arXiv subjects

Yossathorn Tawabutr

Publications and source records attributed to Yossathorn Tawabutr.

At least 19 recordsLinked to original sources

arXiv2026

Constraining Proton Spin at Small $x$ with Valence Quark Model

Recently, a global analysis has been performed for longitudinal spin asymmetries in polarized deep inelastic scattering (DIS) processes, combining the polarized valence quark model with the large-$N_c \& N_f$ helicity evolution equations. With a three-fold reduction in the number of free parameters, the valence quark model results in a six-fold reduction of uncertainty for the resulting prediction of total parton spin inside the proton, when compared to previous analysis performed with traditional moderate-$x$ model inspired by Born approximation. The fit based on valence quark model predicts a positive gluon hPDF and negative $g_1$ structure function at small $x$. However, the resulting increase in the $χ^2$-statistic of the fit warrants further examination into the physical uncertainty of the valence quark model, which is a work in progress. We also summarize other possibilities of future research directions towards the end of this article.

hep-ph↗

arXiv2026

Gluonic nucleon energy correlators and fracture functions for Color Glass Condensate

Nucleon energy correlators (NECs) and fracture functions provide novel tools for probing nucleon and nuclear structure at small $x$ through measurements in the target fragmentation region (TFR) of deep inelastic scattering (DIS). We investigate gluonic NECs and fracture functions using the Color Glass Condensate effective theory at eikonal accuracy. We find that only the unpolarized and linearly polarized gluon components in an unpolarized target are nonvanishing at this order, and that both are determined by the adjoint dipole $S$-matrix. Furthermore, we show that the linearly polarized gluonic NEC $h_{1}^{t,g}$ generates a characteristic $\cos 2ϕ$ azimuthal asymmetry in the DIS energy pattern in the TFR. Unlike analogous observables in the current fragmentation region, this asymmetry is governed by the ratio of the linearly polarized gluon NEC $h_{1}^{t,g}$ to the unpolarized quark NEC $f_{1}^{q}$, making it particularly sensitive to the saturation scale. Our numerical analysis shows that this asymmetry exhibits substantial nuclear suppression, providing a novel window into the onset of gluon saturation at the future Electron-Ion Collider.

hep-ph↗

arXiv2026

Small-$x$ Asymptotics of the Leading-Twist Flavor Singlet Quark TMDs

In this paper, we investigate the small-$x$ behavior of the flavor-singlet, leading-twist quark Transverse Momentum Dependent parton distribution functions (TMDs) using the Light-Cone Operator Treatment. This formalism allows us to express TMD operators at small $x$ in terms of polarized dipole amplitudes, enabling a systematic approach to their small-$x$ evolution. We derive the evolution equations for these TMDs and solve them within the large-$N_c$ approximation under the linearized, Double-Logarithmic Approximation (DLA), where $N_c$ represents the number of quark colors. Expanding on previous work on unpolarized and helicity TMDs, we present the small-$x$ asymptotics for a comprehensive set of TMDs, including the Sivers function, helicity worm-gear, transversity, pretzelosity, Boer-Mulders, and transversity worm-gear distributions. Our results provide a complete picture of the small-$x$ asymptotic behavior for all leading-twist flavor-singlet quark TMDs. We also discuss the implications of our findings for phenomenological applications and outline potential avenues for further research, particularly in understanding non-linear effects and extending beyond the DLA and large-$N_c$ approximations.

hep-ph↗

arXiv2025

Proton spin from small-$x$ with constraints from the valence quark model

We apply the valence quark model recently calculated for polarized proton to constrain the non-perturbative initial condition for the small-$x$ helicity evolution. The remaining free parameters are constrained by performing a global analysis to the available polarized small-$x$ deep inelastic scattering data. A good description of the world data is obtained with only 8 free parameters. The model parameters are tightly constrained by the data, allowing us to predict the proton polarized structure function $g_1^p$ to be negative at small $x$. Furthermore, we obtain the small-$x$ quark and gluon spins to give a contribution $\int_{10^{-5}}^{0.1} dx \left( \frac{1}{2}ΔΣ+ ΔG \right) = 0.76 \pm 0.13$ or $1.70\pm 0.20$ to the proton spin, depending on the applied running coupling prescription.

