Search results for "Vector"
showing 10 items of 2660 documents
Hawking radiation of massive modes and undulations
2012
We compute the analogue Hawking radiation for modes which posses a small wave vector perpendicular to the horizon. For low frequencies, the resulting mass term induces a total reflection. This generates an extra mode mixing that occurs in the supersonic region, which cancels out the infrared divergence of the near horizon spectrum. As a result, the amplitude of the undulation (0-frequency wave with macroscopic amplitude) emitted in white hole flows now saturates at the linear level, unlike what was recently found in the massless case. In addition, we point out that the mass introduces a new type of undulation which is produced in black hole flows, and which is well described in the hydrodyn…
Derivation of spontaneously broken gauge symmetry from the consistency of effective field theory II: Scalar field self-interactions and the electroma…
2019
We extend our study of deriving the local gauge invariance with spontaneous symmetry breaking in the context of an effective field theory by considering self-interactions of the scalar field and inclusion of the electromagnetic interaction. By analyzing renormalizability and the scale separation conditions of three-, four- and five-point vertex functions of the scalar field, we fix the two couplings of the scalar field self-interactions of the leading order Lagrangian. Next we add the electromagnetic interaction and derive conditions relating the magnetic moment of the charged vector boson to its charge and the masses of the charged and neutral massive vector bosons to each other and the tw…
Numerical Multi-Loop Calculations via Finite Integrals and One-Mass EW-QCD Drell-Yan Master Integrals
2017
We study a recently-proposed approach to the numerical evaluation of multi-loop Feynman integrals using available sector decomposition programs. As our main example, we consider the two-loop integrals for the $\alpha \alpha_s$ corrections to Drell-Yan lepton production with up to one massive vector boson in physical kinematics. As a reference, we evaluate these planar and non-planar integrals by the method of differential equations through to weight five. Choosing a basis of finite integrals for the numerical evaluation with SecDec3 leads to tremendous performance improvements and renders the otherwise problematic seven-line topologies numerically accessible. As another example, basis integ…
DsixTools 2.0: The Effective Field Theory Toolkit
2021
$\tt DsixTools$ is a Mathematica package for the handling of the Standard Model Effective Field Theory (SMEFT) and the Low-energy Effective Field Theory (LEFT) with operators up to dimension six, both at the algebraic and numerical level. $\tt DsixTools$ contains a visually accessible and operationally convenient repository of all operators and parameters of the SMEFT and the LEFT. This repository also provides information concerning symmetry categories and number of degrees of freedom, and routines that allow to implement this information on global expressions (such as decay amplitudes and cross-sections). $\tt DsixTools$ also performs weak basis transformations, and implements the full on…
Adiabatic regularization for Dirac fields in time-varying electric backgrounds
2020
The adiabatic regularization method was originally proposed by Parker and Fulling to renormalize the energy-momentum tensor of scalar fields in expanding universes. It can be extended to renormalize the electric current induced by quantized scalar fields in a time-varying electric background. This can be done in a way consistent with gravity if the vector potential is considered as a variable of adiabatic order one. Assuming this, we further extend the method to deal with Dirac fields in four spacetime dimensions. This requires a self-consistent ansatz for the adiabatic expansion, in presence of a prescribed time-dependent electric field, which is different from the conventional expansion u…
No chiral light bending by clumps of axion-like particles
2019
We study the propagation of light in the presence of a parity-violating coupling between photons and axion-like particles (ALPs). Naively, this interaction could lead to a split of light rays into two separate beams of different polarization chirality and with different refraction angles. However, by using the eikonal method we explicitly show that this is not the case and that ALP clumps do not produce any spatial birefringence. This happens due to non-trivial variations of the photon's frequency and wavevector, which absorb time-derivatives and gradients of the ALP field. We argue that these variations represent a new way to probe the ALP-photon couping with precision frequency measuremen…
Normalization of Killing vectors and energy conservation in two-dimensional gravity
1999
We explicitly show that, in the context of a recently proposed 2D dilaton gravity theory, energy conservation requires the ``natural'' Killing vector to have, asymptotically, an unusual normalization. The Hawking temperature $T_H$ is then calculated according to this prescription.
N-quantum approach to quantum field theory at finite T and mu: the NJL model
1999
We extend the N-quantum approach to quantum field theory to finite temperature ($T$) and chemical potential ($\mu$) and apply it to the NJL model. In this approach the Heisenberg fields are expressed using the Haag expansion while temperature and chemical potential are introduced simultaneously through a generalized Bogoliubov transformation. Known mean field results are recovered using only the first term in the Haag expansion. In addition, we find that at finite T and in the broken symmetry phase of the model the mean field approximation can not diagonalize the Hamiltonian. Inclusion of scalar and axial vector diquark channels in the SU(2)$_{rm f}$ $otimes$ SU(3)$_{\rm c}$ version of the …
A comment on the relationship between differential and dimensional renormalization
1992
We show that there is a very simple relationship between differential and dimensional renormalization of low-order Feynman graphs in renormalizable massless quantum field theories. The beauty of the differential approach is that it achieves the same finite results as dimensional renormalization without the need to modify the space time dimension.
Modular invariant dynamics and fermion mass hierarchies around τ = i
2021
We discuss fermion mass hierarchies within modular invariant flavour models. We analyse the neighbourhood of the self-dual point $\tau=i$, where modular invariant theories possess a residual $Z_4$ invariance. In this region the breaking of $Z_4$ can be fully described by the spurion $\epsilon \approx \tau - i$, that flips its sign under $Z_4$. Degeneracies or vanishing eigenvalues of fermion mass matrices, forced by the $Z_4$ symmetry at $\tau=i$, are removed by slightly deviating from the self-dual point. Relevant mass ratios are controlled by powers of $|\epsilon|$. We present examples where this mechanism is a key ingredient to successfully implement an hierarchical spectrum in the lepto…