Massive Scalars Research Articles

Trace anomalies and the graviton-dilaton amplitude

Abstract We consider 3+1 dimensional Quantum Field Theories (QFTs) coupled to the dilaton and the graviton. We show that the graviton-dilaton scattering amplitude receives a universal contribution which is helicity flipping and is proportional to ∆c − ∆a along any RG flow, where ∆c and ∆a are the differences of the UV and IR c- and a-trace anomalies respectively. This allows us to relate ∆c − ∆a to spinning massive states in the spectrum of the QFT. We test our predictions in two simple examples: in the theory of a massive free scalar and in the theory of a massive Dirac fermion (a more complicated example is provided in a companion paper [1]). We discuss possible applications.

Loops, recursions, and soft limits for fermionic correlators in (A)dS

Study of correlation functions in AdS/CFT and in-in correlators in de Sitter space often requires the computation of Witten diagrams. Due to the complexity of evaluating radial integrals for these correlators, several indirect approaches have been developed to simplify computations. However, in momentum space, these methods have been limited to fields with integer spin. In this paper, we formulate tools for evaluating Witten diagrams with spin−12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ extrm{spin}-\\frac{1}{2} $$\\end{document} fields in momentum space and discuss where they differ from the corresponding integer-spin analysis. We formulate our tools explicitly for massless fermions and present how appropriate Weight shifting operators with respect to the external kinematics can be used to obtain the generalization to fermions with integer mass (in units of 1/lAdS). We apply these tools to loop Witten diagrams and also discuss their use for evaluating in-in correlators in dS. In cases where we can evaluate the loop integrals, we find their transcendentality is lower than the corresponding scalar field results. Further, we classify the nature of IR divergences encountered for interacting massive scalars and fermions. We also prove a novel Weinberg-like soft theorem for gauge fields coupled to matter in AdS and show that the universal terms in the leading soft factor are sensitive to the spin of the matter field. These generalize the recently discovered soft theorems for pure Yang-Mills to Yang-Mills with matter.

Amplitude factorization in the electroweak standard model

We provide tools to analyze factorization at the amplitude level for processes involving the entire standard model. We focus in particular on a momentum region, in which the factorization of real and certain virtual corrections appears in a generalized eikonal approximation in which we expand around a quasisoft limit for massive gauge bosons, fermions, and scalars. We use the chirality-flow formalism to express loop exchanges or emissions as operators on chiral structures. This provides key tools for amplitude evolution with parton exchange and branching in the full Standard Model, including the electroweak sector. Published by the American Physical Society 2024

Signatures of light new particles in B→K(*)Emiss

The recent Belle II observation of B→KEmiss challenges theoretical interpretations in terms of Standard Model neutrino final states. Instead, we consider new physics scenarios where up to two new light-invisible particles of spin 0 up to 3/2 are present in the final state. We identify viable scenarios by reconstructing the (binned) likelihoods of the relevant B→K(*)Emiss and also Bs→Emiss experimental analyses and present preferred regions of couplings and masses. In particular, we find that the current data prefer two-body decay kinematics involving the emission of a single massive scalar or a vector particle or, alternatively, three-body decays involving pairs of massive scalars or spin 1/2 fermions. When applicable, we compare our findings with existing literature and briefly discuss some model-building implications. Published by the American Physical Society 2024

The exact relativistic scalar quasibound states of the dyonic Kerr–Sen black hole: quantized energy, and Hawking radiation

We consider Klein–Gordon equation in the Dyonic Kerr–Sen black hole background, which is the charged rotating axially symmetric solution of the Einstein–Maxwell–Dilaton–Axion theory of gravity. The black hole incorporates electric, magnetic, dilatonic and axionic charges and is constructed in 3+1 dimensional spacetime. We begin our investigations with the construction of the scalar field’s governing equation, i.e., the covariant Klein–Gordon equation. With the help of the ansatz of separation of variables, we successfully separate the polar part, and find the exact solution in terms of Spheroidal Harmonics, while the radial exact solution is obtained in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that gives rise to discrete complex-valued energy levels for massive scalar fields. The real part is the scalar field relativistic quantized energy, while the imaginary part represents the quasibound states’s decay. We present all of the sixteen possible exact energy solutions for both massive and massless scalars. We also present the investigation the Hawking radiation of the Dyonic Kerr–Sen black hole’s apparent horizon, via the Sigurd–Sannan method by making use of the obtained exact scalar wave functions. The radiation distribution function, and the Hawking temperature are also obtained.

