Ultraviolet Pole Research Articles

Quantum scale invariance in gauge theories and applications to muon production

We discuss quantum scale invariance in (scale invariant) gauge theories with both ultraviolet (UV) and infrared (IR) divergences. Firstly, their BRST invariance is checked in two apparently unrelated approaches using a scale invariant regularisation (SIR). These approaches are then shown to be equivalent. Secondly, for the Abelian case we discuss both UV and IR quantum corrections present in such theories. We present the Feynman rules in a form suitable for offshell Green functions calculations, together with their one-loop renormalisation. This information is then used for the muon production cross section at one-loop in a quantum scale invariant theory. Such a theory contains not only new UV poles but also IR poles. While the UV poles bring new quantum corrections (in the form of counterterms), finite or divergent, that we compute, it is shown that the IR poles do not bring new physics. The IR quantum corrections, both finite and divergent, cancel out similarly to the way the IR poles themselves cancel in the traditional approach to IR divergences (in the cross section, after summing over virtual and real corrections). Hence, the evanescent interactions induced by the scale-invariant analytical continuation of the SIR scheme do not affect IR physics, as illustrated at one-loop for the muon production ($e^+ e^- \to \mu^+\mu^-$) cross section.

From boundary data to bound states. Part III. Radiative effects

We extend the boundary-to-bound (B2B) correspondence to incorporate radiative as well as conservative radiation-reaction effects. We start by deriving a map between the total change in observables due to gravitational wave emission during hyperbolic-like motion and in one period of an elliptic-like orbit, which is valid in the adiabatic expansion for non-spinning as well as aligned-spin configurations. We also discuss the inverse problem of extracting the associated fluxes from scattering data. Afterwards we demonstrate, to all orders in the Post-Minkowskian expansion, the link between the radiated energy and the ultraviolet pole in the radial action in dimensional regularization due to tail effects. This implies, as expected, that the B2B correspondence for the conservative sector remains unchanged for local-in-time radiation-reaction tail effects with generic orbits. As a side product, this allows us to read off the energy flux from the associated pole in the tail Hamiltonian. We show that the B2B map also holds for non-local-in-time terms, but only in the large-eccentricity limit. Remarkably, we find that all of the trademark logarithmic contributions to the radial action map unscathed between generic unbound and bound motion. However, unlike logarithms, other terms due to non-local effects do not transition smoothly to quasi-circular orbits. We conclude with a discussion on these non-local pieces. Several checks of the B2B dictionary are displayed using state-of-the-art knowledge in Post-Newtonian/Minkowskian theory.

Two-Loop QCD Corrections to Wbb[over ¯] Production at Hadron Colliders.

We present an analytic computation of the two-loop QCD corrections to ud[over ¯]→W^{+}bb[over ¯] for an on-shell W boson using the leading color and massless bottom quark approximations. We perform an integration-by-parts reduction of the unpolarized squared matrix element using finite field reconstruction techniques and identify an independent basis of special functions that allows an analytic subtraction of the infrared and ultraviolet poles. This basis is valid for all planar topologies for five-particle scattering with an off-shell leg.

Conservative dynamics of binary systems to fourth post-Newtonian order in the EFT approach. II. Renormalized Lagrangian

We complete the derivation of the conservative dynamics of binary systems to fourth Post-Newtonian (4PN) order in the effective field theory (EFT) approach. We present a self-contained (ambiguity-free) computation of the renormalized Lagrangian, entirely within the confines of the PN expansion. While we confirm the final results reported in the literature, we clarify several issues regarding intermediate infrared (IR) and ultraviolet (UV) divergences, as well as the renormalization procedure. First, we properly identify the IR and UV singularities using (only) dimensional regularization and the method of regions, which are the pillars of the EFT formalism. This requires a careful study of scaleless integrals in the potential region, as well as conservative contributions from radiation modes due to tail effects. As expected by consistency, the UV divergences in the near region (due to the point-particle limit) can be absorbed into two counter-terms in the worldline effective theory. The counter-terms can then be removed by field redefinitions, such that the renormalization scheme-dependence has no physical effect to 4PN order. The remaining IR poles, which are spurious in nature, are unambiguously removed by implementing the zero-bin subtraction in the EFT approach. The procedure transforms the IR singularities into UV counter-parts. As anticipated, the left-over UV poles explicitly cancel out against UV divergences in conservative terms from radiation-reaction, uniquely determining the gravitational potential. Similar artificial IR/UV poles, which are intimately linked to the split into regions, are manifest at lower orders. Starting at 4PN, both local- and nonlocal-in-time contributions from the radiation region enter in the conservative dynamics. Neither additional regulators nor ambiguity-parameters are introduced at any stage of the computations.

