External Fermions Research Articles

Two-loop vertices with vacuum polarization insertion

We present the analytic evaluation of the second-order corrections to the massive form factors, due to two-loop vertex diagrams with a vacuum polarization insertion, with exact dependence on the external and internal fermion masses, and on the squared momentum transfer. We consider vector, axial-vector, scalar and pseudoscalar interactions between the external fermion and the external field. After renormalization, the finite expressions of the form factors are expressed in terms of polylogarithms up to weight three.

Loops in AdS: from the spectral representation to position space. Part II

We continue the study of AdS loop amplitudes in the spectral representation and in position space. We compute the finite coupling 4-point function in position space for the large-N conformal Gross Neveu model on AdS3. The resummation of loop bubble diagrams gives a result proportional to a tree-level contact diagram. We show that certain families of fermionic Witten diagrams can be easily computed from their companion scalar diagrams. Thus, many of the results and identities of [1] are extended to the case of external fermions. We derive a spectral representation for ladder diagrams in AdS. Finally, we compute various bulk 2-point correlators, extending the results of [1].

UV sensitivity of the axion mass from instantons in partially broken gauge groups

We examine the contribution of small instantons to the axion mass in various UV completions of QCD. We show that the reason behind the potential dominance of such contributions is the non-trivial embedding of QCD into the UV theory. The effects from instantons in the partially broken gauge group appear as “fractional instanton” corrections in the effective theory. These will exhibit unusual dependences on the various scales in the problem whenever the index of embedding is non-trivial. We present a full one-instanton calculation of the axion mass in the simplest product group models, carefully keeping track of numerical prefactors. Rather than using a ’t Hooft operator approximation we directly evaluate the contributions to the vacuum bubble, automatically capturing the effects of closing up external fermion lines with Higgs loops. This approach is manifestly finite and removes the uncertainty associated with introducing a cutoff scale for the Higgs loops. We verify that the small instantons may dominate over the QCD contribution for very high breaking scales and at least three group factors.

On all-order higher-point Dp–D̄p̄ effective actions

In this paper we derive a class of contributions to all orders in α′ to the effective action of D-brane-anti D-brane systems in Type II String Theory, considering an amplitude involving a closed-string Ramond-Ramond state and four open-string states: two tachyons, a scalar and a gauge boson. This type of amplitude arises in both Type IIA and Type IIB strings, and reveals a number of new effective couplings. Furthermore, we derive a series representation for the result that goes beyond a factorized limit that was recently studied, and which is expected to apply to more general six-point amplitudes of superstrings, including external fermions.

Damping rate of a fermion in ultradegenerate chiral matter

We compute the damping rate of a fermion propagating in a chiral plasma when there is an imbalance between the densities of left- and right-handed fermions, after generalizing the hard thermal loop resummation techniques for these systems. In the ultradegenerate limit, for very high energies the damping rate of this external fermion approaches a constant value. Closer to the two Fermi surfaces, however, we find that the rate depends on both the energy and the chirality of the fermion, being higher for the predominant chirality. This comes out as a result of its scattering with the particles of the plasma, mediated by the exchange of Landau damped photons. In particular, we find that the chiral imbalance is responsible for a different propagation of the left and right circular polarised transverse modes of the photon, and that a chiral fermion interacts differently with these two transverse modes. We argue that spontaneous radiation of energetic fermions is kinematically forbidden, and discuss the time regime where our computation is valid.

Skewed Sudakov regime, harmonic numbers, and multiple polylogarithms

On the example of massless QED we study an asymptotic of the vertex when only one of the two virtualities of the external fermions is sent to zero. We call this regime the skewed Sudakov regime. First, we show that the asymptotic is described with a single form factor, for which we derive a linear evolution equation. The linear operator involved in this equation has a discrete spectrum. Its eigenfunctions and eigenvalues are found. The spectrum is a shifted sequence of harmonic numbers. With the spectrum found, we represent the expansion of the asymptotic in the fine structure constant in terms of multiple polylogarithms. Using this representation, the exponentiation of the doubly logarithmic corrections of the Sudakov form factor is recovered. It is pointed out that the form factor of the skewed Sudakov regime is growing with the virtuality of a fermion decreasing at a fixed virtuality of another fermion.

Planar two-loop five-parton amplitudes from numerical unitarity

We compute a complete set of independent leading-color two-loop five-parton amplitudes in QCD. These constitute a fundamental ingredient for the next-to-next-to-leading order QCD corrections to three-jet production at hadron colliders. We show how to consistently consider helicity amplitudes with external fermions in dimensional regularization, allowing the application of a numerical variant of the unitarity method. Amplitudes are computed by exploiting a decomposition of the integrand into master and surface terms that is independent of the parton type. Master integral coefficients are numerically computed in either finite-field or floating-point arithmetic and combined with known analytic master integrals. We recompute leading-color two-loop four-parton amplitudes as a check of our implementation. Results are presented for all independent four- and five-parton processes including contributions with massless closed fermion loops.

