The proper-time 4d path integral is used as a starting point to derive the new explicit parametric form of the quark-antiquark Green's function in gluonic and QED fields, entering as a common Wilson loop. The subsequent vacuum averaging of the latter allows to derive the instantaneous Hamiltonian. The explicit form and solutions are given in the case of the $q\bar q$ mesons in magnetic field.
QED based on $θ$-unexpanded noncomutative space-time in contrast with the noncommutative QED based on $θ$-expanded U(1) gauge theory via the Seiberg-Witten map, is one-loop renormalizable. Meanwhile it suffers from asymptotic freedom that is not in agreement with the experiment. We show that QED part of $U_\star(3)\times U_\star(1)$ gauge group as an appropriate gauge group for the noncommutative QED+QCD, is not only one-loop renormalizable but also has a $β$ function that can be positive, negative and even zero. In fact the $β$ function depends on the mixing parameter $δ_{13}$ as a free param…
We consider for the first time the QED corrections to the evolution of (un)polarized quark and gluon transverse-momentum-dependent distribution and fragmentation functions (TMDs in general). By extending their operator definition to QCD$\times$QED, we provide the mixed new anomalous dimensions up to ${\cal O}(α_sα)$ and the pure QED ones up to ${\cal O}(α^2)$. These new corrections are universal for all TMDs up to the flavor of the considered parton, i.e., the full flavor universality of TMD evolution found in pure QCD is broken in QCD$\times$QED by the presence of the electric charge. In addi…
Transverse-momentum resummation at mixed QCD$\otimes$QED NNLL accuracy for Z boson production at hadron colliders
Instituto de Física Corpuscular (IFIC), CSIC-Universitat de València（粒子物理研究所（IFIC），西班牙瓦伦西亚大学）；CERN（欧洲核子研究中心）；Tif Lab, Dipartimento di Fisica, Universitá di Milano and INFN, Sezione di Milano（米兰大学物理系及意大利国家核物理研究院米兰分部）；Departamento de Física Fundamental e IUFFyM, Universidad de Salamanca（萨拉曼卡大学基础物理系）
The semi-analytical expression for the forth coefficient of the renormalization group $β$-function in the ${\rm{V}}$-scheme is obtained in the case of the $SU(N_c)$ gauge group. In the process of calculations we use the three-loop perturbative approximation for the QCD static potential, evaluated in the $\rm{\overline{MS}}$-scheme. The importance of getting more detailed expressions for the $n_f$-independent three-loop contribution to the static potential,obtained at present by two groups, is emphasised. The comparison of the numerical structure of the four-loop approximations for the RG $β$- …
We present a concise summary of recent results for the vector correlator in massless QCD at order ${\cal O}(α_s^4)$, with all colour factors being given for a generic colour group. As a direct consequence we arrive at: (i) the full QCD contribution to the QED $β$--function of order $α^2\, α_s^4$ in the MSbar- and MOM-schemes; (ii) the full five-loop result of order $α^6$ for the $β$-function of QED with a generic number of single-charged fermions, again for the MSbar- and MOM-schemes.
We report on the computation of the effective actions describing the interaction of gravity both for an abelian and a non-abelian gauge theory, mediated by the trace anomaly.