hep-ph↗

arXiv2025

Nucleon Energy Correlators for the Odderon

We investigate the T-odd nucleon energy correlator (NEC) at small $x$ and establish its connection with the spin-dependent odderon. Probing the T-odd NEC involves measuring a single transverse spin asymmetry (SSA) for the energy pattern in the target fragmentation region in deep inelastic scattering. We find that while the inclusive energy pattern results in a vanishing SSA, a nonzero SSA emerges when restricting the measurement to charged hadrons, which are directly measured in tracking detectors. To describe this effect, we introduce the track-based NEC and evaluate its small-$x$ limit from fracture functions using the energy sum rule. The resulting SSA exhibits an opposite sign between positively and negatively charged hadrons, providing a clear experimental signature of the odderon. Furthermore, by incorporating charge weighting into the NEC, we construct a C-odd tag in the final state, eliminating potential contamination from C-even gluonic contributions. Our results demonstrate that these track-based energy-pattern observables offer a clean and sensitive probe for unveiling odderon dynamics at the future electron-ion collider.

hep-ph↗

arXiv2025

First study of polarized proton-proton scattering with small-$x$ helicity evolution

We perform a phenomenological study of helicity-dependent parton distribution functions (PDFs) using small-$x$ helicity evolution equations, incorporating for the first time single-inclusive jet production data in polarized proton-proton ($pp$) scattering at parton momentum fractions $x < 0.1$. We also simultaneously include double-longitudinal spin asymmetries in inclusive and semi-inclusive deep-inelastic scattering probing $x < 0.1$. Employing the polarized small-$x$ pure-glue calculation of $pp\to gX$ for the jet production cross section, we modify the large-$N_c\&N_f$ KPS-CTT evolution equations by setting $N_f = 0$ to replicate the large-$N_c$ (pure-glue) limit, while retaining external quark flavors for the spinor field operators. We find that the $pp$ data have a considerable impact on the helicity PDFs at small $x$, reducing their uncertainties and leading to a total quark and gluon helicity in the proton for $x < 0.1$ of $-0.04 \pm 0.23$. Combining our analysis with the a recent JAM helicity PDF analysis of the world polarized data, which includes $x > 0.1$, we find a total quark and gluon helicity contribution for $x > 10^{-7}$ of between 0.02 and 0.51.

hep-ph↗

arXiv2024

Quark and Gluon Helicity Evolution at Small $x$: Revised and Updated

We revisit the problem of small Bjorken-$x$ evolution of the gluon and flavor-singlet quark helicity distributions in the shock wave ($s$-channel) formalism. Earlier works on the subject in the same framework resulted in an evolution equation for the gluon field-strength $F^{12}$ and quark "axial current" ${\barψ}γ^+γ^5ψ$ operators (sandwiched between the appropriate light-cone Wilson lines) in the double-logarithmic approximation (DLA: summing powers of $α_s\,\ln^2(1/x)$ with $α_s$ the strong coupling constant). In this work, we observe that an important mixing of the above operators with another gluon operator, $\overleftarrow{D}^i\,{D}^i$, also sandwiched between the light-cone Wilson lines (with the repeated index $i=1,2$ summed over), was missing in the previous works. This operator has the physical meaning of the sub-eikonal (covariant) phase: its contribution to helicity evolution is shown to be proportional to another sub-eikonal operator, $D^i-\overleftarrow{D}^i$, which is related to the Jaffe-Manohar polarized gluon distribution. In this work we include this operator into small-$x$ helicity evolution, and construct a novel evolution mixing all three operators ($D^i-\overleftarrow{D}^i$, $F^{12}$, and ${\barψ}γ^+γ^5ψ$), generalizing the previous results. We also construct closed DLA evolution equations in the large-$N_c$ and large-$N_c\& N_f$ limits, with $N_c$ and $N_f$ the numbers of quark colors and flavors, respectively. Solving the large-$N_c$ equations numerically we obtain the following small-$x$ asymptotics of the quark and gluon helicity distributions $ΔΣ$ and $ΔG$, along with the $g_1$ structure function, \[ΔΣ(x,Q^2)\simΔG(x,Q^2)\sim g_1(x,Q^2)\sim\left(\frac{1}{x}\right)^{3.66\,\sqrt{\frac{α_s\,N_c}{2π}}},\] in complete agreement with the earlier work by Bartels, Ermolaev and Ryskin.

