Browsing by Subject "RENORMALIZATION-GROUP"

Sort by: Order: Results:

Now showing items 1-5 of 5
  • Enckell, Vera-Maria; Enqvist, Kari; Räsänen, Syksy; Tomberg, Eemeli (2018)
    We study inflation with the non-minimally coupled Standard Model Higgs in the case when quantum corrections generate a hilltop in the potential. We consider both the metric and the Palatini formulation of general relativity. We investigate hilltop inflation in different parts of the Higgs potential and calculate predictions for CMB observables. We run the renormalization group equations up from the electroweak scale and down from the hilltop, adding a jump in-between to account for unknown corrections in the intermediate regime. Within our approximation, no viable hilltop inflation is possible for small field values, where the non-minimal coupling has no role, nor for intermediate field values. For large field values, hilltop inflation works. We find the spectral index to be n(s)
  • Lappi, T.; Ramnath, A.; Rummukainen, K.; Weigert, H. (2016)
    We study the effects of a parity-odd "odderon" correlation in Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner renormalization group evolution at high energy. Firstly we show that in the eikonal picture where the scattering is described by Wilson lines, one obtains a strict mathematical upper limit for the magnitude of the odderon amplitude compared to the parity-even Pomeron one. This limit increases with N-c, approaching infinity in the infinite N-c limit. We use a systematic extension of the Gaussian approximation including both two-and three-point correlations which enables us to close the system of equations even at finite N-c. In the large-N-c limit we recover an evolution equation derived earlier. By solving this equation numerically we confirm that the odderon amplitude decreases faster in the nonlinear case than in the linear Balitsky-Fadin-Kuraev-Lipatov limit. We also point out that, in the three-point truncation at finite N-c, the presence of an odderon component introduces azimuthal angular correlations similar to cos(n phi) at all n in the target color field. These correlations could potentially have an effect on future studies of multiparticle angular correlations.
  • Leino, Viljami; Rindlisbacher, Tobias; Rummukainen, Kari; Sannino, Francesco; Tuominen, Kimmo (2020)
    We present the first numerical study of the ultraviolet dynamics of nonasymptotically free gauge-fermion theories at large number of matter fields. As test bed theories, we consider non-Abelian SU(2) gauge theories with 24 and 48 Dirac fermions on the lattice. For these numbers of flavors, asymptotic freedom is lost, and the theories are governed by a Gaussian fixed point at low energies. In the ultraviolet, they can develop a physical cutoff and therefore be trivial, or achieve an interacting safe fixed point and therefore be fundamental at all energy scales. We demonstrate that the gradient flow method can be successfully implemented and applied to determine the renormalized running coupling when asymptotic freedom is lost. Additionally, we prove that our analysis is connected to the Gaussian fixed point as our results nicely match with the perturbative beta function. Intriguingly, we observe that it is hard to achieve large values of the renormalized coupling on the lattice. This might be an early sign of the existence of a physical cutoff and imply that a larger number of flavors is needed to achieve the safe fixed point. A more conservative interpretation of the results is that the current lattice action is unable to explore the deep ultraviolet region where safety might emerge. Our work constitutes an essential step toward determining the ultraviolet fate of nonasymptotically free gauge theories.
  • Ducloue, B.; Iancu, E.; Lappi, T.; Mueller, A. H.; Soyez, G.; Triantafyllopoulos, D. N.; Zhu, Y. (2018)
    We address and solve a puzzle raised by a recent calculation [1] of the cross section for particle production in proton-nucleus collisions to next-to-leading order: the numerical results show an unreasonably large dependence upon the choice of a prescription for the QCD running coupling, which spoils the predictive power of the calculation. Specifically, the results obtained with a prescription formulated in the transverse coordinate space differ by 1 to 2 orders of magnitude from those obtained with a prescription in momentum space. We show that this discrepancy is an artifact of the interplay between the asymptotic freedom of QCD and the Fourier transform from coordinate space to momentum space. When used in coordinate space, the running coupling can act as a fictitious potential which mimics hard scattering and thus introduces a spurious contribution to the cross section. We identify a new coordinate-space prescription, which avoids this problem, and leads to results consistent with those obtained with the momentum-space prescription.