Fri·Sep 28, 2018Friday·September 28, 2018

1. 01*

   Quantum Chameleons

   Philippe Brax🇫🇷 · Sylvain Fichet🇧🇷

   We initiate a quantum treatment of chameleon-like particles, deriving classical and quantum forces directly from the path integral. It is found that the quantum force can potentially dominate the classical one by many orders of magnitude. We calculate the quantum chameleon pressure between infinite plates, which is found to interpolate between the Casimir and the integrated Casimir-Polder pressures, respectively in the limits of full screening and no screening. To this end we calculate the chameleon propagator in the presence of an arbitrary number of one-dimensional layers of material. For the Eöt-Wash experiment, the five-layer propagator is used to take into account the intermediate shielding sheet, and it is found that the presence of the sheet enhances the quantum pressure by two orders of magnitude. As an example of implication, we show that in both the standard chameleon and symmetron models, large and previously unconstrained regions of the parameter space are excluded once the quantum pressure is taken into account.

   hep-phastro-ph.COgr-qcquant-phPRD(2019)·35 citations
2. 02*

   Effective Theories of Dark Mesons with Custodial Symmetry

   Graham D. Kribs🇺🇸 · Adam Martin🇺🇸 · Tom Tong🇺🇸

   Dark mesons are bosonic composites of a new, strongly-coupled sector beyond the Standard Model. We consider several dark sectors with fermions that transform under the electroweak group, as arise from a variety of models including strongly-coupled theories of dark matter (e.g., stealth dark matter), bosonic technicolor (strongly-coupled indcued electroweak symmetry breaking), vector-like confinement, etc. We consider theories with two and four flavors under an $SU(N)$ strong group that acquire variously chiral, vector-like, and mixed contributions to their masses. We construct the non-linear sigma model describing the dark pions and match the ultraviolet theory onto a low energy effective theory that provides the leading interactions of the lightest dark pions with the Standard Model. We uncover two distinct classes of effective theories that are distinguishable by how the lightest dark pions decay: "Gaugephilic": where ${\pi }^0\to Zh$, ${\pi }^{\pm }\to Wh$ dominate once kinematically open, and "Gaugephobic": where ${\pi }^0\to \bar{f}f$, ${\pi }^{\pm }\to {\bar{f}}^{\prime }f$ dominate. Custodial $SU(2)$ plays a critical role in determining the "philic" or "phobic" nature of a model. In dark sectors that preserve custodial $SU(2)$, there is no axial anomaly, and so the decay ${\pi }^0\to \gamma \gamma$ is highly suppressed. In a companion paper, we study dark pion production and decay at colliders, obtaining the constraints and sensitivity at the LHC.

   hep-phJHEP(2019)·35 citations
3. 03*

   Dark Mesons at the LHC

   Graham D. Kribs🇺🇸 · Adam Martin🇺🇸 · Bryan Ostdiek🇺🇸 · Tom Tong🇺🇸

   A new, strongly-coupled dark sector could be accessible to LHC searches now. These dark sectors consist of composites formed from constituents that are charged under the electroweak group and interact with the Higgs, but are neutral under Standard Model color. In these scenarios, the most promising target is the dark meson sector, consisting of dark vector-mesons as well as dark pions. In this paper we study dark meson production and decay at the LHC in theories that preserve a global SU(2) dark flavor symmetry. Dark pions can be pair-produced through resonant dark vector meson production, $pp\to {\rho }_D\to {\pi }_D{\pi }_D$, and decay in one of two distinct ways: gaugephobic, when ${\pi }_D\to f{\bar{f}}^{\prime }$ generally dominates; or gaugephilic, when ${\pi }_D\to W+h,Z+h$ dominates once kinematically open. Unlike QCD, the decay ${\pi }_D^0\to \gamma \gamma$ is virtually absent due to the dark flavor symmetry. We recast a vast set of LHC searches to determine the current constraints on dark meson production and decay. When $m_{{\rho }_D}$ is slightly heavier than $2m_{{\pi }_D}$ and ${\rho }_D^{\pm ,0}$ kinetically mixes with the weak gauge bosons, the 8 TeV same-sign lepton search strategy sets the best bound, $m_{{\pi }_D}>500$ GeV. Yet, when only the ${\rho }_D^0$ kinetically mixes with hypercharge, we find the strongest LHC bound is $m_{{\pi }_D}>130$ GeV, that is only slightly better than what LEP II achieved. We find the relative insensitivity of LHC searches, especially at 13 TeV, can be blamed mainly on their penchant for high mass objects or large MET. Dedicated searches would undoubtedly yield substantially improved sensitivity. We provide a GitHub page to speed the implementation of these searches in future LHC analyses. Our findings provide a strong motivation for model-independent searches of the form $pp\to A\to B+C\to SMSM+SMSM$ where the theoretical prejudice is for SM to be a t,b,$\tau$ or W,Z,h.

   hep-phJHEP(2019)·70 citations
4. 04*

   Is the radion a bulk Higgs doublet?

