arXiv subjects

Junegone Chay

Publications and source records attributed to Junegone Chay.

At least 19 recordsLinked to original sources

arXiv2026

Anatomy of the Quasi-PDF with a Transverse-Momentum Cutoff

The quasi-PDF is fundamentally different from the light-cone PDF, and large-momentum effective theory relates the two through perturbative matching. This has required considerable effort. One of the difficulties in matching is that no single renormalization scheme has been agreed upon for the quasi-PDF, and the resulting variety of prescriptions can obscure the physics underlying the matching. We study how the choice of scheme affects the renormalized quasi-PDF and the matching coefficient, and how the two are related, aiming to identify a scheme in which this dependence becomes transparent. As a first attempt, we consider the transverse-momentum cutoff scheme. It is not used in practice, since a hard momentum cutoff breaks Lorentz invariance, and it has generally been treated as an illustrative example exhibiting the linear divergence of the spatial Wilson line. A careful study, however, reveals a richer structure than expected. The ultraviolet divergence in this scheme depends not only on the cutoff itself, but also on an independent divergence associated with the momentum fraction of the quasi-PDF. Disentangling these two ultraviolet structures, and following the disentangling through the explicit one-loop calculation, uncovers further structure along the way. Once the ultraviolet contributions are correctly separated and assigned to the renormalization counterterm, a finite ambiguity remains, and we use it to restore the quark-number conservation broken by the cutoff. The resulting renormalized quasi-PDF and matching coefficient can be meaningfully compared with the result obtained in dimensional regularization, and we show how the two are reconciled.

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arXiv2026

Isolating Scheme Dependence of Quasi-PDFs in the RI/MOM Scheme

Quasi-parton distribution functions provide a framework for relating lightcone parton distributions to correlation functions in Euclidean lattice QCD. Their connection to lightcone distributions is established through perturbative matching, whose form depends on the renormalization prescription adopted for the quasi-PDF. In the ordinary RI/MOM scheme, the off-shell reference momentum enters both the renormalized quasi-PDF and the matching coefficient. We propose modified finite renormalization schemes in which neither quantity depends on the RI/MOM reference momentum. Starting from the ordinary RI/MOM scheme, we identify the part to be retained in the renormalized quasi-PDF and include the remaining finite part in the counterterm. We consider a minimal RI/MOM scheme and a modified minimal scheme as specific examples. We derive the corresponding one-loop renormalized quasi-PDFs, counterterms, matching coefficients, and renormalization-group equations, and show explicitly that the finite transformation removes the dependence on the RI/MOM reference momentum from both the renormalized quasi-PDF and the counterterm in the modified schemes.

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arXiv2022

N-jettiness for muon jet pairs in electroweak high-energy processes

We study the $N$-jettiness in the electroweak high-energy process for the final muon jet pairs, $e^- e^+ \rightarrow μ^+ \ \mathrm{jet} + μ^- \mathrm{jet}$. Compared to QCD, the main difference is that there exist additional gauge nonsinglet contributions in the weak interaction, which make the factorization more elaborate. Especially the nonsinglet contributions arise due to the Block-Nordsieck violation in electroweak processes, which yields the Sudakov logarithms and the rapidity divergence. They change the evolution of the factorized parts considerably in the $N$-jettiness. There are two possible channels, initiated from the gauge bosons $W W \rightarrow \ell_μ \overline{\ell}_μ$, and from the electrons $\ell_e \overline{\ell}_e \rightarrow \ell_μ \overline{\ell}_μ$, where $\ell$ denotes the weak doublet. The latter was discussed previously, and we complete the analysis by studying the first. The factorization for $W W \rightarrow \ell_μ \overline{\ell}_μ$ can be proceeded in a similar way as in the factorization for $\ell_e\overline{\ell}_e \rightarrow \ell_μ \overline{\ell}_μ$, and the result exhibits a rich structure. The new ingredients in this study consist of the $W$ beam functions, and the complex color structure of the soft functions and the hard functions. The resummation of the large logarithms is performed by solving the renormalization group equations with respect to the renormalization scale and the rapidity scale. In the numerical analysis, we confine to the SU(2) weak gauge interaction, and the numerical results are presented for both channels at next-to-leading-logarithmic accuracy including the singlet and the nonsinglet contributions. The nonsinglet contributions turn out to be appreciable in the 2-jettiness.

