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The results of a high-statistics study of inclusive muon spectra at PETRA are reported. Improved mass limits have been obtained for heavy quarks, heavy leptons, and charged Higgs particles. It is shown that the fragmentation properties of $b$ quarks and $c$ quarks are different, with the mean fragmentation variables $〈z_b〉=0.75\mathrm{}\pm 0.03\pm 0.06$, $〈z_c〉=0.46\mathrm{}\pm 0.02\pm 0.05$ and the average semileptonic branching ratio for the $B$ and $C$ hadrons $R\mathrm{}\left(B\right)=(10.5\mathrm{}\pm 1.5\pm 1.3)\%$, $R\left(C\right)=(11.5\mathrm{}\pm 1.0\pm 1.7)\%$.

We report mass limits on the ${\tilde{Z}}^0$ and ${\tilde{W}}^{\pm }$, supersymmetric partners of the $Z^0$ and $W^{\pm }$, respectively, using the MARK-J detector at PETRA. The experimental signatures in both cases are acoplanar lepton pairs with missing energy. For the ${\tilde{W}}^{\pm }$, an additional signature is a single energetic lepton. No evidence is found for either the ${\tilde{Z}}^0(M_{{\tilde{Z}}^0}<35\mathrm{}\mathrm{GeV})$ or the ${\tilde{W}}^{\pm }(M_{\tilde{W}}<25\mathrm{}\mathrm{GeV})$.

A precision measurement of the nitrogen flux with rigidity (momentum per unit charge) from 2.2 GV to 3.3 TV based on $2.2\times {10}^6$ events is presented. The detailed rigidity dependence of the nitrogen flux spectral index is presented for the first time. The spectral index rapidly hardens at high rigidities and becomes identical to the spectral indices of primary He, C, and O cosmic rays above $\sim 700\mathrm{GV}$. We observed that the nitrogen flux ${\mathrm{\Phi }}_{\mathrm{N}}$ can be presented as the sum of its primary component ${\mathrm{\Phi }}_{\mathrm{N}}^P$ and secondary component ${\mathrm{\Phi }}_{\mathrm{N}}^S$, ${\mathrm{\Phi }}_{\mathrm{N}}={\mathrm{\Phi }}_{\mathrm{N}}^P+{\mathrm{\Phi }}_{\mathrm{N}}^S$, and we found ${\mathrm{\Phi }}_{\mathrm{N}}$ is well described by the weighted sum of the oxygen flux ${\mathrm{\Phi }}_{\mathrm{O}}$ (primary cosmic rays) and the boron flux ${\mathrm{\Phi }}_{\mathrm{B}}$ (secondary cosmic rays), with ${\mathrm{\Phi }}_{\mathrm{N}}^P=(0.090\pm 0.002)\times {\mathrm{\Phi }}_{\mathrm{O}}$ and ${\mathrm{\Phi }}_{\mathrm{N}}^S=(0.62\pm 0.02)\times {\mathrm{\Phi }}_{\mathrm{B}}$ over the entire rigidity range. This corresponds to a change of the contribution of the secondary cosmic ray component in the nitrogen flux from 70% at a few GV to $<30\%$ above 1 TV.

A precision measurement by the Alpha Magnetic Spectrometer on the International Space Station of the positron fraction in primary cosmic rays in the energy range from 0.5 to 350 GeV based on $6.8\times {10}^6$ positron and electron events is presented. The very accurate data show that the positron fraction is steadily increasing from 10 to $\sim 250\mathrm{GeV}$, but, from 20 to 250 GeV, the slope decreases by an order of magnitude. The positron fraction spectrum shows no fine structure, and the positron to electron ratio shows no observable anisotropy. Together, these features show the existence of new physical phenomena.