Fermionic one-loop amplitudes of the RNS superstring

We investigate massless n-point one-loop amplitudes of the open RNS superstring with two external fermions and determine their worldsheet integrands. The contributing correlation functions involving spin-1/2 and spin-3/2 operators from the fermion vertices are evaluated to any multiplicity. Moreover, we introduce techniques to sum these correlators over the spin structures of the worldsheet fermions such as to manifest all cancellations due to spacetime supersymmetry. These spin sums require generalizations of the Riemann identities among Jacobi theta functions, and the results can be expressed in terms of doubly-periodic functions known from the mathematics literature on elliptic multiple zeta values. On the boundary of moduli space, our spin-summed correlators specialize to compact representations of fermionic one-loop integrands for ambitwistor strings.

Higher dimensional generalizations of the SYK model

We discuss a 1+1 dimensional generalization of the Sachdev-Ye-Kitaev model. The model contains N Majorana fermions at each lattice site with a nearest-neighbour hopping term. The SYK random interaction is restricted to low momentum fermions of definite chirality within each lattice site. This gives rise to an ordinary 1+1 field theory above some energy scale and a low energy SYK-like behavior. We exhibit a class of low-pass filters which give rise to a rich variety of hyperscaling behaviour in the IR. We also discuss another set of generalizations which describes probing an SYK system with an external fermion, together with the new scaling behavior they exhibit in the IR.

Vacuum effects in magnetic field with with account for fermion anomalous magnetic moment and axial-vector interaction

We study vacuum polarization effects in the model of Dirac fermions with additional interaction of an anomalous magnetic moment with an external magnetic field and fermion interaction with an axial-vector condensate. The proper time method is used to calculate the one-loop vacuum corrections with consideration for different configurations of the characteristic parameters of these interactions.

Symmetries and Feynman rules for the Ramond sector in open superstring field theory

We examine the symmetries of the action suppelemented by the constraint in the WZW-type open superstring field theory. It is found that this pseudo-action has additional symmetries provided we impose the constraint after the transformation. Respecting these additional symmetries, we propose a prescription for the new Feynman rules for the Ramond sector. It is shown that the new rules reproduce the well-known on-shell four- and five-point amplitudes with external fermions.

The Ramond sector of heterotic string field theory

We attempt to construct the full equations of motion for the Neveu–Schwarz and the Ramond sectors of the heterotic string field theory. Although they are also non-polynomial in the Ramond string field |$\Psi $|⁠, we can construct them order by order in |$\Psi $|⁠. Their explicit forms with the gauge transformations are given up to the next-to-next-to-leading order in |$\Psi $|⁠. We also determine a subset of the terms to all orders. By introducing an auxiliary Ramond string field |$\Xi $|⁠, we construct a covariant action supplemented with a constraint, which should be imposed on the equations of motion. We propose the Feynman rules and show how they reproduce well-known physical four-point amplitudes with external fermions.

Mass corrections to flavor-changing fermion-graviton vertices in the standard model

In a previous study, the flavor-changing fermion-graviton interactions have been analyzed in the framework of the standard model, where analytical results for the relevant form factors were obtained at the leading order in the external fermion masses. These interactions arise at one-loop level by the charged electroweak corrections to the fermion-graviton vertex, when the off-diagonal flavor transitions in the corresponding charged weak currents are taken into account. Due to the conservation of the energy-momentum tensor, the corresponding form factors turn out to be finite and gauge invariant when external fermions are on-shell. Here we extend this previous analysis by including the exact dependence on the external fermion masses. Complete analytical results are provided for all the relevant form factors to the flavor-changing fermion-graviton transitions.

Correspondence between classical and pseudoclassical descriptions of the spin degree of freedom of a relativistic particle in an external field

A generalization of the Lagrangian description of a relativistic color charged spinning particle interacting with external non-Abelian gauge and fermion fields, previously introduced by the authors, is proposed which takes into account the time-varying spin degree of freedom of the particle. For the case under consideration, the degree of freedom is described by a classical commuting Dirac spinor ψα . This spinor has been mapped to new (anticommuting) variables: a pseudovector ξμ , a pseudoscalar ξ5, a pseudotensor *ζμν, a vector $ {{\overset{\scriptscriptstyle\frown}{\xi}}_{\mu}} $ ,and a scalar $ {{\overset{\scriptscriptstyle\frown}{\xi}}_5} $ . The first two of them are usually used in a pseudoclassical description of the spin degree of freedom of a massive spin 1/2 particle. The mapping $ \left( {{\psi_{\alpha}},\;{{\bar{\psi}}_{\alpha}}} \right)\Leftrightarrow \left( {{\xi_{\mu}},\;{\xi_5},\ldots } \right) $ has been examined for oneoneness. It has been shown that to attain one-oneness, it is necessary either to narrow the class of the initial spinor ψα to that of Majorana particles or to double the number of variables in the set of tensors (ξμ ξ5 *ζμν $ {{\overset{\scriptscriptstyle\frown}{\xi}}_{\mu}} $ $ {{\overset{\scriptscriptstyle\frown}{\xi}}_5} $ ).

