We present improved perturbative QCD (pQCD) predictions for Higgs boson hadroproduction at the LHC by applying the principle of maximum conformality (PMC), a procedure which resums the pQCD series using the renormalization group (RG), thereby eliminating the dependence of the predictions on the choice of the renormalization scheme while minimizing sensitivity to the initial choice of the renormalization scale. In previous pQCD predictions for Higgs boson hadroproduction, it has been conventional to assume that the renormalization scale mu(r) of the QCD coupling sigma(s)(mu(r)) is the Higgs mass and then to vary this choice over the range 1/2m(H) < mu(r) < 2m(H) in order to estimate the theory uncertainty. However, this error estimate is only sensitive to the nonconformal beta terms in the pQCD series, and thus it fails to correctly estimate the theory uncertainty in cases where a pQCD series has large higher-order contributions, as is the case for Higgs boson hadroproduction. Furthermore, this ad hoc choice of scale and range gives pQCD predictions which depend on the renormalization scheme being used, in contradiction to basic RG principles. In contrast, after applying the PMC, we obtain next-to-next-to-leading-order RG resummed pQCD predictions for Higgs boson hadroproduction which are renormalization-scheme independent and have minimal sensitivity to the choice of the initial renormalization scale. Taking m(H) = 125 GeV, the PMC predictions for the pp -> HX Higgs inclusive hadroproduction cross sections for various LHC center-of-mass energies are sigma(Incl vertical bar 7 TeV) = 21.21(-1.32)(+1.36) pb, sigma(Incl vertical bar 8 TeV) = 27.37(-1.59)(+1.65) pb, and sigma I-ncl vertical bar 13 TeV = 65.72(-3.01)(+3.46) pb. We also predict the fiducial cross section sigma fid(pp -> H -> gamma gamma): sigma(fid vertical bar 7 TeV) = 30.1(-2.2)(+2.3) fb, sigma(fid vertical bar 8 TeV) = 38.3(-2.8)(+2.9) fb, and sigma(fid vertical bar 13 TeV) = 85.8(-5.3)(+5.7) fb. The error limits in these predictions include the small residual high-order renormalization-scale dependence plus the uncertainty from the factorization scale. The PMC predictions show better agreement with the ATLAS measurements than the LHC Higgs Cross Section Working Group predictions which are based on conventional renormalization-scale setting.

We replace the standard Higgs-mechanism by the Coleman-Weinberg mechanism, and investigate its viability through the addition of a new scalar field. As we showed in a previous study, minimal models of this type can alleviate the hierarchy problem of the Higgs-mass through the so-called Veltman conditions. We here extend the previous analysis by taking into account the important difference between running mass and pole mass of the scalar states. We then investigate whether these theories can account for the 750 GeV excess in diphotons observed by the LHC collaborations. New QCD-colored fermions in the TeV mass range coupled to the new scalar state are needed to describe the excess. We further show, by explicit computation of the running of the couplings, that the model is under perturbative control till just above the masses of the heaviest states of the theory. We further suggest related testable signatures and thereby show that the LHC experiments can test these models.

We study the soft behavior of two seemingly different particles that are both referred to as dilatons in the literature, namely the one that appears in theories of gravity and in string theory and the Nambu-Goldstone boson of spontaneously broken conformal invariance. Our primary result is the discovery of a soft theorem at subsubleading order for each dilaton, which in both cases contains the operator of special conformal transformations. Interesting similarities as well as differences between the dilaton soft theorems are discussed.

Starting from the amplitude with an arbitrary number of massless closed states of the bosonic string, we compute the soft limit when one of the states becomes soft to subsubleading order in the soft momentum expansion, and we show that when the soft state is a graviton or a dilaton, the full string amplitude can be expressed as a soft theorem through subsubleading order. It turns out that there are string corrections to the field theoretical limit in the case of a soft graviton, while for a soft dilaton the string corrections vanish. We then show that the new soft theorems, including the string corrections, can be simply obtained from the exchange diagrams where the soft state is attached to the other external states through the three-point string vertex of three massless states. In the soft-limit, the propagator of the exchanged state is divergent, and at tree-level these are the only divergent contributions to the full amplitude. However, they do not form a gauge invariant subset and must be supplemented with extra non-singular terms. The requirement of gauge invariance then fixes the complete amplitude through subsubleading order in the soft expansion, reproducing exactly what one gets from the explicit calculation in string theory. From this it is seen that the string corrections at subsubleading order arise as a consequence of the three-point amplitude having string corrections in the bosonic string. When specialized to a soft dilaton, it remarkably turns out that the string corrections vanish and that the non-singular piece of the subsubleading term of the dilaton soft theorem is the generator of space-time special conformal transformation.

