We calculate all contributions $\propto T_F$ to the polarized three-loop anomalous dimensions in the M-scheme using massive operator matrix elements and compare to results in the literature. This includes the complete anomalous dimensions $γ_{qq}^{(2),\rm PS}$ and $γ_{qg}^{(2)}$. We also obtain the complete two-loop polarized anomalous dimensions in an independent calculation. While for most of the anomalous dimensions the usual direct computation methods in Mellin $N$-space can be applied since all recurrences factorize at first order, this is not the case for $γ_{qg}^{(2)}$. Due to the necessity of deeper expansions of the master integrals in the dimensional parameter $\varepsilon = D-4$, we had to use the method of arbitrary high moments to eliminate elliptic contributions in intermediate steps. 4000 moments were generated to determine this anomalous dimension and 2640 moments turned out to be sufficient. As an aside, we also recalculate the contributions $\propto T_F$ to the three-loop QCD $β$-function.
We describe on-shell methods for computing one- and two-loop anomalous dimensions in the context of effective field theories containing higher-dimension operators. We also summarize methods for computing one-loop amplitudes, which are used as inputs to the computation of two-loop anomalous dimensions, and we explain how the structure of rational terms and judicious renormalization scheme choices can lead to additional vanishing terms in the anomalous dimension matrix at two loops. We describe the two-loop implications for the Standard Model Effective Field Theory (SMEFT). As a by-product of th…
We report on the calculation of the three-loop polarized and unpolarized flavor non-singlet and the polarized singlet anomalous dimensions using massless off-shell operator matrix elements in a gauge-variant framework. We also reconsider the unpolarized two-loop singlet anomalous dimensions and correct errors in the foregoing literature.
We calculate the unpolarized and polarized three--loop anomalous dimensions and splitting functions $P_{\rm NS}^+, P_{\rm NS}^-$ and $P_{\rm NS}^{\rm s}$ in QCD in the $\overline{\sf MS}$ scheme by using the traditional method of space--like off shell massless operator matrix elements. This is a gauge--dependent framework. For the first time we also calculate the three--loop anomalous dimensions $P_{\rm NS}^{\rm \pm tr}$ for transversity directly. We compare our results to the literature.
We calculate tree-level cross-sections for $W^{+}γ$ and $W^{+}W^{-}$ production in proton-antiproton collisions, with one $W$ decaying to leptons, with anomalous electroweak triple-boson coupling parameters $Δκ$ and $λ$. We compare the unpolarized cross-sections to those for a polarized proton beam, to study how a polarized proton beam would improve experimental tests of anomalous couplings.
The present contribution reports a study of the effects of anomalous gauge and fermionic couplings in the process $e^+e^- -> W^+W^-$ at the Next Linear Collider focusing in particular on the option of polarized beams. We conclude that polarized beams with adjustable degree of polarization would constitute a very significant tool in the search for new physics.
We discuss the polar angle decay distribution in the decay of on-shell and off-shell polarized (W,Z) gauge bosons into massive quark pairs. In particular for the off-shell decays in $H \to (W,Z) + (W^\ast,Z^\ast) (\to q_1\bar q_2)$ it is important to keep the masses of the charm and bottom quarks at their finite values since the scale of the problem is not set by $m_{W,Z}^2$ but by the off-shellness of the gauge boson which varies in the range $(m_1+m_2)^2 \le q^2 \le (m_H-m_{W,Z})^2$.
Interaction of charged leptons with photons is considered for the case when one of the lepton legs is off the mass shell. The effect due to off-mass-shell shift in the anomalous magnetic moment is computed within one-loop approximation. Possible contributions of this effect in the muon $g-2$ measurements are discussed.
Analytic expression for energy and angular dependence of a secondary charged lepton in the decay of a polarized top quark with anomalous $tWb$ couplings in the presence of all anomalous couplings are derived. The angular distribution of the b-quark is derived as well. It is presented that the charged lepton spin correlation coefficient is not very sensitive to the anomalous couplings. However, the b-quark spin correlation coefficient is sensitive to anomalous couplings and could be used as a powerful tool for searching of non-SM coupling.
