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

We present a measurement of the distribution of the variable ${\varphi }_{\eta }^{*}$ for muon pairs with masses between 30 and 500 GeV, using the complete run II data set collected by the D0 detector at the Fermilab Tevatron proton-antiproton collider. This corresponds to an integrated luminosity of $10.4{\mathrm{fb}}^{-1}$ at $\sqrt{s}=1.96\mathrm{TeV}$. The data are corrected for detector effects and presented in bins of dimuon rapidity and mass. The variable ${\varphi }_{\eta }^{*}$ probes the same physical effects as the $Z/{\gamma }^{*}$ boson transverse momentum, but is less susceptible to the effects of experimental resolution and efficiency. These are the first measurements at any collider of the ${\varphi }_{\eta }^{*}$ distributions for dilepton masses away from the $Z\to {\ell }^{+}{\ell }^{-}$ boson mass peak. The data are compared to QCD predictions based on the resummation of multiple soft gluons.

Figure 1

Illustration in the plane transverse to the beam direction of the variables defined in the text and used to analyze the dilepton transverse momentum [1]. The variables $a_T$ and $a_L$ [5] correspond to the decomposition of $p_T^{\ell \ell }$ into two orthogonal components relative to the dilepton thrust axis $\widehat{t}$ [6], as illustrated.

Figure 2

Corrected distributions of $(1/\sigma )\times (d\sigma /d{\varphi }_{\eta }^{*})$ in dimuon events with $70<M_{\ell \ell }<110\mathrm{GeV}$ for (a) $|y|<1$ and (b) $1<|y|<2$ in the restricted range $0<{\varphi }_{\eta }^{*}<0.34$. The insets show an extended range of ${\varphi }_{\eta }^{*}$. The error bars on the data points represent statistical and systematic uncertainties combined in quadrature. The predictions from ResBos [10] are shown as histograms.

Figure 3

Ratio of the corrected distributions of $(1/\sigma )\times (d\sigma /d{\varphi }_{\eta }^{*})$ in dielectron and dimuon data to the predictions of ResBos [10] for $70<M_{\ell \ell }<110\mathrm{GeV}$ for (a) $|y|<1$, (b) $1<|y|<2$, and (c) $|y|>2$. The error bars on the data points represent statistical and systematic uncertainties combined in quadrature. The dielectron data are taken from Ref. [1] and correspond to an integrated luminosity of $7.3{\mathrm{fb}}^{-1}$. The band around the ResBos prediction represents the quadrature sum of uncertainties due to PDFs, QCD scales, and the nonperturbative parameter $a_Z$.

Figure 4

Ratio of the corrected distributions of $(1/\sigma )\times (d\sigma /d{\varphi }_{\eta }^{*})$ in dimuon data to the $\mathrm{NNLL}+\mathrm{NLO}$ predictions of Ref. [8] for $70<M_{\ell \ell }<110\mathrm{GeV}$: (a) $|y|<1$ and (b) $1<|y|<2$. The error bars on the data points represent statistical and systematic uncertainties combined in quadrature. The band around the $\mathrm{NNLL}+\mathrm{NLO}$ prediction represents the uncertainty due to variations in the QCD scales (evaluated by varying the resummation, factorization, and renormalization scales).

Figure 5

Ratio of the $(1/\sigma )(d\sigma /d{\varphi }_{\eta }^{*})$ distribution in the central rapidity region ($|y|<1$) to that in the forward rapidity region ($1<|y|<2$). The corrected dimuon data are compared to the predictions from (a) ResBos [10] and from (b) $\mathrm{NNLL}+\mathrm{NLO}$ [8]. The error bars on the data points represent statistical and systematic uncertainties combined in quadrature, assuming no correlation between the two rapidity regions. The theoretical predictions are represented by histograms and the band shows the theoretical uncertainties, taking correlations between the two rapidity regions into account.

Figure 6

Corrected distributions of $(1/\sigma )\times (d\sigma /d{\varphi }_{\eta }^{*})$ in dimuon events with $30<M_{\ell \ell }<60\mathrm{GeV}$ for (a) $|y|<1$ and (b) $1<|y|<2$ in the restricted range $0<{\varphi }_{\eta }^{*}<0.38$. The insets show an extended range of ${\varphi }_{\eta }^{*}$. The error bars on the data points represent statistical and systematic uncertainties combined in quadrature. The predictions from ResBos [10] are shown as histograms.

Figure 7

Ratio of the corrected distributions of $(1/\sigma )\times (d\sigma /d{\varphi }_{\eta }^{*})$ to ResBos [10] in dimuon events with $30<M_{\ell \ell }<60\mathrm{GeV}$ for (a) $|y|<1$ and (b) $1<|y|<2$. Statistical and systematic uncertainties are combined in quadrature. The band around the ResBos prediction represents the quadrature sum of uncertainties due to PDFs, QCD scales, and the nonperturbative parameter $a_Z$.

Figure 8

Ratio of the corrected distributions of $(1/\sigma )\times (d\sigma /d{\varphi }_{\eta }^{*})$ to the $\mathrm{NNLL}+\mathrm{NLO}$ predictions of Ref. [8, 27] in dimuon events with $30<M_{\ell \ell }<60\mathrm{GeV}$ for (a) $|y|<1$ and (b) $1<|y|<2$. Statistical and systematic uncertainties are combined in quadrature. The band around the $\mathrm{NNLL}+\mathrm{NLO}$ prediction represents the uncertainty due to variations in the QCD scales (evaluated by varying the resummation, factorization, and renormalization scales).

Figure 9

Corrected distributions of $(1/\sigma )\times (d\sigma /d{\varphi }_{\eta }^{*})$ for dimuon events with (a) $160<M_{\ell \ell }<300\mathrm{GeV}$ and (b) $300<M_{\ell \ell }<500\mathrm{GeV}$ for a restricted range of ${\varphi }_{\eta }^{*}$. The insets show an extended range of ${\varphi }_{\eta }^{*}$. The error bars on the data points represent statistical and systematic uncertainties combined in quadrature. The predictions from ResBos [10] are shown as the red histogram.

Figure 10

Ratio of the corrected distributions of $(1/\sigma )\times (d\sigma /d{\varphi }_{\eta }^{*})$ to ResBos [10] for (a) $160<M_{\ell \ell }<300\mathrm{GeV}$ and (b) $300<M_{\ell \ell }<500\mathrm{GeV}$. Statistical and systematic uncertainties are combined in quadrature. The band around the ResBos prediction represents the quadrature sum of uncertainties due to PDFs, QCD scales, and the nonperturbative parameter $a_Z$.

Figure 11

Comparison of corrected distributions of $(1/\sigma )\times (d\sigma /d{\varphi }_{\eta }^{*})$ in dimuon events with $30<M_{\ell \ell }<60\mathrm{GeV}$ and $70<M_{\ell \ell }<130\mathrm{GeV}$ for (a) $|y|<1$ and (b) $1<|y|<2$ in the restricted range $0<{\varphi }_{\eta }^{*}<0.28$. The error bars on the data points represent statistical and systematic uncertainties combined in quadrature. The predictions from ResBos [10] are shown as histograms.