   Marco Merchand🇺🇸 · Marc Sher🇺🇸 · Keith Thrasher🇺🇸

   In 2013, Geller, Bar-Shalom and Soni (GBS) proposed a Randall-Sundrum model with a bulk SU(2) doublet. They found that the doublet could both stabilize the extra dimension and break the electroweak symmetry; the radion and the Higgs boson were then one and the same. This alternative to the Goldberger-Wise mechanism contained enhanced Higgs couplings to gluons and photons, but at the time of the GBS paper, these couplings were phenomenologically acceptable. We note that updated results from the LHC rule out the model as presented. One can expand the parameter space by extending the model to include bulk fermions. We do so, and show that for any choice of parameters, the model remains in conflict with LHC data. We then extend the scalar sector to a two Higgs model, and show that the model contains a phenomenologically unacceptable zero mass scalar. This property will likely apply to all extensions to the scalar sector, and thus we conclude that the radion cannot be part of a bulk doublet.

   hep-phJ.Phys.G(2019)·1 citation
5. 05*

   Three-Body Decay of ${\Lambda }_c^{\ast }(2595)$ and ${\Lambda }_c^{\ast }(2625)$ with the Inclusion of Direct Two-Pion Coupling

   A. J. Arifi🇯🇵 · H. Nagahiro🇯🇵 · A. Hosaka🇯🇵

   We investigate the three-body decays of ${\Lambda }_c^{\ast }(2595)$ and ${\Lambda }_c^{\ast }(2625)$ into ${\Lambda }_c\pi \pi$ by including a direct process going through the two-pion coupling of ${\Lambda }_c^{\ast }{\Lambda }_c\pi \pi$ in addition to the sequential processes going through ${\Sigma }_c(2455)$ and ${\Sigma }_c^{\ast }(2520)$. The strength of the direct coupling is related to that of the Yukawa coupling by the chiral partner structure between ${\Lambda }_c$'s and ${\Sigma }_c$'s, while the strength of the Yukawa coupling is estimated by the quark model. It is found that the direct process gives a considerable contribution especially in the decay of ${\Lambda }_c^{\ast }(2625)$. A clear indication of the direct process is seen in an asymmetric pattern in the angular correlation between the two pions. We discuss the usefulness of the detailed analysis of the decays for the study of the structure of ${\Lambda }_c^{\ast }$.

   hep-phnucl-thPRD(2018)·13 citations
6. 06*

   Spontaneous breaking of $SO(3)$ to finite family symmetries with supersymmetry - an $A_4$ model

   Stephen F. King🇬🇧 · Ye-Ling Zhou🇬🇧

   We discuss the breaking of $SO(3)$ down to finite family symmetries such as $A_4$, $S_4$ and $A_5$ using supersymmetric potentials for the first time. We analyse in detail the case of supersymmetric $A_4$ and its finite subgroups $Z_3$ and $Z_2$. We then propose a supersymmetric $A_4$ model of leptons along these lines, originating from $SO(3)\times U(1)$, which leads to a phenomenologically acceptable pattern of lepton mixing and masses once subleading corrections are taken into account. We also discuss the phenomenological consequences of having a gauged $SO(3)$, leading to massive gauge bosons, and show that all domain wall problems are resolved in this model.

   hep-phJHEP(2018)·36 citations
7. 07*

   Black disk radius constrained by unitarity

   V.A. Khoze🇬🇧 · A.D. Martin🇬🇧 · M.G. Ryskin🇬🇧

   We argue that if the elastic proton-proton cross section increases with energy, the Froissart-like high energy behaviour of the elastic amplitude (which corresponds to a `black disk' of radius $R(s)=c\ln s-\beta \ln (\ln s)$) is the only possibility to satisfy the unitarity equation at each value of the impact parameter, $b$. Otherwise the cross section of events with Large Rapidity Gaps grows faster than the total cross section at the same $b$. That is, these `gap' events require {\it maximal} growth of the high-energy (asymptotic) cross section and of the interaction radius $R(s)$ in order to be consistent with unitarity.

