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1

Kleiss, R., I. Malamos, and G. van den Oord. "Majoranized Feynman rules." European Physical Journal C 64, no. 3 (September 23, 2009): 387–89. http://dx.doi.org/10.1140/epjc/s10052-009-1158-0.

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2

Gates, Evalyn I., and Kenneth L. Kowalski. "Majorana Feynman rules." Physical Review D 37, no. 4 (February 15, 1988): 938–45. http://dx.doi.org/10.1103/physrevd.37.938.

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3

ALUFFI, PAOLO, and MATILDE MARCOLLI. "ALGEBRO-GEOMETRIC FEYNMAN RULES." International Journal of Geometric Methods in Modern Physics 08, no. 01 (February 2011): 203–37. http://dx.doi.org/10.1142/s0219887811005099.

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We give a general procedure to construct "algebro-geometric Feynman rules", that is, characters of the Connes–Kreimer Hopf algebra of Feynman graphs that factor through a Grothendieck ring of immersed conical varieties, via the class of the complement of the affine graph hypersurface. In particular, this maps to the usual Grothendieck ring of varieties, defining "motivic Feynman rules". We also construct an algebro-geometric Feynman rule with values in a polynomial ring, which does not factor through the usual Grothendieck ring, and which is defined in terms of characteristic classes of singular varieties. This invariant recovers, as a special value, the Euler characteristic of the projective graph hypersurface complement. The main result underlying the construction of this invariant is a formula for the characteristic classes of the join of two projective varieties. We discuss the BPHZ renormalization procedure in this algebro-geometric context and some motivic zeta functions arising from the partition functions associated to motivic Feynman rules.
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4

Pinsky, Stephen S., and L. M. Simmons. "Feynman rules for theδexpansion." Physical Review D 38, no. 8 (October 15, 1988): 2518–25. http://dx.doi.org/10.1103/physrevd.38.2518.

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5

Wu, Tai Tsun, and Sau Lan Wu. "Failure of the Feynman R1 gauge for the standard model: An explicit example." International Journal of Modern Physics A 31, no. 04n05 (February 3, 2016): 1650028. http://dx.doi.org/10.1142/s0217751x16500287.

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The decay of the Higgs particle into two photons through a [Formula: see text] loop was calculated in a straightforward way four years ago on the basis of the standard model. This calculation was carried out in the unitary gauge. Nevertheless, all attempts to reproduce this correct answer using the Feynman rules in the [Formula: see text] gauge, or the more general [Formula: see text] gauge, have failed. In this paper, a detailed analysis is carried out to compare the unitary gauge with the [Formula: see text] gauge; through this comparison, the underlying reason is determined why the answer cannot be obtained using the Feynman rules in the [Formula: see text] gauge. This is the first example where the use of the Feynman rules in the [Formula: see text] gauge leads to an incorrect answer, and this incorrect answer cannot be ruled out by any simple argument such as gauge invariance. It means that great care must be exercised in using Feynman rules.
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6

Tikochinsky, Yoel. "Feynman rules for probability amplitudes." International Journal of Theoretical Physics 27, no. 5 (May 1988): 543–49. http://dx.doi.org/10.1007/bf00668836.

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7

Hamber, Herbert W., and Shao Liu. "Feynman rules for simplicial gravity." Nuclear Physics B 472, no. 1-2 (July 1996): 447–77. http://dx.doi.org/10.1016/0550-3213(96)00216-7.

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8

Christensen, Neil D., and Claude Duhr. "FeynRules – Feynman rules made easy." Computer Physics Communications 180, no. 9 (September 2009): 1614–41. http://dx.doi.org/10.1016/j.cpc.2009.02.018.

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9

Bounakis, Marios, and Gerasimos Rigopoulos. "Feynman rules for stochastic inflationary correlators." Journal of Cosmology and Astroparticle Physics 2020, no. 05 (May 26, 2020): 046. http://dx.doi.org/10.1088/1475-7516/2020/05/046.