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arXiv2021

N-jettiness in electroweak high-energy processes

We study $N$-jettiness in electroweak processes at extreme high energies. The description of the scattering process such as $e^- e^+ \rightarrow μ^- μ^+ +X$ is similar to QCD. At present, electroweak processes are prevailed by the processes induced by the strong interaction, but they will be relevant at future $e^- e^+$ colliders at high energy. The main difference between QCD and electroweak processes is that the initial- and final-state particles should appear in the form of hadrons, that is, color singlets in QCD, while there can be weak nonsinglets as well in electroweak interactions. We analyze the factorization theorems for the $N$-jettiness in $e^- e^+ \rightarrow μ^- μ^+ +X$, and compute the factorized parts to next-to-leading logarithmic accuracy. To simplify the comparison with QCD, we only consider the $SU(2)_W$ gauge interaction, and the extension to the Standard Model is straightforward. Put it in a different way, it corresponds to an imaginary world in which colored particles can be observed in QCD, and the richer structure of effective theories is probed. Various nonzero nonsinglet matrix elements are interwoven to produce the factorized results, in contrast to QCD in which there are only contributions from the singlets. Another distinct feature is that the rapidity divergence is prevalent in the contributions from weak nonsinglets due to the different group theory factors between the real and virtual corrections. We verify that the rapidity divergence cancels in all the contributions with a different number of nonsinglet channels. We also consider the renormalization group evolution of each factorized part to resum large logarithms, which are distinct from QCD.

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arXiv2021

Factorization of the dijet cross section in hadron-hadron collisions

The factorization theorem for the dijet cross section is presented in hadron-hadron collisions with a cone-type jet algorithm. We also apply the beam veto to the beam jets consisting of the initial radiation. The soft-collinear effective theory is employed to see the factorization structure transparently when there are four distinct lightcone directions involved. There are various types of divergences such as the ultraviolet and infrared divergences. And when the phase space is divided to probe the collinear and the soft parts, there appears an additional divergence called rapidity divergence. These divergences are sorted out and we will show that all the infrared and rapidity divergences cancel, and only the ultraviolet divergence remains. It is a vital step to justify the factorization. Among many partonic processes, we take $q\overline{q} \rightarrow gg$ as a specific example to consider the dijet cross section. The hard and the soft functions have nontrivial color structure, while the jet and the beam functions are diagonal in operator basis. The dependence of the soft anomalous dimension on the jet algorithm and the beam veto is diagonal in operator space, and is cancelled by that of the jet and beam functions. We also compute the anomalous dimensions of the factorized components, and resum the large logarithms to next-to-leading logarithmic accuracy by solving the renormalization group equation.

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arXiv2021

Consistent treatment of rapidity divergence in soft-collinear effective theory

In soft-collinear effective theory, we analyze the structure of rapidity divergence due to the collinear and soft modes residing in disparate phase spaces. The idea of an effective theory is applied to a system of collinear modes with large rapidity and soft modes with small rapidity. The large-rapidity (collinear) modes are integrated out to obtain the effective theory for the small-rapidity (soft) modes. The full SCET with the collinear and soft modes should be matched onto the soft theory at the rapidity boundary, and the matching procedure becomes exactly the zero-bin subtraction. The large-rapidity region is out of reach for the soft mode, which results in the rapidity divergence. The rapidity divergence in the collinear sector comes from the zero-bin subtraction, which ensures the cancellation of the rapidity divergences from the soft and collinear sectors. In order to treat the rapidity divergence, we construct the rapidity regulators consistently for all the modes. They are generalized by assigning independent rapidity scales for different collinear directions. The soft regulator incorporates the correct directional dependence when the innate collinear directions are not back-to-back, which is discussed in the $N$-jet operator. As an application, we consider the Sudakov form factor for the back-to-back collinear current and the soft-collinear current, where the soft rapidity regulator for a soft quark is developed. We extend the analysis to the boosted heavy quark sector and exploit the delicacy with the presence of the heavy quark mass. We present the resummed results of large logarithms in the form factors for various currents with the light and the heavy quarks, employing the renormalization group evolution on the renormalization and the rapidity scales.

