Measurement of the $\phi^*_\eta$ distribution of muon pairs with masses between 30 and 500 GeV in 10.4 fb$^{-1}$ of $p\bar{p}$ collisions

The dilepton rapidity is defined by y = ( 1 / 2 ) ​ ln ⁡ [ ( E + p z ) / ( E − p z ) ] , y=(1/2)\ln\left[\left(E+p_{z}\right)/\left(E-p_{z}\right)\right], where E E is the energy and p z p_{z} is the momentum component parallel to the proton beam direction. The rapidity is given in terms of the momentum fractions, x 1 x_{1} and x 2 x_{2} of the annihilating quark and antiquark by y = ( 1 / 2 ) ​ ln ⁡ ( x 1 / x 2 ) y=(1/2)\ln\left(x_{1}/x_{2}\right)

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The thrust axis is defined as a unit vector in the direction of p → T ( lepton1 ) − p → T ( lepton2 ) \vec{p}_{T}^{\,\mathrm{(lepton1)}}-\vec{p}_{T}^{\,\mathrm{(lepton2)}} , where p → T ( lepton1 ) \vec{p}_{T}^{\,\mathrm{(lepton1)}} and p → T ( lepton2 ) \vec{p}_{T}^{\,\mathrm{(lepton2)}} are the lepton momentum vectors in the transverse plane

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Pseudorapidity is defined by η = − ln ⁡ [ tan ⁡ ( θ / 2 ) ] \eta=-\ln\left[\tan(\theta/2)\right]

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Following Ref. [ 10 ] the central value of the non-perturbative parameter a Z = 1.1 a_{Z}=1.1 GeV 2 is chosen in ResBos

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Following Ref. [ 1 ] the momentum of MC particle-level electrons are defined as the full-momentum vector sum of any photons or electrons within a cone of Δ ​ R = ( Δ ​ η ) 2 + ( Δ ​ ϕ ) 2 < 0.2 \Delta R=\sqrt{(\Delta\eta)^{2}+(\Delta\phi)^{2}}<0.2 around the electron, where Δ ​ η \Delta\eta ( Δ ​ ϕ \Delta\phi ) is the distance in η \eta ( ϕ \phi ) from the particle-level electron. The dielectron kinematic requirements are: 70 < M ℓ ​ ℓ < 110 70<M_{\ell\ell}<110 GeV, and for both electrons p T p_{T} > > 20 GeV and | η | |\eta| < < 1.1 or 1.5 < < | η | |\eta| < < 3

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