arXiv subjects

Jungil Lee

Publications and source records attributed to Jungil Lee.

At least 19 recordsLinked to original sources

arXiv2026

A purely mechanical system realizing a Coulomb-like interaction

We solve in closed form a one-dimensional relativistic system: two masses interacting only through elastic collisions with a massless mediator bouncing between them. Momenta, times, and positions are hyperbolic functions of the collision index. The mediator energy, interpreted as the pair's effective potential, obeys an exact discrete Coulomb law, $V\propto 1/r$, with a Lorentz-invariant action as coupling. A massive Newtonian mediator instead transmits a $1/r^{3}$ force; one adiabatic invariant traces both laws to the mediator's dispersion relation. Continued to negative mediator energy, the closed forms turn trigonometric, binding a one-dimensional mechanical analog of the Coulomb atom.

physics.class-ph↗

arXiv2026

Resummation of threshold double logarithms in quarkonium fragmentation functions

We develop a formalism for resumming threshold double logarithms that appear in fragmentation functions for production of heavy quarkonia. Threshold singularities appear in fixed-order calculations of quarkonium fragmentation functions in the nonrelativistic QCD factorization formalism due to radiation of soft gluons. Because of this, fixed-order quarkonium fragmentation functions are not positive definite, and can lead to unphysically negative cross sections. This problem can be resolved by resumming threshold logarithms to all orders in perturbation theory, which renders the fragmentation functions finite and ensures the positivity of cross sections. We present a detailed derivation of the resummation formalism and derive the formula for resummed quarkonium fragmentation functions, which can be computed entirely within perturbation theory without the need for nonperturbative model functions.

hep-ph↗

arXiv2025

Resummation of threshold double logarithms in inclusive production of heavy quarkonium

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

hep-ph↗

arXiv2024

Scalar dark matter multiplet of global $O(N)$ symmetry

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

hep-ph↗

arXiv2024

Resummation of threshold double logarithms in hadroproduction of heavy quarkonium

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

hep-ph↗

arXiv2023

Higher-order relativistic corrections to gluon fragmentation into spin-triplet S-wave quarkonium

We compute the relative-order-v^4 contribution to gluon fragmentation into quarkonium in the 3S1 color-singlet channel, using the nonrelativistic QCD (NRQCD) factorization approach. The QCD fragmentation process contains infrared divergences that produce single and double poles in epsilon in 4-2epsilon dimensions. We devise subtractions that isolate the pole contributions, which ultimately are absorbed into long-distance NRQCD matrix elements in the NRQCD matching procedure. The matching procedure involves two-loop renormalizations of the NRQCD operators. The subtractions are integrated over the phase space analytically in 4-2epsilon dimensions, and the remainder is integrated over the phase-space numerically. We find that the order-v^4 contribution is enhanced relative to the order-v^0 contribution. However, the order-v^4 contribution is not important numerically at the current level of precision of quarkonium-hadroproduction phenomenology. We also estimate the contribution to hadroproduction from gluon fragmentation into quarkonium in the 3PJ color-octet channel and find that it is significant in comparison to the complete next-to-leading-order-in-alpha_s contribution in that channel.

hep-ph↗

arXiv2022

Vacuum stability of conformally invariant scalar dark matter models

We discuss vacuum structure and vacuum stability in classically scale-invariant renormalizable models with a scalar dark matter multiplet of global O(N) symmetry together with an electroweak singlet scalar mediator. Our conformally invariant scalar potential generates the electroweak symmetry breaking via the Coleman-Weinberg mechanism, and the new scalar singlet mediator acquires its mass through radiative corrections of the scalar dark matters as well as of the standard model particles. Taking into account the present collider bounds, we find the region of parameter space where the scalar potential is stable and all the massless couplings are perturbative up to the Planck scale. With the obtained parameter sets satisfying the vacuum stability condition, we present the allowed region of new physics parameters satisfying the recent measurement of relic abundance, and predict the elastic scattering cross section of the new scalar multiplet into target nuclei for a direct detection of the dark matter. We also discuss the collider signatures and future discovery potentials of the new scalars.

