We present a short comment on resummation of double-logarithmic (DL) contributions to decays of W and Z -bosons into charged fermion pairs. We show that resummation of DL corrections to the Z -boson decay leads to standard Sudakov form factor with the negative exponent independently of the boson is on-shell or off-shell. In contrast, the Sudakov exponent for the W - decay is negative (positive) when the W-boson is on-shell (off-shell). In this connection we consider applicability of the Dispersion Relations to the case when the imaginary parts contain infrared-divergent contributions.
In this comment we present an analysis of electroweak neutral triple gauge boson couplings projected out of the gauge sector of the extended non-commutative standard model. A brief overview of the current experimental situation is given.
We show that, for all values of $Tan β$ and the light right-handed stop mass for which the electroweak phase transition is strong enough to avoid washout following electroweak baryogenesis, the electroweak vacuum is stable over the lifetime of the observed Universe. Cosmological stability of the electroweak vacuum is violated only if the light right-handed stop is lighter than 100-115GeV.
In the QCD context, the non-singlet structure functions of u and d -quarks are identical, save the initial quark densities. Electroweak radiative corrections, being flavor-dependent, bring further difference between the non-singlets. This difference is calculated in the double-logarithmic approximation and the impact of the electroweak corrections on the non-singlet intercepts is estimated numerically.
We point out that if the majoron-like scheme is implemented within a 331 model, there must exist at least three different mass scales for the scalar vacuum expectation values in the model.
We introduce in an arbitrary supersymmetric version of the standard model without elementary scalars a logarithmic operator which is irrelevant in the limit in which all symmetries are respected. However through a dynamical mechanism of the Nambu Jona Lasinio type this operator may produce two fermion vacuum condensates that may account for electroweak and contribute to supersymmetry breaking. Some of the phenomenological consequences of this set-up are discussed.
We have studied the effects of the complete logarithmic electroweak O(alpha) corrections on the production of vector-boson pairs WZ, ZZ, and WW at the LHC. These corrections are implemented into a Monte Carlo program for pp -> 4f (+γ) with final states involving four or two leptons using the double-pole approximation. We numerically investigate purely leptonic final states and find that electroweak corrections lower the predictions by 5-30% in the physically interesting region of large di-boson invariant mass and large angle of the produced vector bosons.
We consider two-loop leading and next-to-leading logarithmic virtual corrections to arbitrary processes with external massless fermions in the electroweak Standard Model at energies well above the electroweak scale. Using the sector-decomposition method and alternatively the strategy of regions we calculate the mass singularities that arise as logarithms of Q^2/MW^2, where Q is the energy scale of the considered process, and 1/εpoles in D=4-2εdimensions, to one- and two-loop next-to-leading logarithmic accuracy. The derivations are performed within the complete electroweak theory with spontane…
We report on an investigation of various problems related to the theory of the electroweak phase transition. This includes a determination of the nature of the phase transition, a discussion of the possible role of higher order radiative corrections and the theory of the formation and evolution of the bubbles of the new phase. We find in particular that no dangerous linear terms appear in the effective potential. However, the strength of the first order phase transition is 2/3 times less than what follows from the one-loop approximation. This rules out baryogenesis in the minimal version of th…
We consider W-boson scattering at high-energy e+ e- colliders and study one-loop logarithmic electroweak corrections within the Standard Model assuming a light Higgs boson. We present explicit analytical results for W+ W- -> W+ W-. Using the equivalent vector-boson approximation, we have implemented these corrections into a Monte Carlo program for the process e+ e- -> nue anti-nue W+ W-. The quality of the equivalent vector-boson approximation and of the logarithmic high-energy approximation for the electroweak corrections is discussed in detail. The impact of the radiative effects is quantita…
We consider hadronic production of a Z boson in association with a jet and study one- and two-loop electroweak logarithmic corrections in the region of high Z-boson transverse momentum, p_T >> M_Z, including leading and next-to-leading logarithms. Numerical results for the LHC and Tevatron colliders are presented. At the LHC these corrections amount to tens of per cent and will be important for interpretation of the measurements.
In Next Linear Colliders at TeV scale, electroweak double logarithmic corrections, which come from the infrared behaviors of theory can not be neglected. It is well known that in QED and QCD, double logarithmic corrections are resummed to all orders, and these corrections can be exponentiated, resulting in the Sudakov form factor. However it is never trivial that double logarithmic corrections in electroweak theory can be exponentiated, because of the spontaneous breaking of symmetry and the pattern of that. We discuss the electroweak double logarithmic corrections at two loop level and explai…
We compute the MSSM one-loop contributions to the asymptotic energy behaviour of fermion-antifermion pair production at future lepton-antilepton colliders. Besides the conventional logarithms of Renormalization Group origin, extra SUSY linear logarithmic terms appear of "Sudakov-type". In the TeV range their overall effect on a variety of observables can be quite relevant and drastically different from that obtained in the SM case.