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10

Lawrie, I. D. "Feynman rules for nonequilibrium field theory." Journal of Physics A: Mathematical and General 25, no. 24 (December 21, 1992): 6493–505. http://dx.doi.org/10.1088/0305-4470/25/24/005.

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11

Antonov, E. N., I. O. Cherednikov, E. A. Kuraev, and L. N. Lipatov. "Feynman rules for effective Regge action." Nuclear Physics B 721, no. 1-3 (August 2005): 111–35. http://dx.doi.org/10.1016/j.nuclphysb.2005.05.013.

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12

Galperin, A., E. Ivanov, V. Ogievetsky, and E. Sokatchev. "Harmonic supergraphs: Feynman rules and examples." Classical and Quantum Gravity 2, no. 5 (September 1, 1985): 617–30. http://dx.doi.org/10.1088/0264-9381/2/5/005.

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13

Gluza, J., and M. Zraek. "Feynman rules for Majorana-neutrino interactions." Physical Review D 45, no. 5 (March 1, 1992): 1693–700. http://dx.doi.org/10.1103/physrevd.45.1693.

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14

Andraši, A., and J. C. Taylor. "Feynman rules for Coulomb gauge QCD." Annals of Physics 327, no. 10 (October 2012): 2591–603. http://dx.doi.org/10.1016/j.aop.2012.05.011.

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15

Denner, A., H. Eck, O. Hahn, and J. Küblbeck. "Compact Feynman rules for Majorana fermions." Physics Letters B 291, no. 3 (September 1992): 278–80. http://dx.doi.org/10.1016/0370-2693(92)91045-b.

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16

Rowe, ET. "Feynman Rules for Magnetised Spin-O Bosons." Australian Journal of Physics 44, no. 4 (1991): 335. http://dx.doi.org/10.1071/ph910335.

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Solutions of the Klein-Gordon equation are given in the Landau and cylindrical gauges and these are used to calculate explicit forms of the vertex function. From an S-matrix expansion analogous to the spin-i case we obtain the Feynman rules for magnetised spin-O particles: the major differences between the spin-i and spin-O cases are the explicit forms of the respective vertex functions and the addition of a two-photon vertex in the spin-O case. This additional vertex makes possible a whole new class of Feynman diagrams.
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17

Dūdėnas, Vytautas, and Thomas Gajdosik. "Feynman rules for Weyl spinors with mixed Dirac and Majorana mass terms." Lithuanian Journal of Physics 56, no. 3 (October 17, 2016): 149–63. http://dx.doi.org/10.3952/physics.v56i3.3364.

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We present a basic formalism for using the Weyl spinor notation in Feynman rules. We focus on Weyl spinors with mixed Dirac and Majorana mass terms. To clarify the definitions we derive the Feynman rules from the path integral and present two examples: loop corrections for a fermion propagator and a tree level analysis of a seesaw toy model.
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18

Belhaj Mohamed, Mohamed. "Doubling bialgebras of graphs and Feynman rules." Confluentes Mathematici 8, no. 1 (September 27, 2016): 3–30. http://dx.doi.org/10.5802/cml.26.

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19

Denner, A., H. Eck, O. Hahn, and J. Küblbeck. "Feynman rules for fermion-number-violating interactions." Nuclear Physics B 387, no. 2 (November 1992): 467–81. http://dx.doi.org/10.1016/0550-3213(92)90169-c.

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20

Le Bellac, M., and H. Mabilat. "Real-time Feynman rules at finite temperature." Physics Letters B 381, no. 1-3 (July 1996): 262–68. http://dx.doi.org/10.1016/0370-2693(96)00604-1.

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21

Hart, A., G. M. von Hippel, R. R. Horgan, and E. H. Müller. "Automated generation of lattice QCD Feynman rules." Computer Physics Communications 180, no. 12 (December 2009): 2698–716. http://dx.doi.org/10.1016/j.cpc.2009.04.021.

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22

Cheng, Hung, and Er-Cheng Tsai. "Inconsistency of Feynman Rules Derived via Path Integration." Physical Review Letters 57, no. 5 (August 4, 1986): 511–14. http://dx.doi.org/10.1103/physrevlett.57.511.