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arXiv2018

Factorized groomed jet mass distribution in inclusive jet processes

We consider the factorized groomed jet mass distribution in inclusive jet processes using modified mass drop tagger (mMDT), corresponding to soft drop with the angular exponent $β=0$. A grooming procedure is implemented rather than tagging in the sense that grooming always returns a groomed jet, while tagging dose not return a jet when a single particle remains after tagging. We find that the grooming procedure makes the jet mass distribution infrared safe and only ultraviolet divergences appear in each factorized part. The groomed jet mass distributions are investigated in a wide range of the jet mass considering various limits on the jet mass variable $ρ= M_J^2/(p_T^JR)^2$ and the grooming cut $y_c$. Appropriate effective theories in different kinematic regions are employed to resum large logarithms, in which the analysis in the region $ρ\sim y_c \ll 1$ is included due to the different type of factorization. The analytic computation of the factorized groomed jet mass distribution is presented by resumming the large logarithms in the jet mass, and $y_c$. Numerically, the effect of the resummation is notably enhanced, compared with the calculation at next-to-leading order, and nonglobal logarithms are estimated to be small.

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arXiv2018

Threshold Factorization Redux

We reanalyze the factorization theorems for Drell-Yan process and for deep inelastic scattering near threshold, as constructed in the framework of the soft-collinear effective theory (SCET), from a new, consistent perspective. In order to formulate the factorization near threshold in SCET, we should include an additional degree of freedom with small energy, collinear to the beam direction. The corresponding collinear-soft mode is included to describe the parton distribution function (PDF) near threshold. The soft function is modified by subtracting the contribution of the collinear-soft modes in order to avoid double counting on the overlap region. As a result, the proper soft function becomes infrared finite, and all the factorized parts are free of rapidity divergence. Furthermore, the separation of the relevant scales in each factorized part becomes manifest. We apply the same idea to the dihadron production in $e^+ e^-$ annihilation near threshold, and show that the resultant soft function is also free of infrared and rapidity divergences.

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arXiv2015

Analysis of exclusive $k_T$ jet algorithms in electron-positron annihilation

We study the factorization of the dijet cross section in $e^+ e^-$ annihilation using the generalized exclusive jet algorithm which includes the cone-type, the JADE, the $k_T$, the anti-$k_T$ and the Cambridge/Aachen jet algorithms as special cases. In order to probe the characteristics of the jet algorithms in a unified way, we consider the generalized $k_T$ jet algorithm with an arbitrary weight of the energies, in which various types of the $k_T$-type algorithms are included for specific values of the parameter. We show that the jet algorithm respects the factorization property for the parameter $α<2$. The factorized jet function and the soft function are well defined and infrared safe for all the jet algorithms except the $k_T$ algorithm. The $k_T$ algorithm ($α=2$) breaks the factorization since the jet and the soft functions are infrared divergent and are not defined for $α=2$, though the dijet cross section is infrared finite. In the jet algorithms which enable factorization, we give a phenomenological analysis using the resummed and the fixed-order results.

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arXiv2015

Factorization of the dijet cross section with the Georgi jet algorithm in $e^+ e^-$ annihilation

We consider the dijet cross section in $e^+ e^-$ annihilation using the Georgi jet algorithm, or the maximizing jet algorithm. The cross section is factorized into the hard, collinear and soft parts. Each factorized function is computed to next-to-leading order, and is shown to be infrared finite. The large logarithms are resummed at next-to-leading logarithmic accuracy. By analyzing the phase space for the jet algorithm, the Georgi algorithm turns out to be equivalent to the Sterman-Weinberg and the cone-type algorithms.

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arXiv2015

Factorization of the dijet cross section in electron-positron annihilation with jet algorithms

We analyze the effects of jet algorithms on each factorized part of the dijet cross sections in $e^+ e^-$ scattering using the soft-collinear effective theory. The jet function and the soft function with a cone-type jet algorithm and the Sterman-Weinberg jet algorithm are computed to next-to-leading order in $α_s$, and are shown to be infrared finite using the dimensional regularization. The integrated and unintegrated jet functions are presented, and compared with other types of jet functions.

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arXiv2013

Proper factorization theorems in high-energy scattering near the endpoint

Consistent factorization theorems in high-energy scattering near the threshold are presented in the framework of the soft-collinear effective theory. Traditional factorization theorem separates the soft and collinear parts successfully, but a final step should be supplemented if each part encounters infrared divergence. We present factorization theorems in which the infrared divergences appear only in the parton distribution functions and the infrared divergence is removed by carefully separating and reorganizing collinear and soft parts. The underlying physical idea is to isolate and remove the soft contributions systematically from the collinear part in loop corrections order by order. After this procedure, each factorized term in the scattering cross sections is free of infrared divergence, and can be safely computed using perturbation theory. This factorization procedure can be applied to various high-energy scattering processes. We show factorization theorems in Drell-Yan processes, deep inelastic scattering and Higgs production near the endpoint.

