arXiv subjects

E. Remiddi

Publications and source records attributed to E. Remiddi.

At least 19 recordsLinked to original sources

arXiv2009

Quest for precision in hadronic cross sections at low energy: Monte Carlo tools vs. experimental data

We present the achievements of the last years of the experimental and theoretical groups working on hadronic cross section measurements at the low energy e+e- colliders in Beijing, Frascati, Ithaca, Novosibirsk, Stanford and Tsukuba and on tau decays. We sketch the prospects in these fields for the years to come. We emphasise the status and the precision of the Monte Carlo generators used to analyse the hadronic cross section measurements obtained as well with energy scans as with radiative return, to determine luminosities and tau decays. The radiative corrections fully or approximately implemented in the various codes and the contribution of the vacuum polarisation are discussed.

hep-ph↗

arXiv2007

The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges

We compute the (three) master integrals for the crossed ladder diagram with two exchanged quanta of equal mass. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the singular (plus some regular) points, which are then matched numerically with high accuracy. The expansions allow a fast and precise numerical calculation of the three master integrals (better than 15 digits with less than 30 terms in the whole real axis). A conspicuous relation with the equal-mass sunrise in two dimensions is found. Comparison with a previous large momentum expansion is made finding complete agreement.

hep-ph↗

arXiv2006

Two-Loop N_F=1 QED Bhabha Scattering Differential Cross Section

We calculate the two-loop virtual, UV renormalized corrections at order α^4 (N_F=1) in QED to the Bhabha scattering differential cross section, for arbitrary values of the squared c.m. energy s and momentum transfer t, and on-shell electrons and positrons of finite mass m. The calculation is carried out within the dimensional regularization scheme; the remaining IR divergences appear as polar singularities in (D-4). The result is presented in terms of 1- and 2-dimensional harmonic polylogarithms, of maximum weight 3.

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arXiv2006

Two-Loop N_F =1 QED Bhabha Scattering: Soft Emission and Numerical Evaluation of the Differential Cross-section

Recently, we evaluated the virtual cross-section for Bhabha scattering in pure QED, up to corrections of order alpha^4 (N_F =1). This calculation is valid for arbitrary values of the squared center of mass energy s and momentum transfer t; the electron and positron mass m was considered a finite, non vanishing quantity. In the present work, we supplement the previous calculation by considering the contribution of the soft photon emission diagrams to the differential cross-section, up to and including terms of order alpha^4 (N_F=1). Adding the contribution of the real corrections to the renormalized virtual ones, we obtain an UV and IR finite differential cross-section; we evaluate this quantity numerically for a significant set of values of the squared center of mass energy s.

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arXiv2006

Two-Parton Contribution to the Heavy-Quark Forward-Backward Asymmetry in NNLO QCD

Forward-backward asymmetries, $A_{FB}^Q$, are important observables for the determination of the neutral-current couplings of heavy quarks in inclusive heavy quark production, $e^+ e^- \to γ^*, Z^* \to Q +X$. In view of the measurement perspectives on $A_{FB}^Q$ at a future linear collider, precise predictions of $A_{FB}^Q$ are required for massive quarks. We compute the contribution of the $Q \bar Q$ final state to $A_{FB}^Q$ to order $\as^2$ in the QCD coupling. We provide general formulae, and we show that this contribution to $A_{FB}^Q$ is infrared-finite. We evaluate these two-parton contributions for $b$ and $c$ quarks on and near the $Z$ resonance, and for $t$ quarks above threshold. Moreover, near the $t \bar t$ threshold we obtain, by expanding in the heavy-quark velocity $β$, an expression for $A_{FB}^{t \bar t}$ to order $\as^2$ and NNLL in $β$. This quantity is equal, to this order in $β$, to the complete forward-backward asymmetry $A_{FB}^t$.

hep-ph↗

arXiv2006

Heavy-Quark Form Factors and Threshold Cross Section at O(α_S^2)

During the last year, analytic expressions for the two-loop QCD corrections to the form factors for the vector, axial-vector, scalar and pseudo-scalar vertices involving a pair of heavy quarks, $Q \bar{Q}$, were calculated. The results are valid for arbitrary momentum transfer and mass of the heavy quarks. These form factors have a number of applications, including anomalous couplings, the $e^{+}e^{-} \to Q \bar Q$ cross section, and the forward-backward asymmetry of heavy quarks. Here the $Q {\bar Q}$ threshold cross section is presented with some new second order axial vector contributions.