We present results on the calculation of the polarized 2- and 3-loop anomalous dimensions in a massive computation of the associated operator matrix element. We also discuss the treatment of $γ_5$ and derive results in the M-scheme.10
We provide analytical $O(α_s)$ results for the three polarized decay structure functions $H_{++},\,H_{00}$ and $H_{--}$ that describe the decay of a polarized $W$ boson into massive quark--antiquark pairs. As an application we consider the decay $t\to b+W^+$ involving the helicity fractions $ρ_{mm}$ of the $W^+$ boson followed by the polarized decay $\hbox{$W^+(\uparrow)$}\to q_1\bar{q}_2$ described by the polarized decay structure functions $H_{mm}$. We thereby determine the $O(α_s)$ polar angle decay distribution of the cascade decay process $t\to b+W^+(\to q_1\bar{q}_2)$. As a second exampl…
We investigate the potential of $eγ$ collisions to probe anomalous $Wtb$ couplings via the polarized single top quark production process $e^{+} γ\to t \bar{b} \bar{ν_{e}}$. We find 95% confidence level limits on the anomalous coupling parameters $F_{2L}$ and $F_{2R}$ with an integrated luminosity of $500 fb^{-1}$ and $\sqrt{s}=0.5, 1$ and 1.5 TeV energies. The effects of top quark spin polarization on the anomalous $Wtb$ couplings are discussed. It is shown that polarization leads to a considerable improvement in the sensitivity limits.
We examine anomalous ZZH and gammaZH interactions in the process e+e- -> HZ followed by Z -> l+l- at a linear collider. We study the effects of beam polarization, both longitudinal and transverse, in probing these anomalous couplings. We study various correlations constructed out of the initial and final state lepton momenta and the spins of electron and positron. We evaluate the sensitivity of these observables to probe anomalous couplings at the linear collider.
We compute the O(1/N_f) correction to the predominantly gluonic flavour singlet twist-2 anomalous dimension used in polarized deep inelastic scattering. It is consistent with known two loop perturbation theory and we determine the three loop contribution at O(1/N_f). The treatment of the epsilon-tensor in the large N_f d-dimensional critical point formalism is also discussed.
The energy spectra of the lepton(s) in eebar --> ttbar --> l^{+-}X/ l^+l^- X' at next linear colliders (NLC) are analyzed a model-independent way for arbitrary longitudinal beam polarizations as a general test of possible anomalous top-quark couplings.
Future high luminosity polarized deep--inelastic scattering experiments will improve both the knowledge of the spin sub--structure of the nucleons and contribute further to the precision determination of the strong coupling constant, as well as, reveal currently yet unknown higher twist contributions in the polarized sector. For all these tasks to be performed, it is necessary to know the QCD leading twist scaling violations of the measured structure functions. Here an important ingredient consists in the polarized singlet anomalous dimensions and splitting functions in QCD. We recalculate the…
We use the on-shell S-matrix and form factors to compute anomalous dimensions of higher dimension operators in the Standard Model Effective Field Theory. We find that in many instances, these computations are made simple by using the on-shell method. We first compute contributions to anomalous dimensions of operators at dimension-six that arise at one-loop. Then we calculate two-loop anomalous dimensions for which the corresponding one-loop contribution is absent, using this powerful method.
On-shell amplitude methods allow to derive one-loop renormalization effects from just tree-level amplitudes, with no need of loop calculations. We derive a simple formula to obtain the anomalous dimensions of higher-dimensional operators from a product of tree-level amplitudes. We show how this works for dimension-6 operators of the Standard Model, providing explicit examples of the simplicity, elegance and efficiency of the method. Many anomalous dimensions can be calculated from the same Standard Model tree-level amplitude, displaying the attractive recycling aspect of the on-shell method. W…
We study the potential of the next-generation $e^+ e^-$ linear colliders with longitudinally polarized beams, to restrict the values of the anomalous trilinear couplings $WWγ$ and $WWZ$ from the measurement of the process $e^+ e^-\to W^+ W^-$. Along with initial $e^+e^-$ polarization, we account also for the possibilities offered by cross sections for polarized final $W$, in order to disentangle the constraints on the various constants. The results show the essential role of the initial beams polarization in improving the bounds obtained from the unpolarized case.
Critical exponents are computed for a variety of twist-2 composite operators, which occur in polarized and unpolarized deep inelastic scattering, at leading order in the 1/N_f expansion. The resulting d-dimensional expressions, which depend on the moment of the operator, are in agreement with recent explicit two and three loop perturbative calculations. An interesting aspect of the critical point approach which is used, is that the anomalous dimensions of the flavour singlet eigenoperators, which diagonalize the perturbative mixing matrix, are computed directly. We also elucidate the treatment…
We consider the possibility of observing deviations from the Standard Model gauge-boson self-couplings at a future $500$~GeV $e^+ e^-$ linear collider. We concentrate on the case in which the electroweak symmetry breaking sector is strongly interacting and there are no new resonances within reach of the collider. We find a sensitivity to the anomalous couplings that is two orders of magnitude higher than that achievable at LEP II. We also show how a polarized electron beam extends the reach of the collider, allowing experiments to probe different directions in parameter space.
