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Marcello Ciafaloni

Publications and source records attributed to Marcello Ciafaloni.

At least 19 recordsLinked to original sources
arXiv2019

Infrared features of gravitational scattering and radiation in the eikonal approach

Following a semi-classical eikonal approach --- justified at transplanckian energies order by order in the deflection angle $Θ_s\sim\frac{4G\sqrt{s}}{b} \equiv \frac{2 R}{b}$ --- we investigate the infrared features of gravitational scattering and radiation in four space-time dimensions, and we illustrate the factorization and cancellation of the infinite Coulomb phase for scattering and the eikonal resummation for radiation. As a consequence, both the eikonal phase $2δ(E,b)$ and the gravitational-wave (GW) spectrum $\frac{\mathrm{d}E^{GW}}{\mathrm{d}ω}$ are free from infrared problems in a frequency region extending from zero to (and possibly beyond) $ω=1/R$. The infrared-singular behavior of $4$-D gravity leaves a memory in the deep infrared region ($ωR \ll ωb < 1$) of the spectrum. At $\mathcal{O}(ωb)$ we confirm the presence of logarithmic enhancements of the form already pointed out by Sen and collaborators on the basis of non leading corrections to soft-graviton theorems. These, however, do not contribute to the unpolarized and/or azimuthally-averaged flux. At $\mathcal{O}(ω^2 b^2)$ we find instead a positive logarithmically-enhanced correction to the total flux implying an unexpected maximum of its spectrum at $ωb \sim 0.5$. At higher orders we find subleading enhanced contributions as well, which can be resummed, and have the interpretation of a finite rescattering Coulomb phase of emitted gravitons.

hep-th↗
arXiv2017

Radiation enhancement and "temperature" in the collapse regime of gravitational scattering

We generalize the semiclassical treatment of graviton radiation to gravitational scattering at very large energies $\sqrt{s}\gg m_P$ and finite scattering angles $Θ_s$, so as to approach the collapse regime of impact parameters $b \simeq b_c \sim R\equiv 2G\sqrt{s}$. Our basic tool is the extension of the recently proposed, unified form of radiation to the ACV reduced-action model and to its resummed-eikonal exchange. By superimposing that radiation all-over eikonal scattering, we are able to derive the corresponding (unitary) coherent-state operator. The resulting graviton spectrum, tuned on the gravitational radius $R$, fully agrees with previous calculations for small angles $Θ_s\ll 1$ but, for sizeable angles $Θ_s(b)\leq Θ_c = O(1)$ acquires an exponential cutoff of the large $ωR$ region, due to energy conservation, so as to emit a finite fraction of the total energy. In the approach-to-collapse regime of $b\to b_c^+$ we find a radiation enhancement due to large tidal forces, so that the whole energy is radiated off, with a large multiplicity $\langle N \rangle\sim Gs \gg 1$ and a well-defined frequency cutoff of order $R^{-1}$. The latter corresponds to the Hawking temperature for a black hole of mass notably smaller than $\sqrt{s}$.

hep-th↗
arXiv2017

Unitarity restoring graviton radiation in the collapse regime of scattering

We investigate graviton radiation in gravitational scattering at small impact parameters $b b$, so as to suggest a possible completion of the unitarity sum. In fact, such energy radiation at large distances turns out to compensate and to gradually reduce to nothing the amount of energy $E'$ being trapped at small-$b$'s, by thus avoiding the quantum tunneling suppression of the elastic scattering and suggesting a unitary evolution. We finally look at the coherent radiation sample so obtained and we find that, by energy conservation, it develops an exponential frequency damping corresponding to a "quasi-temperature" of order $\hbar/R$, which is naturally related to a Hawking radiation and is suggestive of a black-hole signal at quantum level.

hep-th↗
arXiv2016

Radiation enhancement and "temperature" in the collapse regime of gravitational scattering

We generalize the semiclassical treatment of graviton radiation to gravitational scattering at very large energies $\sqrt{s}\gg m_P$ and finite scattering angles $Θ_s$, so as to approach the collapse regime of impact parameters $b \simeq b_c \sim R\equiv 2G\sqrt{s}$. Our basic tool is the extension of the recently proposed, unified form of radiation to the ACV reduced-action model and to its resummed-eikonal exchange. By superimposing that radiation all-over eikonal scattering, we are able to derive the corresponding (unitary) coherent-state operator. The resulting graviton spectrum, tuned on the gravitational radius $R$, fully agrees with previous calculations for small angles $Θ_s\ll 1$ but, for sizeable angles $Θ_s(b)\leq Θ_c = O(1)$ acquires an exponential cutoff of the large $ωR$ region, due to energy conservation, so as to emit a finite fraction of the total energy. In the approach-to-collapse regime of $b\to b_c^+$ we find a radiation enhancement due to large tidal forces, so that the whole energy is radiated off, with a large multiplicity $\langle N \rangle\sim Gs \gg 1$ and a well-defined frequency cutoff of order $R^{-1}$. The latter corresponds to the Hawking temperature for a black hole of mass notably smaller than $\sqrt{s}$.

