A test of lepton flavor universality in B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$ and B$^{\pm}$$\to$ K$^{\pm}$e$^+$e$^-$ decays, as well as a measurement of differential and integrated branching fractions of a nonresonant B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$ decay are presented. The analysis is made possible by a dedicated data set of proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded in 2018, by the CMS experiment at the LHC, using a special high-rate data stream designed for collecting about 10 billion unbiased b hadron decays. The ratio of the branching fractions $\mathcal{B}$(B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$) to $\mathcal{B}$(B$^{\pm}$$\to$ K$^{\pm}$e$^+$e$^-$) is determined from the measured double ratio $R$(K) of these decays to the respective branching fractions of the B$^\pm$$\to$ J/$\psi$K$^\pm$ with J/$\psi$$\to$$\mu^+\mu^-$ and e$^+$e$^-$ decays, which allow for significant cancellation of systematic uncertainties. The ratio $R$(K) is measured in the range 1.1 $\lt q^2 \lt$ 6.0 GeV$^2$, where $q$ is the invariant mass of the lepton pair, and is found to be $R$(K) = 0.78$^{+0.47}_{-0.23}$, in agreement with the standard model expectation $R$(K) $\approx$ 1. This measurement is limited by the statistical precision of the electron channel. The integrated branching fraction in the same $q^2$ range, $\mathcal{B}$(B$^{\pm}$$\to$ K$^{\pm}\mu^+\mu^-$) = (12.42 $\pm$ 0.68) $\times$ 10$^{-8}$, is consistent with the present world-average value and has a comparable precision.
The differential $\text{B}^+ \to \text{K}^+\mu^+\mu^-$ branching fraction measured in the individual $q^2$ bins. The uncertainties in the yields are statistical uncertainties from the fit, while the branching fraction uncertainties include both the statistical and systematic components.
Differential branching fraction $d\mathcal{B}/dq^2$, with theoretical predictions obtained with the HEPFiT, SuperIso, Flavio, and EOS packages. The HEPFiT predictions are available only for $q^2 < 8\ \mathrm{GeV}^2$.
Relative uncertainties in the differential branching fraction measurement of $\mathrm{B}^+\to\mathrm{K}^+\mu^+\mu^-$ per $q^2$ bin.
The strong interaction coupling constant α s has been measured with a new method, the planar triple energy correlation in the reaction e + e - → hadrons at center-of-mass energies ranging from 14 GeV to 46.78 GeV. A complete second-order perturbative QCD calculation was used. Λ MS = 110 ± 30 −55 +70 MeV is found.
Energy-energy-correlations (EEC) have been measured with the JADE detector at c.m. energies of 14 GeV, 22 GeV and in the region 29 GeV<Ecm<36 GeV. Corrected results are presented of EEC and their asymmetry, which can be directly compared to theoretical predictions. At 〈Ecm〉=34 GeV a comparison with second order QCD predictions yields good agreement for the string model fragmentation resulting in a value of the strong coupling constant αs=0.165±0.01 (stat.). The independent fragmentation models, which yield values of αs between 0.10 and 0.15 depending on the treatment of energy and momentum conservation and of the gluon splitting, do not provide a satisfactory description of the data over the full angular range.
