Massless Leptons Research Articles

QCD corrections to the Darwin coefficient in inclusive semileptonic B→Xuℓν¯ℓ decays

In this paper, we compute αs corrections to the matching coefficients of the dimension-six operators in the heavy quark expansion of the inclusive semileptonic heavy hadron decay rate and leptonic invariant mass spectrum with a massless quark and both a massive or massless lepton in the final state, analytically. The obtained results can be applied to the inclusive semileptonic B→Xuℓν¯ℓ (ℓ=e, μ, τ) and D→Xℓν¯ℓ (ℓ=e, μ) decays. The main application of our results is the background subtraction of the B→Xuℓν¯ℓ decay in the measurement of the B→Xcℓν¯ℓ decay, which is important for the precise extraction of Vcb and R(D(*)). They also play a role in the computation of lifetimes of heavy hadrons. Published by the American Physical Society 2024

Lepton-pair scattering with an off-shell and an on-shell photon at two loops in massless QED

We compute the two-loop QED helicity amplitudes for the scattering of a lepton pair with an off-shell and an on-shell photon, 0 → ℓℓ¯γγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\ell \\overline{\\ell}\\gamma \\gamma $$\\end{document}*, using the approximation of massless leptons. We express all master integrals relevant for the scattering of four massless particles with a single external off-shell leg up to two loops in a basis of algebraically independent multiple polylogarithm, which guarantees an efficient numerical evaluation and compact analytic representations of the amplitudes. Analytic forms of the amplitudes are reconstructed from numerical evaluations over finite fields. Our results complete the amplitude-level ingredients contributing to the N3LO predictions of electron-muon scattering eμ → eμ, which are required to meet the precision goal of the future MUonE experiment.

Mixed QCD-electroweak corrections to dilepton production at the LHC in the high invariant mass region

We compute mixed QCD-electroweak corrections to the neutral-current Drell-Yan production of a pair of massless leptons in the high invariant mass region. Our computation is fully differential with respect to the final state particles. At relatively low values of the dilepton invariant mass, mℓℓ ∼ 200 GeV, we find unexpectedly large mixed QCD-electroweak corrections at the level of −1%. At higher invariant masses, mℓℓ ∼ 1 TeV, we observe that these corrections can be well approximated by the product of QCD and electroweak corrections. Hence, thanks to the well-known Sudakov enhancement of the latter, they increase at large invariant mass and reach e.g. −3% at mℓℓ = 3 TeV. Finally, we note that the inclusion of mixed corrections reduces the theoretical uncertainty related to the choice of electroweak input parameters to below the percent level.

Theoretical predictions for inclusive B→Xuτν¯ decay

With the expected large increase in datasets, previously not measured decays will be studied at Belle II. We derive standard model predictions for the $B\ensuremath{\rightarrow}{X}_{u}\ensuremath{\tau}\overline{\ensuremath{\nu}}$ decay rate and distributions. The region in the lepton energy spectrum where higher-dimension operators in the local operator product expansion need to be resummed into the $b$-quark light-cone distribution function is a significantly greater fraction of the phase space than for massless leptons. The finite $\ensuremath{\tau}$ mass has the novel effect of shifting and squeezing how the distribution function enters the lepton energy spectrum. We also derive new predictions for the $\ensuremath{\tau}$ polarization.

Next-to-next-to-leading order event generation for Z-boson pair production matched to parton shower

We present a novel next-to-next-to-leading order (NNLO) QCD calculation matched to parton shower for the production of a pair of Z bosons decaying to four massless leptons, pp→ℓ+ℓ−ℓ′+ℓ′−+X, at the LHC. Spin correlations, interferences and off-shell effects are included throughout. Our result is based on the resummed beam-thrust spectrum, which we evaluate at next-to-next-to-leading-logarithmic (NNLLT0′) accuracy for the first time for this process, and makes use of the Geneva Monte Carlo framework for the matching to Pythia8 shower and hadronisation models. We compare our predictions with data from the ATLAS and CMS experiments at 13TeV, finding a good agreement.