A unitarity compatible approach to one-loop amplitudes with massive fermions

We explain how one-loop amplitudes with massive fermions can be computed using only on-shell information. We first use the spinor-helicity formalism in six dimensions to perform generalised unitarity cuts in d dimensions. We then show that divergent wave-function cuts can be avoided, and the remaining ambiguities in the renormalised amplitudes can be fixed, by matching to universal infrared poles in 4 − 2ϵ dimensions and ultraviolet poles in 6 − 2ϵ dimensions. In the latter case we construct an effective Lagrangian in six dimensions and reduce the additional constraint to an on-shell tree-level computation.

Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD.

Virtual two-loop corrections to scattering amplitudes are a key ingredient to precision physics at collider experiments. We compute the full set of planar master integrals relevant to five-point functions in massless QCD, and use these to derive an analytical expression for the two-loop five-gluon all-plus-helicity amplitude. After subtracting terms that are related to the universal infrared and ultraviolet pole structure, we obtain a remarkably simple and compact finite remainder function, consisting only of dilogarithms.

Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes

We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N=4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude's integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N=8 supergravity integrand, whose graph numerators are double copies (squares) of the N=4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop four-point supergravity amplitude makes manifest the same ultraviolet power counting as the corresponding N=4 super-Yang-Mills amplitude. We determine the amplitude's ultraviolet pole in the critical dimension of D=11/2, the same dimension as for N=4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after simplification) describes the ultraviolet divergence of N=8 supergravity as the subleading-in-1/N_c^2 single-trace divergence in N=4 super-Yang-Mills theory.

Five-point amplitudes inN=4super-Yang-Mills theory andN=8supergravity

We present the complete integrands of five-point superamplitudes in $\mathcal{N}=4$ super-Yang-Mills theory and $\mathcal{N}=8$ supergravity, at one and two loops, for four-dimensional external states and $D$-dimensional internal kinematics. For $\mathcal{N}=4$ super-Yang-Mills theory we give the amplitudes for general gauge group---including all nonplanar contributions. The results are constructed using integral diagrams that manifestly satisfy the conjectured duality between color and kinematics, providing additional nontrivial evidence in favor of the duality for multipoint and multiloop amplitudes. We determine the ultraviolet poles by integrating the amplitudes in the dimensions where logarithmic divergences first occur. We introduce new kinematic prefactors which offer a convenient decomposition of the external state structure of the nonplanar five-point amplitudes in the maximally supersymmetric theories to all loop orders.

Exact one-loop running couplings in the standard model

Taking the dominant couplings in the standard model to be the quartic scalar coupling, the Yukawa coupling of the top quark, and the SU(3) gauge coupling, we consider their associated running couplings to one-loop order. Despite the nonlinear nature of the differential equations governing these functions, we show that they can be solved exactly. The nature of these solutions is discussed and their singularity structure is examined. It is shown that for a sufficiently small Higgs mass, the quartic scalar coupling decreases with increasing energy scale and becomes negative, indicative of vacuum instability. This behavior changes for a Higgs mass greater than 168 GeV, beyond which this couplant increases with increasing energy scales and becomes singular prior to the ultraviolet pole of the Yukawa coupling. Upper and lower bounds on the Higgs mass corresponding to new physics at the TeV scale are obtained and compare favourably with the numerical results of the one-loop and two-loop analyses with inclusion of electroweak couplings.PACS Nos.: 11.10.Hi, 14.80.Bn

Ultraviolet poling of pure fused silica by high-intensity femtosecond radiation

We demonstrate UV poling of a pure fused silica sample by applying to it an electric field of 200 kV/cm and irradiating it with high-intensity (∼40GW∕cm2) femtosecond (220 fs) laser pulses at 264 nm.