We present high-statistics, precision measurements of the detailed time and energy dependence of the primary cosmic-ray electron flux and positron flux over 79 Bartels rotations from May 2011 to May 2017 in the energy range from 1 to 50 GeV. For the first time, the charge-sign dependent modulation during solar maximum has been investigated in detail by leptons alone. Based on $23.5\times {10}^6$ events, we report the observation of short-term structures on the timescale of months coincident in both the electron flux and the positron flux. These structures are not visible in the $e^{+}/e^{-}$ flux ratio. The precision measurements across the solar polarity reversal show that the ratio exhibits a smooth transition over $830\pm 30$ days from one value to another. The midpoint of the transition shows an energy dependent delay relative to the reversal and changes by $260\pm 30$ days from 1 to 6 GeV.

We present the precision measurement of the daily proton fluxes in cosmic rays from May 20, 2011 to October 29, 2019 (a total of 2824 days or 114 Bartels rotations) in the rigidity interval from 1 to 100 GV based on $5.5\times {10}^9$ protons collected with the Alpha Magnetic Spectrometer aboard the International Space Station. The proton fluxes exhibit variations on multiple timescales. From 2014 to 2018, we observed recurrent flux variations with a period of 27 days. Shorter periods of 9 days and 13.5 days are observed in 2016. The strength of all three periodicities changes with time and rigidity. The rigidity dependence of the 27-day periodicity is different from the rigidity dependences of 9-day and 13.5-day periods. Unexpectedly, the strength of 9-day and 13.5-day periodicities increases with increasing rigidities up to $\sim 10\mathrm{GV}$ and $\sim 20\mathrm{GV}$, respectively. Then the strength of the periodicities decreases with increasing rigidity up to 100 GV.

We use the reaction $e^{+}$$e^{\mathrm{-}}$→hadrons, in the Mark J detector at the DESY electron-positron collider PETRA, to determine the hadronic cross section up to 46.78 GeV. The production of a top quark with a charge equal to (2/3) is excluded up to 46.6 GeV with 95% C.L. The observed rise in the cross section at higher energies is consistent with the electroweak prediction for a $Z^0$ mass of 93 GeV. We describe some unusual muon inclusive events.

A direct test is presented of higher-order QED (${\alpha }^4$) at large momentum transfers (up to ∼100 Ge${\mathrm{V}}^2$). These tests were carried out with the MARK-J detector at PETRA by comparing the measured cross section for the process $e^{+}{e}^{-}\to e^{+}{e}^{-}{\mu }^{+}{\mu }^{-}$ with the prediction of QED for $12 \mathrm{GeV}<~\sqrt{s}<~36.7 \mathrm{GeV}$. The cross sections and the various kinematic distributions agree with QED.

We report the observation of new properties of primary cosmic rays He, C, and O measured in the rigidity (momentum/charge) range 2 GV to 3 TV with $90\times {10}^6$ helium, $8.4\times {10}^6$ carbon, and $7.0\times {10}^6$ oxygen nuclei collected by the Alpha Magnetic Spectrometer (AMS) during the first five years of operation. Above 60 GV, these three spectra have identical rigidity dependence. They all deviate from a single power law above 200 GV and harden in an identical way.

A precision measurement by AMS of the positron fraction in primary cosmic rays in the energy range from 0.5 to 500 GeV based on 10.9 million positron and electron events is presented. This measurement extends the energy range of our previous observation and increases its precision. The new results show, for the first time, that above $\sim 200\mathrm{GeV}$ the positron fraction no longer exhibits an increase with energy.

We report the properties of primary cosmic-ray sulfur (S) in the rigidity range 2.15 GV to 3.0 TV based on $0.38\times {10}^6$ sulfur nuclei collected by the Alpha Magnetic Spectrometer experiment (AMS). We observed that above 90 GV the rigidity dependence of the S flux is identical to the rigidity dependence of Ne-Mg-Si fluxes, which is different from the rigidity dependence of the He-C-O-Fe fluxes. We found that, similar to N, Na, and Al cosmic rays, over the entire rigidity range, the traditional primary cosmic rays S, Ne, Mg, and C all have sizeable secondary components, and the S, Ne, and Mg fluxes are well described by the weighted sum of the primary silicon flux and the secondary fluorine flux, and the C flux is well described by the weighted sum of the primary oxygen flux and the secondary boron flux. The primary and secondary contributions of the traditional primary cosmic-ray fluxes of C, Ne, Mg, and S (even $Z$ elements) are distinctly different from the primary and secondary contributions of the N, Na, and Al (odd $Z$ elements) fluxes. The abundance ratio at the source for $\mathrm{S}/\mathrm{Si}$ is $0.167\pm 0.006$, for $\mathrm{Ne}/\mathrm{Si}$ is $0.833\pm 0.025$, for $\mathrm{Mg}/\mathrm{Si}$ is $0.994\pm 0.029$, and for $\mathrm{C}/\mathrm{O}$ is $0.836\pm 0.025$. These values are determined independent of cosmic-ray propagation.