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arXiv2013

Factorization theorem for high-energy scattering near the endpoint

A consistent factorization theorem is presented in the framework of effective field theories. Conventional factorization suffers from infrared divergences in the soft and collinear parts. We present a factorization theorem in which the infrared divergences appear only in the parton distribution functions by carefully reorganizing collinear and soft parts. The central idea is extracting the soft contributions from the collinear part to avoid double counting. Combining it with the original soft part, an infrared-finite kernel is obtained. This factorization procedure can be applied to various high-energy scattering processes.

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arXiv2012

Structure of divergences in Drell-Yan process with small transverse momentum

We consider the structure of divergences in Drell-Yan process with small transverse momentum. The factorization proof is not trivial because various kinds of divergences are intertwined in the collinear and soft parts at high orders. We prescribe a method to disentangle the divergences in the framework of the soft-collinear effective theory. The rapidity divergence is handled by introducing the $δ$ regulator in the collinear Wilson lines. The collinear part, which consists of the transverse-momentum-dependent parton distribution function (TMDPDF), is free of the rapidity divergence after the soft zero-bin subtraction. There still remains the problem of mixing between the ultraviolet and infrared divergences, which forbids the renormalization group description. We show that the mixing is cancelled by the soft function. This suggests that the collinear and soft parts should be treated as a whole in constructing a consistent factorization theorem. The renormalization group behavior of the combined collinear and soft parts is presented explicitly at one loop. We also show that the integrated PDF can be obtained by integrating the TMDPDF over the transverse momentum.

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arXiv2010

N=4 Supersymmetric Yang-Mills theory in soft-collinear effective theory

We formulate N=4 supersymmetric Yang-Mills theory in terms of soft-collinear effective theory. The effective Lagrangian in soft-collinear effective theory is developed according to the power counting by a small parameter η\sim p_{\perp}/Q. All the particles in this theory are in the adjoint representation of the SU(N) gauge group, and we derive the collinear gauge-invariant Lagrangian in the adjoint and fundamental representations respectively. We consider collinear and ultrasoft Wilson lines in this theory, and show the ultrasoft factorization of the collinear Lagrangian by redefining the collinear fields with the use of the ultrasoft Wilson lines. The vertex correction for a vector fermion current at one loop is explicitly presented as an example to illustrate how the computation is performed in the effective theory.

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arXiv2010

Endpoint behavior of high-energy scattering cross sections

In high-energy processes near the endpoint, there emerge new contributions associated with spectator interactions. Away from the endpoint region, these new contributions are suppressed compared to the leading contribution, but the leading contribution becomes suppressed as we approach the endpoint and the new contributions become comparable. We present how the new contributions scale as we reach the endpoint and show that they are comparable to the suppressed leading contributions in deep-inelastic scattering by employing a power counting analysis. The hadronic tensor in deep-inelastic scattering is shown to factorize including the spectator interactions, and it can be expressed in terms of the lightcone distribution amplitudes of initial hadrons. We also consider the contribution of the spectator contributions in Drell-Yan processes. Here the spectator interactions are suppressed compared to double parton annihilation according to the power counting.

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arXiv2007

Transverse-momentum-dependent parton distribution function in soft-collinear effective theory

Transverse-momentum-dependent parton distribution functions are analyzed in semi-inclusive deep inelastic scattering at low transverse momentum using soft-collinear effective theory. The transverse-momentum-dependent parton distribution functions are defined on the lightcone without distorting the lightcone path nor adding additional soft Wilson lines. In this approach, the comparison between the integrated and unintegrated parton distribution functions becomes transparent. The procedure of computing radiative corrections in dimensional regularization is explained in detail, and the divergence, which is a product of infrared and ultraviolet divergence, is cancelled. The renormalization group equation for the transverse-momentum-dependent parton distribution functions is derived. It depends only on the relevant physical quantities and exhibits a nontrivial scaling behavior because the longitudinal momentum fraction and the transverse momentum are coupled in the renormalization group equation.

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arXiv2007

Possible complex annihilation and B -> K pi direct CP asymmetry

We point out that a sizable strong phase could be generated from the penguin annihilation in the soft-collinear effective theory for B meson decays. Keeping a small scale suppressed by O(Lambda/m_b), Lambda being a hadronic scale and m_b the b quark mass, in the denominators of internal particle propagators without expansion, the resultant strong phase can accommodate the data of the B^0 -> K^-+ pi^+- direct CP asymmetry. Our study reconciles the opposite conclusions on the real or complex penguin annihilation amplitude drawn in the soft-collinear effective theory and in the perturbative QCD approach based on k_T factorization theorem.

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