In a recent letter Marciano and Sirlin (Phys. Rev. Lett. 96, 032002, (2006)) presented an improved calculation of the electroweak radiative correction to derive a precision value of the quark mixing angle $V_{ud}$ by improving the continuation from long to short distance contributions. At the precision level considered by them, however, there is a more important contribution from weak magnetism that was not included by their calculation. The addition of the weak magnetism contribution to the superallowed beta-decay radiative corrections lowers $V_{ud}$ by 0.00023, which is compared with the in…
Starting from a theoretical representation of the electroweak component of four-fermion neutral current processes that uses as theoretical input the experimental measurements at the Z peak, we consider the asymptotic high energy behaviour in the Standard Model at one loop of those gauge-invariant combinations of self-energies, vertices and boxes that contribute all the different observables. We find that the logarithmic contribution due to the renormalization group running of the various couplings is numerically overwhelmed by single and double logarithmic terms of purely electroweak (Sudakov-…
We demonstrate that in the process of deducing the constraint on the electroweak mixing angle $θ_{W}$ in our paper, we have indeed been working with three mass scales while implementing (331) model.
The first model of Foot, Kobakhidze and Volkas described in their work in arXiv:0704.1165 [hep-ph] is a tailored version of our model on broken scale invariance in the standard model presented in hep-th/0403039.
Accounting for double-logarithmic contributions to high-energy (>> 100 GeV) e^+ e^- annihilation into a quark or a lepton pair in the kinematics where the final particles are colinear to the e^+e^- beams leading to a sizable difference between the forward and backward scattering amplitudes, i.e. to the forward-backward asymmetry. When the annihilation is accompanied by emission of n electroweak bosons in the multi-Regge kinematics, it turns out that the cross sections of the photon and Z production have the identical energy dependence and asymptotically their ratio depends only on the Weinberg…
We investigate the Sudakov double logarithmic corrections to the form factor of fermion in the SU(2)XU(1) electroweak theory. We adopt the familiar Feynman gauge and present explicit calculations at the two loop level. We show that the leading logarithmic corrections coming from the infrared singularities are consistent with the "postulated" exponentiated electroweak Sudakov form factor. The similarities and differences in the "soft" physics between the electroweak theory and the unbroken non-abelian gauge theory (QCD) will be clarified.
We calculate the leading-logarithmic and next-to-leading-logarithmic electroweak corrections to the charm-top-quark contribution to the effective $|ΔS| = 2$ Lagrangian, relevant for the parameter $ε_K$. We find that these corrections lead to a $-0.5\%$ shift in the corresponding Wilson coefficient. Moreover, our calculation removes an implicit ambiguity in the standard-model prediction of $ε_K$, by fixing the renormalization scheme of the electroweak input parameters.
This PhD thesis is concerned with one-loop virtual electroweak corrections to arbitrary processes in the high-energy limit. Complete results are presented for the leading and subleading logarithms of large ratios of energy scales to mass scales. These results include the logarithmic dependence on the photon and weak-boson masses, on the light-fermion masses, as well as on the Higgs- and top-masses in the heavy-Higgs and heavy-top limit. All sources of electroweak logarithmic corrections are taken into account, including the exchange of soft and/or collinear electroweak gauge bosons as well as …
We have studied the effect of one-loop logarithmic electroweak radiative corrections on WZ and $Wγ$ production processes at the LHC. We present analytical results for the leading-logarithmic electroweak corrections to the corresponding partonic processes du -> WZ, Wgamma. Using the leading-pole approximation we implement these corrections into Monte Carlo programs for $pp\to lν_l l'\bar l', lν_lγ$. We find that electroweak corrections lower the predictions by 5-20% in the physically interesting region of large transverse momentum and small rapidity separation of the gauge bosons.
We discuss recent results for the asymptotic behavior of fermion scattering amplitudes in the Sudakov limit. The results include next-to-next-to-leading logarithmic electroweak corrections and are used for the analysis of fermion-antifermion pair production in e+e- annihilation at high energy. The importance of the subleading logarithmic contributions is emphasized and the fermionic contributions to the Abelian form factor at two loops are discussed.
