Using the method of massive operator matrix elements, we calculate the subleading QED initial state radiative corrections to the process $e^+e^- \rightarrow γ^*/Z^*$ for the first three logarithmic contributions from $O(α^3 L^3), O(α^3 L^2), O(α^3 L)$ to $O(α^5 L^5), O(α^5 L^4), O(α^5 L^3)$ and compare their effects to the leading contribution $O(α^6 L^6)$ and one more subleading term $O(α^6 L^5)$. The calculation is performed in the limit of large center of mass energies squared $s \gg m_e^2$. These terms supplement the known corrections to $O(α^2)$, which were completed recently. Given the high precision at future colliders operating at very large luminosity, these corrections are important for concise theoretical predictions. The present calculation needs the calculation of one more two--loop massive operator matrix element in QED. The radiators are obtained as solutions of the associated Callen--Symanzik equations in the massive case. The radiators can be expressed in terms of harmonic polylogarithms to weight {\sf w = 6} of argument $z$ and $(1-z)$ and in Mellin $N$ space by generalized harmonic sums. Numerical results are presented on the position of the $Z$ peak and corrections to the $Z$ width, $Γ_Z$. The corrections calculated result into a final theoretical accuracy for $δM_Z$ and $δΓ_Z$ which is estimated to be of O(30 keV) at an anticipated systematic accuracy at the FCC\_ee of \sim 100 keV. This precision cannot be reached, however, by including only the corrections up to $O(α^3)$.
It was shown by F. Low in the 1950s that the subleading terms of soft photon S-matrix elements obey a universal linear relation. In this paper we give a new interpretation to this old relation, for the case of massless QED, as an infinitesimal symmetry of the S-matrix. The symmetry is shown to be locally generated by a vector field on the conformal sphere at null infinity. Explicit expressions are constructed for the associated charges as integrals over null infinity and shown to generate the symmetry. These charges are local generalizations of electric and magnetic dipole charges.
We consider the subleading contributions of the hadronic vacuum polarization, involving the $π^0γ^*γ^*$ transition form factor, to the muon anomalous magnetic moment $g-2$. Various models for the form factor, based on hadronic ansatzes and holographic principles, are considered: They are the Wess-Zumino-Witten, vector meson dominance, lowest meson dominance (one and two vector resonances) models, and AdS/QCD. The model parameters are determined by fitting the experimental data for the $e^+ e^- \rightarrow π^0 γ$ total cross section. We report numerical results of the corrections to the muon $g…
We calculate the complete $O(α^2)$ initial state radiation corrections to $e^+ e^-$ annihilation into a neutral vector boson in a direct analytic computation without any approximation. The corrections are represented in terms of iterated incomplete (elliptic) integrals over alphabets of square--root valued letters. Performing the limit $s \gg m_e^2$, we find discrepancies with the earlier results of Ref.~\cite{Berends:1987ab} and confirm results obtained in Ref.~\cite{Blumlein:2011mi} where the effective method of massive operator matrix elements has been used, which works for all but the powe…
We have calculated one loop quantum electrodynamic corrections to the process $ γγ\rightarrowμ^+μ^-γ$, where all photons are on mass shell and the muon mass is taken into account. The result is obtained in the analytical form and is implemented as functions in the C programming language, which can be used to calculate the cross-section, the differential cross section, and to construct generators. We also present numerical results for corrections to the cross section and to the differential cross section.
We study the Ward identity for the effective photon-electron vertex summing the ladder diagrams contributing to the electrical conductivity in hot QED at leading logarithmic order. It is shown that the Ward identity requires the inclusion of a new diagram in the integral equation for the vertex that has not been considered before. The real part of this diagram is subleading and therefore the final expressions for the electrical conductivity at leading logarithmic order are not affected.
