arXiv subjects

Shanmuka Shivashankara

Publications and source records attributed to Shanmuka Shivashankara.

7 recordsLinked to original sources

arXiv2026

Regularized Compton double scattering via unitarity

When two initially entangled photons each undergo Compton scattering, the scattered electrons become correlated. However, the final reduced density matrix of one scattered pair is not influenced by the other scattered pair due to unitarity. Herein, we keep unitarity up to tree level for Compton double scattering and obtain different results than recent literature. The initial four particles, where the initial photons are entangled, are written as a superposition of two states with a relative phase. The final density matrix has two area divergences that are regularized with unitarity. The regularization procedure, i.e. solving for the roots of a polynomial that represents the probability for no scattering, suggests a novel definition of the scattering cross-section. Vieta's formulas relate these divergences to finite cross-sections. For an initial pure state, the formulas for the final density matrix and the correlation of final electronic polarizations are given. The correlation implies double scattering is analogous to Young's diffraction experiment. The two initial superposed states are the circular apertures while the Feynman amplitudes are the interfering complex light fields.

hep-ph↗

arXiv2025

Unitarity constrains the quantum information metrics for particle interactions

Unitarity provides mathematical and physical constraints on quantum information systems. e.g., in entanglement swapping, unitarity requires the same von Neumann entanglement entropy generation for either a particle interaction or an act of measurement. For the first time, the language of non-relativistic quantum mechanics is presented to derive the density matrix for hard scattering. We show that unitarity allows for finding the latter's cross section without using the scattering amplitude or the Lippmann-Schwinger equation plus Green's function. We also show the language of relativistic quantum mechanics can be used to derive the momentum entropy or Sackur-Tetrode equation for the inelastic scattering of an electron from a proton. The latter entropy derives from a Shannon entropy and an additional entropy that evokes the uncertainty principle. This article's presentation allows particle physicists to readily begin calculating quantum information metrics such as correlations and mutual information for any particle interaction.

hep-th↗

arXiv2024

Regularized Entanglement Entropy of Electron-Positron Scattering with a Witness Photon

Regularized quantum information metrics are calculated for the scattering process $e^-e^+ \rightarrow γ,Z\rightarrow μ^-μ^+$ that has a witness photon entangled with the initial electron-positron state. Unitarity implies the correct regularization of divergences that appear in both the final density matrix and von Neumann entanglement entropies. The entropies are found to quantify uncertainty or randomness. The variation of information, entanglement entropy, and correlation between the muon's and witness photon's helicities are found to convey equivalent information. The magnitude of the muon's expected helicity rises (falls) as the helicity entropy falls (rises). Area, or the scattering cross section, is a source of entropy for the muon's helicity entropy and momentum entropy. The muon's differential angular entropy distribution is similar to the differential angular cross section distribution, capturing the forward-backward asymmetry at high center of mass energies.

hep-th↗

arXiv2023

Entanglement Entropy Distributions of a Muon Decay

Divergences that occur in density matrices of decay and scattering processes are shown to be regularized by tracing and unitarity or the optical theorem. These divergences are regularized by the lifetime of the decaying particle or the total scattering cross section. Also, this regularization is shown to give the expected helicities of final particles. The density matrix is derived for the weak decay of a polarized muon at rest, $μ^- \rightarrow ν_μ (e^- \bar ν_e)$, with Lorentz invariant density matrix entries and unitarity upheld at tree level. The electron's von Neumann entanglement entropy distributions are calculated with respect to both the electron's emission angle and energy. The angular entropy distribution favors an electron emitted backwards with respect to the muon's polarization given a minimum volume regularization. The kinematic entropy distribution is maximal at half the muon's rest mass energy. These results are similar to the electron's angular and kinematic decay rate distributions. Both the density matrix and entanglement entropy can be cast either in terms of ratios of areas or volumes.

hep-ph↗

arXiv2023

Entanglement Entropy of Compton Scattering with a Witness

Unitarity and the optical theorem are used to derive the reduced density matrices of Compton scattering in the presence of a witness particle. Two photons are initially entangled wherein one photon participates in Compton scattering while the other is a witness, i.e. does not interact with the electron. Unitarity is shown to require that the entanglement entropy of the witness photon does not change after its entangled partner undergoes scattering. The final mutual information of the electronic and witness particle's polarization is nonzero for low energy Compton scattering. This indicates that the two particles become correlated in spite of no direct interaction. Assuming an initial maximally entangled state, the change in entanglement entropy of the scattered photon's polarization is calculated in terms of Stokes parameters. A common ratio of areas occurs in the final reduced density matrix elements, von Neumann entropies, Stokes parameter, and mutual information. This common ratio consists of the Thomson scattering cross-section and an accessible regularized scattering area.

hep-th↗

arXiv2015

$Λ_b \to Λ_c τ\barν_τ$ Decay in the Standard Model and with New Physics

Recently hints of lepton flavor non-universality emerged when the BaBar Collaboration observed deviations from the standard model predictions in $R(D^{(*)}) \equiv {\cal B}({\bar B} \to D^{(*)+} τ^- {\barν}_τ) / {\cal B}({\bar B} \to D^{(*)+} \ell^- {\barν}_\ell)$ ($\ell =e,μ$). Another test of this non-universality can be in the semi leptonic $Λ_{b}\toΛ_{c}τ\barν_τ$ decay. In this work we present predictions for this decay in the standard model and in the presence of new-physics operators with different Lorentz structures. We present the most general four-fold angular distribution for this decay including new physics. For phenomenology, we focus on predictions for the decay rate and the differential distribution in the momentum transfer squared $q^2$. In particular, we calculate $R_{Λ_{b}} = \frac{BR[Λ_b \to Λ_c τ\barν_τ]}{BR[Λ_b \to Λ_c \ell \barν_{\ell}]}$ where $\ell$ represents $μ$ or $e$, and find the standard model prediction to be around $0.3$ while the new physics operators can increase or slightly decrease this value.

hep-ph↗

arXiv2015

Simultaneous Explanation of the $R_K$ and $R(D^{(*)})$ Puzzles

At present, there are several hints of lepton flavor non-universality. The LHCb Collaboration has measured $R_K\equiv{\cal B}(B^+ \to K^+ μ^+ μ^-)/{\cal B}(B^+ \to K^+ e^+ e^-)$, and the BaBar Collaboration has measured $R(D^{(*)}) \equiv {\cal B}({\bar B} \to D^{(*)+} τ^- {\barν}_τ) / {\cal B}({\bar B} \to D^{(*)+} \ell^- {\barν}_\ell)$ ($\ell = e,μ$). In all cases, the experimental results differ from the standard model predictions by 2-3$σ$. Recently, an explanation of the $R_K$ puzzle was proposed in which new physics (NP) generates a neutral-current operator involving only third-generation particles. Now, assuming the scale of NP is much larger than the weak scale, this NP operator must be made invariant under the full $SU(3)_C \times SU(2)_L \times U(1)_Y$ gauge group. In this Letter, we note that, when this is done, a new charged-current operator can appear, and this can explain the $R(D^{(*)})$ puzzle. A more precise measurement of the double ratio $R(D)/R(D^*)$ can rule out this model.

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