Thermal one- and two-graviton Green’s functions in the temporal gauge

The thermal one- and two-graviton Green's function are computed using a temporal gauge. In order to handle the extra poles which are present in the propagator, we employ an ambiguity-free technique in the imaginary-time formalism. For temperatures T high compared with the external momentum, we obtain the leading T^4 as well as the subleading T^2 and log(T) contributions to the graviton self-energy. The gauge fixing independence of the leading T^4 terms as well as the Ward identity relating the self-energy with the one-point function are explicitly verified. We also verify the 't Hooft identities for the subleading T^2 terms and show that the logarithmic part has the same structure as the residue of the ultraviolet pole of the zero temperature graviton self-energy. We explicitly compute the extra terms generated by the prescription poles and verify that they do not change the behavior of the leading and sub-leading contributions from the hard thermal loop region. We discuss the modification of the solutions of the dispersion relations in the graviton plasma induced by the subleading T^2 contributions.

Behavior of the thermal gluon self-energy in the Coulomb gauge

We study, to one loop order, the behavior of the gluon self-energy in the noncovariant Coulomb gauge at finite temperature. The cancellation of the peculiar energy divergences, which arise in such a gauge, is explicitly verified in the complete two point function of the Yang-Mills theory. At high temperatures, the leading ${T}^{2}$ term is determined to be transverse and nonlocal, in agreement with the results obtained in covariant gauges. The coefficient of the sub-leading $\mathrm{ln}(T)$ contribution is nontransverse but local and coincides (up to a multiplicative constant) with that of the ultraviolet pole term of the zero temperature amplitude.

Critical behavior atm-axial Lifshitz points: Field-theory analysis and ε-expansion results

The critical behavior of d-dimensional systems with an n-component order parameter is reconsidered at (m,d,n)-Lifshitz points, where a wave-vector instability occurs in an m-dimensional subspace of ${R}^{d}.$ Our aim is to sort out which ones of the previously published partly contradictory \ensuremath{\epsilon}-expansion results to second order in $\ensuremath{\epsilon}=4+m/2\ensuremath{-}d$ are correct. To this end, a field-theory calculation is performed directly in the position space of $d=4+m/2\ensuremath{-}\ensuremath{\epsilon}$ dimensions, using dimensional regularization and minimal subtraction of ultraviolet poles. The residua of the dimensionally regularized integrals that are required to determine the series expansions of the correlation exponents ${\ensuremath{\eta}}_{l2}$ and ${\ensuremath{\eta}}_{l4}$ and of the wave-vector exponent ${\ensuremath{\beta}}_{q}$ to order ${\ensuremath{\epsilon}}^{2}$ are reduced to single integrals, which for general $m=1,\dots{},d\ensuremath{-}1$ can be computed numerically, and for special values of m, analytically. Our results are at variance with the original predictions for general m. For $m=2$ and $m=6,$ we confirm the results of Sak and Grest [Phys. Rev. B 17, 3602 (1978)] and Mergulh\~ao and Carneiro's recent field-theory analysis [Phys. Rev. B 59, 13 954 (1999)].