A precise SM prediction for the direct CP violation in the $K \rightarrow ππ$ decay process is of great importance in confronting experiments and constraining new physics. The state-of-art lattice QCD study of this process will soon achieve a precision that QED effects can no longer be neglected. The inclusion of QED in such calculations is planned, and the formalism to relate the finite-volume matrix element obtained from these calculations to the physical amplitude is underway. Here, we report on the progress towards an extension of the Lellouch-Lüscher formalism in presence of QED, with the…
The precise knowledge of the QED initial state corrections is of instrumental importance in studying high luminosity measurements in $e^+e^-$ annihilation at facilities like LEP, the International Linear Collider ILC, CLIC, a Giga-$Z$ facility, and the planned FCC\_ee. Logarithmic corrections of up to $O(α^6 L^5)$ are necessary with various subleading terms taken into account. This applies to both the inclusive measurement of processes like $e^+ e^- \rightarrow γ^*/Z^*$ and also the forward-backward asymmetry. As has been shown recently, techniques from massive QCD, such as the computation of …
In view of the recent interest in the decays of mesons into a pair of light leptons, a computation of the QED radiative corrections to the decay of $π^{0}$ into an electron-positron pair is presented here. The results indicate that the peak value of the differential decay rate is reduced by about $50 \%$, because of soft-photon radiation. The number of $e^{+}e^{-}$ pairs having invariant masses in an energy bin of 0.5 MeV centered around $m_π$ is found to be about $20 \%$ smaller than the one it would be if radiative corrections were neglected.
We investigate in detail the stimulated photon emission in pulse-shaped Laguerre-Gauss beams of arbitrary mode decomposition within the framework of Euler-Heisenberg effective theory. We elaborate on the analytic structure of the photon emission amplitude and identify its dominant and sub-dominant parts by analyzing each signature's phase scaling. We identify three distinct nonlinear signatures: the orbital angular momentum (OAM) flip ($\ell:1 \rightarrow -1$) , higher harmonic generation ($\ell:1 \rightarrow 2$) and harmonic reduction ($\ell:1 \rightarrow 0$). We estimate signal photon yield …
Parton showers are crucial components of high-energy physics calculations. Improving their modelling of QCD is an active research area since shower approximations are stumbling blocks for precision event generators. Naively, the interference between sub-dominant Standard-Model interactions and QCD can be of similar size to subleading QCD corrections. This article assesses the impact of QCD/QED interference effects in parton showers, by developing a sophisticated shower including QED, QCD at fixed color, and employing complete tree-level matrix element corrections for individual $N_C=3$ color c…
We present numerical results on the recently completed $O(α^2)$ initial state corrections to the process $e^+e^- \rightarrow γ^*/Z^*$, which is a central process at past and future high energy and high luminsoity colliders for precision measurements of the properties of the $Z$-boson, the Higgs boson, and the top quark. We observe differences to an earlier result \cite{Berends:1987ab} in the non-logarithmic contributions at $O(α^2)$. The new result leads to a 4 MeV shift in the $Z$ width considering the lower end $s_0 = 4 m_τ^2$ of the radiation region, which is larger than the present accurac…
We consider in detail various theoretical uncertainties of the perturbative predictions for the decay width of $H^0\rightarrow b\overline{b}$ process in the region $50\ GeV< M_H\leq 2M_W$. We calculate the order $O(α_s^2)$-contributions to the expression for $Γ_{Hb\overline{b}}$ through the pole quark mass and demonstrate that they are important for the elimination of the numerical difference between the corresponding expression and the one through the running $b$-quark mass. The order $O(αα_s)$ and $O(α^2)$ massless and order $O(m_b^2/M_H^2)$ massive corrections to $Γ_{Hb\overline{b}}$ are al…
The angle-dependent cusp anomalous dimension governs divergences coming from soft gluon exchanges between heavy particles, such as top quarks. We focus on the matter-dependent contributions and compute the first truly non-planar terms. They appear at four loops and are proportional to a quartic Casimir operator in color space. Specializing our general gauge theory result to U(1), we obtain the full QED four-loop angle-dependent cusp anomalous dimension. While more complicated functions appear at intermediate steps, the analytic answer depends only on multiple polylogarithms with singularities …
We give detailed results of $\mathcal{O}(α)$ QED corrections (both real emission and virtual corrections) to $B\to K\ell^+\ell^-$ modes. Requiring the real emission to be gauge invariant, the structure of the contact term(s) is fixed. The calculation is done with a fictitious photon mass as the IR regulator and results are shown to be independent of it, establishing cancellation of the soft divergences. Results are presented for a choice of photon energy, $k_{max}$, and photon angle $θ_{cut}$. The QED effects are negative, thereby reducing the rate compared to that without QED effects. Electro…
The resummation of the $α\ln^2(z)$ non-singlet contributions is performed for initial state QED corrections. As examples, the effect of the resummation on neutral-current deep-inelastic scattering and the $e^+ e^- \rightarrow μ^+ μ^-$ scattering cross section near the $Z^0$-peak is investigated.