A critical point in the distribution of lepton energies from the decay of a spin-1 resonance

We consider a spin-1 resonance produced with an arbitrary spectrum of velocities and decaying into a pair of massless leptons, and we study the probability density function of the energy of the leptons in the laboratory frame. A special case is represented by the production of W bosons in proton-proton collisions, for which the energy of the charged lepton from the decaying W can be measured with sufficient accuracy for a high-precision measurement of MW . We find that half of the resonance mass is a special value of the lepton energy, since the probability density function at this point is in general not analytic for a narrow-width resonance. In particular, the higher-order derivatives of the density function are likely to develop singularities, such as cusps or poles. A finite width of the resonance restores the regularity, for example by smearing cusps and poles into local stationary points. The quest for such points offers a handle to estimate the resonance mass with much reduced dependence on the underlying production and decay dynamics of the resonance.

Angular analyses of exclusive B¯→XJℓ1ℓ2 decays for spin J≤4

As an update to our previous calculation for spin $J\leq2$, we present the angular moments for exclusive $\overline{B} \to X_J \ell_1 \ell_2$, where $\ell_1$ is a charged massless lepton and $\ell_2$ is a charged or neutral massless lepton, and $X_J$ is a mesonic system with spin $J\leq4$. The expected applications include higher resonances in the $[K\pi]$ system in $\overline{B}^0 \to K^- \pi^+ \mu^- \mu^+$ at LHCb in Run~II, and in the $[\pi \pi]$ system for $ \overline{B} \to \pi \pi \ell^- \bar{\nu}_\ell$ at Belle~II. For the $J\leq2$ case, we also provide a set of consistency relations among the measured moments observables and validate them against the latest measurements from LHCb.

Modification of {$\mit \Delta $}(1232) in the Neutrino Nucleus Reaction

The remarkable observations in the pion induced and charge exchange reactions on a nucleus are the significant shift and broadening of the $\Delta (1232)$-peak relative to free pion nucleon scattering. For the forward going massless leptons, the weak process $(\nu_l,l)$ on a nucleon, according to Adler's partially conserved axial current theorem, is connected to the pion nucleon scattering. This mechanism is also applicable to the nucleus. Therefore, the modification of the $\Delta$-peak in a nucleus can be seen in the $(\nu_l,l)$ reaction since it is connected to the pion nucleus scattering. To investigate this issue quantitatively, the double differential cross sections of the forward going ejectile $l$ energy distribution in the $(\nu_l,l)$ reaction are calculated in the $\Delta$-excitation region for both proton and nucleus. The measured pion nucleon and pion nucleus scattering cross sections in the quoted energy region are used in these reactions as input. Since the $(\nu_l,l)$ reaction is connected to the pion induced scattering, the features of the previous reaction is shown analogous to those of the later.

Angular analyses of exclusiveB¯→Xℓ1ℓ2with complex helicity amplitudes

We present the differential rates for exclusive $\Bbar\to X \ell_1 \ell_2$, where $\ell_1$ is a charged massless lepton and $\ell_2$ is a charged or neutral massless lepton, and $X$ is a mesonic system up to spin 2. The cases of interest are semileptonic (SL) $\Bbar\to \xcu\ellm \barnuell$ decays, and $\Bbar \to X_s \ellm \ellp$ where the the di-lepton can be $c \bar{c}$ resonances or non-resonant electroweak penguins (EWP). We consider helicity amplitudes having non-zero relative phases that can be potential new sources for CP-violation. Our motivations for these additional phases include a complex right-handed admixture in the hadronic weak charged current for the SL decays and complex Wilson coefficients in the effective Hamiltonians for the EWP decays. We demonstrate the efficacy of a novel technique of projecting out the individual angular moments in the full rate expression in a model-independent fashion. Our work is geared towards ongoing data analyses at $\babar$ and LHCb.

Heavy pseudoscalar leading-twist distribution amplitudes within QCD theory in background fields