hep-th↗
arXiv2015

Unified limiting form of graviton radiation at extreme energies

We derive the limiting form of graviton radiation in gravitational scattering at transplanckian energies ($E\gg M_P$) and small deflection angles. We show that --- owing to the graviton's spin 2 --- such limiting form unifies the soft- and Regge- regimes of emission, by covering a broad angular range, from forward fragmentation to deeply central region. The single-exchange emission amplitudes have a nice expression in terms of the transformation phases of helicity amplitudes under rotations. As a result, the multiple-exchange emission amplitudes can be resummed via an impact parameter $b$-space factorization theorem that takes into account all coherence effects. We then see the emergence of an energy spectrum of the emitted radiation which, being tuned on $\hbar/R \sim M_P^2/E \ll M_P$, is reminiscent of Hawking's radiation. Such a spectrum is much softer than the one naïvely expected for increasing input energies and neatly solves a potential energy crisis. Furthermore, by including rescattering corrections in the (quantum) factorization formula, we are able to recover the classical limit and to find the corresponding quantum corrections. Perspectives for the extrapolation of such limiting radiation towards the classical collapse regime (where $b$ is of the order of the gravitational radius $R$) are also discussed.

hep-th↗
arXiv2015

Emerging Hawking-like Radiation from Gravitational Bremsstrahlung Beyond the Planck Scale

We argue that, as a consequence of the graviton's spin-2, its bremsstrahlung in trans-planckian-energy ($E\gg M_P$) gravitational scattering at small deflection angle can be nicely expressed in terms of helicity-transformation phases and their transfer within the scattering process. The resulting spectrum exhibits deeply sub-planckian characteristic energies of order $M_P^2/E \ll M_P$ (reminiscent of Hawking radiation), a suppressed fragmentation region, and a reduced rapidity plateau, in broad agreement with recent classical estimates.

hep-th↗
arXiv2014

Rescattering corrections and self-consistent metric in Planckian scattering

Starting from the ACV approach to transplanckian scattering, we present a development of the reduced-action model in which the (improved) eikonal representation is able to describe particles' motion at large scattering angle and, furthermore, UV-safe (regular) rescattering solutions are found and incorporated in the metric. The resulting particles' shock-waves undergo calculable trajectory shifts and time delays during the scattering process --- which turns out to be consistently described by both action and metric, up to relative order $R^2/b^2$ in the gravitational radius over impact parameter expansion. Some suggestions about the role and the (re)scattering properties of irregular solutions --- not fully investigated here --- are also presented.

hep-th↗
arXiv2010

Anomalous Sudakov Form Factors

While radiative corrections of infrared origin normally depress high energy amplitudes (Sudakov form factors), we find that in some cases resummation of leading effects produces exponentials with positive exponents, giving rise to amplitudes that grow indefinitely with energy. The effect happens in broken gauge theories like the electroweak sector of the Standard Model, and is related to the existence of amplitudes that do not respect the gauge symmetry, and that contrary to expectations do not vanish in the very high energy limit, but rather become dominant. As a working example we consider a model with two chiral abelian gauge groups $U'(1)\otimes U(1)$ with large mass splitting $M_{Z'} \gg M_{Z} $, and we compute leading radiative corrections corrections to the decay of the heavy extra ${Z'}$ boson into light fermions. For proper fermionic charges, the chirality breaking magnetic dipole moment, although mass suppressed, becomes the dominant contribution to the $Z'$ width at very high energies.

hep-ph↗
arXiv2004

The gluon splitting function at moderately small x

It is widely believed that at small x, the BFKL resummed gluon splitting function should grow as a power of 1/x. But in several recent calculations it has been found to decrease for moderately small-x before eventually rising. We show that this `dip' structure is a rigorous feature of the P_gg splitting function for sufficiently small alpha_s, the minimum occurring formally at ln 1/x of order 1/sqrt(alpha_s). We calculate the properties of the dip, including corrections of relative order sqrt(alpha_s), and discuss how this expansion in powers of sqrt(alpha_s), which is poorly convergent, can be qualitatively matched to the fully resummed result of a recent calculation, for realistic values of alpha_s. Finally, we note that the dip position, as a function of alpha_s, provides a lower bound in x below which the NNLO fixed-order expansion of the splitting function breaksdown and the resummation of small-x terms is mandatory.