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23

van Eijck, M. A., R. Kobes, and Ch G. van Weert. "Transformations of real-time finite-temperature Feynman rules." Physical Review D 50, no. 6 (September 15, 1994): 4097–109. http://dx.doi.org/10.1103/physrevd.50.4097.

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24

Kobes, R. "Feynman rules for response functions at thermal equilibrium." Physical Review B 45, no. 7 (February 15, 1992): 3230–35. http://dx.doi.org/10.1103/physrevb.45.3230.

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25

Cheng, Hung, and Er Cheng Tsai. "Ghostless Feynman rules in non-Abelian gauge theories." Physical Review D 34, no. 12 (December 15, 1986): 3858–62. http://dx.doi.org/10.1103/physrevd.34.3858.

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26

Parthasarathy, R. "Quantisation in a nonlinear gauge and Feynman rules." Journal of Physics A: Mathematical and General 21, no. 24 (December 21, 1988): 4593–607. http://dx.doi.org/10.1088/0305-4470/21/24/014.

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27

Gough, John. "Quantum stochastic Feynman rules and extended Wigner statistics." Journal of Physics A: Mathematical and General 31, no. 8 (February 27, 1998): 2021–30. http://dx.doi.org/10.1088/0305-4470/31/8/013.

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28

Thomas, Philipp, Christian Fleck, Ramon Grima, and Nikola Popović. "System size expansion using Feynman rules and diagrams." Journal of Physics A: Mathematical and Theoretical 47, no. 45 (October 29, 2014): 455007. http://dx.doi.org/10.1088/1751-8113/47/45/455007.

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29

Nogueira, P. "From Feynman rules to conserved quantum numbers, III." Computer Physics Communications 260 (March 2021): 107740. http://dx.doi.org/10.1016/j.cpc.2020.107740.

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30

Nogueira, P. "From Feynman rules to conserved quantum numbers, I." Computer Physics Communications 214 (May 2017): 83–90. http://dx.doi.org/10.1016/j.cpc.2017.01.025.

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31

Nogueira, P. "From Feynman rules to conserved quantum numbers, II." Computer Physics Communications 215 (June 2017): 13–19. http://dx.doi.org/10.1016/j.cpc.2017.01.027.

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32

Franke, F. "Neutralinos and Higgs Bosons in the Next-To-Minimal Supersymmetric Standard Model." International Journal of Modern Physics A 12, no. 03 (January 30, 1997): 479–533. http://dx.doi.org/10.1142/s0217751x97000529.

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The purpose of this paper is to present a complete and consistent list of the Feynman rules for the vertices of neutralinos and Higgs bosons in the Next-To-Minimal Supersymmetric Standard Model (NMSSM), which does not yet exist in the literature. The Feynman rules are derived from the full expression for the Lagrangian and the mass matrices of the neutralinos and Higgs bosons in the NMSSM. Some crucial differences between the vertex functions of the NMSSM and the Minimal Supersymmetric Standard Model (MSSM) are discussed.
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33

RADYUSHKIN, A. "QUARK COUNTING RULES: OLD AND NEW APPROACHES." International Journal of Modern Physics A 25, no. 02n03 (January 30, 2010): 502–12. http://dx.doi.org/10.1142/s0217751x10048792.

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I discuss the subject of powerlike asymptotic behavior of hadronic form factors in pre-QCD analyses of soft (Feynman/Drell-Yan) and hard (West) mechanisms, and also recent derivation of 1/Q2 asymptotics of meson form factors in AdS/QCD. At the end, I briefly comment on "light-front holography" ansatz.
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34

DAI, YUAN-BEN, CHUAN-SHENG XIONG, and WEI-DONG ZHAO. "ON STOCHASTIC QUANTIZATION OF WITTEN'S FIELD THEORY OF INTERACTING STRING." Modern Physics Letters A 02, no. 10 (October 1987): 753–59. http://dx.doi.org/10.1142/s0217732387000938.

