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Register a new userRevisiting QCD corrections to the forward-backward charge asymmetry of heavy quarks in electron-positron collisions at the Z pole: really a problem?
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Juan Alcaraz Maestre
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We review in some detail the QCD corrections to the measurement of the forward-backward charge asymmetry of heavy quarks in the $mathrm{e^+e^-rightarrow Qoverline{Q}(g)}$ process at the Z pole. We show that the size of these corrections can be reduced by an order of magnitude by using simple cuts on jet acollinearity. Such a reduction is expected to lead to systematic uncertainties at the $Delta mathrm{A_{FB}^{0,Q}} approx 10^{-4}$ level, opening up the path to high precision electroweak measurements with heavy flavors at future high luminosity $mathrm{e^+e^-}$ colliders like the FCC-ee.
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The bottom quark forward-backward asymmetry $A_{rm{FB}}$ is a key observable in electron-positron collisions at the $Z^{0}$ peak. In this paper, we employ the Principle of Maximum Conformality (PMC) to fix the $alpha_s$-running behavior of the next-to-next-to-leading order QCD corrections to $A_{rm{FB}}$. The resulting PMC scale for this $A_{rm{FB}}$ is an order of magnitude smaller than the conventional choice $mu_r=M_Z$. This scale has the physically reasonable behavior and reflects the virtuality of its QCD dynamics, which is independent to the choice of renormalization scale. Our analyses show that the effective momentum flow for the bottom quark forward-backward asymmetry should be $mu_rll M_Z$ other than the conventionally suggested $mu_r=M_Z$. Moreover, the convergence of perturbative QCD series for $A_{rm{FB}}$ is greatly improved using the PMC. Our prediction for the bare bottom quark forward-backward asymmetry is refined to be $A^{0,b}_{rm FB}=0.1004pm0.0016$, which diminishes the well known tension between the experimental determination for this (pseudo) observable and the respective Standard Model fit to $2.1sigma$.
The forward-backward (FB) asymmetry of $b$ quarks in $e^+e^-$ collisions at the Z pole measured at LEP, $A_{FB}^{0,b} = 0.0992pm0.0016$, remains today the electroweak precision observable with the largest disagreement (2.4$sigma$) with respect to the Standard Model prediction, $(A_{FB}^{0,b})_{_{rm th}} = 0.1030 pm 0.0002$. Beyond the dominant statistical uncertainties, QCD effects, such as $b$-quark showering and hadronization, are the leading sources of $A_{FB}^{0,b}$ systematic uncertainty, and have not been revised in the last twenty years. We reassess the QCD uncertainties of the eight original $A_{FB}^{0,b}$ LEP measurements, using modern parton shower PYTHIA-8 and PYTHIA-8 + VINCIA simulations with nine different implementations of soft and collinear radiation as well as of parton fragmentation. Our analysis, combined with NNLO massive $b$-quark corrections independently computed recently, indicates total propagated QCD uncertainties of $sim$0.7% and $sim$0.3% for the lepton-charge and jet-charge analyses, respectively, that are about a factor of two smaller than those of the original LEP results. Accounting for such updated QCD effects leads to a new $A_{FB}^{0,b} = 0.0996pm0.0016$ average, with a data-theory tension slightly reduced from 2.4$sigma$ to 2.1$sigma$. Confirmation or resolution of this long-term discrepancy requires a new high-luminosity $e^+e^-$ collider collecting orders-of-magnitude more data at the Z pole to significantly reduce the $A_{FB}^{0,b}$ statistical uncertainties.
We study logarithmically enhanced electromagnetic corrections to the decay rate in the high dilepton invariant mass region as well as corrections to the forward backward asymmetry (FBA) of the inclusive rare decay $bar{B} to X_s ell^+ ell^-$. As expected, the relative effect of these corrections in the high dilepton mass region is around -8% for the muonic final state and therefore much larger than in the low dilepton mass region. We also present a complete phenomenological analysis, to improved NNLO accuracy, of the dilepton mass spectrum and the FBA integrated in the low dilepton mass region, including a new approach to the zero of the FBA. The latter represents one of the most precise predictions in flavour physics with a theoretical uncertainty of order 5%. We find $(q_0^2)_{mumu} = (3.50 pm 0.12) gev^2$. For the high dilepton invariant mass region, we have ${cal B}(bar Bto X_smumu)_{rm high} = (2.40^{+0.69}_{-0.62}) times 10^{-7}$. The dominant uncertainty is due to the $1/m_b$ corrections and can be significantly reduced in the future. For the low dilepton invariant mass region, we confirm previous results up to small corrections.
Expressions for Sudakov form factors for heavy quarks are presented. They are used to construct resummed jet rates in electron-positron annihilation. Predictions are given for production of bottom quarks at LEP and top quarks at the Linear Collider.
Models of top condensation can provide both a compelling solution to the hierarchy problem as well as an explanation of why the top-quark mass is large. The spectrum of such models, in particular topcolor-assisted technicolor, includes top-pions, top-rhos and the top-Higgs, all of which can easily have large top-charm or top-up couplings. Large top-up couplings in particular would lead to a top forward-backward asymmetry through $t$-channel exchange, easily consistent with the Tevatron measurements. Intriguingly, there is destructive interference between the top-mesons and the standard model which conspire to make the overall top pair production rate consistent with the standard model. The rate for same-sign top production is also small due to destructive interference between the neutral top-pion and the top-Higgs. Flavor physics is under control because new physics is mostly confined to the top quark. In this way, top condensation can explain the asymmetry and be consistent with all experimental bounds. There are many additional signatures of topcolor with large tu mixing, such as top(s)+jet(s) events, in which a top and a jet reconstruct a resonance mass, which make these models easily testable at the LHC.
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