   hep-phPLB(2018)·7 citations
8. 08*

   The fate of quarkonia in heavy-ion collisions at LHC energies: a unified description of the sequential suppression patterns

   Pietro Faccioli🇵🇹 · Carlos Lourenco🇨🇭

   Measurements made at the LHC have shown that the production of the $\mathrm{J}/\psi$, $\psi$(2S), ${\rm Y}$(1S) and ${\rm Y}$(2S) quarkonia is suppressed in Pb-Pb collisions, with respect to the extrapolation of the pp production yields. The $\psi$(2S) and ${\rm Y}$(2S) states are more strongly suppressed than the ground states and the level of the suppression changes with the centrality of the collision. We show that the measured patterns can be reproduced by a simple model, where all quarkonia are treated in a unified way, starting from the recent realisation that, in pp collisions, the probability of quarkonium formation has a universal dependence on the binding-energy of the bound state. The hot-medium suppression effect is parametrized by a penalty factor in the binding energy, identical for all (S- and P-wave) charmonium and bottomonium states, including those that indirectly contribute to the measured results through feed-down decays. This single parameter, computed through a global fit of all available suppression patterns, fully determines the hierarchy of nuclear effects, for all states and centrality bins. The resulting faithful description of the data provides convincing evidence in favour of the conjecture of sequential quarkonium suppression induced by QGP formation.

   hep-phnucl-thEPJC(2018)·9 citations
9. 09*

   Top-Quark Physics at the LHC

   Sven-Olaf Moch🇩🇪 · Jürgen Reuter🇩🇪

   We report on the precision determination of the top-quark mass to next-to-next-to-leading order in QCD in well-defined renormalization schemes using data from the Large Hadron Collider for single-top and top-quark pair production. We also discuss the calibration of the so-called Monte Carlo top-quark mass parameter which is determined from a comparison to events with top-quark decay products. The implications of the measured value of the top-quark mass for conclusions about the stability of the electroweak vacuum state of our Universe are illustrated. At future lepton colliders, we provide for the first time matched exclusive calculations valid both at the top threshold and in the continuum, also fully differentially. In addition, we calculate fully off-shell top-pair production (also with an associated Higgs boson) at next-to-leading order in QCD, which allows to extract the top-Yukawa coupling with an unprecedented precision.

   hep-phhep-ex1 citation
10. 10*

    Radiative decays of the heavy tensor mesons in light cone QCD sum rules

    T. M. Aliev (1)🇹🇷 · M. Savci (1) ((1) Middle East Technical University/Ankara/Turkey)

    The transition form factors of the radiative decays of the heavy tensor mesons to heavy pseudoscalar and heavy vector mesons are calculated in the framework of the light cone QCD sum rules method at the point $Q^2=0$. Using the obtained values of the transition form factors at the point $Q^2=0$ the corresponding decay widths are estimated. The results show that the radiative decays of the heavy--light tensor mesons can be measurable in the future planned experiments at LHCb.

    hep-phPRD(2019)·6 citations
11. 11*

    Phenomenology of Relativistic $3\to 3$ Reaction Amplitudes within the Isobar Approximation

    JPAC Collaboration: A. Jackura🇺🇸 · C. Fernández-Ramírez🇲🇽 · V. Mathieu🇺🇸 · M. Mikhasenko🇩🇪 · J. Nys🇧🇪 · A. Pilloni🇮🇹 · K. Saldaña🇺🇸 · N. Sherrill🇺🇸 · A. P. Szczepaniak🇺🇸

    Further progress in hadron spectroscopy necessitates the phenomenological description of three particle reactions. We consider the isobar approximation, where the connected part of the $3\to 3$ amplitude is first expressed as a sum over initial and final pairs, and then expanded into a truncated partial wave series. The resulting unitarity equation is automatically fulfilled by the $B$-matrix solution, which is an integral equation for the partial wave amplitudes, analogous to the $K$-matrix parameterization used to describe $2\to 2$ amplitudes. We study the one particle exchange and how its analytic structure impacts rescattering solutions such as the triangle diagram. The analytic structure is compared to other parameterizations discussed in the literature. We briefly discuss the analogies with recent formalisms for extracting $3\to 3$ scattering amplitudes in lattice QCD.

    hep-phhep-latEPJC(2019)·57 citations
12. 12*

    $0\nu \beta \beta$ in left-right theories with Higgs doublets and gauge coupling unification