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35

Sokolovski, Dmitri, and Alexandre Matzkin. "Wigner’s Friend Scenarios and the Internal Consistency of Standard Quantum Mechanics." Entropy 23, no. 9 (September 9, 2021): 1186. http://dx.doi.org/10.3390/e23091186.

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Wigner’s friend scenarios involve an Observer, or Observers, measuring a Friend, or Friends, who themselves make quantum measurements. In recent discussions, it has been suggested that quantum mechanics may not always be able to provide a consistent account of a situation involving two Observers and two Friends. We investigate this problem by invoking the basic rules of quantum mechanics as outlined by Feynman in the well-known “Feynman Lectures on Physics”. We show here that these “Feynman rules” constrain the a priori assumptions which can be made in generalised Wigner’s friend scenarios, because the existence of the probabilities of interest ultimately depends on the availability of physical evidence (material records) of the system’s past. With these constraints obeyed, a non-ambiguous and consistent account of all measurement outcomes is obtained for all agents, taking part in various Wigner’s Friend scenarios.
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36

CHOI, CHUL-WOO, and RICHARD J. GONSALVES. "FEYNCHOIS: A FEYNMAN DIAGRAM GENERATOR." International Journal of Modern Physics E 17, no. 05 (May 2008): 940–64. http://dx.doi.org/10.1142/s0218301308010283.

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A Feynman diagram generator, named FeynChois, is described. It provides the user with a full GUI (Graphical User Interface) environment which enables the generation diagrams automatically with several mouse operations. The diagram generator is built on an Application Programming Interface (API) called ViewableBeans which provides a framework for programming graphically representable objects. We also present a means for describing Feynman rules in a computer friendly manner using the XML (Extensible Markup Language) format.
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37

Egorov, Vadim, and Timofei Rusalev. "Quantum field-theoretical descriprion of neutrino oscillations in T2K experiment." EPJ Web of Conferences 222 (2019): 03002. http://dx.doi.org/10.1051/epjconf/201922203002.

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We consider neutrino oscillations in the T2K experiment using a new quantum field-theoretical approach to the description of processes passing at finite space-time intervals. It is based on the Feynman diagram technique in the coordinate representation, supplemented by modified rules of passing to the momentum representation. Effectively this leads to the Feynman propagators in the momentum representation being modified, while the rest of the Feynman rules remain unchanged. The approach does not make use ofwave packets, the initial and final particle states are described by plane waves, which essentially simplifies the calculations. The oscillation fading out due to momentum distribution of the initial particles is taken into account. The obtained results reproduce the predictions of the standard description and confirm that the far detector position corresponds to the first minimum for muon production probability and the first maximum for electron production probability.
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38

Kaneko, T. "A package of generating Feynman rules in GRACE system." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 502, no. 2-3 (April 21, 2003): 555–57. http://dx.doi.org/10.1016/s0168-9002(03)00500-x.

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39

Furnstahl, R. J., and Brian D. Serot. "Covariant Feynman rules at finite temperature: Time-path formulation." Physical Review C 44, no. 5 (November 1, 1991): 2141–74. http://dx.doi.org/10.1103/physrevc.44.2141.

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40

Takeda, Shinji. "Automatic generation of Feynman rules in the Schrödinger functional." Nuclear Physics B 811, no. 1-2 (April 2009): 36–65. http://dx.doi.org/10.1016/j.nuclphysb.2008.11.022.

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41

De Doncker, E., A. Almulihi, and F. Yuasa. "Transformed Lattice Rules for Feynman Loop Integrals on GPUs." Journal of Physics: Conference Series 1136 (December 2018): 012002. http://dx.doi.org/10.1088/1742-6596/1136/1/012002.

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42

Cheon, Il-Tong. "Photon Propagator in Finite Space and Modified Feynman Rules." Journal of the Physical Society of Japan 61, no. 5 (May 15, 1992): 1535–38. http://dx.doi.org/10.1143/jpsj.61.1535.