We investigate the deconfining phase transition in QCD_4 and QED_4 at finite temperature using a perturbative deformation of topological quantum field theory (TQFT). A modified maximal abelian gauge (MAG) is utilized in the analysis. In this case, we can derive the linear potential studying the 2D theory through Parisi-Sourlas (PS) dimensional reduction. The mechanism of deconfining phase transition is proposed. It is geometrical to discuss the thermal effect on the linear potential. All we have to do is to investigate the behavior of topological objects as such instantons and vortices on a cy…
The covariant quantization of QED and QCD requires the introduction of subsidiary gauge-fixing and ghost fields and it is crucial to understand the role of these in the energy-momentum tensor, and in the momentum and angular momentum operators. These issues were studied in \cite{Leader:2011za}, and key results from this study were utilized in the major review of angular momentum in \cite{Leader:2013jra}. Damski \cite{Damski:2021feu} has rightly criticized as incorrect the derivation of certain equations in \cite{Leader:2011za}. We show, however, that the key results of \cite{Leader:2011za} whi…
Conformal symmetry has important consequences for strong interactions at short distances and provides powerful tools for practical calculations. Even if the Lagrangians of Quantum Chromodynamics (QCD) and Electrodynamics (QED) are invariant under conformal transformations, this symmetry is broken by quantum corrections. The signature of the symmetry breaking is encoded in the presence of massless poles in correlators involving stress-energy tensors. We present a general study of the correlation functions $\langle TJJ\rangle$ and $\langle TTJJ\rangle$ of conformal field theory (CFT) in the flat…
We present a general study of 3-point functions of conformal field theory (CFT) in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWIs), introduced in recent works. We investigate and detail the structure of the CWIs and their non-perturbative solutions, and compare them to perturbation theory, taking QED and QCD as examples. Exact solutions of CFT's in the flat background limit in momentum space are matched by the perturbative realizations in free field theories, showing that the origin the conformal anomaly is…
We compute the mixed QCD$\otimes$QED corrections to the production of on-shell $Z$ bosons at the LHC at a fully-exclusive level. We also include the factorised NLO QCD correction to $Z$ boson production and NLO QED correction to $Z$ boson decay into two leptons. We make use of an abelianised version of the nested soft-collinear subtraction formalism to perform this computation. We study the phenomenological impact of the mixed QCD$\otimes$QED corrections for a number of observables relevant for LHC phenomenology.
An approximation algorithm is proposed to transform truncated QCD (or QED) series for observables. The approximation is a modification of the Baker-Gammel approximants, and is independent of the renormalization scale (RScl) $μ$ -- the coupling parameter $α(μ)$ in the series and in the resulting approximants can evolve according to the perturbative renormalization group equation (RGE) to any chosen loop order. The proposed algorithm is a natural generalization of the recently proposed method of diagonal Padé approximants, the latter making the result RScl-invariant in large-$β_0$ approximation …
The conventional results for hard thermal loops, which are the building blocks of resummed perturbation theory in thermal field theories, have collinear singularities when external momenta are light-like. It is shown that by taking into account asymptotic thermal masses these singularities are removed. The thus improved hard thermal loops can be summarized by compact gauge-invariant effective actions, generalizing the ones found by Taylor and Wong, and by Braaten and Pisarski.
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 review the history of analytical approaches to particle production from external strong fields in QED and QCD, and numerical studies of the back reaction problem for the electric field in QED. We discuss the formulation of the backreaction problem for the chromoelectric field in QCD both in leading and next to leading order in flavor large-N QCD.
We report on two recent results based on the evaluation of five-loop massless propagators in QCD and QED: (i) corrections of order $α_s^4$ to the absorptive part of the polarization function in QCD with $n_f=3$;(ii) the five-loop contribution to the $β$ function of quenched QED.
The lectures are a practical introduction to perturbative calculations in QED and QCD. I discuss methods of calculation of one- and two-loop diagrams in dimensional regularization, MSbar and on-shell renormalization schemes, decoupling of heavy-particle loops.
We present the theory of QED x QCD resummation and its interplay with shower/matrix element matching in precision LHC physics scenarios. We illustrate the theory using single heavy gauge boson production at hadron colliders.
We present next-to-next-to leading order (NNLO) quantum electrodynamics (QED) corrections to the production of the Higgs boson in bottom quark annihilation at the Large Hadron Collider (LHC) in the five flavor scheme. We have systematically included the NNLO corrections resulting from the interference of quantum chromodynamics (QCD) and QED interactions. We have investigated the infrared (IR) structure of the bottom quark form factor up to two loop level in QED and in QCD$\times$QED using K+G equation. We find that the IR poles in the form factor are controlled by the universal cusp, collinear…
In this paper we briefly outline the quadrature method for estimating uncertainties in a function of several variables and apply it to estimate the numerical uncertainties in QCD-QED rescaling factors. We employ here the one-loop order in QED and three-loop order in QCD evolution equations of fermion mass renormalization. Our present calculations are found to be new and also reliable compared to the earlier values employed by various authors.
Decoupling of a heavy flavour in QCD is discussed in a pedagogical way. First we consider a simpler case: decoupling of muons in QED. All calculations are done up to 2 loops.
