It has been claimed that the electroweak vacuum may be unstable during inflation due to large fluctuations of the order H in the case of a high inflationary scale as suggested by BICEP2. We compute the standard model Higgs effective potential including UV-induced curvature corrections at one-loop level. We find that for a high inflationary scale a large curvature mass is generated due to renormalization group running of nonminimal coupling ξ, which either stabilizes the potential against fluctuations for ξEW≳6×10(-2), or destabilizes it for ξEW≲2×10(-2) when the generated curvature mass is negative. Only in the narrow intermediate region may the effect of the curvature mass be significantly smaller.

No abstract

We investigate the dynamics of the Higgs field at the end of inflation in the minimal scenario consisting of an inflaton field coupled to the Standard Model only through the non-minimal gravitational coupling ξ of the Higgs field. Such a coupling is required by renormalisation of the Standard Model in curved space, and in the current scenario also by vacuum stability during high-scale inflation. We find that for ξ 1, rapidly changing spacetime curvature at the end of inflation leads to significant production of Higgs particles, potentially triggering a transition to a negative-energy Planck scale vacuum state and causing an immediate collapse of the Universe.PACS numbers: 98.80. Cq, 04.62.+v The Standard Model (SM) of particle physics can be consistently extrapolated to the Planck scale without any new physics, but the current measurements of the Higgs boson and top quark masses suggest that the current vacuum state of the Universe would then not be stable. This instability depends sensitively on the top mass m t , which is subject to significant experimental and theoretical uncertainty [19], but for the best fit values, the Higgs potential turns negative above the instability scale Λ I ∼ 1011 GeV [21]. This implies that the current vacuum would eventually decay into a negative-energy Planck scale true vacuum, but its lifetime exceeds the age of the universe by a wide margin [1].Whether such a metastable universe could have survived the cosmological evolution, especially inflation, has recently attracted significant interest [3][4][5]. In most of the simplest models of inflation, the Hubble rate during inflation is comparable to the current upper bound H 9 × 10 13 GeV [8]. It may therefore well be above the instability scale, in which case production of Higgs fluctuations could push the field over the potential barrier into the true Planck-scale vacuum [3]. This instability problem is exacerbated by spacetime curvature induced running of the couplings, which makes the Higgs selfcoupling negative even at low field values [4][5][6].Notably, vacuum stability can still be maintained even during inflation without any new physics coupled to the SM fields [4], thanks to the Higgs-curvature coupling ξRĤ †Ĥ . This coupling is inevitably generated by radiative corrections and when assuming the SM to be valid up to the Planck scale it is the only relevant new term when probing sub-Planckian scales. The current experimental constraints are extremely weak, |ξ| 2.6×1015 [7]. With a positive coupling, this term increases the height of the potential barrier between the vacua, thereby increasing the lifetime of the metastable vacuum. Vacuum stability is maintained for all inflationary scales compatible with the tensor bound [8], provided the electroweak scale value of the running coupling ξ(µ) lies above ξ EW 0.1 [4].In this letter, we investigate the instability problem at the end of inflation, again assuming no new physics or higher-dimensional operators but taking the gravitational coupling ξ into account. In contrast with...

Employing a nonperturbative gauge invariant definition of the Debye screening mass m D in the effective field theory approach to finite temperature QCD, we use 3D lattice simulations to determine the leading O ͑g 2 ͒ and to estimate the next-to-leading O ͑g 3 ͒ corrections to m D in the high temperature region. The O ͑g 2 ͒ correction is large and modifies qualitatively the standard power-counting hierarchy picture of correlation lengths in high temperature QCD. [S0031-9007(97)04353-6] PACS numbers: 11.10. Wx, 11.15.Ha, 12.38.Mh QCD matter, a spatially and temporally extended system of matter described by the laws of quantum chromodynamics, goes at high temperatures into a quark-gluon plasma phase, in which color is no more confined and chiral symmetry is restored. An essential quantity, describing coherent static interactions in the plasma, is the inverse screening length of color electric fields, the Debye mass m D . The Debye mass enters in many essential characteristics of static properties of the plasma. Its numerical value is important for phenomenological discussions of formation of the quark-gluon plasma, for the analysis of J͞C and Y suppression in heavy ion collisions, for the computation of parton equilibration rates, etc. (see, e.g., [1]).The definition and computation of the Debye mass for Abelian QED plasma is well understood [2]. The electromagnetic current j m is a gauge-invariant quantity, and the Debye mass can be extracted from the two-point gauge invariant correlation function of j 0 in the plasma. There are no massless charged particles in QED, which allows an infrared-safe perturbative computation of the Debye mass in powers of the electromagnetic coupling e. This has been done to order e 5 [3]. The situation in QCD is much more complicated. First, the corresponding current in QCD, j a m , is not a gauge-invariant quantity. Second, there are massless charged gluons which give rise to infrared divergences and prevent the perturbative determination of the Debye mass beyond leading order.A nonperturbative gauge-invariant definition of the Debye mass in vectorlike theories with zero chemical potential was suggested in [4]. According to it, m D can be defined from the large distance exponential falloff of correlators of gauge-invariant time-reflection odd The aim of this Letter is a nonperturbative determination of the high temperature limit of the Debye mass, at T . a few 3 T c . We will see that the effective 3D approach to high temperature gauge theories, developed in [5][6][7] (for a review, see [8]) allows a simple and transparent gauge-invariant definition of the Debye mass [4], while 3D lattice Monte Carlo simulations provide an economical way to determine its value. The corrections to the leading result we shall find are numerically large; thus many computations in the phenomenology of quark-gluon plasma in heavy ion collisions should be reanalyzed.The theory we shall study is QCD with N f massless quark flavors and with the gauge group SU͑N͒ with N 2, 3. At high temperatures and zero...