915 research outputs found
Analytic Computation of three-point energy correlator in QCD
The energy correlator measures the energy deposited in multiple detectors as a function of the angles among them. In this paper, an analytic formula is given for the three-point energy correlator with full angle dependence at leading order in electron-positron annihilation. This is the first analytic computation of trijet event shape observables in QCD, which provides valuable data for phenomenological studies. The result is computed with direct integration, where appropriate parameterizations of both phase space and kinematic space are adopted to simplify the calculation. With full shape dependence, our result provides the expansions in various kinematic regions such as equilateral, triple collinear and squeezed limits, which benefit studies on both factorization and large logarithm resummation
Numerical Strategies of Computing the Luminosity Distance
We propose two efficient numerical methods of evaluating the luminosity
distance in the spatially flat {\Lambda}CDM universe. The first method is based
on the Carlson symmetric form of elliptic integrals, which is highly accurate
and can replace numerical quadratures. The second method, using a modified
version of Hermite interpolation, is less accurate but involves only basic
numerical operations and can be easily implemented. We compare our methods with
other numerical approximation schemes and explore their respective features and
limitations. Possible extensions of these methods to other cosmological models
are also discussed.Comment: 4 pages, 2 figures. v2: A minor error in the last equation has been
corrected (conclusions are not affected). v3: Accepted by MNRA
An improved method to test the Distance--Duality relation
Many researchers have performed cosmological-model-independent tests for the
distance duality (DD) relation. Theoretical work has been conducted based on
the results of these tests. However, we find that almost all of these tests
were perhaps not cosmological-model-independent after all, because the distance
moduli taken from a given type Ia supernovae (SNe Ia) compilation are dependent
on a given cosmological model and Hubble constant. In this Letter, we overcome
these defects and by creating a new cosmological-model-independent test for the
DD relation. We use the original data from the Union2 SNe Ia compilation and
the angular diameter distances from two galaxy cluster samples compiled by De
Filippis et al. and Bonamente et al. to test the DD relation. Our results
suggest that the DD relation is compatible with observations, and the spherical
model is slightly better than the elliptical model at describing the intrinsic
shape of galaxy clusters if the DD relation is valid. However, these results
are different from those of previous work.Comment: 5 pages, 2 figures, published on ApJ
Energy-energy correlation in hadronic Higgs decays: analytic results and phenomenology at NLO
In this work we complete the investigation of the recently introduced
energy-energy correlation (EEC) function in hadronic Higgs decays at
next-to-leading order (NLO) in fixed-order perturbation theory in the limit of
vanishing light quark masses. The full analytic NLO result for the previously
unknown EEC in the channel is given in terms of classical
polylogarithms and cross-checked against a numerical calculation. In addition
to that, we discuss further corrections to predictions of the Higgs EEC event
shape variable, including quark mass corrections, effects of parton shower and
hadronization. We also estimate the statistical error on the measurements of
the Higgs EEC at future Higgs factories and compare with the current
perturbative uncertainty.Comment: 24 pages, 4 figure
The contribution to the non-singlet splitting function at four-loop order
We report a new result for the contribution to the four-loop
anomalous dimensions of non-singlet, twist-two operators in Quantum
Chromodynamics. This result is obtained through computations of off-shell
operator matrix elements. Employing integration-by-parts reductions and
differential equations with respect to a tracing parameter allowed us to derive
analytic results valid for arbitrary Mellin moment .Comment: 13 pages, 1 figure, ancillary file with resul
Complete contributions to four-loop pure-singlet splitting functions
The scale evolution of parton distributions is determined by universal
splitting functions. As a milestone towards the computation of these functions
to four-loop order in QCD, we compute all contributions to the pure-singlet
quark-quark splitting functions that involve two closed fermion loops. The
splitting functions are extracted from the pole terms of off-shell operator
matrix elements, and the workflow for their calculation is outlined. We
reproduce known results for the non-singlet four-loop splitting functions and
validate our new pure-singlet results against fixed Mellin moments.Comment: 25 pages, 2 figure
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