Kemal Tezgin

Physicist

Research

My research focuses on exploring theoretical and computational tools to delve more into the rich structure of strong interactions. In particular, I am interested in the three-dimensional distributions of energy, momentum, angular momentum, pressure, and shear force of quarks and gluons inside the nucleon. These distributions enable one to visualize the nucleon in three dimensions and help to resolve some of the long-standing mysteries in QCD, including the spin puzzle and the source of nucleon mass. Another portion of my research focuses on generalized parton distribution functions (GPDs), which reveal correlations between collinear momenta and the distribution of partons on the transverse plane to its motion, alongside transverse momentum dependent parton distribution functions (TMDs), which describe the three-dimensional momentum distribution of partons within the nucleon.

One part of my research is on obtaining those three-dimensional distributions by using physically motivated models of strong interactions, such as the chiral quark-soliton model and the MIT bag model. Another part of my research is to obtain model-independent relations in these subjects. The following sections describe some my research in more detail.

1. Energy Momentum Tensor and the D-term in the Bag Model

The energy-momentum tensor form factors (EMT FFs) contain a wealth of information about the nucleon. Fundamental properties of the nucleon, such as mass and spin, are encoded in those form factors. Recently, there has been a growing interest in obtaining another fundamental property of the matter: the D-term, which is also encoded in those form factors. At the density level, the EMT FFs carry information on the distributions of energy, angular momentum, pressure, and shear force inside the nucleon [1, 2].

In [3] and [4], we have computed the EMT FFs and their associated 3D and 2D densities, such as energy, angular momentum, pressure, and shear force inside the nucleon, in the MIT bag model [5], in the large-Nc limit. The consistency of the bag model allowed us to test in a lucid way many theoretical concepts related to EMT FFs and their associated densities.

2. Monopole and Quadrupole Contributions to the Angular Momentum Density

There has been a consensus in the literature that the angular momentum density inside the nucleon can be decomposed into monopole and quadrupole contributions [6]. In [7], we have shown that those two contributions are intertwined with each other and can be characterized by the same function. Thus, the nucleon angular momentum density can be described either by the monopole or the quadrupole contribution alone. The relation between the two contributions is a model-independent result, and our bag model study [3] respects this relation, which gives us further evidence on the consistency of the model.

3. Chiral-odd GPDs in the Bag Model

In addition to PDFs, which describe parton distributions of a fast-moving hadron along the collinear direction, GPDs [8, 9] carry information of partons inside the nucleon in three dimensions [10]. Moreover, GPDs give access to the angular momentum carried by quarks and gluons inside the nucleon [8]. In [11], we have obtained chiral-odd, twist-2 GPDs in the bag model. Furthermore, in a subsequent work to appear, we have analyzed the large-Nc behavior of chiral-odd GPDs, which gives us access to model-independent information on the scaling behavior of those GPDs.

4. EpIC Monte Carlo Event Generator for Exclusive Processes

There is a continuous need for effective simulation tools for exclusive processes, particularly to assess the impact of future data on visualizing the nucleon in three dimensions. We developed the EpIC Monte Carlo event generator [12] to partially fulfill this demand. The EpIC event generator leverages the PARTONS framework [13], offering a variety of model options and a flexible structure. Additionally, it incorporates second-order radiative corrections using the collinear approximation. As a result, EpIC provides a comprehensive set of features that enable deeper studies of nucleon structure through impact studies [14] at future electron-ion colliders.

5. Semi-inclusive Deep Inelastic Scattering in Wandzura-Wilczek-type Approximation

The Wandzura-Wilczek-type approximation, which consists in systematically assuming that antiquark-gluon-quark correlators are much smaller than antiquark-quark correlators [15], is a useful and physically motivated approximation to soften the complexity of describing semi-inclusive deep inelastic scattering (SIDIS) cross section in terms of partonic degrees of freedom. Up to subleading-twist accuracy, and under the validity of factorization at subleading-twist, the SIDIS cross section can be expressed in terms of 24 TMDs and 24 fragmentation functions [16].