We report on the calculation of first-order QED corrections for the $γp\rightarrow l^+l^-p^{\prime}$ process. An upcoming experiment at MAMI (Mainz) aims to compare the cross sections of muon- and electron-pair production in this reaction to test lepton universality. Precise knowledge of the electromagnetic radiative corrections is needed for these measurements. As a first step, we present the leading QED radiative corrections in the soft-photon approximation when accounting for the finite lepton mass. For the kinematics at MAMI, we find corrections of the percent level for muons, and of order…
We showcase the calculation of the master integrals needed for the two loop mixed QCD-QED virtual corrections to the neutral current Drell-Yan process $(q\bar{q}\rightarrow l^+ l^-)$. After establishing a basis of 51 master integrals, we cast the latter into canonical form by using the Magnus algorithm. The dependence on the lepton mass is then expanded such that potentially large logarithmic contributions are kept. After determining all boundary constants, we give the coefficients of the Taylor series around four space-time dimensions in terms of generalized polylogarithms up to weight four.
The noncommutative QED (NCQED) has a non-Abelian nature due to the presence of 3- and 4-photon vertices in the lagrangian. Thus, NCQED predicts a new physics contribution to the $γγ\rightarrowγγ$ scattering already at the tree level. We have examined NCQED by studying the light-by-light process at the 14 TeV LHC with intact protons. Our results show that the NC scale up to $Λ_{\mathrm{NC}} = 1.65(1.35)$ TeV can be probed in the $pp\rightarrow p(γγ)p \rightarrow p'(γγ)p'$ collision for the time-space (space-space) NC parameters. These bounds are stronger than the limits that can be obtained in …
The ${\cal O}(α)$ radiative corrections to the process $p\,p\hskip-7pt\hbox{$^{^{(\!-\!)}}$} \rightarrow γ^*, \, Z \rightarrow \ell^+ \ell^-$ ($\ell=e,\,μ$) are calculated. Factorizing the collinear singularity associated with initial state photon bremsstrahlung into the parton distribution functions, we find that initial state corrections have a much smaller effect than final state radiative corrections. Due to mass singular logarithmic terms associated with photons emitted collinear with one of the final state leptons, QED radiative corrections strongly affect the shape of the di-lepton inva…
We present the double real radiation contributions to the $t \bar t$ hadronic production cross section stemming from the partonic process $gg\rightarrow t\bar{t}q\bar{q}$. We explicitly construct the antenna subtraction terms for this gluon-gluon initiated process starting from the double soft behaviour of the double real radiation matrix elements using soft currents. Those subtraction terms, given in leading and subleading colour contributions, require the use of new genuine NNLO four-parton antenna functions involving massive fermions. Those are also presented together with their infrared li…
In this work, the radiative corrections to the production of a light Higgs boson ($h^0$) with a pair of lightest neutralinos (${\tildeχ}_1^0$) in $e^+ e^-$ collisions within MSSM are presented, including the on-shell renormalization scheme in the loop calculations. We have studied the QED corrections as well as the weak corrections, where the contribution from both corrections is significant and needs to be taken into account in the future linear colliders experiments. The result includes the numerical calculations for two different SUSY scenarios---Higgsino and Gaugino scenarios--- for $e^+ e…
The QED initial state corrections are calculated to the forward-backward asymmetry for $e^+e^- \rightarrow γ^*/{Z^{0}}^*$ in the leading logarithmic approximation to $O(α^6 L^6)$ extending the known corrections up to $O(α^2 L^2)$ in analytic form. We use the method of massive on-shell operator matrix elements and present the radiators both in Mellin-$N$ and momentum fraction $z$-space. Numerical results are presented for various energies around the $Z$-peak by also including energy cuts. These corrections are of relevance for the precision measurements at the FCC$\_$ee.