    Chayan Majumdar🇮🇳 · Sudhanwa Patra🇮🇳 · Supriya Senapati🇮🇳 · Urjit A. Yajnik🇮🇳

    We consider a version of Left-Right Symmetric Model in which the scalar sector consists of a Higgs bidoublet ($\Phi$) with $B-L=0$, Higgs doublets ($H_{L,R}$) with $B-L=1$ and a charged scalar (${\delta }^{+}$) with $B-L=2$ leading to radiatively generated Majorana masses for neutrinos and thereby, leads to new physics contributions to neutrinoless double beta decay ($0\nu \beta \beta$). We show that such a novel framework can be embedded in a non-SUSY $SO(10)$ GUT leading to successful gauge coupling unification at around $10^{16}$ GeV with the scale of left-right symmetry breaking around $10^{10}$ GeV. The model can also be extended to have left-right symmetry breaking at TeV scale, enabling detection of $W_R,Z_R$ bosons in LHC and future collider searches. In the context of neutrinoless double beta decay, this model can saturate the present bound from GERDA and KamLAND-Zen experiments. Also, we briefly explain how keV-MeV range RH neutrino arising from our model can saturate various astrophysical and cosmological constraints and can be considered as warm Dark Matter (DM) candidate to address various cosmological issues. We also discuss on left-right theories with Higgs doublets without having scalar bidoublet leading to fermion masses and mixings by inclusion of vector like fermions.

    hep-phNPB(2020)·8 citations
13. 13*

    Leading-logarithmic threshold resummation of the Drell-Yan process at next-to-leading power

    Martin Beneke🇩🇪 · Alessandro Broggio🇩🇪 · Mathias Garny🇩🇪 · Sebastian Jaskiewicz🇩🇪 · Robert Szafron🇩🇪 · Leonardo Vernazza🇳🇱 · Jian Wang🇩🇪

    We resum the leading logarithms ${\alpha }_s^n{\ln }^{2n-1}(1-z)$, $n=1,2,\dots$ near the kinematic threshold $z=Q^2/\hat{s}\to 1$ of the Drell-Yan process at next-to-leading power in the expansion in $(1-z)$. The derivation of this result employs soft-collinear effective theory in position space and the anomalous dimensions of subleading-power soft functions, which are computed. Expansion of the resummed result leads to the leading logarithms at fixed loop order, in agreement with exact results at NLO and NNLO and predictions from the physical evolution kernel at N${}^3$LO and N${}^4$LO, and to new results at the five-loop order and beyond.

    hep-phhep-thJHEP(2019)·129 citations
14. 14*

    Accurate simulation of W, Z and Higgs boson decays in Sherpa

    Frank Krauss🇬🇧 · Jonas M. Lindert🇬🇧 · Robin Linten🇬🇧 · Marek Schönherr🇨🇭

    We discuss the inclusion of next-to-next-to leading order electromagnetic and of next-to leading order electroweak corrections to the leptonic decays of weak gauge and Higgs bosons in the SHERPA event generator. To this end, we modify the Yennie-Frautschi-Suura scheme for the resummation of soft photon corrections and its systematic improvement with fixed-order calculations, to also include the effect of virtual corrections due to the ex- change of weak gauge bosons. We detail relevant technical aspects of our implementation and present numerical results for observables relevant for high-precision Drell-Yan and Higgs boson production and decay simula- tions at the LHC.

    hep-phEPJC(2019)·25 citations
15. 15*

    Unitarizing non-Minimal Inflation via a Linear Contribution to the Frame Function

    C. Pallis🇬🇷

    We show that non-minimal inflation, based on the phi^4 potential, may be rendered unitarity conserving and compatible with the Planck results for 4.6x10^(-3)<~r21=c2R/c1R^2<~1, if we introduce a linear contribution (c1R phi) to the frame function which takes the form fR=1+c1R phi+c2R phi^2. Supersymmetrization of this model can be achieved by considering two gauge singlet superfields and combining a linear-quadratic superpotential term, with a class of logarithmic or semi-logarithmic Kaehler potentials with prefactor for the logarithms including the inflaton field -(2n+3) or -2(n+1) where -0.01<~ n<~0.013.