At future linear $e^+e^-$ collider experiments in the TeV range, Sudakov double logarithms originating from massive boson exchange can lead to significant corrections to the cross sections of the observable processes. These effects are important for the high precision objectives of the Next Linear Collider. We use the infrared evolution equation, based on a gauge invariant dispersive method, to obtain double logarithmic asymptotics of scattering amplitudes and discuss how it can be applied, in the case of broken gauge symmetry, to the Standard Model of electroweak processes. We discuss the dou…
For superpartner masses not much heavier than the weak scale $M=M_{\rm W}$, large logarithmic corrections of the Sudakov type arise at TeV energies. In this paper we summarize recent results of supersymmetric (susy) electroweak radiative corrections for sfermion and charged Higgs production at $e^+e^-$ colliders in the MSSM. The results are given to subleading logarithmic (SL) accuracy to all orders in perturbation theory in the ``light'' susy-mass scenario. Prospects for the determination of $\tan β\geq 10$ are discussed which is independent of soft susy-breaking terms to SL accuracy.
We review a recent calculation of the two-loop next-to-leading logarithmic electroweak corrections to the form factors for massless chiral fermions coupling to an SU(2)xU(1) singlet gauge boson.
The dominant electroweak double logarithmic corrections to the process $e^+e^-\to f\bar f$ at high energy are found in all orders of perturbation theory. In contrast to results in simple Yang-Mills theories these corrections do not exponentiate.
For energies far above the electroweak scale, large electroweak radiative corrections occur that grow logarithmically with energy and can easily reach several tens of per cent in the TeV range. Recent work on these corrections is reviewed.
We present results on the two-loop leading and angular-dependent next-to-leading logarithmic virtual corrections to arbitrary processes at energies above the electroweak scale. In the `t Hooft-Feynman gauge the relevant Feynman diagrams involving soft and collinear gauge bosons γ, Z, W^\pm coupling to external legs are evaluated in the eikonal approximation in the region where all kinematical invariants are much larger than the electroweak scale. The logarithmic mass singularities are extracted from massive multi-scale loop integrals using the Sudakov method and alternatively the sector-decomp…
We sum up the next-to-next-to-leading logarithmic virtual electroweak corrections to the high energy asymptotics of the neutral current four-fermion processes for light fermions to all orders in the coupling constants using the evolution equation approach. From this all order result we derive finite order expressions through next-to-next-to leading order for the total cross section and various asymmetries. We observe an amazing cancellation between the sizable leading, next-to-leading and next-to-next-to-leading logarithmic contributions at TeV energies.
Using soft-collinear effective theory, the leading-log radiative electroweak corrections are written in a closed and analytical form for the hadronic cross section of Higgs production through vector boson fusion, qq->qqH, one of the most promising channels for studying the Higgs boson at the LHC. The simple leading-log resummation is compared with a full next-to-leading-log calculation, and its accuracy is found to be of order 1% up to 10 TeV, i.e. better than the accuracy of PDFs. Corrections are found to be larger than predicted by one-loop fixed order approximations at LHC energies. The met…
We analyze Higgs condensate bubble expansion during a first-order electroweak phase transition in the early Universe. The interaction of particles with the bubble wall can be accompanied by the emission of multiple soft gauge bosons. When computed at fixed order in perturbation theory, this process exhibits large logarithmic enhancements which must be resummed to all orders when the wall velocity is large. We perform this resummation both analytically and numerically at leading logarithmic accuracy. The numerical simulation is achieved by means of a particle shower in the broken phase of the e…
We study a combination of amplitudes for neutrino scattering that can isolate a (gauge-invariant) difference of chirality-preserving neutrino electroweak radii for $ν_μ$ and $ν_τ$. This involves both photon and $Z_μ$ exchange contributions. It is shown that the construction singles out the contributions of the hypercharge gauge field $B_μ$ in the standard model. We comment on how gauge-dependent terms from the charge radii cancel with other terms in the relative electroweak radii defined.
We present results for the complete one-loop electroweak logarithmic corrections for general processes at high energies and fixed angles. Our results are applicable to arbitrary matrix elements that are not mass-suppressed. We give explicit results for 4-fermion processes and gauge-boson-pair production in electron-positron annihilation.
We determine the real parts of electroweak matching conditions relevant for top quark pair production close to threshold in e+e- annihilation at next-to-next-to-leading logarithmic (NNLL) order. Numerically the corrections are comparable to the NNLL QCD corrections.
At energies much larger than the mass of the weak gauge bosons, electroweak radiative corrections can lead to significant corrections. At 1 TeV the one loop corrections can be of ${\cal O} (20 %)$ due to large contributions of the Sudakov type. We summarize recent progress in the evaluation and resummation of the double and single logarithmic corrections to general scattering amplitudes for fermions, transversely as well as longitudinally polarized external lines.