We study the phase diagram and the stability of the ground state for certain four-dimensional gauge-Yukawa theories whose high-energy behaviour is controlled by an interacting fixed point. We also provide analytical and numerical results for running couplings, their crossover scales, the separatrix, and the Coleman-Weinberg effective potential. Classical and quantum stability of the vacuum is established.

The Principle of Maximum Conformality (PMC) eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero beta-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I); the other, more recent, method (PMC-II) uses the R-delta-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio Re+e- and the Higgs partial width Gamma(H -> b (b) over bar). Both methods lead to the same resummed ('conformal') series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {beta(i)}-terms in the pQCD expansion are taken into account. We also show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.

We compute the leading double-soft behavior for gluons and for the scalars obtained by dimensional reduction of a higher dimensional pure gauge theory, from the scattering amplitudes of gluons and scalars living in the world-volume of a Dp-brane of the bosonic string. In the case of gluons, we compute both the double-soft behavior when the two soft gluons are contiguous as well as when they are not contiguous. From our results, that are valid in string theory, one can easily get the double-soft limit in gauge field theory by sending the string tension to infinity.

We elucidate and extend the conditions that map gauge-Yukawa theories at low energies into time-honored gauged four-fermion interactions at high energies. These compositeness conditions permit us to investigate theories of composite dynamics through gauge-Yukawa theories. Here we investigate whether perturbative gauge-Yukawa theories can have a strongly coupled limit at high energy that can be mapped into a four-fermion theory. Interestingly, we are able to precisely carve out a region of the perturbative parameter space supporting such a composite limit. This has interesting implications on our current view on models of particle physics. As a template model we use an SU(N-C) gauge theory with N-F Dirac fermions transforming according to the fundamental representation of the gauge group. The fermions further interact with a gauge singlet complex N-F x N-F Higgs boson that ceases to be a physical degree of freedom at the ultraviolet composite scale, where it gives away to the four-fermion interactions. We compute the hierarchy between the ultraviolet and infrared composite scales of the theory and show that they are naturally large and well separated. Our results show that some weakly coupled gauge-Yukawa theories can be viewed, in fact, as composite theories. It is therefore tantalizing to speculate that the standard model, with its phenomenological perturbative Higgs sector, could hide, in plain sight, a composite theory.

A key problem in making precise perturbative QCD (pQCD) predictions is how to set the renormalization scale of the running coupling unambiguously at each finite order. The elimination of the uncertainty in setting the renormalization scale in pQCD will greatly increase the precision of collider tests of the Standard Model and the sensitivity to new phenomena. Renormalization group invariance requires that predictions for observables must also be independent on the choice of the renormalization scheme. The well-known Brodsky-Lepage-Mackenzie (BLM) approach cannot be easily extended beyond next-to-next-to-leading order of pQCD. Several suggestions have been proposed to extend the BLM approach to all orders. In this paper we discuss two distinct methods. One is based on the Principle of Maximum Conformality (PMC), which provides a systematic all-orders method to eliminate the scale and scheme ambiguities of pQCD. The PMC extends the BLM procedure to all orders using renormalization group methods; as an outcome it significantly improves the pQCD convergence by eliminating renormalon divergences. An alternative method is the sequential extended BLM (seBLM) approach, which has been primarily designed to improve the convergence of pQCD series. The seBLM, as originally proposed, introduces auxiliary fields and follows the pattern of the beta(0)-expansion to fix the renormalization scale. However, the seBLM requires a recomputation of pQCD amplitudes including the auxiliary fields; due to the limited availability of calculations using these auxiliary fields, the seBLM has only been applied to a few processes at low orders. In order to avoid the complications of adding extra fields, we propose a modified version of seBLM which allows us to apply this method to higher orders. We then perform detailed numerical comparisons of the two alternative scale-setting approaches by investigating their predictions for the annihilation cross section ratio Re+e- at four-loop order in pQCD.

We study the behavior of the scattering amplitudes of the bosonic string involving a soft massless state (graviton, dilaton and Kalb-Ramond antisymmetric tensor) and closed string tachyons or other closed string massless states. For a soft graviton we confirm the results, obtained in ref. [37] using just gauge invariance, up to terms of O(q(1)) for external tachyons and up to terms of O(q(0)) for external massless closed string states. Furthermore, we also derive the behavior of the scattering amplitude when a dilaton or a Kalb-Ramond field becomes soft. These results are new and cannot, to our knowledge, be derived by using gauge invariance. It turns out, in the cases examined, that the soft amplitude for a dilaton or for an antisymmetric tensor is obtained by saturating the tensor, M (mu nu) , derived from gauge invariance for gravitons, with their respective polarization tensors. Thus extra terms that could have appeared in M (mu nu) in the case of a soft dilaton, in fact do not appear.