    hep-phastro-ph.COhep-thPLB(2019)·7 citations
16. 16*

    Gravitationally bound axions and how one can discover them

    Xunyu Liang🇨🇦 · Ariel Zhitnitsky🇨🇦

    As recently advocated in \cite{Fischer:2018niu}, there is a fundamentally new mechanism for the axion production in the Sun and Earth. However, the role of very slow axions in previous studies were neglected because of its negligible contribution to the total axion production by this new mechanism. In the present work we specifically focus on analysis of the non-relativistic axions which will be trapped by the Sun and Earth due to the gravitational forces. The corresponding emission rate of these low energy axions (below the escape velocity) is very tiny. However, these axions will be accumulated by the Sun and Earth during their life-times, i.e. 4.5 billion of years, which greatly enhances the discovery potential. The computations are based on the so-called Axion Quark Nugget (AQN) Dark Matter Model. This model was originally invented as a natural explanation of the observed ratio ${\Omega }_{\mathrm{dark}}\sim {\Omega }_{\mathrm{visible}}$ when the DM and visible matter densities assume the same order of magnitude values, irrespectively to the axion mass $m_a$ or initial misalignment angle ${\theta }_0$.This model, without adjustment of any parameters, gives a very reasonable intensity of the extreme UV (EUV) radiation from the solar corona as a result of the AQN annihilation events with the solar material. This extra energy released in corona represents a resolution, within AQN framework, a long standing puzzle known in the literature as the "solar corona heating mystery". The same annihilation events also produce the axions. The flux of these axions is unambiguously fixed in this model and expressed in terms of the EUV luminosity from solar corona. We make few comments on the potential discovery of these gravitationally bound axions.

    hep-phastro-ph.HEastro-ph.SRPRD(2019)·19 citations
17. 17*

    Analytic (3+1)-dimensional gauged Skyrmions, Heun and Whittaker-Hill equations and resurgence

    Fabrizio Canfora🇨🇱 · Marcela Lagos🇨🇱 · Seung Hun Oh🇰🇷 · Julio Oliva🇨🇱 · Aldo Vera🇨🇱

    We show that one can reduce the coupled system of seven field equations of the (3+1)-dimensional gauged Skyrme model to the Heun equation (which, for suitable choices of the parameters, can be further reduced to the Whittaker-Hill equation) in two non-trivial topological sectors. Hence, one can get a complete analytic description of gauged solitons in (3+1) dimensions living within a finite volume in terms of classic results in the theory of differential equations and Kummer's con uent functions. We consider here two types of gauged solitons: gauged Skyrmions and gauged time-crystals (namely, gauged solitons periodic in time, whose time-period is protected by a winding number). The dependence of the energy of the gauged Skyrmions on the Baryon charge can be determined explicitly. The theory of Kummer's confluent functions leads to a quantization condition for the period of the time-crystals. Likewise, the theory of Sturm-Liouville operators gives rise to a quantization condition for the volume occupied by the gauged Skyrmions. The present analysis also discloses that resurgent techniques are very well suited to deal with the gauged Skyrme model as well. In particular, we discuss a very nice relation between the electromagnetic perturbations of the gauged Skyrmions and the Mathieu equation which allows to use many of the modern resurgence techniques to determine the behavior of the spectrum of these perturbations.

    ↳ hep-thgr-qchep-phPRD(2018)·36 citations
18. 18*

    Manifestation of important role of nuclear forces in emission of photons in scattering of pions off nuclei

    Sergei P. Maydanyuk (1 and 2)🇨🇳 · Peng-Ming Zhang (1)🇨🇳 · Li-Ping Zou (1) ((1) Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, China, (2) Institute for Nuclear Research, National Academy of Sciences of Ukraine, Ukraine)🇨🇳

    Bremsstrahlung of photons emitted during the scattering of ${\pi }^{+}$-mesons off nuclei is studied for the first time. Role of interactions between ${\pi }^{+}$-mesons and nuclei in the formation of the bremsstrahlung emission is analyzed in details. We discover essential contribution of emitted photons from nuclear part of Johnson-Satchler potential to the full spectrum, in contrast to the optical Woods-Saxon potential. We observe unusual essential influence of the nuclear part of both potentials on the spectrum at high photon energies. This phenomenon opens a new experimental way to study and check non-Coulomb and nuclear interactions between pions and nuclei via measurements of the emitted photons. We provide predictions of the bremsstrahlung spectra for pion scattering off ${}^{44}\mathrm{Ca}$.