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arXiv2005

QCD Corrections to Static Heavy Quark Form Factors

Interactions of heavy quarks, in particular of top quarks, with electroweak gauge bosons are expected to be very sensitive to new physics effects related to electroweak symmetry breaking. These interactions are described by the so-called static form factors, which include anomalous magnetic moments and the effective weak charges. We compute the second-order QCD corrections to these static form factors, which turn out to be sizeable and need to be taken into account in searches for new anomalous coupling effects.

hep-ph↗

arXiv2005

Decays of Scalar and Pseudoscalar Higgs Bosons into Fermions: Two-loop QCD Corrections to the Higgs-Quark-Antiquark Amplitude

As a first step in the aim of arriving at a differential description of neutral Higgs boson decays into heavy quarks, $h \to Q {\bar Q}X$, to second order in the QCD coupling $α_S$, we have computed the $hQ{\bar Q}$ amplitude at the two-loop level in QCD for a general neutral Higgs boson which has both scalar and pseudoscalar couplings to quarks. This amplitude is given in terms of a scalar and a pseudoscalar vertex form factor, for which we present closed analytic expressions in terms of one-dimensional harmonic polylogarithms of maximum weight 4. The results hold for arbitrary four-momentum squared, $q^2$, of the Higgs boson and of the heavy quark mass, $m$. Moreover we derive the approximate expressions of these form factors near threshold and in the asymptotic regime $m^2/q^2 \ll 1$.

hep-ph↗

arXiv2005

Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case

We present a double precision routine in Fortran for the precise and fast numerical evaluation of the two Master Integrals (MIs) of the equal mass two-loop sunrise graph for arbitrary momentum transfer in d=2 and d=4 dimensions. The routine implements the accelerated power series expansions obtained by solving the corresponding differential equations for the MIs at their singular points. With a maximum of 22 terms for the worst case expansion a relative precision of better than a part in 10^{15} is achieved for arbitrary real values of the momentum transfer.

hep-ph↗

arXiv2005

Two-Loop QCD Corrections to the Heavy Quark Form Factors: Anomaly Contributions

We present closed analytic expressions for the order $α_s^2$ triangle diagram contributions to the matrix elements of the singlet and non-singlet axial vector currents between the vacuum and a quark-antiquark state. We have calculated these vertex functions for arbitrary momentum transfer and for four different sets of internal and external quark masses. We show that both the singlet and non-singlet vertex functions satisfy the correct chiral Ward identities. Using the exact expressions for the finite axial vector form factors, we check the quality and the convergence of expansions at production threshold and for asymptotic energies.

hep-ph↗

arXiv2004

Two-Loop QCD Corrections to the Heavy Quark Form Factors: Axial Vector Contributions

We consider the Z Q Qbar vertex to second order in the QCD coupling for an on-shell massive quark-antiquark pair and for arbitrary momentum transfer of the Z boson. We present closed analytic expressions for the two parity-violating form factors of that vertex at the two-loop level in QCD, excluding the contributions from triangle diagrams. These form factors are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.

hep-ph↗

arXiv2004

Two-loop QCD Corrections to the Heavy Quark Form Factors: the Vector Contributions

We present closed analytic expressions of the electromagnetic vertex form factors for heavy quarks at the two-loop level in QCD for arbitrary momentum transfer. The calculation is carried out in dimensional regularization. The electric and magnetic form factors are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.