Silica glass: A material for photonics

Recent studies on two aspects of silica glass as a photonic material will be described. Part A of this review will be focused on structural disorder and structural relaxations in silica glass. With regard to the structural disorder, investigations have been made to improve transparency and to shift the optical absorption edge in the ultraviolet towards shorter wavelengths. Remarkable advances have been achieved in the understanding of both light scattering, which is a dominant factor in the optical losses in silica fibers, and the absorption edge. Freezing of the structural disorder was observed, and structural relaxations are found to be important for improving the transparency, whereas for the absorption edge thermal vibration effects seem to be more predominant than the structural disorder. From the results, the present authors have tried to control the structural relaxation for developing silica glass with an ultimate optical transparency, finding that a very tiny amount of the proper impurity species gives rise to structural subrelaxations, which are effective in reducing the Rayleigh scattering. The scattering was reduced by 13% by addition of only 10 wt ppm Na2O, for example. In part B of this review the second-order optical nonlinearity induced in Ge-doped silica glass will be described based on recent experiments carried out by the group of present authors. A large second-order optical nonlinearity has been successfully induced in the glass by simultaneous applications of a high dc electric field and ultraviolet (UV) irradiation, so-called UV poling. The nonlinearity induced by UV poling in bulk and film samples has achieved a magnitude of χ(2), comparable to or even larger than those of LiNbO3 and other crystals. Surprisingly enough, the nonlinearity induced by this method then decays after the UV poling as an exact single-exponential function of time, very much unlike the usual decay processes observed in glasses. Evidence is presented associating the nonlinearity with GeE′ defect centers created from oxygen deficient vacancies through photochemical reactions. The decay or degradation can be made much slower with the addition of proper impurities which work as electron scavengers. In addition, we have found that crystallites are generated in the glass by the UV poling, which leads to an increase in the third-order nonlinearity, χ(3), approximately 15 times larger than before the treatment. As a whole, the evidence strongly suggests that a major origin of the second-order nonlinearity induced in the glass is a combined effect of a large third-order nonlinearity associated with the crystallites and an internal space-charge field, where the charges to build up the field are produced during the formation of GeE′ centers.

Finite temperature gluon self-energy in a class of temporal gauges

The approach which relates thermal Green functions to forward scattering amplitudes of on-shell thermal particles is applied to the calculation of the gluon self-energy, in a class of temporal gauges. We show to all orders that, unlike the case of covariant gauges, the exact self-energy of the gluon is transverse at finite temperature. The leading T^2 and the sub-leading ln(T) contributions are obtained for temperatures T high compared with the external momentum. The logarithmic contributions have the same structure as the ultraviolet pole terms which occur at zero temperature.

Induced Defects and Increase of Second-Order Nonlinearity in Ultraviolet-Poled GeO2–SiO2 Glass

We report on enhancement by thermal defects control of the second-order optical nonlinearity in GeO2–SiO2 glass induced by ultraviolet (UV) poling. The present work is based on the previous results which suggest GeE' centers as the most relevant ingredient to produce the induced nonlinearity, and heat treatment in a vacuum before UV poling has been found to increase the induced second-harmonic generation (SHG). The result is thought to be related to an increase of oxygen deficient defects, which function as precursors of the photoinduced GeE' centers. To obtain larger d coefficient, optimization of pre-heat treatment conditions, temperature and time duration, have been investigated. The largest value of d33 coefficient thus far obtained is 5.1±0.2 pm/V in UV-poled GeO2–SiO2 glass of 15 mole% GeO2 content with the pre-heat treatment at 1200°C for 5 h, which exceeds d13, the second largest coefficient of LiNbO3.

Structure of the graviton self-energy at finite temperature

We study the graviton self-energy function in a general gauge, using a hard thermal loop expansion which includes terms proportional to T^4, T^2 and log(T). We verify explicitly the gauge independence of the leading T^4 term and obtain a compact expression for the sub-leading T^2 contribution. It is shown that the logarithmic term has the same structure as the ultraviolet pole part of the T=0 self-energy function. We argue that the gauge-dependent part of the T^2 contribution is effectively canceled in the dispersion relations of the graviton plasma, and present the solutions of these equations.

Vanishing quantum vacuum energy in eleven-dimensional supergravity on the round seven-sphere

Quantum corrections to the vacuum energy are evaluated at one-loop order in eleven-dimensional supergravity on the round seven-sphere S 7 and are shown to vanish. The cancellation is also shownfor all ultraviolet poles at z = 11 2 , 10 2 , … , corresponding to divergences of eleventh and lower powers of momentum cut-off Λ