We discuss differences between on-shell and off-shell treatments in the search for anomalous neutral triple gauge couplings in $\mathrm{e^+ e^-}$ collisions. We find that the usual on-shell framework represents an optimal starting point, covering all scenarios in which a reasonable experimental sensitivity is expected. We show that off-shell effects lead to negligible deviations at the experimental level, provided that $\mathrm{e^+ e^-}\to\mathrm{f}\bar{\mathrm{f}}γ$ and $\mathrm{e^+ e^-}\to\mathr performed in regions where $\mathrm{Z}^*\to\mathrm{f}\bar{\mathrm{f}},\mathrm{f^\prime}\math prod…
We explore the possibility of deriving model independent limits on the anomalous trilinear electroweak gauge boson couplings from high energy $e^+e^-\to W^+W^-$, by combining the cross sections for the different initial and final states polarizations integrated with suitable kinematical cuts. In the case of the CP conserving couplings the limits can be disentangled, and are given by simple mathematical expressions. Numerical results show the advantages of this approach, in particular the important role of polarization in improving the bounds.
In searching for indications of new physics scalar particle and unparticle couplings in e^+ e^- \to t\bar t, we consider the role of transversely polarized initial beams at e^+ e^- colliders. By using a general relativistic spin density matrix formalism for describing the particles spin states, we find analytical expressions for the squared amplitude of the process with t or \bar t polarization measured, including the anomalous coupling contributions. Thanks to the transversely polarized initial beams these contributions are first order anomalous coupling corrections to the Standard Model (SM)…
The linearized Einstein equation describing graviton propagation through a chiral medium appears to be helicity dependent. We analyze features of the corresponding spectrum in a collision-less regime above a flat background. In the long wave-length limit, circularly polarized metric perturbations travel with a helicity dependent group velocity that can turn negative giving rise to a new type of an anomalous dispersion. We further show that this chiral anomalous dispersion is a general feature of polarized modes propagating through chiral plasmas extending our result to the electromagnetic sect…
In this paper we investigate the renormalization of ${\cal N}=1$ supersymmetric quantum electrodynamics, regularized by higher derivatives, in the on-shell scheme. It is demonstrated that in this scheme the exact Novikov, Shifman, Vainshtein, and Zakharov (NSVZ) equation relating the $β$-function to the anomalous dimension of the matter superfields is valid in all orders of the perturbation theory. This implies that the on-shell scheme enters the recently constructed continuous set of NSVZ subtraction schemes. To verify this statement, we compare the anomalous dimension of the matter superfiel…
The angular and energy distributions of the final lepton in e ebar t tbar --> l^{+-} X at next linear colliders (NLC) are analyzed a model-independent way for arbitrary longitudinal beam polarizations as sensitive tests of possible anomalous top-quark couplings. The angular-energy distribution is expressed as a combination of independent functions of the angle and the energy, where each anomalous parameter is the coefficient of an individual term. Every parameter could be thereby determined simultaneously via the optimal-observable procedure. On the other hand, anomalous tbW couplings totally …
The differential cross-sections for processes of the type e+ e- to W+ W- to l nu q anti-q are determined with account of background contributions and of anomalous triple gauge boson couplings. Analytic expressions for dsigma/ds1 ds2 dcostheta, where theta is the production angle of the W boson, are numerically integrated with the Fortran package GENTLE. QED corrections are taken into account in the leading logarithmic approximation. The importance of the various contributions is studied for center-of-mass energies of 190 GeV, 500 GeV, and 1 TeV.