We discuss the elements of QED X QCD exponentiation and its interplay with shower/ME matching and IR-improved DGLAP theory in precision LHC physics scenarios. Applications to single heavy gauge boson production at hadron colliders are illustrated.
We present the QCD and QED corrections to the fermion-loop contributions to light-by-light scattering, gamma gamma to gamma gamma, in the ultrarelativistic limit where the kinematic invariants are much larger than the masses of the charged fermions.
We study in the quasiclassical approximation the radiation reaction and its influence on the space-time evolution for the small relativistic dipole moving in a constant external electromagnetic field in QED.
We review some recent results about the computation of mixed QCD-QED corrections beyond the leading order in perturbation theory. We start by considering the effects induced in the Altarelli-Parisi equations and the partonic distributions. In particular, we describe the computation of one-loop mixed QCD-QED and two-loop QED terms in the splitting kernels, which are relevant to account for the presence of photon distributions. In the last part, we briefly talk about the implementation of these corrections in the context of the $q_T$-subtraction/resummation formalism.
I discuss the basic ideas of the light-cone path integral approach to the induced radiation in QED and QCD and recent applications to the induced parton energy loss.
In this paper we present a new and efficient analytical solutions for evolving the QED$\otimes$QCD DGLAP evolution equations in mellin space and obtain the parton distribution functions (PDFs) in perturbative QCD including the QED corrections. The validity of our analytical solutions, which have done in the next to leading order QCD and the leading order QED approximations, are checked with the initial parton distributions from newly released CT14QED global analysis code (Phys. Rev.D93,114015(2016)). The evolved parton distributions are in good agreement with CT14QED code and also with those f…
We present the results of our recent calculation of $ε^{\prime}/ ε$ at the Next-to-Leading (NLO) order in QCD and QED, in the framework of $\DSone$ Effective Hamiltonians. The operator matrix elements are taken from lattice QCD, at a scale $μ=2\,\,\mbox{GeV}$. NLO corrections seem to lower the value of $ε^{\prime}/ε$, favouring the experimental result of E731. Contributions from different operators are analyzed and dependence on $\mt$, $μ$ and $Λ_{\sss QCD}$ discussed. (Talk given at the XXVIIIth Rencontres de Moriond, ``Electro-Weak Interactions and Unified Theories'', March 13-19 1993).
We compute the on-shell wave function renormalization constant to four-loop order in QCD and present numerical results for all coefficients of the SU$(N_c)$ colour factors. We extract the four-loop HQET anomalous dimension of the heavy quark field and also discuss the application of our result to QED.
We study the mixed effect of QCD and QED corrections to the evolution of parton distribution functions (PDFs). The Altarelli-Parisi splitting functions are extended to one order higher in QED, reaching ${\cal O}(α\, α_S^2)$ accuracy. This also involves extending DGLAP equations to include charge separation effects, that are ignored for pure QCD corrections. Besides that, these effects are crucial for the determination of the photon distribution, which plays an increasingly important role in nowadays phenomenological analysis.
With an eye toward LHC processes in which theoretical precisions of 1 percent are desired, we introduce the theory of the simultaneous YFS resummation of QED and QCD to compute the size of the expected resummed soft radiative threshold effects in precision studies of heavy particle production at the LHC. Our results show that both QED and QCD soft threshold effects must be controlled to be on the conservative side to achieve such precision goals.
The effective kinematic diagram technique is applied to study inelastic form factors of electron and quark in QED and QCD. The explicit expressions for these form factors in the double-logarithmic approximation are presented. The self-consistency of the results is shown by demonstrating the fulfillment of the Kinoshita-Lee-Nauenberg theorem.
By using path integral formulation of QCD and QED we prove that the factorization theorem is valid for light-like Wilson line but is not valid for non-light-like Wilson line. This conclusion is shown to be consistent with Ward identity and Grammer-Yennie approximation. Hence we find that the factorization theorem is violated in all the previous studies which used the non-light-like Wilson line in the definition of the (transverse momentum dependent) parton distribution function and fragmentation function at high energy colliders.