In this paper, we study the leading-twist distribution amplitude (DA) of the heavy pseudoscalars (HPs), such as $\eta_c$, $\eta_b$ and $B_c$, within the QCD theory in the background fields. New sum rules up to dimension-six condensates for both the HP decay constants and their leading-twist DA moments are presented. From the sum rules for the HP decay constants, we obtain $f_{\eta_c} = 453 \pm 4 \textrm{MeV}$, $f_{B_c} = 498 \pm 14 \textrm{MeV}$, and $f_{\eta_b} = 811 \pm 34 \textrm{MeV}$. Basing on the sum rules for the HPs' leading-twist DA moments, we construct a new model for the $\eta_c$, $\eta_b$ and $B_c$ leading-twist DAs. Our present HP DA model can also be adaptable for the light pseudo-scalar DAs, such as the pion and kaon DAs. Thus, it shall be applicable for a wide range of QCD exclusive processes. As an application, we apply the $\eta_c$ leading-twist DA to calculate the $B_c \to \eta_c$ transition form factor $f_+^{B_c \to \eta_c}(q^2)$. At the maximum recoil region, we obtain $f_+^{B_c \to \eta_c}(0) = 0.612^{+0.053}_{-0.052}$. After further extrapolating the TFF $f_+^{B_c \to \eta_c}(q^2)$ to its allowable $q^2$ region, we predict the branching ratio for the semi-leptonic decay $B_c \to \eta_c l \nu$. We obtain ${\cal B}(B_c \to \eta_c l \nu)=\left(7.70^{+1.65}_{-1.48}\right) \times 10^{-3}$ for massless leptons, which is consistent with the LCSRs estimation obtained in the literature.

Lepton pair emission in the top quark decayt→bW+ℓ−ℓ+

The heaviness of the top quark makes its 2-body decay mode $t \to bW^+$ to be dominant, at such level that hardly any other decay mode reaches a detectable branching ratio (BR) within the SM. Here we study the decay $t \to bW^+\ell^-\ell^+$ ($\ell=e, \mu, \tau$), which diverges for massless leptons, and it can reach a BR $\sim \mathcal{O}(10^{-5}\sim 10^{-6})$ for reasonable values of the low energy cut in the lepton-pair invariant mass. This rate surpasses almost any other rare decays such as $t \to cX$ ($X=\gamma,Z,g,H, W^+W^-$), and thus offers the possibility of being detectable. Furthermore, the estimate of this channel is relevant because it can mimic the signal arising from the lepton number violating decay $t\to bW^-\ell^+\ell^+$, when the $W$ boson decays into lepton channels.

Subtraction scheme for next-to-next-to-leading order computations

We use the known soft and collinear limits of tree- and one-loop scattering amplitudes---computed over a decade ago---to explicitly construct a subtraction scheme for next-to-next-to-leading order (NNLO) computations. Our approach combines partitioning of the final-state phase-space together with the technique of sector decomposition, following recent suggestions in Ref. [34]. We apply this scheme to a toy example: the NNLO QED corrections to the decay of the $Z$ boson to a pair of massless leptons. We argue that the main features of this subtraction scheme remain valid for computations of processes of arbitrary complexity with NNLO accuracy.

On the new physics reach of the decay mode $ {\bar{B}_d} \to {\bar{K}^{*0}}{\ell^{+} }{\ell^{-} } $

We present a complete method to construct QCD-protected observables based on the exclusive 4-body $B$-meson decay $\bar{B} \to \bar{K}^{*0}\ell^+\ell^-$ in the low dilepton mass region. The core of the method is the requirement that the constructed quantities should fulfil the symmetries of the angular distribution. We have identified all symmetries of the angular distribution in the limit of massless leptons and explore: a new non-trivial relation between the coefficients of the angular distribution, the possibility to fully solve the system for the $K^{*}$ amplitudes, and the construction of non-trivial observables. We also present a phenomenological analysis of the new physics sensitivity of angular observables in the decay based on QCD factorisation. We further analyse the CP-conserving observables, $A_{T}^{(2)}$, $A_{T}^{(3)}$ and $A_{T}^{(4)}$. They are practically free of theoretical uncertainties due to the soft form factors for the full range of dilepton masses rather than just at a single point as for $A_{FB}$. They also have a higher sensitivity to specific new physics scenarios compared to observables such as $A_{FB}$. Moreover, we critically examine the new physics reach of CP-violating observables via a complete error analysis due to scale dependences, form factors and $\Lambda/m_b$ corrections. We have developed an ensemble method to evaluate the error on observables from $\Lambda/m_b$ corrections. Finally, we explore the experimental prospects of CP-violating observables and find that they are rather limited. Indeed, the CP-conserving (averaged) observables $A_{T}^{(i)}$ (with $i=2,3,4$) will offer a better sensitivity to large CP phases and may be more suitable for experimental analysis.