University of Oxford（牛津大学）；CERN（欧洲核子研究组织）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Arizona State University（亚利桑那州立大学）；University of Amsterdam（阿姆斯特丹大学）
One of the most-studied signals for physics beyond the standard model in the production of gauge bosons in electron-positron collisions is that due to the anomalous triple gauge boson couplings in the $Z γ$ final state. In this work, we study the implications of this at the ILC with polarized beams for signals that go beyond traditional anomalous triple neutral gauge boson couplings. Here we report a dimension-8 CP-conserving $Z γZ$ vertex that has not found mention in the literature. We carry out a systematic study of the anomalous couplings in general terms and arrive at a classification. We…
We establish the general off-shell structure of the three neutral gauge boson self-couplings V1*V2*V3*, with applications to the Z*Z*Z*, Z*Z*gamma*, gamma*gamma*Z* cases. New coupling forms appear which do not exist when two gauge bosons are on-shell. We give the contribution arising from a fermionic triangle loop. It covers both the standard model (SM) and possible new physics (NP) contributions like those arising in the MSSM. For what concerns NP contributions with a high scale, we discuss the validity of an effective Lagrangian involving a limited set of parameters. Finally we write the gen…
We study the anomalous $W^+W^-V$ ($V=γ,Z$) couplings in $e^+e^-\to W^+W^-$ using the complete set of polarization observables of $W$ boson with longitudinally polarized electron ($e^-$) and positron ($e^+$) beams. For the effective $W^+W^-V$ couplings, we use the most general Lorentz invariant form factor parametrization as well as $SU(2)\times U(1)$ invariant dimension-$6$ effective operators. We estimate simultaneous limits on the anomalous couplings using the Markov-Chain--Monte-Carlo (MCMC) method for an $e^+e^-$ collider running at center of mass energy of $\sqrt{s}=500$ GeV and the integ…
We investigate the transition of the polarized photon structure function $g_1^γ(x,Q^2,P^2)$ when the target photon shifts from on-shell ($P^2=0$) to far off-shell ($P^2\gg Λ^2$) region. The analysis is performed to the next-to-leading order in QCD. The first moment of $g_1^γ$ which vanishes for the real photon, turns to be a negative value when target photon becomes off-shell. The explicit $P^2$-dependence of the first moment sum rule as well as of the structure function $g_1^γ(x,Q^2,P^2)$ as a function of $x$ is studied in the framework of the vector meson dominance model.
Using on-shell methods, we present a new perturbative non-renormalization theorem for operator mixing in massless four-dimensional quantum field theories. By examining how unitarity cuts of form factors encode anomalous dimensions we show that longer operators are often restricted from renormalizing shorter operators at the first order where there exist Feynman diagrams. The theorem applies quite generally and depends only on the field content of the operators involved. We apply our theorem to operators of dimension five through seven in the Standard Model Effective Field Theory, including exa…
We study the anomalous $W^+W^-V$ ($V=γ,Z$) couplings in $e^+e^-\to W^+W^-$ using the complete set of polarization observables of $W$ boson with longitudinally polarized beams. We use most general Lorentz invariant form factors parametrization as well as $SU(2)\times U(1)$ invariant dimension $6$ effective operators for the effective $W^+W^-V$ couplings. We estimate simultaneous limits on the anomalous couplings in both the parametrizations using cross section, forward backward asymmetry and polarization observables of $W$ boson with different kinematical cuts using Markov-Chain--Monte-Carlo (M…
We examine the contributions of various couplings in general ZZH and gammaZH interactions arising from new physics to the Higgs production process e+e- --> HZ, followed by the decay of the Z into a charged-lepton pair. We take into account possible longitudinal or transverse beam polarization likely to be available at a linear collider. We show how expectation values of certain simple observables in suitable combinations with appropriate longitudinal beam polarizations can be used to disentangle various couplings from one another. Longitudinal polarization can also improve the sensitivity for …
We show that in the Mclerran-Venugopalan model, an axial asymmetrical valence quark distributions in the transverse plane of a transversely polarized proton can give rise to a spin dependent odderon. Such polarized odderon is responsible for the transverse single spin asymmetries(SSAs) for jet production in the backward region of pp collisions and open charm production in semi-inclusive DIS process.
Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector
CERN（欧洲核子研究中心）；Dipartimento di Fisica e Astronomia “G. Galilei”, Università degli Studi di Padova（帕多瓦大学物理与天文学系）；Istituto Nazionale di Fisica Nucleare, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）
We examine the potential of the $ep\toν_{e}qγX$ and $ep\toν_{e}qZX$ processes to search for the anomalous couplings of $WWγ$ and $WWZ$ vertices at the LHeC with the electron beam energy of $E_{e}=60$ GeV and $E_{e}=140$ GeV. The difference of maximum and minimum bounds on the anomalous couplings, ($δΔκ_γ$, $δλ_γ$) and ($δΔκ_{Z}$, $δλ_{Z}$) are obtained as ($0.990$, $0.122$) and ($0.362$, $0.012$) without electron beam polarization at the beam energy of $E_{e}=140$ GeV for an integrated luminosity of $L_{int}=100$ fb$^{-1}$, respectively. With the possibility of $e-$beam polarization, we obtain…
A covariant formulation of spin-dependent deep-inelastic scattering from nuclei is presented. In the relativistic impulse approximation the inclusive nuclear cross section is described in terms of the amplitude for forward, virtual-photon scattering from an off-mass-shell nucleon. The general structure of the off-shell nucleon hadronic tensor is derived, and the leading behavior of the off-shell nucleon structure functions computed in the Bjorken limit. The formalism, which is valid for nucleons bound inside nuclei with spin 1/2 or 1, is applied to the case of the deuteron.
