Visualization of internal forces inside the proton in a classical relativistic model
DOI:
https://doi.org/10.31349/SuplRevMexFis.3.0308090Keywords:
Energy-momentum tensor, D-term, classical modelAbstract
A classical model of a stable particle of finite size is studied. The model parameters can be chosen such that the described particle has the mass and radius of a proton. Using the energy-momentum tensor (EMT), we show how the presence of long-range forces alters some notions taken for granted in short-range systems. We focus our attention on the D-term form factor. The important conclusion is that a more careful definition of the D-term may be required when long-range forces are present.
References
Mira Varma and Peter Schweitzer. Effects of long-range forces on the D-term and the energy-momentum structure. Phys. Rev.
D, 102(1):014047, 2020.
Iwo Białynicki Birula. Simple relativistic model of a finite size particle. Phys. Lett. A, 182:346–352, 1993.
I. Yu. Kobzarev and L. B. Okun. Gravitational Interaction of Fermions. Zh. Eksp. Teor. Fiz., 43:1904–1909, 1962.
H. Pagels. Energy-Momentum Structure Form Factors of Particles. Phys. Rev., 144:1250–1260, 1966.
X.-D. Ji. Off forward parton distributions. J. Phys. G, 24:1181–1205, 1998.
A. V. Radyushkin. Generalized parton distributions. 10 2000.
K. Goeke, M. V. Polyakov, and M. Vanderhaeghen. Hard exclusive reactions and the structure of hadrons. Prog. Part. Nucl. Phys., 47:401–515, 2001.
M. Diehl. Generalized parton distributions. Phys. Rept., 388:41–277, 2003.
A. V. Belitsky and A. V. Radyushkin. Unraveling hadron structure with generalized parton distributions. Phys. Rept., 418:1–387, 2005.
S. Boffi and B. Pasquini. Generalized parton distributions and the structure of the nucleon. Riv. Nuovo Cim., 30(9):387–448, 2007.
M. V. Polyakov and C. Weiss. Skewed and double distributions in pion and nucleon. Phys. Rev. D, 60:114017, 1999.
M. V. Polyakov. Generalized parton distributions and strong forces inside nucleons and nuclei. Phys. Lett. B, 555:57–62, 2003.
M. V. Polyakov and P. Schweitzer. Forces inside hadrons: pressure, surface tension, mechanical radius, and all that. Int. J. Mod. Phys. A, 33(26):1830025, 2018.
C. Lorc ́e, Herv ́e Moutarde, and A. P. Trawi ́nski. Revisiting the mechanical properties of the nucleon. Eur. Phys. J. C, 79(1):89,
A. Freese and G. A. Miller. Forces within hadrons on the light front. Phys. Rev. D, 103:094023, 2021.
J. Yu. Panteleeva and M. V. Polyakov. Forces inside the nucleon on the light front from 3D Breit frame force distributions: Abel tomography case. Phys. Rev. D, 104(1):014008, 2021.
S. Kumano, Q.-T. Song, and O. V. Teryaev. Hadron tomography in meson-pair production and gravitational form factors. PoS, SPIN2018:074, 2019.
V. D. Burkert, L. Elouadrhiri, and F. X. Girod. The pressure distribution inside the proton. Nature, 557(7705):396–399, 2018.
K. Kumeriˇcki. Measurability of pressure inside the proton. Nature, 570(7759):E1–E2, 2019.
V. D. Burkert, L. Elouadrhiri, and F. X. Girod. Determination of shear forces inside the proton. 4 2021.
K. Goeke, J. Grabis, J. Ossmann, M. V. Polyakov, P. Schweitzer, A. Silva, and D. Urbano. Nucleon form-factors of the energy momentum tensor in the chiral quark-soliton model. Phys. Rev. D, 75:094021, 2007.
K. Goeke, J. Grabis, J. Ossmann, P. Schweitzer, A. Silva, and D. Urbano. The pion mass dependence of the nucleon formfactors of the energy momentum tensor in the chiral quark-soliton model. Phys. Rev. C, 75:055207, 2007.
C. Cebulla, K. Goeke, J. Ossmann, and P. Schweitzer. The Nucleon form-factors of the energy momentum tensor in the Skyrme model. Nucl. Phys. A, 794:87–114, 2007.