Resonant reheating

We investigate a novel reheating scenario proceeding through s-channel inflaton annihilation, mediated by a massive scalar. If the inflaton ϕ oscillates around the minimum of a monomial potential ∝ ϕ n, we reveal the emergence of resonance phenomena originating from the dynamic evolution of the inflaton mass for n>2. Consequently, a resonance appears in both the radiation and the temperature evolution during the reheating process. By solving the coupled Boltzmann equations, we present solutions for radiation and temperature. We find non-trivial temperature characteristics during reheating, depending on the value of n and the masses of the inflaton and mediator. Some phenomenological aspects of the model are explored. As a concrete example, we show that the same mediator participates in the genesis of dark matter, modifying the standard freeze-in dynamics. In addition, we demonstrate that the resonant reheating scenario could be tested by next-generation low- and high-frequency gravitational wave detectors.

Conformal Graphs as Twisted Partition Functions.

We show that a class of L-loop conformal ladder graphs are intimately related to twisted partition functions of free massive complex scalars in d=2L+1 dimensions. The graphs arise as four-point functions in certain two- and four-dimensional conformal fishnet models. The twisted thermal two-point function of the scalars becomes a generator of conformal ladder graphs for all loops. We argue that this correspondence is seeded by a system of two decoupled harmonic oscillators twisted by an imaginary chemical potential. We find a number of algebraic and differential relations among the conformal graphs that mirror the underlying free dynamics.

Analytic formulae for inflationary correlators with dynamical mass

Massive fields can imprint unique oscillatory features on primordial correlation functions or inflationary correlators, which is dubbed the cosmological collider signal. In this work, we analytically investigate the effects of a time-dependent mass of a scalar field on inflationary correlators, extending previous numerical studies and implementing techniques developed in the cosmological bootstrap program. The time-dependent mass is in general induced by couplings to the slow-roll inflaton background, with particularly significant effects in the case of non-derivative couplings. By linearly approximating the time dependence, the mode function of the massive scalar is computed analytically, on which we derive analytic formulae for two-, three-, and four-point correlators with the tree-level exchange of the massive scalar. The obtained formulae are utilized to discuss the phenomenological impacts on the power spectrum and bispectrum, and it is found that the scaling behavior of the bispectrum in the squeezed configuration, i.e., the cosmological collider signal, is modified from a time-dependent Boltzmann suppression. By investigating the scaling behavior in detail, we are in principle able to determine the non-derivative couplings between the inflaton and the massive particle.

UV and IR effects in axion quality control

Motivated by recent discussions and the absence of exact global symmetries in UV completions of gravity we re-examine the axion quality problem (and naturalness issues more generally) using antisymmetric Kalb-Ramond (KR) fields rather than their pseudoscalar duals, as suggested by string and higher dimensional theories. Two types of axions can be identified: a model independent S-type axion dual to a two form Bμν in 4D and a T-type axion coming directly as 4D scalar Kaluza-Klein (KK) components of higher-dimensional tensor fields. For T-type axions our conclusions largely agree with earlier workers for the axion quality problem, but we also reconcile why T-type axions can couple to matter localized on 3-branes with Planck suppressed strength even when the axion decay constants are of order the KK scale. For S-type axions, we review the duality between form fields and massive scalars and show how duality impacts naturalness arguments about the UV sensitivity of the scalar potential. In particular UV contributions on the KR side suppress contributions on the scalar side by powers of m/M with m the axion mass and M the UV scale. We re-examine how the axion quality problem is formulated on the dual side and compare to recent treatments. We study how axion quality is affected by the ubiquity of p-form gauge potentials (for both p = 2 and p = 3) in string vacua and identify two criteria that can potentially lead to a problem. We also show why most fields do not satisfy these criteria, but when they do the existence of multiple fields also provides mechanisms for resolving it. We conclude that the quality problem is easily evaded.

Exact massive and massless scalar quasibound states solutions of the Einstein–Maxwell-dilaton (EMD) black hole

In this letter, we will focus on the Klein–Gordon equation with static spherically symmetric black hole solution of the Einstein–Maxwell-dilaton (EMD) theory as its 3+1 background space-time. The Klein–Gordon equation represents quasibound states of both massive and massless scalar fields which are localized in the black hole potential well. By using the covariant Klein–Gordon equation, we investigate the behaviour of both massive and massless scalars in the EMD black hole space-time. We successfully exactly solved the relativistic wave equation and are going to present the novel exact results in this letter. The exact solutions, the wave functions and the energy levels, describe the decaying nature of the relativistic scalar field bound in the curved space-time. The massive scalar quasibound state has complex-valued energy levels where the real part is the massive scalar’s energy while the imaginary part represents the decay. For the massless scalar quasibound state, pure imaginary energy levels are discovered. In this letter, by using the obtained exact scalar particle’s wave functions, we also consider the Hawking radiation of the apparent horizon of the EMD black hole that is calculated via Damour–Ruffini method. In principle, the investigation of black hole quasibound states could provide possibility for laboratory testing of effects whose nature are absolutely related with quantum effects in gravity.