Nonperturbative effects in semileptonicBcdecays

We discuss the impact of the soft degrees of freedom inside the B_c meson on its rate in the semi-leptonic decay B_c -> X l nu_l where X denotes light hadrons below the D^0 threshold. In particular we identify contributions involving soft hadrons which are non-vanishing in the limit of massless leptons. These contributions become relevant for a measurement of the purely leptonic B_c decay rate, which due to helicity suppression involves a factor m_l^2 and thus is much smaller than the contributions involving soft hadrons.

Group independent color decomposition of next-to-leading order matrix elements for e+e−→ four partons

We present the next-to-leading order partonic cross sections involving an electroweak vector boson and four massless partons (quarks, gluons or gluinos) in a general gauge theory with a simple Lie Group. The vector boson couples to a massless lepton pair and a quark-antiquark pair. The cross sections are given in terms of group independent kinematical functions multiplying the eigenvalues of the quadratic Casimir operator of the Lie group. This kind of color decomposition is required for the calculation of O( α s 3 ) corrections to the group independent kinematical functions in the four-jet production cross sections in electron-positron annihilation. The knowledge of these corrections facilitates the simultaneous precision measurement of the strong coupling and the color charge factors using the four-jet LEP or SLC data as well as the test whether these data favour or exclude the existence of a light gluino.

One-loop amplitudes for e +e − -+ [formula omitted][formula omitted

We present the one-loop helicity amplitudes for processes involving a vector boson V ( V = W, Z, or y *) and four massless quarks, 0 → V qq QQ , where V couples to a massless lepton pair. These amplitudes are required for next-to-leading order O α s 3) numerical programs for four jet production at e + e − colliders, for W, Z or Drell-Yan production in association with two jets at hadron colliders, and for three jet production in deeply inelastic scattering experiments. We obtained the amplitudes presented here by using their analytic properties to constrain their form.

New Mechanism for Leptogenesis.

Unified theories containing a $U(1)_{B-L}$ gauge symmetry predict heavy Majorana right-handed neutrinos. In such theories, cosmic strings may form at the $B-L$ breaking scale. If the Higgs field forming the strings is also the Higgs field which gives mass to the right-handed neutrinos, there are right-handed neutrinos trapped as transverse zero modes in the core of the strings. When cosmic string loops decay, they release these neutrinos. This is an out-of-equilibrium process. The released neutrinos acquire heavy Majorana mass and decay into massless leptons and electroweak Higgs particles to produce a lepton asymmetry, which is converted into a baryon asymmetry via sphaleron transitions.

Neutrino mass in dense matter

For massless leptons interacting with massive vector bosons in a hot and dense medium the possibility of the generation of an effective mass is investigated. By using the one-loop approximation of the neutrino self-energy in the Weinberg-Salam model in the unitary gauge, expressions are found for the dispersion equations of quasiparticles in the low momentum limit. A negative effective mass can be defined for neutrinos, whereas for holes and antineutrinos this mass is positive.

A measurement of the τ leptonic branching fractions

A sample of 25000 Z 0 → τ + τ − events collected by the DELPHI experiment at LEP in 1991 and 1992 is used to measure the leptonic branching fractions of the τ lepton. The results are B(τ → eν ν) = (17.51 ± 0.39) % and B(τ → μν ν) = (17.02 ± 0.31) %. The ratio of the muon and electron couplings to the weak charged current is measured to be g μ g e = 1.000 ± 0.013 , satisfying e-μ universality. The leptonic branching fraction corrected to the value for a massless lepton, assuming e-μ universality, is found to be B(τ → lν ν) = (17.50 ± 0.25) %.

CLASSIFICATION OF SYMMETRY BREAKING PATTERNS IN HETEROTIC STRINGS ON Z3 ORBIFOLD

Symmetry breaking patterns of E8×E′8 on Z3 orbifold are completely analyzed for physically acceptable models by using a kind of Weyl transformation and modular invariance. It is shown that SU(3)×SU(2)×U(1)n cannot be obtained by using any kind of a shift vector and Wilson lines and that the minimal group including SU(3)×SU(2)×U(1) is SU(3)2×U(1)n which is realized by a shift vector and Wilson lines. All models accessible to realistic low energy theories are listed out and an example is described to get SU(3)×SU(2)×UY(1) by using Higgs mechanism with anomalous U(1) channel. The example is able to give massless quark, lepton and Higgs to suppress proton decay by Planck mass scale and to make left-handed neutrino massless.