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Two-particle azimuthal ($\Delta\phi$) and pseudorapidity ($\Delta\eta$) correlations using a trigger particle with large transverse momentum ($p_T$) in $d$+Au, Cu+Cu and Au+Au collisions at $\sqrt{s_{{NN}}}$ =\xspace 62.4 GeV and 200~GeV from the STAR experiment at RHIC are presented. The \ns correlation is separated into a jet-like component, narrow in both $\Delta\phi$ and $\Delta\eta$, and the ridge, narrow in $\Delta\phi$ but broad in $\Delta\eta$. Both components are studied as a function of collision centrality, and the jet-like correlation is studied as a function of the trigger and associated $p_T$. The behavior of the jet-like component is remarkably consistent for different collision systems, suggesting it is produced by fragmentation. The width of the jet-like correlation is found to increase with the system size. The ridge, previously observed in Au+Au collisions at $\sqrt{s_{{NN}}}$ = 200 GeV, is also found in Cu+Cu collisions and in collisions at $\sqrt{s_{{NN}}}$ =\xspace 62.4 GeV, but is found to be substantially smaller at $\sqrt{s_{{NN}}}$ =\xspace 62.4 GeV than at $\sqrt{s_{{NN}}}$ = 200 GeV for the same average number of participants ($ \langle N_{\mathrm{part}}\rangle$). Measurements of the ridge are compared to models.
Dependence of the widths in $\Delta\eta$ on $p_T^{\mathrm{associated}}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ for 0-95% $d$+Au, 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV and $\sqrt{s_{NN}}$ = 200 GeV, 0-80% Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV, and 0-12% and 40-80% Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.
We present two-dimensional (2D) two-particle angular correlations on relative pseudorapidity $\eta$ and azimuth $\phi$ for charged particles from Au-Au collisions at $\sqrt{s_{\rm NN}} = 62$ and 200 GeV with transverse momentum $p_t \geq 0.15$ GeV/$c$, $|\eta| \leq 1$ and $2\pi$ azimuth. Observed correlations include a {same-side} (relative azimuth $< \pi/2$) 2D peak, a closely-related away-side azimuth dipole, and an azimuth quadrupole conventionally associated with elliptic flow. The same-side 2D peak and away-side dipole are explained by semihard parton scattering and fragmentation (minijets) in proton-proton and peripheral nucleus-nucleus collisions. Those structures follow N-N binary-collision scaling in Au-Au collisions until mid-centrality where a transition to a qualitatively different centrality trend occurs within a small centrality interval. Above the transition point the number of same-side and away-side correlated pairs increases rapidly {relative to} binary-collision scaling, the $\eta$ width of the same-side 2D peak also increases rapidly ($\eta$ elongation) and the $\phi$ width actually decreases significantly. Those centrality trends are more remarkable when contrasted with expectations of jet quenching in a dense medium. Observed centrality trends are compared to {\sc hijing} predictions and to the expected trends for semihard parton scattering and fragmentation in a thermalized opaque medium. We are unable to reconcile a semihard parton scattering and fragmentation origin for the observed correlation structure and centrality trends with heavy ion collision scenarios which invoke rapid parton thermalization. On the other hand, if the collision system is effectively opaque to few-GeV partons the observations reported here would be inconsistent with a minijet picture.
FIG. 3. Fit parameters for $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ correlation data from Au-Au collisions at $\sqrt{s_{N N}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ computed at fixed energy $(200 \mathrm{GeV})$. The SS $2 \mathrm{D}$ Gaussian amplitudes, $\eta_{\Delta}$ widths, and $\phi_{\Delta}$ widths are shown in the left, center, and right panels, respectively of the top row. The bottom row shows from left to right the amplitudes for the dipole, quadrupole, and SS peak width aspect ratio $\sigma_{\eta_{\Delta}} / \sigma_{\phi_{\Delta}} .$ Fitting errors are indicated by error bars where larger than the symbols. Solid lines connect the points for clarity. The dotted and dashed curves indicate Glauber linear superposition estimates for 62 - and 200 -GeV peak amplitudes respectively, as discussed in the text. The quadrupole data are consistent with Ref. [60]. The hatched regions indicate the full range of systematic uncertainties listed in Appendix F. The vertical dark bands indicate estimated $v$ equivalents for $N-N$ collisions and $b=0$ Au-Au collisions.