hep-ph↗
arXiv2003

Extending the QCD Perturbative Domain to Higher Energies

After a brief introduction to low-x QCD and to resummation approaches, I illustrate the predictions for the gluon Green function and splitting function of a recent renormalization-group improved small-x resummation scheme. I argue, on this basis, that the range of validity of perturbative calculations is considerably extended in rapidity with respect to leading log expectations. The perturbative high-energy exponents are predicted in a phenomenologically interesting range, and significant preasymptotic effects are found. In particular, the splitting function shows a shallow dip in the moderate-x region, followed by the expected small-x power increase.

hep-ph↗
arXiv2001

Diffusion corrections to the hard pomeron

The high-energy behaviour of two-scale hard processes is investigated in the framework of small-x models with running coupling, having the Airy diffusion model as prototype. We show that, in some intermediate high-energy regime, the perturbative hard Pomeron exponent determines the energy dependence, and we prove that diffusion corrections have the form hinted at before in particular cases. We also discuss the breakdown of such regime at very large energies, and the onset of the non-perturbative Pomeron behaviour.

hep-ph↗
arXiv2001

Enhanced Electroweak Corrections to Inclusive Boson Fusion Processes at the TeV Scale

Electroweak radiative corrections with double-log enhancements occur in inclusive observables at the TeV scale because of a lack of compensation of virtual corrections with real emission due to the nonabelian (weak isospin) charges of the accelerator beams. Here we evaluate such Bloch-Nordsieck violating corrections in the case of initial longitudinal bosons, which is experimentally provided by boson fusion processes, and is related to the Goldstone-Higgs sector. All four states of this sector are involved in the group structure of the corrections, and cause in particular a novel double log effect due to hypercharge mixing in the longitudinal states. We study both the light- and the heavy-Higgs cases, and we analyze the symmetry breaking pattern of the corrections. The latter turn out to be pretty large, in the 5-10 % range, and show an interesting Higgs mass dependence, even for processes without Higgs boson in the final state.

hep-ph↗
arXiv2001

Bloch-Nordsieck Violation in Spontaneously Broken Abelian Theories

We point out that, in a spontaneously broken U(1) gauge theory, inclusive processes, whose primary particles are mass eigenstates that do not coincide with the gauge eigenstates, are not free of infrared logarithms. The charge mixing allowed by symmetry breaking and the ensuing Bloch-Nordsieck violation are here analyzed in a few relevant cases and in particular for processes initiated by longitudinal gauge bosons. Of particular interest is the example of weak hypercharge in the Standard Model where, in addition, left-right mixing effects arise in transversely polarized fermion beams.

hep-ph↗
arXiv2000

QCD factorization with heavy quarks

We further analyze the definition and the calculation of the heavy quark impact factor at next-to-leading (NL) $\log s$ level, and we provide its analytical expression in a previously proposed k-factorization scheme. Our results indicate that k-factorization holds at NL level with a properly chosen energy scale, and with the same gluonic Green's function previously found in the massless probe case.

hep-ph↗
arXiv2000

On factorisation at small x

We investigate factorisation at small x using a variety of analytical and numerical techniques. Previous results on factorisation in collinear models are generalised to the case of the full BFKL equation, and illustrated in the example of a collinear model which includes higher twist terms. Unlike the simplest collinear model, the BFKL equation leads to effective anomalous dimensions containing higher-twist pieces which grow as a (non-perturbative) power at small x. While these pieces dominate the effective splitting function at very small x they do not lead to a break-down of factorisation insofar as their effect on the predicted scaling violations remains strongly suppressed.

hep-ph↗
arXiv2000

Heavy Quark Impact Factor at Next-to-leading Level

We further analyze the definition and the calculation of the heavy quark impact factor at next-to-leading (NL) log(s) level, and we provide its analytical expression in a previously proposed k-factorization scheme. Our results indicate that k-factorization holds at NL level with a properly chosen energy scale, and with the same gluonic Green's function previously found in the massless probe case.

hep-ph↗
arXiv1999

Renormalization Group Improved BFKL Equation

I report on the recent proposal of a generalized small-x equation which, in addition to exact leading and next-to-leading BFKL kernels, incorporates renormalization group constraints in the relevant collinear limits.

hep-ph↗