The new version of the SANCphot integrator has been prepared for fast and stable numerical calculations up to two loops for polarized light-by-light scattering. One-loop modules based on the helicity formalism with massive particles and two-loop modules with massless particles inside the loops are used. The presented study is driven by the potential of polarized photon beams to probe the high energy region. This study is a contribution to the research program of the CEPC project being under development in China.
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.
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 …
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 Effects of the Massless O(alpha_s^2), O(αα_s), O(α^2) QCD and QED Corrections and of the Massive Contributions to Gamma(H^0\rightarrow b\overline{b})
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 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 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…
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 …
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.
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 h…
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…
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…
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 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.
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…
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 …
We have performed the first $n_f = 2+1+1$ lattice QCD computations of the properties (masses and decay constants) of ground-state charmonium mesons. Our calculation uses the HISQ action to generate quark-line connected two-point correlation functions on MILC gluon field configurations that include $u/d$ quark masses going down to the physical point, tuning the $c$ quark mass from $M_{J/ψ}$ and including the effect of the $c$ quark's electric charge through quenched QED. We obtain $M_{J/ψ}-M_{η_c}$ (connected) = 120.3(1.1) MeV and interpret the difference with experiment as the impact on $M_{η_…
In this work we investigate the lattice Landau gauge photon propagator together with the average number of Dirac strings in the compact formulation of QED for the pure gauge version of the theory as a function of the coupling constant. Their $β$ dependence show that these two quantities can be used to identify the confinement-deconfinement transition and that the nature of this transition is first order. Our results show that in the confined phase the propagator is always finite, the theory has a mass gap and the number of Dirac strings present in the configuration is two orders of magnitude l…
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 $\…
We investigate the theoretical predictions for thrust distribution in the electron positron annihilation to three-jets process at NNLO for different values of the number of flavors, $N_f$. To determine the distribution along the entire renormalization group flow from the highest energies to zero energy we consider the number of flavors near the upper boundary of the conformal window. In this regime of number of flavors the theory develops a perturbative infrared interacting fixed point. We then consider also the QED thrust obtained as the limit $N_c \rightarrow 0$ of the number of colors. In t…
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…
In the framework of the electroweak standard model, we investigated, in the center of mass frame, the Higgs boson production in the presence of an intense laser field via ${e}^{+} {e}^{-}$ annihilation $({e}^{+} {e}^{-}\rightarrow ZH)$. By comparing our results with those obtained by Djouadi \cite{1} for laser-free process, we show that the circularly polarized laser field affects significantly the $s$-channel Higgs boson production. We find that for a given number of exchanged photons, laser field strength and frequency, the total cross section decreases by several orders of magnitude. These …
We derive the momentum distribution for two soft and collinear gluons emitted from an off-shell quark, modeled by a $qγ\rightarrow qgg$ scattering process and computed using the maximal helicity violating (MHV) technique. We find the explicit non-Abelian corrections to the independent emission Poisson distribution in QED and demonstrate the efficiency of the MHV technique in perturbative QCD calculations. The gluonic two particle correlation function is highly suggestive of that measured in high-multiplicity $pp$ and $pA$ collisions, with a tight correlation in angle but broad correlation in r…
We compute the Standard Model semileptonic vector and axial-vector form factors for $B_s\to D_s^*$ decay across the full $q^2$ range using lattice QCD. We use the Highly Improved Staggered Quark (HISQ) action for all valence quarks, enabling us to normalise weak currents nonperturbatively. We use gluon field configurations including $u$, $d$, $s$ and $c$ HISQ sea quarks and multiple HISQ heavy quarks with masses from the $c$ mass up to that of the $b$ on our finest lattices. We determine the physical form factors, with which we construct the differential and total rates for $Γ(B_s^0\to D_s^{*-…
The charged Higgs pair production via photon-photon collisions is investigated in the framework of two Higgs doublet model (2HDM), taking into account a full set of one-loop-level scattering amplitudes, i.e., including electroweak (EW) corrections together with soft and hard QED radiation. The numerical evaluation is carried out for three different scenarios, so-called non-alignment, low-$m_H$ and short-cascade, defined in the presence of the up-to-date experimental constraints and consistent with theoretical constraints as well. The total cross sections of $γγ\rightarrow H^{-}H^{+}$ are scann…
We calculate the leading-order QED radiative corrections to the process $e^- p\rightarrow e^- p l^- l^+ $ in the soft-photon approximation, in two different energy regimes which are of relevance to extract nucleon structure information. In the low-energy region, this process is studied to better constrain the hadronic corrections to precision muonic Hydrogen spectroscopy. In the high-energy region, the beam-spin asymmetry for double virtual Compton scattering allows to directly access the Generalized Parton Distributions. We find that the soft-photon radiative corrections have a large impact o…
We consider reduced quantum electrodynamics (RQED$_{d_γ,d_e}$) a model describing fermions in a $d_e$-dimensional space-time and interacting via the exchange of massless bosons in $d_γ$-dimensions ($d_e \leq d_γ$). We compute the two-loop mass anomalous dimension, $γ_m$, in general RQED$_{4,d_e}$ with applications to RQED$_{4,3}$ and QED$_4$. We then proceed on studying dynamical (parity-even) fermion mass generation in RQED$_{4,d_e}$ by constructing a fully gauge-invariant gap equation for RQED$_{4,d_e}$ with $γ_m$ as the only input. This equation allows for a straightforward analytic computa…
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>…
We study the mirror world with dark matter arising from the thermal freeze-out of the lightest, stable mirror particle -- the mirror electron. The dark matter abundance is achieved for mirror electrons of mass 225 GeV, fixing the mirror electroweak scale near $10^8$ GeV. This highly predictive scenario is realized by an axion that acts as a portal between the two sectors through its coupling to the QCD and mirror QCD sectors. The axion is more massive than the standard QCD axion due to additional contributions from mirror strong dynamics. Still, the strong CP problem is solved by this "heavy" …