We derive an analytic expression for one-loop effective action of QCD+QED at zero and finite temperatures by using the Schwinger's proper time method. The result is a nonlinear effective action not only for electromagnetic and chromo-electromagnetic fields but also the Polyakov loop, and thus reproduces the Euler-Heisenberg action in QED, QCD, and QED+QCD, and also the Weiss potential for the Polyakov loop at finite temperature. As applications of this "Euler-Heisenberg-Weiss" action in QCD+QED, we investigate quark pair productions induced by QCD+QED fields at zero temperature and the Polyako…
For the first time a rigorous quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD is given. The rate of photon (gluon) radiation by an electron (quark) in medium is expressed through the Green's function of a two-dimensional Schrödinger equation with an imaginary potential. In QED this potential is proportional to the dipole cross section for scattering of $e^{+}e^{-}$ pair off an atom, in QCD it is proportional to the cross section of interaction with color centre of the color singlet quark-antiquark-gluon system.
A numerical estimative error of the magnitude of the vacuum polarization effect due to electron-positron by a factor of $10^3$ in [PRL97(2006)100403; 269901(E)] invalidates the study carried in this work in its present context.
We present results of numerical solutions of Schwinger-Dyson equations for the finite-temperature quark and electron propagators. It is shown that both strongly coupled QED and QCD undergo a chiral symmetry restoring phase transition as the temperature is increased. We go beyond the bare vertex or "rainbow" approximation by applying the finite-temperature Ward-Takahashi identity to constrain the non-perturbative vertex function.
In some processes at the LHC, theoretical precisions of 1 percent are desired. With an eye toward such precisions, we introduce the theory of the simultaneous YFS resummation of QED and QCD to compute the size of the expected resummed soft radiative threshold effects in precision studies of heavy particle production at the LHC. Our results, that the soft QED threshold effects are at the level of 0.3 percent whereas the soft QCD threshold effects enter at the level of 20 percent, show that both must be controlled to be on the conservative side to achieve such precision goals.
The large N_f self-consistency programme is reviewed. As an application the QCD beta-function is computed at O(1/N_f) and the anomalous dimensions of polarized twist-2 singlet operators are determined at the same order.
We compute the free energy density for gauge theories, with fermions, at high temperature and zero chemical potential. Specifically, we analytically compute the free energy through $O(g^4)$, which requires the evaluation of three-loop diagrams. This computation extends our previous result for pure gauge QCD.
Evolution equations of YFS and DGLAP types in leading order are considered. They are compared in terms of mathematical properties and solutions. In particular, it is discussed how the properties of evolution kernels affect solutions. Finally, comparison of solutions obtained numerically are presented.
Bound state problem in the relativistic QED is investigated by the functional integral methods. The ortho- para- positron mass difference is calculated. Contribution of the "nonphysical"$~$ time variable turned out to be important and leads to the nonanalytic dependence of the bound state mass of the order $α^{2\over3}$. It is shown that the relativistic and non-relativistic QED gives different results for this mass shift. In addition so-called abnormal states as "time excitations" arise. Sequential application of relativistic QED to bound state problem is in contradiction with real ortho- and…
The resummation of $O(α^{l+1} \ln^{2l} x)$ terms in the evolution kernels of non--singlet combinations of structure functions is investigated for both QED abd QCD. Numerical results are presented for unpolarized and polarized structure functions.
Using the Schwinger-Keldysh closed time path integral formalism we show that the magnetic screening mass in QED and QCD at one loop level is non-zero as long as the single particle distribution function f(\vec{k}) is non-isotropic, {i.e.} it depends on the direction of the momentum. For isotropic distribution functions such as those corresponding to thermal equilibrium the magnetic screening mass at one loop level is found to be zero which is consistent with finite temperature field theory. The non-zero magnetic screening mass in non-isotropic non-equlibrium situations has fundamental importan…
The effect of sea quark electromagnetic charge on meson masses is investigated, and first results for full QED+QCD low-energy constants are presented. The electromagnetic charge for sea quarks is incorporated in quenched QED+full QCD lattice simulations by a reweighting method. The reweighting factor, which connects quenched and unquenched QED, is estimated using a stochastic method on 2+1 flavor dynamical domain-wall quark ensembles.
We present the elements of three applications of resummation methods in non-Abelian gauge theories: (1), QED X QCD exponentiation and shower/ME matching for LHC physics; (2), IR improvement of DGLAP theory; (3), resummed quantum gravity and the final state of Hawking radiation. In all cases, the extension of the YFS approach, originally introduced for Abelian gauge theory, to non-Abelian gauge theories, QCD and quantum general relativity, leads to new results and solutions which we briefly summarize.
