Goldstone's theorem does not apply straightforwardly to the case of spontaneously broken scale invariance. We elucidate under what conditions a light scalar degree of freedom, identifiable with the dilaton, can naturally arise. Our construction can be considered an explicit dynamical solution to the cosmological constant problem in the scalar version of gravity.
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 na\"ively 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.Comment: 45 pages, 15 figures, new result, some corrections and additional comment
Abstract:We consider the transverse-momentum (q T ) distribution of a diphoton pair produced in hadron collisions. At small values of q T , we resum the logarithmically-enhanced perturbative QCD contributions up to next-to-next-to-leading logarithmic accuracy. At intermediate and large values of q T , we consistently combine resummation with the known next-to-leading order perturbative result. All perturbative terms up to order α 2 S are included in our computation which, after integration over q T , reproduces the known nextto-next-to-leading order result for the diphoton pair production total cross section. We present a comparison with LHC data and an estimate of the perturbative accuracy of the theoretical calculation by performing the corresponding variation of scales. In general we observe that the effect of the resummation is not only to recover the predictivity of the calculation at small transverse momentum, but also to improve substantially the agreement with the experimental data.
We present an upgraded calculation of the effects of resonance-continuum interference for the Higgs boson decaying to two photons at the Large Hadron Collider, at next-to-leading order in the strong coupling α S , O(α 3 S ), and including transverse-momentum (q T ) resummation at next-to-leading logarithmic accuracy. We study the importance of the interference contribution in different transverse-momentum regions, with a particular focus on the low q T region q 2 T << Q 2 (with Q 2 being the invariant diphoton mass) where resummation becomes essential for a reliable calculation.
Di-lepton searches for Beyond the Standard Model (BSM) Z bosons that rely on the analysis of the Breit-Wigner (BW) line shape are appropriate in the case of narrow resonances, but likely not sufficient in scenarios featuring Z states with large widths. Conversely, alternative experimental strategies applicable to wide Z resonances are much more dependent than the default bump search analyses on the modelling of QCD higher-order corrections to the production processes, for both signal and background. For heavy Z boson searches in the di-lepton channel at the CERN Large Hadron Collider (LHC), the transverse momentum qT of the di-lepton system peaks at qT ∼ < 10 −2 M ll , where M ll is the di-lepton invariant mass. We exploit this to treat the QCD corrections by using the logarithmic resummation methods in M ll /qT to all orders in the strong coupling constant αs. We carry out studies of Z states with large width at the LHC by employing the program reSolve, which performs QCD transverse momentum resummation up to Next-to-Next-to-Leading Logarithmic (NNLL) accuracy. We consider two benchmark BSM scenarios, based on the Sequential Standard Model (SSM) and dubbed 'SSM wide' and 'SSM enhanced'. We present results for the shape and size of Z boson signals at the differential level, mapped in both cross section (σ) and Forward-Backward Asymmetry (AFB), and perform numerical investigations of the experimental sensitivity at the LHC Run 3 and High-Luminosity LHC (HL-LHC).
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