hep-ph↗

arXiv2024

Contribution to the Proton Spin Puzzle from Helicity at small Bjorken $x$

The contribution to proton helicity from the spins of quarks and gluons at small Bjorken $x$ can be conveniently studied through the small-$x$ helicity evolution. Recently, it has been employed in a global analysis that includes polarized inclusive and semi-inclusive deep-inelastic scattering measurements at small $x$. The analysis demonstrates an excellent agreement between the evolution and the data, but its predictions contain large uncertainties owing to the large number of free parameters in the initial conditions. The latest development aims to mitigate this issue by employing the valence quark model in the polarized proton target in order to replace most of the free parameters in the initial conditions by the physical information from the proton model.

hep-ph↗

arXiv2024

Polarized Dipole Scattering Amplitudes meet the Valence Quark Model

The recently revised small-$x$ helicity evolution, resumming the double-logarithmic factor, $α_s\ln^2(1/x)$, allows for the study of helicity distributions of quarks and gluons at small Bjorken $x$, corresponding to high center-of-mass energy. In this work, we calculate the moderate-$x$ initial conditions in the regime, $α_s \ln^2(1/x)\sim 1$, for the small-$x$ helicity evolution using a light-front valence quark model of the proton, which provides additional physical information about the target. The perturbative emission and absorption of a gluon by the valence quarks are also included. The results, given in Eqs. (35), provide a new set of initial conditions with a significantly reduced number of free parameters than conventional models. Consequently, the predictive power of small-$x$ helicity evolution is expected to improve once the initial conditions from this work are incorporated.

hep-ph↗

arXiv2024

Complete Next-to-Leading Order Calculation of Single Inclusive $π^0$ Production in Forward Proton-Nucleus Collisions

We present the first fully consistent calculation of inclusive $π^0$ production at forward rapidities at next-to-leading order (NLO) accuracy in proton-lead collisions at $\sqrt{s}=8.16$ TeV within the Color Glass Condensate approach. The center-of-mass energy dependence is determined by the Balitsky-Kovchegov equation with the initial condition constrained at NLO accuracy by the proton structure function measurements. We find that the LHCb data further constrain this non-perturbative input, and that both the NLO corrections to the evolution equation and to the impact factor have significant effects on the nuclear modification factor $R_{p\mathrm{Pb}}$. The complete NLO calculation is shown to be in qualitative agreement with the LHCb data, and the predictions are found to be sensitive to the details of the applied deep inelastic scattering (DIS) fit. These results demonstrate the need to perform global analyses of DIS and LHC data in order to probe gluon saturation phenomena at precision level at very small momentum fraction $x$.

hep-ph↗

arXiv2023

Global analysis of polarized DIS & SIDIS data with improved small-$x$ helicity evolution