We consider virtual electroweak corrections to the form factors for massless chiral fermions coupling to an SU(2)xU(1) singlet gauge boson in the asymptotic region $s\gg M_W^2$, where the invariant mass $s$ of the external gauge boson is much higher than the weak-boson mass scale. Using the sector-decomposition method we compute mass singularities, which arise as logarithms of $s/M_W^2$ and $1/ε$ poles in $D=4-2ε$ dimensions, to one- and two-loop next-to-leading logarithmic accuracy. In this approximation we include all contributions of order $α^l ε^{k} log^{j+k}(s/M_W^2)$, with $l=1,2$ and $j…
In this study we examine post-inflationary cosmologies dominated by a scalar field with the equation of state: p_phi=w_phi rho_phi (0 leq w_phi leq 1) in order to facilitate baryogenesis at the electroweak scale. We take a more conventional approach from one in Ref. 1 [Joyce, Prokopec] and assume that the Universe reheats by the scalar field decay before the nucleosynthesis epoch, and find a larger expansion rate at the electroweak scale than the one obtained in Ref. 1. The decaying field models suffer however from an entropy release that dilutes the baryon number produced at the electroweak s…
We summarize results for the complete one-loop electroweak logarithmic corrections for general processes at high energies and fixed angles. Our results are applicable to arbitrary matrix elements that are not mass-suppressed. We give explicit results for W-boson-pair production in e^+e^- annihilation.
We compute the dominant logarithmically enhanced two-loop electroweak corrections to the electron-positron scattering differential cross section in the high energy limit for large scattering angles. Depending on the scattering angle and energy the two-loop corrections may exceed one percent and are important for the high-precision luminosity spectrum determination at a future linear collider.
Accounting for the double-logarithmic (DL) contributions to amplitude of Z to f \bar{f} leads to the Sudakov suppression. In contrast, resumming DL contributions to amplitudes of W to f \bar{f}' results into an exponential with a positive exponent, i.e. into the enhancement. This effect is intrinsic property of the theories with non-Abelian gauge groups.
We study the application of the joint resummation to electroweak boson production at hadron colliders. The joint resummation formalism resums both threshold and transverse momentum corrections to the transverse momentum distribution at next-to-leading logarithmic accuracy. We obtain a good description of the transverse momentum distribution of Z bosons produced at the Tevatron collider.
The Standard Model of electroweak interactions is shown to include a gauge theory for the observed scalar and pseudoscalar mesons. This is done by exploiting the consequences of embedding the SU(2)left X U(1) group into the chiral group of strong interactions and by considering explicitly the Higgs boson and its three companions inside the standard scalar 4-plet as composite. No extra scale of interaction is needed. Quantizing by the Feynman path integral reveals how, in the `Nambu Jona-Lasinio approximation', the quarks and the Higgs boson become unobservable, and the theory anomaly-free. Nev…
We show that in Composite Higgs models, the coupling of the Higgs resonance to a pair of $W$ bosons is weaker than the corresponding Standard Model coupling, provided the Higgs arises from electroweak doublets only. This is partly due to the effects of the nonlinear realization of the chiral symmetries at the compositeness scale.
The soft function relevant for the production of an electroweak boson (photon, W, Z or H) with large transverse momentum at a hadron collider is computed at next-to-next-to-leading order. This is the first two-loop computation of a soft function involving three light-cone directions. With the result, the threshold resummation for these processes can now be performed at next-to-next-to-next-to-leading logarithmic accuracy.
The leading logarithmic approximation method fails to yield the correct asymptotic behavior in some realistic situations: inclusion of the beta-terms to which the LLA method is insensitive may change a power growth to merely logarithmic. The results of [hep-ph/0101058] indicate that the problem of large-s behavior of total cross sections belongs to this class. Similarly, a reference to the LLA method cannot be sufficient to justify constructions such as the kT jet algorithm.
When scattering amplitudes are calculated in the double-logarithmic approximation, it is possible to relate the double-logarithmic on-shell and off-shell amplitudes. Explicit relations are obtained for scattering amplitudes in QED, QCD, and the ElectroWeak Standard Model. The off-shell amplitudes are considered in the hard and the Regge kinematic limits. We compare our results in both the Feynman and Coulomb gauges.
Recent results for the asymptotic behavior of fermion scattering amplitudes in the Sudakov limit are presented including next-to-leading logarithmic corrections. These are used for the analysis of the dominant electroweak corrections to the fermion-antifermion pair production in $e^+e^-$ annihilation at high energy.
