation parity into $S$-wave charmonium pairs at leading order in strong coupling constant. Relativistic are resummed for a class color-singlet contributions all orders charm-quark velocity ${v}_{c}$ rest frame. Almost every process that consider this work has negative ranging from $\ensuremath{-}20$ $\ensuremath{-}35%$....

We test the nonrelativistic QCD factorization conjecture for inclusive quarkonium production at two loops by carrying out a covariant calculation of quantum chromodynamics (NRQCD) long-distance matrix element (LDME) heavy-quark pair in an $S$-wave, color-octet state to fragment into color-singlet arbitrary orbital angular momentum. The NRQCD universality LDME requires that infrared divergences it contains be independent direction Wilson line appears its definition. find this case our...

Abstract We compute the electrostatic potential of a uniformly charged triangle. Barycentric coordinates are employed to express field point, parametrization surface integral, and gradient operator. The resultant analytic expression for is expressed in terms side lengths triangle, altitude point from plane which triangle placed, barycentric relative Our results good agreement with available numerical results. asymptotic behavior investigated special limits that satisfy known values....

We compute leading-power fragmentation corrections to $J/\psi$ photoproduction at DESY HERA, making use of the nonrelativistic QCD factorization approach. Our calculations include parton production cross sections through order $\alpha_s^3$, functions though $\alpha_s^2$, and leading logarithms transverse momentum divided by charm-quark mass all orders in $\alpha_s$. find that corrections, beyond those are included next-to-leading $\alpha_s$, small relative fixed-order contributions...

We derive a general formula for the inertia tensor of three-body system. By employing three independent Lagrange undetermined multipliers to express vectors corresponding sides in terms position vertices, we present covariant expression particles different masses. If $m_a/a=m_b/b=m_c/c=\rho$, then center mass coincides with incenter triangle and moment about normal axis passing is $I=\rho abc$, where $m_a$, $m_b$, $m_c$ are masses at $A$, $B$, $C$, respectively, $a$, $b$, $c$ lengths line...

Abstract We consider the normal mode problem of a vibrating string loaded with n identical beads equal spacing, which involves an eigenvalue problem. Unlike conventional approach to solving this by considering difference equation for components eigenvector, we modify introducing matrix-valued Lagrange undetermined multipliers, regularize secular and make non-singular. Then, eigenvector can be obtained from regularized multiplying indeterminate inverse matrix. find that matrix is nothing but...

We resum threshold double logarithms that appear in inclusive production of heavy quarkonium. This resolves the catastrophic failure fixed-order perturbation theory where quarkonium cross sections at large transverse momentum can turn negative due to radiative corrections. find resummation is imperative for describing measured prompt rates $J/\psi$ momentum.

We study two types of models involving a scalar dark matter multiplet global $O(N)$ symmetry. These are distinguished by the absence (Type I) or presence II) mediator with $Z_{2}$ derive allowed regions for mass and new couplings based on constraints from Higgs invisible decay, relic abundance matter, spin-independent matter-nucleon scattering cross section. Within parameter space, we also discuss vacuum stability potential perturbativity in both models. find that Type I model cannot achieve...