We analyze the world polarized deep-inelastic scattering (DIS) and semi-inclusive DIS (SIDIS) data at low values of $x < 0.1$, using small-$x$ evolution equations for the flavor singlet and nonsinglet helicity parton distribution functions (hPDFs). The hPDFs for quarks, antiquarks, and gluons are extracted and evolved to lower values of $x$ to make predictions for the future Electron-Ion Collider (EIC). We improve on our earlier work by employing the more realistic large-$N_c\, \& N_f$ limit of the revised small-$x$ helicity evolution, and incorporating running coupling corrections along with SIDIS data into the fit. We find an anti-correlation between the signs of the gluon and $C$-even quark hPDFs as well as the $g_1$ structure function. While the existing low-$x$ polarized DIS and SIDIS data are insufficient to constrain the initial conditions for the polarized dipole amplitudes in the helicity evolution equations, future EIC data will allow more precise predictions for hPDFs and the $g_1$ structure function for $x$ values beyond those probed at the EIC. Using the obtained hPDFs, we discuss the contributions to the proton spin from quark and gluon spins at small $x$.

hep-ph↗

arXiv2023

Recent Developments of Small-$x$ Evolution for Quark and Gluon Helicity

Helicity of quarks and gluons inside the proton at small Bjorken $x$ is one of the missing pieces of the proton spin puzzle, with limited experimental results due to various challenges. To address the problem, we derive under the framework of color glass condensate (CGC) effective theory a renormalization group equation in rapidity for the parton helicity distributions, which resums double-logarithmic factor, $α_s\ln^2(1/x)$, with $α_s$ being the strong coupling constant. With running coupling, the equation produces results at Bjorken $x\leq 0.1$ that are consistent with the world polarized scattering data. There is an evidence for a significant parton helicity contribution from the small-$x$ region. However, the helicity estimate still contains a large uncertainty that will dramatically reduce with the upcoming measurements from the Electron-Ion Collider (EIC). Ongoing attempts to reduce the uncertainty of our helicity prediction in the medium term will also be discussed.

hep-ph↗

arXiv2023

Small-$x$ Quark and Gluon Helicity Contributions to the Proton Spin Puzzle

A small-$x$ helicity evolution has been derived in 2016-18 and received an important modification in 2022. This article discusses its general framework and summarizes the recent theoretical developments, including the asymptotic behaviors of helicity PDFs and $g_1$ structure function at small $x$. The latest fits to various polarized scattering data are also discussed. The results from this research program will provide important theoretical inputs for the future polarized small-$x$ measurements at the electron-ion collider (EIC).

hep-ph↗

arXiv2023

Single-Inclusive Particle Production from $pA$ Collision at Next-to-Leading Order

We present the first fully consistent NLO calculation of the single-inclusive forward hadron production in proton-nucleus (pA) collisions under the color glass condensate (CGC) framework. In the dilute-dense limit, the NLO cross-section can be written as a convolution of the NLO impact factor, NLO parton distribution function (PDF), NLO fragmentation function (FF) and dipole-target scattering amplitude which satisfies the NLO small-$x$ Balitsky-Kovchegov (BK) evolution. We demonstrate that, without the NLO corrections to the impact factor, we obtain a significant Cronin peak when the dipole amplitude satisfies the NLO BK equation. This would contradict the recent LHCb results. However, the Cronin peak becomes suppressed when the NLO correction to the impact factor is included. This is the main result of this work. The dependence on resummation schemes for the NLO BK evolution will also be discussed.