Event shape and charged particle inclusive distributions are measured using 750000 decays of the Z to hadrons from the DELPHI detector at LEP. These precise data allow a decisive confrontation with models of the hadronization process. Improved tunings of the JETSET, ARIADNE and HERWIG parton shower models and the JETSET matrix element model are obtained by fitting the models to these DELPHI data as well as to identified particle distributions from all LEP experiments. The description of the data distributions by the models is critically reviewed with special importance attributed to identified particles.
Difference in Hemisphere Masses. Corrected to final state particles.
An updated analysis using about 1.5 million events recorded at $\sqrt{s} = M_Z$ with the DELPHI detector in 1994 is presented. Eighteen infrared and collinear safe event shape observables are measured as a function of the polar angle of the thrust axis. The data are compared to theoretical calculations in ${\cal O} (\alpha_s^2)$ including the event orientation. A combined fit of $\alpha_s$ and of the renormalization scale $x_{\mu}$ in $\cal O(\alpha_s^2$) yields an excellent description of the high statistics data. The weighted average from 18 observables including quark mass effects and correlations is $\alpha_s(M_Z^2) = 0.1174 \pm 0.0026$. The final result, derived from the jet cone energy fraction, the observable with the smallest theoretical and experimental uncertainty, is $\alpha_s(M_Z^2) = 0.1180 \pm 0.0006 (exp.) \pm 0.0013 (hadr.) \pm 0.0008 (scale) \pm 0.0007 (mass)$. Further studies include an $\alpha_s$ determination using theoretical predictions in the next-to-leading log approximation (NLLA), matched NLLA and $\cal O(\alpha_s^2$) predictions as well as theoretically motivated optimized scale setting methods. The influence of higher order contributions was also investigated by using the method of Pad\'{e} approximants. Average $\alpha_s$ values derived from the different approaches are in good agreement.
Energy Energy Correlation EEC.
Deep-inelastic ep scattering data taken with the H1 detector at HERA and corresponding to an integrated luminosity of 106 pb^{-1} are used to study the differential distributions of event shape variables. These include thrust, jet broadening, jet mass and the C-parameter. The four-momentum transfer Q is taken to be the relevant energy scale and ranges between 14 GeV and 200 GeV. The event shape distributions are compared with perturbative QCD predictions, which include resummed contributions and analytical power law corrections, the latter accounting for non-perturbative hadronisation effects. The data clearly exhibit the running of the strong coupling alpha_s(Q) and are consistent with a universal power correction parameter alpha_0 for all event shape variables. A combined QCD fit using all event shape variables yields alpha_s(mZ) = 0.1198 \pm 0.0013 ^{+0.0056}_{-0.0043} and alpha_0 = 0.476 \pm 0.008 ^{+0.018} _{-0.059}.
Normalised distribution of the squared Jet Mass (RHO), for Q = 14.0 to 16.0 GeV and X = 0.00841 .
Precise measurements of the spin structure functions of the proton $g_1^p(x,Q^2)$ and deuteron $g_1^d(x,Q^2)$ are presented over the kinematic range $0.0041 \leq x \leq 0.9$ and $0.18 $ GeV$^2$ $\leq Q^2 \leq 20$ GeV$^2$. The data were collected at the HERMES experiment at DESY, in deep-inelastic scattering of 27.6 GeV longitudinally polarized positrons off longitudinally polarized hydrogen and deuterium gas targets internal to the HERA storage ring. The neutron spin structure function $g_1^n$ is extracted by combining proton and deuteron data. The integrals of $g_1^{p,d}$ at $Q^2=5$ GeV$^2$ are evaluated over the measured $x$ range. Neglecting any possible contribution to the $g_1^d$ integral from the region $x \leq 0.021$, a value of $0.330 \pm 0.011\mathrm{(theo.)}\pm0.025\mathrm{(exp.)}\pm 0.028$(evol.) is obtained for the flavor-singlet axial charge $a_0$ in a leading-twist NNLO analysis.
Correlation matrix for G1 for the P target in 15 X bins (Q**2 > 1 GeV**2), averaged over Q**2.
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