    ↳ nucl-thhep-phnucl-exPRC(2018)·11 citations
19. 19*

    Light-Neutrino Exchange and Long-Distance Contributions to $0\nu 2\beta$ Decays: An Exploratory Study on $\pi \pi \to ee$

    Xu Feng🇨🇳 · Lu-Chang Jin🇺🇸 · Xin-Yu Tuo🇨🇳 · Shi-Cheng Xia🇨🇳

    We present an exploratory lattice QCD calculation of the neutrinoless double beta decay $\pi \pi \to ee$. Under the mechanism of light-neutrino exchange, the decay amplitude involves significant long-distance contributions. The calculation reported here, with pion masses $m_{\pi }=420$ and 140 MeV, demonstrates that the decay amplitude can be computed from first principles using lattice methods. At unphysical and physical pion masses, we obtain that amplitudes are $24\%$ and $9\%$ smaller than the predication from leading order chiral perturbation theory. Our findings provide the lattice QCD inputs and constraints for effective field theory. A follow-on calculation with fully controlled systematic errors will be possible with adequate computational resources.

    ↳ hep-lathep-phnucl-exnucl-thPRL(2019)·48 citations
20. 20*

    1/N corrections to $F_1$ and $F_2$ structure functions of vector mesons from holography

    Nicolas Kovensky🇦🇷 · Gustavo Michalski🇦🇷 · Martin Schvellinger🇦🇷

    The structure functions $F_1$ and $F_2$ of the hadronic tensor of vector mesons are obtained at order $1/N$ and strong coupling using the gauge/gravity duality. We find that the large $N$ limit and the high energy one do not commute. Thus, by considering the high energy limit first, our results of the first moments of $F_1$ for the rho meson agree well with those from lattice QCD, with an important improvement of the accuracy with respect to the holographic dual calculation in the planar limit.

    ↳ hep-thhep-lathep-phPRD(2019)·10 citations
21. 21*

    Deep Learning and Holographic QCD

    Koji Hashimoto🇯🇵 · Sotaro Sugishita🇯🇵 · Akinori Tanaka🇯🇵 · Akio Tomiya🇺🇸

    We apply the relation between deep learning (DL) and the AdS/CFT correspondence to a holographic model of QCD. Using a lattice QCD data of the chiral condensate at a finite temperature as our training data, the deep learning procedure holographically determines an emergent bulk metric as neural network weights. The emergent bulk metric is found to have both a black hole horizon and a finite-height IR wall, so shares both the confining and deconfining phases, signaling the cross-over thermal phase transition of QCD. In fact, a quark antiquark potential holographically calculated by the emergent bulk metric turns out to possess both the linear confining part and the Debye screening part, as is often observed in lattice QCD. From this we argue the discrepancy between the chiral symmetry breaking and the quark confinement in the holographic QCD. The DL method is shown to provide a novel data-driven holographic modeling of QCD, and sheds light on the mechanism of emergence of the bulk geometries in the AdS/CFT correspondence.

    ↳ hep-thhep-lathep-phPRD(2018)·76 citations
22. 22*

    High-Temperature QCD: theory overview

    Massimo D'Elia🇮🇹

    We review the recent progress achieved in the theoretical investigation of Quantum Chromodynamics in the high temperature regime, with a focus on results achieved by lattice QCD simulations. The discussion covers the structure of the phase diagram and the properties of the strongly interacting medium at finite T and small baryon chemical potential.

    ↳ hep-lathep-phhep-thNPA(2019)·43 citations
23. 23*

    Quantum decay law: Critical times and the Equivalence of approaches

    D. F. Ramírez Jiménez🇨🇴 · N. G. Kelkar🇨🇴

    Methods based on the use of Green's functions or the Jost functions and the Fock-Krylov method are apparently very different approaches to understand the time evolution of unstable states. We show that the two former methods are equivalent up to some constants and as an outcome find an analytic expression for the energy density of states in the Fock-Krylov amplitude in terms of the coefficients introduced in the Green's functions and the Jost functions methods. This model-independent density is further used to obtain an analytical expression for the survival amplitude and study its behaviour at large times. Using these expressions, we investigate the origin of the oscillatory behaviour of the decay law in the region of the transition from the exponential to the non-exponential at large times. With the objective to understand the failure of nuclear and particle physics experiments in observing the non-exponential decay law predicted by quantum mechanics for large times, we derive analytical formulae for the critical transition time, $t_c$, from the exponential to the inverse power law behaviour at large times. Evaluating ${\tau }_c=\Gamma t_c$ for some particle resonances and narrow nuclear states which have been tested experimentally to verify the exponential decay law, we conclude that the large time power law in particle and nuclear decay is hard to find experimentally.

    ↳ quant-phhep-phnucl-exnucl-thJ.Phys.A(2019)·17 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.