Scalar-graviton amplitudes and celestial holography

We compute scattering amplitudes involving one massive scalar and two, three, or four gravitons. We show that when the conformal dimension of the massive scalar is set to zero, the resulting celestial correlators depend only on the coordinates of the gravitons. Such correlators of gravitons are well-defined and do not suffer from divergences associated with the Mellin transform of usual graviton amplitudes. Moreover, they are non-distributional and take the form of standard CFT correlators. We show that they are consistent with the usual OPEs but the statement of the soft theorem is modified.

Gravitational action for a massive Majorana fermion in 2d quantum gravity

We compute the gravitational action of a free massive Majorana fermion coupled to two-dimensional gravity on compact Riemann surfaces of arbitrary genus. The structure is similar to the case of the massive scalar. The small-mass expansion of the gravitational yields the Liouville action at zeroth order, and we can identify the Mabuchi action at first order. While the massive Majorana action is a conformal deformation of the massless Majorana CFT, we find an action different from the one given by the David-Distler-Kawai (DDK) ansatz.

Effective gravitational action for 2D massive Majorana fermions on arbitrary genus Riemann surfaces

We explore the effective gravitational action for two-dimensional massive Euclidean Majorana fermions in a small mass expansion, continuing and completing the study initiated in a previous paper [1]. We perform a detailed analysis of local zeta functions, heat kernels, and Green’s functions of the Dirac operator on arbitrary Riemann surfaces. We obtain the full expansion of the effective gravitational action to all orders in m2. For genus one and larger, this requires the understanding of the role of the zero-modes of the (massless) Dirac operator which is worked out.Besides the Liouville action, at order m0, which only involves the background metric and the conformal factor σ, the various contributions to the effective gravitational action at higher orders in m2 can be expressed in terms of integrals of the renormalized Green’s function at coinciding points of the squared (massless) Dirac operator, as well as of higher Green’s functions. In particular, at order m2, these contributions can be re-written as a term ∫ e2σσ characteristic of the Mabuchi action, much as for 2D massive scalars, as well as several other terms that are multi-local in the conformal factor σ and involve the Green’s functions of the massless Dirac operator and the renormalized Green’s function, but for the background metric only, and certain area-like parameters related to the zero-modes.

Casimir free energy for massive scalars: A comparative study of various approaches

We compute the Casimir thermodynamic quantities for a massive real scalar field between two parallel plates with the Dirichlet boundary conditions, using three different general approaches and present explicit solutions for each. The Casimir thermodynamic quantities include the Casimir Helmholtz free energy, pressure, energy, and entropy. The three general approaches that we use are based on the fundamental definition of Casimir thermodynamic quantities, the analytic continuation method, and the zero temperature subtraction method. Within the analytic continuation approach, we use two distinct methods which are based on the utilization of the zeta function and the Schlömilch summation formula. We include the renormalized versions of the latter two approaches as well, whereas the first approach does not require one. Within each general approach, we obtain the same results in a few different ways to ascertain the selected cancellations of infinities have been done correctly. We show that, as expected, the results based on the zeta function and the Schlömilch summation formula are equivalent. We then do a comparative study of the three different general approaches and their results and show that they are in principle not equivalent to each other, and they yield equivalent results only in the massless case. In particular, we show that the Casimir energy calculated only by the first approach has all three properties of going to zero as the temperature, mass of the field or the distance between the plates increases. Moreover, we show that in this approach the Casimir entropy reaches a positive constant in the high temperature limit, which can explain the linear term in the Casimir free energy. We use the results obtained by the fundamental approach as our reference for the correct results.

Calculations of Scalaron Decay Probabilities

The particle production through the scalaron decays is considered for several different channels. The central part of the work is dedicated to a study of the decay probability into two complex minimally coupled massless scalars. The calculations are performed by two different independent methods. In addition we calculated the decay probability into real minimally coupled massless scalars, conformally coupled massive scalars, massive fermions, and gauge bosons. The results are compared with the published papers which in some cases disagree with each other.