hep-ph↗

arXiv2022

Renormalization of the radiative jet function

We show how to compute directly the renormalization/evolution of the radiative jet function that appears in the factorization theorems for $B\to γ\ellν$ and $H\to γγ$ through a $b$-quark loop. We point out that, in order to avoid double counting of soft contributions, one should use in the factorization theorems a subtracted radiative jet function, from which soft contributions have been removed. The soft-contribution subtractions are zero-bin subtractions in the terminology of soft-collinear effective theory. We show that they can be factored from the radiative jet function and that the resulting soft-subtraction function gives rise to a nonlocal renormalization of the subtracted radiative jet function. This is a novel instance in which zero-bin subtractions lead to a nonlocality in the renormalization of a subtracted quantity that is not present in the renormalization of the unsubtracted quantity. We demonstrate the use of our formalism by computing the order-$α_s$ evolution kernel for the subtracted radiative jet function. Our result is in agreement with the result that had been inferred previously by making use of the factorization theorem for $B\to γ\ellν$, but that had been ascribed to the unsubtracted radiative jet function.

hep-ph↗

arXiv2021

Analyticity, renormalization, and evolution of the soft-quark function

We compute the renormalization and evolution of the soft-quark function that appears in the factorization theorem for Higgs-boson decays to two photons through a $b$-quark loop. Our computation confirms a conjecture by Liu, Mecaj, Neubert, Wang, and Fleming for the form of the renormalization and evolution of the soft-quark function in order $α_s$. We also work out the analyticity structure of the soft-quark function by making use of light-cone perturbation theory.

hep-ph↗

arXiv2020

Derivation of Jacobian Formula with Dirac Delta Function

We demonstrate how to make the coordinate transformation or change of variables from Cartesian coordinates to curvilinear coordinates by making use of a convolution of a function with Dirac delta functions whose arguments are determined by the transformation functions between the two coordinate systems. By integrating out an original coordinate with a Dirac delta function, we replace the original coordinate with a new coordinate in a systematic way. A recursive use of Dirac delta functions allows the coordinate transformation successively. After replacing every original coordinate into a new curvilinear coordinate, we find that the resultant Jacobian of the corresponding coordinate transformation is automatically obtained in a completely algebraic way. In order to provide insights on this method, we present a few examples of evaluating the Jacobian explicitly without resort to the known general formula.

physics.gen-ph↗

arXiv2020

Proof of Cramer's rule with Dirac Delta Function

We present a new proof of Cramer's rule by interpreting a system of linear equations as a transformation of $n$-dimensional Cartesian-coordinate vectors. To find the solution, we carry out the inverse transformation by convolving the original coordinate vector with Dirac delta functions and changing integration variables from the original coordinates to new coordinates. As a byproduct, we derive a generalized version of Cramer's rule that applies to a partial set of variables, which is new to our best knowledge. Our formulation of finding a transformation rule for multi-variable functions shall be particularly useful in changing a partial set of generalized coordinates of a mechanical system.

math.GM↗

arXiv2020

Mechanical Snell's Law

We investigate the motion of a massive particle constrained to move along a path consisting of two line segments on a vertical plane under an arbitrary conservative force. By fixing the starting and end points of the track and varying the vertex horizontally, we find the least-time path. We define the angles of incidence and refraction similar to the refraction of a light ray. It is remarkable that the ratio of the sines of these angles is identical to the ratio of the average speeds on the two partial paths as long as the horizontal component of the conservative force vanishes.

physics.class-ph↗

arXiv2020

Bra-Ket Representation of the Inertia Tensor

We employ Dirac's bra-ket notation to define the inertia tensor operator that is independent of the choice of bases or coordinate system. The principal axes and the corresponding principal values for the elliptic plate are determined only based on the geometry. By making use of a general symmetric tensor operator, we develop a method of diagonalization that is convenient and intuitive in determining the eigenvector. We demonstrate that the bra-ket approach greatly simplifies the computation of the inertia tensor with an example of an $N$-dimensional ellipsoid. The exploitation of the bra-ket notation to compute the inertia tensor in classical mechanics should provide undergraduate students with a strong background necessary to deal with abstract quantum mechanical problems.