As a result of the approximation, certain relations among TMDs and fragmentation functions emerge and the leading contributions come from 6 TMDs and 2 fragmentation functions. In [17], we have systematically analyzed the consequences of the approximation by employing the Gaussian Ansatz for transverse momentum dependence of the TMDs and fragmentation functions. We observed that the approximation works reasonably well for leading-twist asymmetries. However, for certain subleading-twist asymmetries, the approximation is not able to capture the dynamics, which hints at sizable antiquark-gluon-quark correlations in those structure functions.

6. Applications of Resurgence Theory in Physics

Significant progress has been made in understanding the relationship between the perturbative energy expansion around a potential minimum and the non-perturbative tunneling effects between degenerate vacua in quantum mechanics [18, 19]. Much of this progress is due to resurgence theory [20], which asserts that asymptotic expansions around different saddle points systematically affect each other. A direct implication of this idea in physics has been discussed in [21, 22], where a direct relationship was found between the early terms of a perturbative energy expansion and the early terms of instanton/anti-instanton fluctuation terms for stable genus-one potentials, such as the double well and sine-Gordon potentials. The relationship between those two early terms is commonly referred to as perturbative/non-perturbative (P/NP) relation.

In our work [23, 24], we demonstrated that the P/NP relation also applies to non-stable genus-one potentials. For example, in the case of the anharmonic cubic potential, we calculated the decay rate of a particle at the potential minimum using only the perturbative energy expansion around that point. More recently [25], we unified the cubic and quartic anharmonic oscillators under a single potential with a deformation parameter, showing that their resurgent structures—specifically, the connection between perturbative expansions around the perturbative saddle and non-perturbative saddles—can be described by a parameter-dependent first-order partial differential equation. In our latest work [26], we studied the effects of the deformation parameter on generic genus-one potentials, which can be expressed in terms of Jacobi elliptic functions, and extended the P/NP relation to any elliptic curve. The new formulation accounts for the non-vanishing residue effects of the momentum at its pole, thereby considering the additional independent cycle in the topology of the space where the particle’s dynamics are defined.

References

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  2. M. V. Polyakov and P. Schweitzer, Int. J. Mod. Phys. A 33, no. 26, 1830025 (2018).
  3. M. Neubelt, A. Sampino, J. Hudson, K. Tezgin, and P. Schweitzer, Phys. Rev. D 101, 3, 034013 (2020).
  4. C. Lorcé, P. Schweitzer, and K. Tezgin, Phys. Rev. D 106, no. 1, 014012 (2022).
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  6. C. Lorcé, L. Mantovani, and B. Pasquini, Phys. Lett. B 776, 38 (2018).
  7. P. Schweitzer and K. Tezgin, Phys. Lett. B 796, 47 (2019).
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  11. K. Tezgin, B. Maynard, and P. Schweitzer, Phys. Rev. D 110, no. 5, 5 (2024).
  12. E.C. Aschenauer et al., Eur. Phys. J. C 82, no. 9, 819 (2022).
  13. B. Berthou et al., Eur. Phys. J. C 78, no. 6, 478 (2018).
  14. E.C. Aschenauer et al., to appear.
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  22. G. V. Dunne and M. Unsal, Phys. Rev. D 89, no. 10, 105009 (2014).
  23. I. Gahramanov and K. Tezgin, Phys. Rev. D 93, no. 6, 065037 (2016).
  24. I. Gahramanov and K. Tezgin, Int. J. Mod. Phys. A 32, no. 05, 1750033 (2017).
  25. A. Çavusoglu, C. Kozçaz, and K. Tezgin, arXiv:2311.17850.
  26. A. Çavusoglu, C. Kozçaz, and K. Tezgin, arXiv:2408.02628.