Non-Perturbative Self-Consistent Model in SU(N) Gauge Field Theory

Non-perturbative quasi-classical model in a gauge theory with the Yang-Mills (YM) field is developed. The self-consistent solutions of the Dirac equation in the SU (N ) gauge field, which is in the eikonal approximation, and the Yang-Mills (YM) equations containing the external fermion current are solved. It shown that the developed model has the self-consistent solutions of the Dirac and Yang-Mills equations at N ≥ 3. In this way, the solutions take place provided that the fermion and gauge fields exist simultaneously, so that the fermion current completely compensates the current generated by the gauge field due to self-interaction of it.

External leg corrections in the unitarity method

Unitarity cuts diverge in the channel of a single massive external fermion. We propose an off-shell continuation of the momentum that allows a finite evaluation of the unitarity cuts. If the cut is taken with complete amplitudes on each side, our continuation and expansion around the on-shell configuration produces the finite contribution to the bubble coefficient. Finite parts in the expansion of the external leg counterterms must be included explicitly as well.

One-loop QCD and Higgs bosons to partons processes using six-dimensional helicity and generalized unitarity

We combine the six-dimensional helicity formalism of Cheung and O'Connell with D-dimensional generalized unitarity to obtain a new formalism for computing one-loop amplitudes in dimensionally regularized QCD. With this procedure, we simultaneously obtain the pieces that are constructible from four-dimensional unitarity cuts and the rational pieces that are missed by them, while retaining a helicity formalism. We illustrate the procedure using four- and five-point one-loop amplitudes in QCD, including examples with external fermions. We also demonstrate the technique's effectiveness in next-to-leading order QCD corrections to Higgs processes by computing the next-to-leading order correction to the Higgs plus three positive-helicity gluons amplitude in the large top-quark mass limit.

Two-loop QED operator matrix elements with massive external fermion lines

The two-loop massive operator matrix elements for the fermionic local twist-2 operators with external massive fermion lines in Quantum Electrodynamics (QED) are calculated up to the constant terms in the dimensional parameter ε = D − 4 . We investigate the hypothesis of Berends et al. (1988) [1] that the 2-loop QED initial state corrections to e + e − annihilation into a virtual neutral gauge boson, except power corrections of O ( ( m f 2 / s ) k ) , k ⩾ 1 , can be represented in terms of these matrix elements and the massless 2-loop Wilson coefficients of the Drell–Yan process.

Chromoelectric dipole moment of the top quark in models with vectorlike multiplets

The chromoelectric dipole moment of the top quark is calculated in a model with a vector like multiplet which mixes with the third generation in an extension of the MSSM. Such mixings allow for new CP violating phases. Including these new CP phases, the chromoelectric dipole moment that generates an electric dipole of the top in this class of models is computed. The top chromoelectric dipole moment operator arises from loops involving the exchange of the W, the Z as well as from the exchange involving the charginos, the neutralinos, the gluino, and the vector like multiplet and their superpartners. The analysis of the chromoelectric dipole moment operator of the top is more complicated than for the light quarks because the mass of the external fermion, in this case the top quark mass, cannot be ignored relative to the masses inside the loops. A numerical analysis is presented and it is shown that the contribution to the top EDM could lie in the range ($10^{-19}-10^{-18})$ ecm consistent with the current limits on the EDM of the electron, the neutron and on atomic EDMs. A top EDM of size $(10^{-19}-10^{-18})$ ecm could be accessible in collider experiments such as at the LHC and at the ILC.

The self-consistent quasi-classical model in [formula omitted] gauge field theory

The quasi-classical model in a gauge theory with the Yang–Mills (YM) field is developed. The self-consistent solutions of the Dirac equation in the external SU(N) gauge field and the Yang–Mills equations containing the external fermion current are obtained when the the Yang–Mills field is in the eikonal approximation. The derived solutions are quantized in the quasi-classical approach. It is shown that the solutions take place provided that the dimension of the gauge group is N⩾3. In this way, the fermion and gauge fields exist simultaneously, so that the fermion current completely compensates the current generated by the gauge field due to its self-interaction. The obtained solution are considered in the context of QCD.