Thermal one point functions, large d and interior geometry of black holes

We study thermal one point functions of massive scalars in AdSd+1 black holes. These are induced by coupling the scalar to either the Weyl tensor squared or the Gauss-Bonnet term. Grinberg and Maldacena argued that the one point functions sourced by the Weyl tensor exponentiate in the limit of large scalar masses and they contain information of the black hole geometry behind the horizon. We observe that the one point functions behave identically in this limit for either of the couplings mentioned earlier. We show that in an appropriate large d limit, the one point function for the charged black hole in AdSd+1 can be obtained exactly. These black holes in general contain an inner horizon. We show that the one point function exponentiates and contains the information of both the proper time between the outer horizon to the inner horizon as well as the proper length from the inner horizon to the singularity. We also show that Gauss-Bonnet coupling induced one point functions in AdSd+1 black holes with hyperbolic horizons behave as anticipated by Grinberg-Maldacena. Finally, we study the one point functions in the background of rotating BTZ black holes induced by the cubic coupling of scalars.

Next-to-leading-order solution to Kerr-Newman black hole superradiance

The superradiant instabilities of Kerr-Newman black holes with charged or uncharged massive spin-0 fields are calculated analytically to the next-to-leading order in the limit of $\alpha\sim r_g \mu \ll 1$. A missing factor of $1/2$ in the previous leading-order result is identified. The next-to-leading order result has a compact form and is in good agreement with existing numerical calculations. The percentage error increases with $\alpha$, from a few percent for $\alpha\sim 0.1$ to about $50\%$ for $\alpha\sim 0.4$. Massive neutral scalars too heavy to be produced with Kerr black hole superradiance may exist in the superradiant region of Kerr-Newman black holes.

Effects of Compactification on Free Massive Scalar Fields in Five-Dimensional Space-Time with an Extra Time Dimension: Analysing Some Results

Effects of Compactification on Free Massive Scalar Fields in Five-Dimensional Space-Time with an Extra Time Dimension: Analysing Some Results

Radiative corrections to stop-antistop annihilation into gluons and light quarks

We present the full one-loop supersymmetry-QCD corrections to stop-antistop annihilation into gluons and light quarks within the Minimal Supersymmetric Standard Model including Sommerfeld enhancement effects from the exchange of multiple gluons between the incoming particles. These corrections are important as stop (co)annihilation becomes the dominant contribution to the relic density for scenarios with a small mass difference between the neutralino and the stop which are less constrained by current LHC searches and consistent with the observation of a 125 GeV SM-like Higgs boson. We discuss important technical details of our one-loop, real emission, and resummation calculations where we pay particular attention to the cancellation of infrared divergences and the associated application of the dipole formalism for massive initial scalars. The corrections have been implemented in the dark matter precision tool dm@nlo which allows us to study numerically the impact of these corrections on the annihilation cross section. We find that for the chosen reference scenario the dominant correction comes from the Sommerfeld effect and that the pure NLO correction is below 3%. The inclusion of these radiative corrections is still large enough to decrease the relic density by more than 10% and shift the cosmologically preferred parameter region by a few GeV relative to the standard micromegas result. Therefore, the inclusion of these corrections is mandatory if the experimental errors are taken as upper and lower bounds of the theory value.

Cosmological bootstrap in slow motion

Speed matters. How the masses and spins of new particles active during inflation can be read off from the statistical properties of primordial density fluctuations is well understood. However, not when the propagation speeds of the new degrees of freedom and of the curvature perturbation differ, which is the generic situation in the effective field theory of inflationary fluctuations. Here we use bootstrap techniques to find exact analytical solutions for primordial 2-,3- and 4-point correlators in this context. We focus on the imprints of a heavy relativistic scalar coupled to the curvature perturbation that propagates with a reduced speed of sound cs, hence strongly breaking de Sitter boosts. We show that akin to the de Sitter invariant setup, primordial correlation functions can be deduced by acting with suitable weight-shifting operators on the four-point function of a conformally coupled field induced by the exchange of the massive scalar. However, this procedure requires the analytical continuation of this seed correlator beyond the physical domain implied by momentum conservation. We bootstrap this seed correlator in the extended domain from first principles, starting from the boundary equation that it satisfies due to locality. We further impose unitarity, reflected in cosmological cutting rules, and analyticity, by demanding regularity in the collinear limit of the four-point configuration, in order to find the unique solution. Equipped with this, we unveil that heavy particles that are lighter than H/cs leave smoking gun imprints in the bispectrum in the form of resonances in the squeezed limit, a phenomenon that we call the low speed collider. We characterise the overall shape of the signal as well as its unusual logarithmic mass dependence, both vividly distinct from previously identified signatures of heavy fields. Eventually, we demonstrate that these features can be understood in a simplified picture in which the heavy field is integrated out, albeit in a non-standard manner resulting in a single-field effective theory that is non-local in space. Nonetheless, the latter description misses the non-perturbative effects of spontaneous particle production, well visible in the ultra-squeezed limit in the form of the cosmological collider oscillations, and it breaks down for masses of order the Hubble scale, for which only our exact bootstrap results hold.