The master integrals for the mixed QCD-QED two-loop virtual corrections to the charged-current Drell-Yan process $q\bar{q}^{\prime} \rightarrow \ell ν$ are computed analytically by using the differential equation method. A suitable choice of master integrals makes it successful to cast the differential equation system into the canonical form. We keep the dependence on charged lepton mass in the building of differential equations and then expand the system against the ratio of small charged lepton mass to large $W$-boson mass. In such a way the final results will contain large logarithms of the…
The complete set of ${\cal O}(α)$ QED corrections with soft photon exponentiation to the process $ep \rightarrow eX$ in mixed variables ($y=y_h,Q^2=Q_l^2$) is calculated in the quark parton model, including the lepton-quark interference and the quarkonic corrections which were unknown so far. The interference corrections amount to few percent or less and become negligible at small $x$. The leading logarithmic terms proportional to $\ln(Q^2/m_q^2)$ from radiation off quarks are discussed and the non-logarithmic quarkonic corrections found to be negligible for almost all experimentally accessibl…
Having taken the QED radiative correction and one-loop weak corrections into account, we have computed the unpolarized forward-backward asymmetry in the process $e^+e^- -> μ^+μ^-$ at a very reasonable accuracy. Special attention to the effects around the LEP 200 energy, induced by the possible $Z'$ boson of the left-right symmetric model $SU(2)_{L} \times SU(2)_{R} \times U(1)_{B-L}$, is paid. The numerical results of the directly measurable asymmetry $A_{FB}^μ$ versus the CMS energies are presented in figures. One may be convinced by the results that precise measurements on the asymmetry in f…
We complete the analytic evaluation of the master integrals for the two-loop non-planar box diagrams contributing to the top-pair production in the quark-initiated channel, at next-to-next-to-leading order in QCD. The integrals are determined from their differential equations, which are cast into a canonical form using the Magnus exponential. The analytic expressions of the Laurent series coefficients of the integrals are expressed as combinations of generalized polylogarithms, which we validate with several numerical checks. We discuss the analytic continuation of the planar and the non-plana…
More accurate $σ(\mathcal{G} \,\mathcal{G}\rightarrow h)$, $Γ(h \rightarrow \mathcal{G} \,\mathcal{G}, \mathcal{A} \mathcal{A}, \barΨ Ψ)$ and Higgs width results via the geoSMEFT
We present the full $\mathcal{O}(α)$ electroweak radiative corrections to the process $e^+e^- \rightarrow t \bar{t} γ$ at the International Linear Collider (ILC). The computation is performed with the help of the GRACE-Loop system. We present the total cross-section and the top quark forward-backward asymmetry ($A_{FB}$) as a function of the center-of-mass energy and compare them with the process $e^+e^- \rightarrow t \bar{t}$. We find that the value of $A_{FB}$ in $t \bar{t} γ$ production is larger than $A_{FB}$ in $t\bar{t}$ production. It is an important result for the measurement of the to…
We classify the possible deviations from the Standard Model in the QED-dominated $\mathrm{e^+e^-}\rightarrowγγ$ process under the assumption of a preserved $SU(2)_L \times U(1)_Y$ symmetry. We find that the only deviations really observable in practice correspond to a correction of the differential cross section by a factor $(1 + \frac{c_8~s^2}{8παΛ^4}~\sin^2θ)$, where $Λ$ is the scale of new physics, $θ$ is the polar angle of any of the final state photons and $c_8$ is a constant of order 1. We also provide sensitivity estimates for QED deviations at future $\mathrm{e^+e^-}$ facilities. An $\…