We describe a calculation of the on-shell renormalization factors in QCD and QED at the three loop level. Explicit results for the fermion mass renormalization factor Zm and the on-shell fermion wave function renormalization constant Z2 are given. We find that at O(alpha_s^3) the wave function renormalization constant Z2 in QCD becomes gauge dependent also in the on-shell scheme, thereby disproving the ``gauge-independence'' conjecture based on an earlier two-loop result. As a byproduct, we derive an O(alpha_s^3) contribution to the anomalous dimension of the heavy quark field in HQET.
Upon using the same theoretical framework, I describe two interesting decay processes: the electromagnetic plasmon decay into neutrinos, which can be the dominant cooling mechanism for red giants and white dwarfs, and the gluonic plasmon decay into quarks, which can be measured in ultra-relativistic heavy-ion collisions.
We consider the transverse-momentum ($q_T$) distribution of $Z$ bosons produced in hadronic collisions. At small values of $q_T$, we perform the analytic resummation of the logarithmically enhanced QED contributions up to next-to-leading logarithmic accuracy, including the mixed QCD-QED contributions at leading logarithmic accuracy. Resummed results are consistently matched with the next-to-leading fixed-order results (i.e. $\mathcal{O}(α^2)$) at small, intermediate and large values of $q_T$. We combine the QED corrections with the known QCD results at next-to-next-to-leading order ($\mathcal{…
We use the theory of YFS resummation to compute the size of the expected resummed soft radiative threshold effects in precision studies of heavy particle production at the LHC, where accuracies of 1 percent are desired in some processes. We find that the soft QED threshold effects are at the level of 0.3 percent whereas the soft QCD threshold effects enter at the level of 20 percent and hence both must be controlled to be on the conservative side to achieve such goals.
We discuss the origin of the anomalous $T\ln T^{-1}$ behavior of the low-temperature entropy and specific heat in ultradegenerate QED and QCD and report on a recent calculation which is complete to leading order in the coupling and which contains an infinite series of anomalous terms involving also fractional powers in $T$. This result involves dynamical hard-dense-loop resummation and interpolates between Debye screening effects at larger temperatures and non-Fermi-liquid behavior from only dynamically screened magnetic fields at low temperature.
We analytically solved the QED $\otimes$ QCD coupled DGLAP evolution equations at leading order (LO) quantum electrodynamics (QED) and next to leading order (NLO) quantum chromodynamics (QCD) approximations, using the Laplace transform method and then computed the proton structure function in terms of the unpolarized parton distributions functions. Our analyitical solutions for parton densities are in good agreement with those from APFEL (A PDF Evolution Library) (Computer Physics Communications 185, 1647-1668 (2014)) and CT14QED (Phys. Rev. D 93, 114015 (2016)) global parameterizations. We al…
First order QCD and leading QED corrections to Higgs boson production in the channel $e^-p \to νH^0 X; H^0 \to b\bar{b}$ are calculated for the kinematical conditions at LEP $\otimes$ LHC ($\sqrt{s} = 1360 \GeV$) and the interesting mass range $80 < M_H < 150 \GeV$. In the DIS scheme the QCD corrections (not including the corrections to the branching ratio, which are well-known) are found to be about 1\% for the total cross section and $-13\%$ to $-10\%$ for the observable cross section as defined by appropriate cuts. The latter results depend on the definition of these cuts. The QED correctio…
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.
In this talk, we describe the recent progress on the inclusion of mixed QCD-QED corrections for collider observables. In particular, we developed a formalism to extend $q_T$-resummation to deal with simultaneous emission of gluons and photons. We applied it to $Z$ production at colliders, and briefly discuss extensions to more complicated final states.
Magnetic susceptibility of the quark matter in QCD is calculated in a closed form for an arbitrary chemical potential μ. For small μ, μ<<T, eB << T^2, a strong dependence on temperature T is found due to Polyakov line factors. In the opposite case of small T, eB > T^2, the oscillations as functions of eB occur, characteristic of the de Haas-van Alphen effect. Results are compared with available lattice data.