The QCD structure of the electroweak bosons is reviewed and the lepton structure function is defined and calculated. The leading order splitting functions of electron into quarks are extracted, showing an important contribution from $γ$-$Z$ interference. Leading logarithmic QCD evolution equations are constructed and solved in the asymptotic region where log$^2$ behaviour of the parton densities is observed. Possible applications with clear manifestation of 'resolved' photon and weak bosons are discussed.
In this work we give a detailed description of a method for the calculation of QCD corrections to electroweak processes in dimensional regularization that does not require any definition of the gamma_5 matrix in d dimensions. This method appears particularly convenient in order to limit the algebraic complexity of higher order calculations. As an example, we compute the leading logarithmic corrections to the b -> s gamma decay.
Electroweak corrections associated with the instability of the top quark to the next-to-next-to-leading logarithmic (NNLL) total top pair threshold cross section in e+e- annihilation are determined. Our method is based on absorptive parts in electroweak matching conditions of the NRQCD operators and the optical theorem. The corrections lead to ultraviolet phase space divergences that have to be renormalized and lead to NLL mixing effects. Numerically, the corrections can amount to several percent and are comparable to the known NNLL QCD corrections.
We discuss two-loop leading and angular-dependent next-to-leading logarithmic electroweak virtual corrections to arbitrary processes at energies above the electroweak scale. The relevant Feynman diagrams involving soft-collinear gauge bosons gamma, Z, W, have been evaluated in eikonal approximation. We present results obtained from the analytic evaluation of massive loop integrals. To isolate mass singularities we used the Sudakov method and alternatively the sector decomposition method in the Feynman-parameter representation.
We present in this talk the one-loop electroweak precision constraints in the Littlest Higgs model, including the logarithmically enhanced contributions from both fermion and scalar loops. We find the one-loop contributions are comparable to the tree level corrections in some regions of parameter space. A low cutoff scale is allowed for a non-zero triplet VEV. Constraints on various other parameters in the model are also discussed. The role of triplet scalars in constructing a consistent renormalization scheme is emphasized.
We study the resummation of singular distributions for electroweak-boson production at large transverse momentum in hadronic collisions. We describe the factorization properties of the cross section near partonic threshold and construct the resummed cross section at next-to-leading logarithmic accuracy in moment space in terms of soft gluon anomalous dimensions. We present full analytical results for the expansion of the resummed cross section up to next-to-next-to-leading order. Our results can be applied to W, Z, and virtual gamma production at hadron colliders.
We consider the effect of next-to-leading order (NLO) electroweak corrections to Standard Model 2-to-2 processes, taking into account the potentially large double logarithms originating from both real and virtual corrections. A study of the leading Sudakov logarithms is presented and Bloch-Nordsieck (BN) violations are discussed for processes at the CERN Large Hadron Collider. In particular, we focus on the processes Z/photon+jet and also the ratio of Z to photon production. This ratio is known to be insensitive to NLO QCD corrections but this is not expected to be the case for the electroweak…
Electroweak radiative corrections give rise to large negative, double-logarithmically enhanced corrections in the TeV region. These are partly compensated by real radiation and, moreover, affected by selecting isospin-noninvariant external states. We investigate the impact of real gauge boson radiation more quantitatively by considering different restricted final state configurations. We consider successively a massive abelian gauge theory, a spontaneously broken SU(2) theory and the electroweak Standard Model. We find that details of the choice of the phase space cuts, in particular whether a…
Recently the two-loop next-to-leading logarithmic (NLL) virtual corrections to arbitrary processes with massless external fermions have been calculated. Within the spontaneously broken electroweak theory the one- and two-loop mass singularities have been derived to NLL accuracy and expressed as universal correction factors depending only on the quantum numbers of the external particles. This talk summarizes the results for massless fermionic processes and presents new aspects arising in the extension of the corresponding loop calculations to massive external fermions. As a preliminary result, …
Within the standard electroweak model we point out that the $3\times 3$ matrix of quark mixing is characterized by three universal (rephasing-invariant) quantities: one of them for $CP$ violation and the other two for off-diagonal asymmetries. Unitarity of the quark mixing matrix can in principle be tested through a variety of measurements which are irrelevant to the existence of $CP$-violating effects.
The production of charm quark jets in association with electroweak gauge bosons at the LHC can be used as a tool to constrain quark parton distribution functions (PDFs). Motivated by recent measurements at the Tevatron and LHC, we calculate cross sections for $W/Z+c$, comparing these to $W/Z+\textrm{jet}$, for various PDF sets. The cross-section differences can be understood in terms of the different underlying PDFs, with the strange quark distribution being particularly important for $W+c$ production. We suggest measurements of appropriately defined ratios and comment on how these measurement…