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43

Jones, Bradley, and Karen Yeats. "Tree hook length formulae, Feynman rules and B-series." Annales de l’Institut Henri Poincaré D 2, no. 4 (2015): 413–30. http://dx.doi.org/10.4171/aihpd/22.

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44

Chan, Hue Sun. "Temporal-gauge finite-time Feynman rules and Gauss’s law." Physical Review D 34, no. 8 (October 15, 1986): 2433–39. http://dx.doi.org/10.1103/physrevd.34.2433.

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45

Burnel, A. "Spacelike axial-gauge Feynman rules: A consistent nonambiguous derivation." Physical Review D 36, no. 6 (September 15, 1987): 1846–51. http://dx.doi.org/10.1103/physrevd.36.1846.

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46

Zwiebach, Barton. "A note on covariant Feynman rules for closed strings." Physics Letters B 213, no. 1 (October 1988): 25–29. http://dx.doi.org/10.1016/0370-2693(88)91040-4.

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47

Hart, A., G. M. von Hippel, R. R. Horgan, and L. C. Storoni. "Automatically generating Feynman rules for improved lattice field theories." Journal of Computational Physics 209, no. 1 (October 2005): 340–53. http://dx.doi.org/10.1016/j.jcp.2005.03.010.

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48

ABE, MITSUO. "WIGHTMAN FUNCTIONS IN THE COVARIANT OPERATOR FORMALISM AND THE OSTENDORF RULES." International Journal of Modern Physics A 08, no. 17 (July 10, 1993): 2895–914. http://dx.doi.org/10.1142/s0217751x9300117x.

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The Ostendorf rules, which generalize Feynman rules for τ functions to Wightman functions, are discussed in the light of the consistency with the operator solution and the energy-positivity condition (or the spectral condition). For the exactly solvable model called the one-loop model, it is shown that the Ostendorf rules are strictly justified.
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49

ABECASIS, C., and O. S. ZANDRON. "DIAGRAMMATICS AND FEYNMAN RULES IN THE LAGRANGIAN THEORY BASED ON THE spl(2,1) GRADED ALGEBRA." International Journal of Modern Physics B 21, no. 01 (January 10, 2007): 97–115. http://dx.doi.org/10.1142/s0217979207035881.

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From the path-integral method, the diagrammatics and Feynman rules for the Lagrangian theory based on the spl(2,1) graded algebra are constructed. The first-order Lagrangian we have obtained is written in terms of the graded Hubbard operators. By using functional techniques, the correlation generating functional is given in terms of the proper effective Lagrangian of the model. Once the Feynman rules, propagators and vertices were found, a physical discussion about the free propagators is given. Finally, the expressions of the boson self-energy and the renormalized boson propagator are used to study the hole effects on the magnetic properties of the high-T c cuprates.
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50

Wang, Zhi-Gang. "Two-particle contributions and nonlocal effects in the QCD sum rules for the axial vector tetraquark candidate Zc(3900)." International Journal of Modern Physics A 35, no. 24 (August 24, 2020): 2050138. http://dx.doi.org/10.1142/s0217751x20501389.

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In this article, we study the [Formula: see text] with the QCD sum rules in details by including the two-particle scattering state contributions and nonlocal effects between the diquark and antidiquark constituents. The two-particle scattering state contributions cannot saturate the QCD sum rules at the hadron side, the contribution of the [Formula: see text] plays an unsubstitutable role, we can saturate the QCD sum rules with or without the two-particle scattering state contributions. If there exists a repulsive barrier or spatial distance between the diquark and antidiquark constituents, the Feynman diagrams can be divided into the factorizable and nonfactorizable diagrams. The factorizable diagrams consist of two-colored clusters and lead to a stable tetraquark state. The nonfactorizable Feynman diagrams correspond to the tunneling effects, which play a minor important role in the QCD sum rules, and are consistent with the small width of the [Formula: see text]. It is feasible to apply the QCD sum rules to study the tetraquark states, which begin to receive contributions at the order [Formula: see text], not at the order [Formula: see text].
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