On the infrared divergence and global colour in $$ \mathcal{N} $$ = 4 Yang-Mills theory

Ding, Su Yu; Karczmarek, Joanna L.; Semenoff, Gordon W.

doi:10.1007/jhep07(2020)228

Cited by 4 publications

(5 citation statements)

References 46 publications

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“…While the greatest source of uncertainty in the anomalous magnetic moment of the muon seems to come from hadronic contributions 42,43 it may be that our computation of the vertex function in addition to our computation of the vacuum polarization tensor 30 may have some relevance in regard to solution of the problem of the muon g -2 anomaly. //std::cout << "q_0 = " << q_0 << "\n"; q[1] = sinh(xi) * p_0 + cosh(xi) * p [1]; q[2] = p [2]; q[3] = p [3]; q_0 = omega_m(q); average_b += psi(q_0,q); //std::cout << "now q_0 = " << q_0 << "\n"; integral_b += psi(q_0, q)/p_0; integral_3 += psi(q_0,q) / (q_0* q_0 * p_0); integral_4 += partial_0_psi(q_0, q) / (q_0 * p_0);…”

Section: Discussionmentioning

confidence: 99%

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UV and IR divergence-free calculation of the vertex function at arbitrary momentum transfer

Mashford¹

2022

Preprint

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The vertex function is analyzed using covariant spectral regularization without encountering any divergence, either UV or IR. The mathematics of covariant spectral regularization for covariant matrix valued measures with one Lorentz index on open subsets of Minkowski space is described. This is then applied to the case of the vertex function and expressions for the densities associated with the vertex function in the t channel and the s channel with respect to Lebesgue measure on Minkowski space are obtained. These densities are well defined, non-divergent and analytic over their domains of definition and can be used in QFT calculations. The limit of the expression for the vertex function in the t channel at low energy and low momenta is computed resulting in the classical result for the leading order (LO) contribution to the anomalous magnetic moment of the electron. Also the density for the vertex function in the s channel is used to compute the (LO) vertex correction contribution to the high energy limit of the cross section for the process e + e − → µ + µ − without divergence or the need to consider final state radiation.

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Section: Discussionmentioning

confidence: 99%

“…Infrared divergence is a significant problem in many areas of physics, from Yang-Mills theory 3,4 , cosmology 5 and quantum gravity 6 to high energy physics 7 .…”

Section: Conclusion 36mentioning

confidence: 99%

UV and IR divergence-free calculation of the vertex function at arbitrary momentum transfer

Mashford¹

2022

Preprint

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“…IR divergence is a significant problem in many areas of physics, from Yang-Mills theory [3,4], cosmology [5] and quantum gravity [6] to high energy physics [7].…”

Section: Introductionmentioning

confidence: 99%

UV and IR divergence-free calculation of the vertex function at arbitrary values of its arguments

Mashford

2023

Preprint

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The mathematics of covariant spectral regularization for covariant matrix valued measures with one Lorentz index on open subsets of Minkowski space is described. This is then applied to the case of the vertex function and expressions for the densities associated with the vertex function in the t channel and the s channel with respect to Lebesgue measure on Minkowski space are obtained. These densities are well defined, non-divergent and analytic over their domains of definition and are obtained without using renormalization or needing to consider final state radiation. The limit of the expression for the vertex function in the t channel at low energy and low momenta is computed resulting in the classical result for the leading order (LO) contribution to the anomalous magnetic moment of the electron. Also the density for the vertex function in the s channel is used to compute the NLO vertex correction contribution to the high energy limit of the cross section for the process e+ e−→µ + µ−.

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“…Much of the structure of the IR dynamics is dictated by symmetry, independently of the details of the UV completion of the theory [1][2][3][4][5][6][7][8][9][10][11][12]. It is important to provide measures of the entanglement between the hard and soft degrees of freedom [13][14][15][16][17][18][19], and to uncover implications for the structure of the S-matrix (in both gauge theories and gravity) [20][21][22][23][24], black hole physics [25][26][27][28][29][30][31] and holography [32][33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Soft photon radiation and entanglement

2021

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We study the entanglement between soft and hard particles produced in generic scattering processes in QED. The reduced density matrix for the hard particles, obtained via tracing over the entire spectrum of soft photons, is shown to have a large eigenvalue, which governs the behavior of the Renyi entropies and of the non-analytic part of the entanglement entropy at low orders in perturbation theory. The leading perturbative entanglement entropy is logarithmically IR divergent. The coefficient of the IR divergence exhibits certain universality properties, irrespectively of the dressing of the asymptotic charged particles and the detailed properties of the initial state. In a certain kinematical limit, the coefficient is proportional to the cusp anomalous dimension in QED. For Fock basis computations associated with two-electron scattering, we derive an exact expression for the large eigenvalue of the density matrix in terms of hard scattering amplitudes, which is valid at any finite order in perturbation theory. As a result, the IR logarithmic divergences appearing in the expressions for the Renyi and entanglement entropies persist at any finite order of the perturbative expansion. To all orders, however, the IR logarithmic divergences exponentiate, rendering the large eigenvalue of the density matrix IR finite. The all-orders Renyi entropies (per unit time, per particle flux), which are shown to be proportional to the total inclusive cross-section in the initial state, are also free of IR divergences. The entanglement entropy, on the other hand, retains non-analytic, logarithmic behavior with respect to the size of the box (which provides the IR cutoff) even to all orders in perturbation theory.

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On the infrared divergence and global colour in $$ \mathcal{N} $$ = 4 Yang-Mills theory

Cited by 4 publications

References 46 publications

UV and IR divergence-free calculation of the vertex function at arbitrary momentum transfer

UV and IR divergence-free calculation of the vertex function at arbitrary momentum transfer

UV and IR divergence-free calculation of the vertex function at arbitrary values of its arguments

Soft photon radiation and entanglement

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