The decreasing uncertainties in theoretical predictions and experimental measurements of several hadronic observables related to weak processes, which in many cases are now smaller than $\mathrm{O}(1\%)$, require theoretical calculations to include subleading corrections that were neglected so far. Precise determinations of leptonic and semi-leptonic decay rates, including QED and strong isospin-breaking effects, can play a central role in solving the current tensions in the first-row unitarity of the CKM matrix. In this work we present the first RBC/UKQCD lattice calculation of the isospin-br…
SuperB experiment could represent an ideal environment to test a new U (1) symmetry related to light dark forces candidates. A promising discovery channel is represented by the resonant production of a boson U, followed by its decay into lepton pairs. Beyond approximations adopted in the literature, an exact tree level calculation of the radiative processes $e+ e- \rightarrow γ, U \rightarrow μ^+ μ^- γ, e^+ e^- γ$ and corresponding QED backgrounds is performed, including also the most important higher-order corrections. The calculation is implemented in a release of the generator BabaYaga@NLO …
The ratio of di-lepton production cross sections on a proton, using the $γp\rightarrow l^+ l^- p$ process, above and below di-muon production threshold allows to extract the effective lepton-proton interaction, which is required to be identical for electrons and muons if lepton universality is exact. To test for a scenario of broken universality at the percent level, of the size which could explain the different proton charge radii extracted from electron scattering and from muonic hydrogen spectroscopy, we evaluate all one-loop QED corrections to this process, including the full lepton mass d…
A total and differential cross-section calculation for the Electroweak Standard Model reaction $e^+ e^- \rightarrow (Z^0 Z^0) \rightarrow f_1\bar{f_1}f_2\bar{f_2}(γ)$\ including the effects of the finite $Z^0$\ width and, for the first time, all QED initial state radiative corrections (ISR) is presented. A semi-analytical technique is used: All angular phase space integrations, five for the tree level process, seven if ISR is included, are carried out analytically. The remaining phase space variables are the invariant masses of the two decaying $Z^0$\ bosons for tree level plus the reduced cen…
We discuss how colour flows can be used to simplify the computation of matrix elements, and in the context of parton shower Monte Carlos with accuracy beyond leading-colour. We show that, by systematically employing them, the results for tree-level matrix elements and their soft limits can be given in a closed form that does not require any colour algebra. The colour flows that we define are a natural generalization of those exploited by existing Monte Carlos; we construct their representations in terms of different but conceptually equivalent quantities, namely colour loops and dipole graphs,…
In this work we revisit the algorithm of Denner and Pozzorini for the calculation of one-loop electroweak Sudakov logarithms and we automate it in the MadGraph5_aMC@NLO framework. We adapt the formulas for modern calculations, keeping light-quarks and photons strictly massless and dealing with infrared divergences via dimensional regularisation. We improve the approximation by taking into account additional logarithms that are angular dependent. We prove that an imaginary term has been previously omitted and we show that it cannot be in general neglected for $2\rightarrow n$ processes with $n>…
Due to the angular condition in the light-front dynamics (LFD), the extraction of the electromagnetic form factors for spin-1 particles can be uniquely determined taking into account implicitly non-valence and/or the zero-mode contributions to the matrix elements of the electromagnetic current. No matter which matrix elements of the electromagnetic current is used to extract the electromagnetic form factors, the same unique result is obtained. As physical observables, the electromagnetic form factors obtained from matrix elements of the current in LFD must be equal to those obtained in the ins…