We compute the eighth-order fermionic corrections involving two and three closed massless fermion loops to the anomalous magnetic moment of the muon. The required four-loop on-shell integrals are classified and explicit analytical results for the master integrals are presented. As further applications we compute the corresponding four-loop QCD corrections to the mass and wave function renormalization constants for a massive quark in the on-shell scheme.
Spin correlations in the t-channel single top quark production and its subsequent decay are investigated for the case of contributions involving anomalous Wtb couplings. We obtain analytical expressions for the differential widths for the three-particle decay of a polarized t quark in its rest frame and also expressions for the differential cross sections of the full process of production and decay of the t quark ($2\to 4$) as a function of the energy of a charged lepton and two angles of orientation of the quantization axis of the t-quark spin. The expression is presented in the most general …
The superfluid phase diagrams of a two-dimensional cold polarized Fermi gas in the BCS-BEC crossover are systematically and analytically investigated. In the BCS-Leggett mean field theory, the transition from unpolarized superfluid phase to normal phase is always of first order. For a homogeneous system, the two critical Zeeman fields and the critical population imbalance are analytically determined in the whole coupling parameter region, and the superfluid-normal mixed phase is shown to be the ground state between the two critical fields. The density profile in the presence of a harmonic trap…
We study the potential for using $eγ$\ collisions produced by backscattered laser photons to investigate WW$γ$\ couplings. We present results for Next Linear Collider energies of 500 GeV and 1 TeV. We find that where statistics allow, off W mass shell results can be quite important, complementing on W mass shell results from this and other studies. It is shown that $eγ$\ colliders would prove quite valuable in the investigations of W-boson physics.
We examine the contribution of general Z*ZH and gamma*ZH three-point interactions arising from new physics to the Higgs production process e+e- -> HZ. From Lorentz covariance, each of these vertices may be written in terms of three (complex) form factors, whose real and imaginary parts together make six independent couplings. We take into account possible longitudinal or transverse beam polarization likely to be available at a linear collider. We show how partial cross sections and angular asymmetries in suitable combinations with appropriate beam polarizations, can be used to disentangle vari…
The contribution of the anomalous quark-gluon interaction induced by instantons to the polarized and unpolarized gluon distributions in nucleon is estimated. It is shown that this interaction leads to negative gluon polarization in nucleon.
Extensions to the Standard Model that use strictly off-shell degrees of freedom - the fakeons - allow for new measurable interactions at energy scales usually precluded by the constraints that target the on-shell propagation of new particles. Here we employ the interactions between a new fake scalar doublet and the muon to explain the recent Fermilab measurement of its anomalous magnetic moment. Remarkably, unlike in the case of usual particles, the experimental result can be matched for fakeon masses below the electroweak scale without contradicting the stringent precision data and collider b…
New heavy neutral gauge bosons Z' are predicted by many models of physics beyond the Standard Model. It is quite possible that Z's are heavy enough to lie beyond the discovery reach of the CERN Large Hadron Collider LHC, in which case only indirect signatures of Z' exchanges may emerge at future colliders, through deviations of the measured cross sections from the Standard Model predictions. We discuss in this context the foreseeable sensitivity to Z's of W^\pm-pair production cross sections at the e^+e^- International Linear Collider (ILC), especially as regards the potential of distinguishin…
We investigate the feasibility of probing anomalous top-quark couplings of $Wtb$, $Z t \bar{t}$, and $γt \bar{t}$ in terms of an effective Lagrangian with dimension-six operators at future $e^+e^-$ linear colliders with a c. m. energy $\sqrt s \sim 500-800$ GeV. We first examine the constraints on these anomalous couplings from the $Z\to b \bar{b}$ data at LEP I and from unitarity considerations. We then consider in detail the effects of anomalous couplings on $t \bar{t}$ spin correlations in the top-pair production and decay with three spin bases: the helicity, beamline and off-diagonal bases…
By means of a model-independent analysis, we discuss the constraints on anomalous trilinear gauge-boson couplings that can be obtained from the study of electron-positron annihilation into $W$ pairs at LC with \sqrt{s}=0.5 TeV and 1 TeV. We consider the general CP conserving anomalous effective Lagrangian, as well as some specific models with reduced number of independent couplings. The analysis is based on combinations of observables with initial and final state polarizations, that allow to separately constrain the different couplings and to improve the corresponding numerical bounds.