J.-H. Jung, U. Yakhshiev, and H.-C. Kim. Energy–momentum tensor form factors of the nucleon within a π–ρ–ω soliton model. J. Phys. G, 41:055107, 2014.
H.-C. Kim, P. Schweitzer, and U. Yakhshiev. Energy-momentum tensor form factors of the nucleon in nuclear matter. Phys. Lett. B, 718:625–631, 2012.
J.-H. Jung, U. Yakhshiev, H.-C. Kim, and P. Schweitzer. In medium modified energy-momentum tensor form factors of the
nucleon within the framework of a π-ρ-ω soliton model. Phys. Rev. D, 89(11):114021, 2014.
M. Mai and P. Schweitzer. Energy momentum tensor, stability, and the D-term of Q-balls. Phys. Rev. D, 86:076001, 2012
M. Mai and P. Schweitzer. Radial excitations of Q-balls, and their D-term. Phys. Rev. D, 86:096002, 2012.
M. Cantara, M. Mai, and P. Schweitzer. The energy-momentum tensor and D-term of Q-clouds. Nucl. Phys. A, 953:1–20, 2016.
I. E. Gulamov, E. Ya. Nugaev, A. G. Panin, and M. N. Smolyakov. Some properties of U(1) gauged Q-balls. Phys. Rev. D, 92(4):045011, 2015.
E. Ya. Nugaev and A. V. Shkerin. Review of Nontopological Solitons in Theories with U(1)-Symmetry. J. Exp. Theor. Phys., 130(2):301–320, 2020.
J. Hudson and P. Schweitzer. D term and the structure of pointlike and composed spin-0 particles. Phys. Rev. D, 96(11):114013, 2017.
J. Hudson and P. Schweitzer. Dynamic origins of fermionic D-terms. Phys. Rev. D, 97(5):056003, 2018.
P. E. Shanahan and W. Detmold. Pressure Distribution and Shear Forces inside Proton. Phys. Rev. Lett., 122(7):072003, 2019.
P. E. Shanahan and W. Detmold. Gluon gravitational form factors of the nucleon and the pion from lattice QCD. Phys. Rev. D, 99(1):014511, 2019.
I. V. Anikin. Gravitational form factors within light-cone sum rules at leading order. Phys. Rev. D, 99(9):094026, 2019.
M. J. Neubelt, A. Sampino, J. Hudson, K. Tezgin, and P. Schweitzer. Energy momentum tensor and the D-term in the bag model. Phys. Rev. D, 101(3):034013, 2020.
K. Azizi and U. ̈Ozdem. Nucleon’s energy–momentum tensor form factors in light-cone QCD. Eur. Phys. J. C, 80(2):104, 2020.
J. Yu. Panteleeva and M. V. Polyakov. Quadrupole pressure and shear forces inside baryons in the large Nclimit. Phys. Lett. B,
:135707, 2020.
J.-Y. Kim, H.-C. Kim, M. V. Polyakov, and H.-D. Son. Strong force fields and stabilities of the nucleon and singly heavy baryon Σc. Phys. Rev. D, 103(1):014015, 2021.
D. Chakrabarti, C. Mondal, A. Mukherjee, S. Nair, and X. Zhao. Gravitational form factors and mechanical properties of proton in a light-front quark-diquark model. Phys. Rev. D, 102:113011, 2020.
S. Owa, A. W. Thomas, and X. G. Wang. Effect of the pion field on the distributions of pressure and shear in the proton. 6 2021.
J. More, A. Mukherjee, S. Nair, and S. Saha. Gravitational form factors and mechanical properties of a quark at one loop in light-front Hamiltonian QCD. 12 2021.
J. F. Donoghue, B. R. Holstein, B. Garbrecht, and T. Konstandin. Quantum corrections to the Reissner-Nordstr ̈om and Kerr-Newman metrics. Phys. Lett. B, 529:132–142, 2002. [Erratum: Phys.Lett.B 612, 311–312 (2005)].
A. Metz, B. Pasquini, and S. Rodini. The gravitational form factor D(t) of the electron. Phys. Lett. B, 820:136501, 2021.
B. Kubis and U.-G. Meissner. Virtual photons in the pion formfactors and energy momentum tensor. Nucl. Phys. A, 671:332–
, 2000. [Erratum: Nucl.Phys.A 692, 647–648 (2001)]
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Mira Varma, Peter Schweitzer (Author)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Suplemento de la Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.