hep-ph↗

arXiv2004

Analytic treatment of the two loop equal mass sunrise graph

The two loop equal mass sunrise graph is considered in the continuous d-dimensional regularisation for arbitrary values of the momentum transfer. After recalling the equivalence of the expansions at d=2 and d=4, the second order differential equation for the scalar Master Integral is expanded in (d-2) and solved by the variation of the constants method of Euler up to first order in (d-2) included. That requires the knowledge of the two independent solutions of the associated homogeneous equation, which are found to be related to the complete elliptic integrals of the first kind of suitable arguments. The behaviour and expansions of all the solutions at all the singular points of the equation are exhaustively discussed and written down explicitly.

hep-ph↗

arXiv2004

Planar box diagram for the (N_F = 1) 2-loop QED virtual corrections to Bhabha scattering

In this paper we present the master integrals necessary for the analytic calculation of the box diagrams with one electron loop (N_{F}=1) entering in the 2-loop (α^3) QED virtual corrections to the Bhabha scattering amplitude of the electron. We consider on-shell electrons and positrons of finite mass m, arbitrary squared c.m. energy s, and momentum transfer t; both UV and soft IR divergences are regulated within the continuous D-dimensional regularization scheme. After a brief overview of the method employed in the calculation, we give the results, for s and t in the Euclidean region, in terms of 1- and 2-dimensional harmonic polylogarithms, of maximum weight 3. The corresponding results in the physical region can be recovered by analytical continuation. For completeness, we also provide the analytic expression of the 1-loop scalar box diagram including the first order in (D-4).

hep-ph↗

arXiv2004

Vertex diagrams for the QED form factors at the 2-loop level

We carry out a systematic investigation of all the 2-loop integrals occurring in the electron vertex in QED in the continuous $D$-dimensional regularization scheme, for on-shell electrons, momentum transfer $t=-Q^2$ and finite squared electron mass $m_e^2=a$. We identify all the Master Integrals (MI's) of the problem and write the differential equations in $Q^2$ which they satisfy. The equations are expanded in powers of $ε= (4-D)/2$ and solved by the Euler's method of the variation of the constants. As a result, we obtain the coefficients of the Laurent expansion in $ε$ of the MI's up to zeroth order expressed in close analytic form in terms of Harmonic Polylogarithms.

hep-ph↗

arXiv2004

The analytic value of a 4-loop sunrise graph in a particular kinematical configuration

The 4-loop sunrise graph with two massless lines, two lines of equal mass M and a line of mass m, for external invariant timelike and equal to m^2 is considered. We write differential equations in x=m/M for the Master Integrals of the problem, which we Laurent-expand in the regularizing continuous dimension d around d=4, and then solve exactly in x up to order (d-4)^3 included; the result is expressed in terms of Harmonic PolyLogarithms of argument x and maximum weight 7. As a by product, we obtain the x=1 value, expected to be relevant in QED 4-loop static quantities like the electron (g-2). The analytic results were checked by an independent precise numerical calculation

hep-ph↗

arXiv2004

Master Integrals for the 2-loop QCD virtual corrections to the Forward-Backward Asymmetry

We present the Master Integrals needed for the calculation of the two-loop QCD corrections to the forward-backward asymmetry of a quark-antiquark pair produced in electron-positron annihilation events. The abelian diagrams entering in the evaluation of the vector form factors were calculated in a previous paper. We consider here the non-abelian diagrams and the diagrams entering in the computation of the axial form factors, for arbitrary space-like momentum transfer Q^2 and finite heavy quark mass m. Both the UV and IR divergences are regularized in the continuous D-dimensional scheme. The Master Integrals are Laurent-expanded around D=4 and evaluated by the differential equation method; the coefficients of the expansions are expressed as 1-dimensional harmonic polylogarithms of maximum weight 4.

hep-ph↗

arXiv2003

Numerical evaluation of the general massive 2-loop 4-denominator self-mass master integral from differential equations

The differential equation in the external invariant p^2 satisfied by the master integral of the general massive 2-loop 4-denominator self-mass diagram is exploited and the expansion of the master integral at p^2=0 is obtained analytically. The system composed by this differential equation with those of the master integrals related to the general massive 2-loop sunrise diagram is numerically solved by the Runge-Kutta method in the complex p^2 plane. A numerical method to obtain results for values of p^2 at and close to thresholds and pseudo-thresholds is discussed in details.

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