hep-ph↗

arXiv2023

Helicity of Quarks and Gluons at Small Bjorken $x$

The proton spin puzzle is a longstanding problem in high-energy nuclear physics: how the proton spin distributes among the spin and orbital angular momenta of the quarks and gluons inside. Two of the unresolved pieces of the puzzle are the contributions to quark and gluon spins from the region of small Bjorken $x$. This dissertation fills the gap by constructing the evolution of these quantities into the small-$x$ region using a modified dipole formalism. The dominant contributions to the evolution equations resum powers of $α_s\ln^2(1/x)$, where $α_s$ is the strong coupling constant. In general, these evolution equations do not close. However, once the large-$N_c$ or large-$N_c\& N_f$ limit is taken, they turn into a system of linear integral equations that can be solved iteratively. At large $N_c$, the evolution equations are shown to be consistent with the gluon sector of the polarized DGLAP evolution in the small-$x$ limit. We numerically solve the equations in the large-$N_c$ and large-$N_c\& N_f$ limits and obtain the exponential growth in $\ln(1/x)$ for $N_f \leq 5$, with the intercept decreasing with $N_f$. For the large-$N_c$ limit, we have $α_h = 3.66$, which agrees up to the uncertainty with the earlier work by Bartels, Ermolaev and Ryskin. Furthermore, at $N_f=6$, the asymptotic form attains an oscillation in $\ln(1/x)$ on top of the exponential growth, with the period spanning several units of rapidity. Finally, parts of the single-logarithmic corrections to the small-$x$ helicity evolution is also derived, resumming powers of $α_s\ln(1/x)$. There, the effects of the unpolarized small-$x$ evolution and the running coupling are also included for consistency. The complete single-logarithmic corrections can be derived based on the framework established here. Altogether, these equations will provide the most precise small-$x$ helicity evolution to date.

hep-ph↗

arXiv2023

Helicity Evolution at Small $x$: Revised Asymptotic Results at Large $N_c\& N_f$

We present a numerical solution of the revised version of the small-$x$ helicity evolution equations at large $N_c$ and $N_f$. (Here $N_c$ and $N_f$ are the numbers of quark colors and flavors, respectively.) The evolution equations are double-logarithmic in the Bjorken $x$ variable, resumming powers of $α_s \, \ln^2 (1/x)$ with $α_s$ the strong coupling constant. The large-$N_c \& N_f$ evolution we consider includes contributions of small-$x$ quark emissions and is thus more realistic than the large-$N_c$ one, which only involves gluon emissons. The evolution equations are written for the so-called ``polarized dipole amplitudes", which are related to the helicity distribution functions and the $g_1$ structure function. Unlike the previously reported solution of the earlier version of helicity evolution equations at large $N_c \& N_f$, our solution does not exhibit periodic oscillations in $\ln (1/x)$ for $N_f < 2 N_c$, while only showing occasional sign reversals. For $N_f = 2 N_c$, we report oscillations with $\ln (1/x)$, similar to those found earlier. We determine the intercept of our evolution for $N_f < 2 N_c$ as well as the parameters of the oscillatory behavior for $N_f = 2 N_c$. We compare our results to the existing resummation and finite-order calculations for helicity-dependent quantities in the literature.

hep-ph↗

arXiv2022

Single-Logarithmic Corrections to Small-$x$ Helicity Evolution

The small-$x$ quark helicity evolution equations at double-logarithmic order, with the kernel $\simα_s\ln^2(1/x)$, have been derived previously. In this work, we derive the single-logarithmic corrections to the equations, to order $α_s\ln(1/x)$ of the evolution kernel. The new equations include the effects of the running coupling and the unpolarized small-$x$ evolution, both of which are parametrically significant at single-logarithmic order. The large-$N_c$ and large-$N_c\& N_f$ approximations to the equation are computed. (Here, $N_c$ and $N_f$ are the numbers of quark colors and flavors, respectively.) Their solutions will provide more precise estimates of the quark helicity distribution at small $x$, contributing to the resolution of the proton spin puzzle.

hep-ph↗

arXiv2022

Helicity Evolution at Small $x$: the Single-Logarithmic Contribution

We calculate single-logarithmic corrections to the small-$x$ flavor-singlet helicity evolution equations derived recently in the double-logarithmic approximation. The new single-logarithmic part of the evolution kernel sums up powers of $α_s \ln(1/x)$, which are an important correction to the dominant powers of $α_s \ln^2(1/x)$ summed up by the double-logarithmic kernel at small values of Bjorken $x$ and with $α_s$ the strong coupling constant. The single-logarithmic terms arise separately from either the longitudinal or transverse momentum integrals. Consequently, the evolution equations we derive employing the light-cone perturbation theory simultaneously include the small-$x$ evolution kernel and the leading-order polarized DGLAP splitting functions. We further enhance the equations by calculating the running coupling corrections to the kernel.

hep-ph↗