We report the observation of new properties of primary cosmic rays, neon (Ne), magnesium (Mg), and silicon (Si), measured in the rigidity range 2.15 GV to 3.0 TV with $1.8\times {10}^6\mathrm{Ne}$, $2.2\times {10}^6\mathrm{Mg}$, and $1.6\times {10}^6\mathrm{Si}$ nuclei collected by the Alpha Magnetic Spectrometer experiment on the International Space Station. The Ne and Mg spectra have identical rigidity dependence above 3.65 GV. The three spectra have identical rigidity dependence above 86.5 GV, deviate from a single power law above 200 GV, and harden in an identical way. Unexpectedly, above 86.5 GV the rigidity dependence of primary cosmic rays Ne, Mg, and Si spectra is different from the rigidity dependence of primary cosmic rays He, C, and O. This shows that the Ne, Mg, and Si and He, C, and O are two different classes of primary cosmic rays.

We present the precision measurement of 2824 daily helium fluxes in cosmic rays from May 20, 2011 to October 29, 2019 in the rigidity interval from 1.71 to 100 GV based on $7.6\times {10}^8$ helium nuclei collected with the Alpha Magnetic Spectrometer (AMS) aboard the International Space Station. The helium flux and the helium to proton flux ratio exhibit variations on multiple timescales. In nearly all the time intervals from 2014 to 2018, we observed recurrent helium flux variations with a period of 27 days. Shorter periods of 9 days and 13.5 days are observed in 2016. The strength of all three periodicities changes with time and rigidity. In the entire time period, we found that below $\sim 7\mathrm{GV}$ the helium flux exhibits larger time variations than the proton flux, and above $\sim 7\mathrm{GV}$ the helium to proton flux ratio is time independent. Remarkably, below 2.4 GV a hysteresis between the helium to proton flux ratio and the helium flux was observed at greater than the $7\sigma$ level. This shows that at low rigidity the modulation of the helium to proton flux ratio is different before and after the solar maximum in 2014.

Precision measurements of cosmic ray positrons are presented up to 1 TeV based on 1.9 million positrons collected by the Alpha Magnetic Spectrometer on the International Space Station. The positron flux exhibits complex energy dependence. Its distinctive properties are (a) a significant excess starting from $25.2\pm 1.8\mathrm{GeV}$ compared to the lower-energy, power-law trend, (b) a sharp dropoff above $284_{-64}^{+91}\mathrm{GeV}$, (c) in the entire energy range the positron flux is well described by the sum of a term associated with the positrons produced in the collision of cosmic rays, which dominates at low energies, and a new source term of positrons, which dominates at high energies, and (d) a finite energy cutoff of the source term of $E_s=810_{-180}^{+310}\mathrm{GeV}$ is established with a significance of more than $4\sigma$. These experimental data on cosmic ray positrons show that, at high energies, they predominantly originate either from dark matter annihilation or from other astrophysical sources.