physics.class-ph↗

arXiv2020

Three-Body Inertia Tensor

We derive a general formula for the inertia tensor of a three-body system. By employing three independent Lagrange undetermined multipliers to express the vectors corresponding to the sides in terms of the position vectors of the vertices, we present the general covariant expression for the inertia tensor of the three particles of different masses. If $m_a/a=m_b/b=m_c/c=ρ$, then the center of mass coincides with the incenter of the triangle and the moment of inertia about the normal axis passing the center of mass is $I=ρabc$, where $m_a$, $m_b$, and $m_c$ are the masses of the particles at $A$, $B$, and $C$, respectively, and $a$, $b$, and $c$ are the lengths of the line segments $\overline{BC}$, $\overline{CA}$, and $\overline{AB}$, respectively. The derivation and the corresponding results are closely related to the famous Heron's formula for the area of a triangle.

physics.class-ph↗

arXiv2020

Covariant calculation of a two-loop test of nonrelativistic QCD factorization

We test the nonrelativistic QCD factorization conjecture for inclusive quarkonium production at two loops by carrying out a covariant calculation of the nonrelativistic quantum chromodynamics (NRQCD) long-distance matrix element (LDME) for a heavy-quark pair in an $S$-wave, color-octet state to fragment into a heavy-quark pair in a color-singlet state of arbitrary orbital angular momentum. The NRQCD factorization conjecture for the universality of the LDME requires that infrared divergences that it contains be independent of the direction of the Wilson line that appears in its definition. We find this to be the case in our calculation. The results of our calculation differ in some respects from those of a previous calculation that was carried out by Nayak, Qiu, and Sterman using light-cone methods. We have identified the sources of some of these differences. The results of both calculations are consistent with the NRQCD factorization conjecture. However, the general principle that underlies this confirmation of NRQCD factorization at two-loop order has yet to be revealed.

hep-ph↗

arXiv2020

Top FCNC induced by a Z' boson

We consider a Z' model where the Z' boson couples only to up and top quarks. As a simple setup, one can consider a family-dependent $U(1)'$ symmetry, under which only right-handed up-type quarks are charged. After symmetry breaking, the right-handed quarks mix with each other and top flavor-changing neutral currents (FCNCs) mediated by the Z' boson can be generated at tree level. We take into account several processes to probe the top FCNCs, and find that the same sign top quark pair production or the triple top quark production is the most capable of testing the top FCNCs. We also consider a few non-FCNC processes to probe the Z' boson, for example, dijet production at the LHC.

hep-ph↗

arXiv2019

Pseudoscalar Quarkonium+gamma Production at NLL+NLO accuracy

We consider the exclusive pseudoscalar heavy-quarkonium (eta_{b,c}) production in association with a photon at future lepton colliders where the collider energies of O(10^2) GeV are far greater than the quarkonium mass. At these energies, the logarithm of mass to collision energy becomes increasingly large hence its resummation becomes particularly important. By making use of the light-cone-distribution factorization formula, we resum the logarithms up to next-to-leading-logarithmic accuracy (NLL) that corresponds to order-alpha_s accuracy. We combine the resummed result with a known fixed-order result at next-to-leading order (NLO) such that both resummed-logarithmic terms and non-logarithmic terms are included at the same order in alpha_s. This allowed us to provide reliable predictions at accuracies of order alpha_s ranging from relatively low energies near quarkonium mass to the collider energies of O(10^2) GeV. We also include the leading relativistic corrections resummed at leading-logarithmic accuracy. Our prediction at the Belle energy is comparable with fixed-order predictions in literatures while it shows a large deviation from a recent Belle's upper limit by about 4 sigma. Finally, we make predictions for the energies of future Z and Higgs factories.

hep-ph↗

arXiv2019

Scalar dark matter in the conformally invariant extension of the standard model

We study a classically scale-invariant model with an electroweak singlet scalar mediator together with a scalar dark matter multiplet of global $O(N)$ symmetry. Our most general conformally invariant scalar potential generates the electroweak symmetry breaking via the Coleman-Weinberg mechanism, and the new scalar singlet acquires its mass through radiative corrections of the SM particles and the scalar dark matter. Taking into account the collider bounds, we present the allowed region of new physics parameters satisfying the recent measurement of relic abundance. With the obtained parameter sets, we predict the elastic scattering cross section of the new scalar multiplet into target nuclei for a direct detection of the dark matter. We also perform a full analysis with arbitrary set of parameters for $N \geq 2$, and discuss the implication of the constraints from the on-going direct and indirect detections of dark matter.

hep-ph↗