We present the precision measurements of 11 years of daily cosmic positron fluxes in the rigidity range from 1.00 to 41.9 GV based on $3.4\times {10}^6$ positrons collected with the Alpha Magnetic Spectrometer (AMS) aboard the International Space Station. The positron fluxes show distinctly different time variations from the electron fluxes at short and long timescales. A hysteresis between the electron fluxes and the positron fluxes is observed with a significance greater than $5\sigma$ at rigidities below 8.5 GV. On the contrary, the positron fluxes and the proton fluxes show similar time variation. Remarkably, we found that positron fluxes are modulated more than proton fluxes with a significance greater than $5\sigma$ for rigidities below 7 GV. These continuous daily positron fluxes, together with AMS daily electron, proton, and helium fluxes over an 11-year solar cycle, provide unique input to the understanding of both the charge-sign and mass dependencies of cosmic rays in the heliosphere.

The Mark J Collaboration at the DESY $e^{+}$$e^{\mathrm{-}}$ collider PETRA presents results on the electroweak reactions ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{-}}$→${\mathrm{\mu }}^{+}$${\mathrm{\mu }}^{\mathrm{-}}$${\mathrm{\tau }}^{+}$${\mathrm{\tau }}^{\mathrm{-}}$,${\mathrm{\mu }}^{+}$${\mathrm{\mu }}^{\mathrm{-}}$γ, and $e^{+}$$e^{\mathrm{-}}$${\mu }^{+}$${\mu }^{\mathrm{-}}$. The c.m. energy range is 12 to 46.78 GeV. In the ${\mu }^{+}$${\mu }^{\mathrm{-}}$ and ${\tau }^{+}$${\tau }^{\mathrm{-}}$ channels the total cross sections and the forward-backward asymmetries are reported and compared with other experiments. The results are in excellent agreement with the standard model. The weak-neutral-current vector and axial-vector coupling constants are determined. The values for muons and τ’s are compatible with universality and with the predictions of the standard model. In the ${\mu }^{+}$${\mu }^{\mathrm{-}}$γ channel, all measured distributions, including the forward-backward muon asymmetry, are in excellent agreement with the electroweak theory. Our data on the two-photon process, $e^{+}$$e^{\mathrm{-}}$${\mu }^{+}$${\mu }^{\mathrm{-}}$, agrees with QED to order ${\alpha }^4$ over the entire energy range and the $Q^2$ range from 0.7 to 166 ${\mathrm{GeV}}^2$.

Precision measurements by the Alpha Magnetic Spectrometer on the International Space Station of the primary cosmic-ray electron flux in the range 0.5 to 700 GeV and the positron flux in the range 0.5 to 500 GeV are presented. The electron flux and the positron flux each require a description beyond a single power-law spectrum. Both the electron flux and the positron flux change their behavior at $\sim 30\mathrm{GeV}$ but the fluxes are significantly different in their magnitude and energy dependence. Between 20 and 200 GeV the positron spectral index is significantly harder than the electron spectral index. The determination of the differing behavior of the spectral indices versus energy is a new observation and provides important information on the origins of cosmic-ray electrons and positrons.

A precision measurement by AMS of the antiproton flux and the antiproton-to-proton flux ratio in primary cosmic rays in the absolute rigidity range from 1 to 450 GV is presented based on $3.49\times 10^5$ antiproton events and $2.42\times 10^9$ proton events. The fluxes and flux ratios of charged elementary particles in cosmic rays are also presented. In the absolute rigidity range $\sim 60$ to $\sim 500\mathrm{GV}$, the antiproton $\overline{p}$, proton $p$, and positron $e^{+}$ fluxes are found to have nearly identical rigidity dependence and the electron $e^{-}$ flux exhibits a different rigidity dependence. Below 60 GV, the ($\overline{p}/p$), ($\overline{p}/e^{+}$), and ($p/e^{+}$) flux ratios each reaches a maximum. From $\sim 60$ to $\sim 500\mathrm{GV}$, the ($\overline{p}/p$), ($\overline{p}/e^{+}$), and ($p/e^{+}$) flux ratios show no rigidity dependence. These are new observations of the properties of elementary particles in the cosmos.

We use the reaction $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$, in the Mark J detector at the DESY high-energy $e^{+}{e}^{-}$ collider PETRA, to test the standard electroweak theory and find good agreement. We also set limits on the parameters of several extended gauge theories.