More extensive and precise results are reported on the parameters of Z decay. On the basis of 20 000 Z decays collected with the ALEPH detector at LEP we find M z =91.182±0.026 (exp.) ±0.030 (beam) GeV, Γ z =2.541±0.056 GeV and σ had 0 =41.4±0.8 nb. The partial widths for the hadronic and leptonic channels are Γ had =1804±44 MeV, Γ e + e − =82.1±3.4 MeV, Γ μ + μ − =87.9±6.0 MeV and Γ τ + τ − =86.1±5.6 MeV, in good agreement with the standard model. On the basis of the average leptonic width Γ ℓ + ℓ − =83.9±2.2 MeV, the effective weak mixing angle is found to be sin 2 θ w ( M z )=0.231±0.008. Usin g the partial widths calculated in the standard model, the number of light neutrino families is N ν =3.01±0.15 (exp.)±0.05 (theor.).
No description provided.
The properties of theZ resonance are measured on the basis of 190 000Z decays into fermion pairs collected with the ALEPH detector at LEP. Assuming lepton universality,Mz=(91.182±0.009exp±0.020L∶P) GeV,ГZ=(2484±17) MeV, σhad0=(41.44±0.36) nb, andГjad/Гℓℓ=21.00±0.20. The corresponding number of light neutrino species is 2.97±0.07. The forward-back-ward asymmetry in leptonic decays is used to determine the ratio of vector to axial-vector coupling constants of leptons:gv2(MZ2)/gA2(MZ2)=0.0072±0.0027. Combining these results with ALEPH results on quark charge and\(b\bar b\) asymmetries, and τ polarization, sin2θW(MZ2). In the contex of the Minimal Standard Model, limits are placed on the top-quark mass.
Statistical errors only.
No description provided.
Hadronic and leptonic cross-sections and forward-backward asymmetries are measured using 5.7 pb −1 of data taken with the ALEPH detector at LEP at centre-of-mass energies of 130 and 136 GeV. The results agree with Standard Model expectations. The measurement of hadronic cross-sections far away from the Z resonance improves the determination of the interference between photon and Z exchange. Constraints on models with extra Z bosons are presented.
Data with tight SPRIME cut.
Forward-Backward Asymmetry for tight SPRIME cuts.
Based on 520 000 fermion pairs accumulated during the first three years of data collection by the ALEPH detector at LEP, updated values of the resonance parameters of theZ are determined to beMZ=(91.187±0.009) GeV, ΓZ=(2.501±0.012) GeV, σhad0=(41.60±0.27) nb, andRℓ=20.78±0.13. The corresponding number of light neutrino species isNν=2.97±0.05. The forward-backward asymmetry in lepton-pair decays is used to determine the ratio of vector to axial-vector couplings of leptons:gV2(MZ2)/gA2(MZ2)=0.0052±0.0016. Combining this with ALEPH measurements of theb andc quark asymmetries and τ polarization gives sin2θWeff=0.2326±0.0013. Assuming the minimal Standard Model, and including measurements ofMW/MZ fromp\(\bar p\) colliders and neutrino-nucleon scattering, the mass of the top quark is\(M_{top} = 156 \pm \begin{array}{*{20}c} {22} \\ {25} \\ \end{array} \pm \begin{array}{*{20}c} {17} \\ {22Higgs} \\ \end{array} \) GeV.
Data from 1990 running period.
Data from 1991 running period.
Data for 1991 running period.
We report on the properties of theZ resonance from 62 500Z decays into fermion pairs collected with the ALEPH detector at LEP, the Large Electron-Positron storage ring at CERN. We findMZ=(91.193±0.016exp±0.030LEP) GeV, ΓZ=(2497±31) MeV, σhad0=(41.86±0.66)nb, and for the partial widths Γinv=(489±24) MeV, Γhad(1754±27) MeV, Γee=(85.0±1.6)MeV, Γμμ=(80.0±2.5) MeV, and Γττ=(81.3±2.5) MeV, all in good agreement with the Standard Model. Assuming lepton universality and using a lepton sample without distinction of the final state we measure Γu=(84.3±1.3) MeV. The forward-backward asymmetry in leptonic decays is used to determine the vector and axial-vector weak coupling constants of leptors,gv2(MZ2)=(0.12±0.12)×10−2 andgA2(MZ2)=0.2528±0.0040. The number of light neutrino species isNν=2.91±0.13; the electroweak mixing angle is sin2θW(MZ2)=0.2291±0.0040.
No description provided.
A measurement of the total $pp$ cross section at the LHC at $\sqrt{s}=8$ TeV is presented. An integrated luminosity of $500$ $\mu$b$^{-1}$ was accumulated in a special run with high-$\beta^{\star}$ beam optics to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable $t$. The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the $-t$ range from $0.014$ GeV$^2$ to $0.1$ GeV$^2$ to extrapolate $t\rightarrow 0$, the total cross section, $\sigma_{\mathrm{tot}}(pp\rightarrow X)$, is measured via the optical theorem to be: $\sigma_{\mathrm{tot}}(pp\rightarrow X) = {96.07} \; \pm 0.18 \; ({{stat.}}) \pm 0.85 \; ({{exp.}}) \pm 0.31 \; ({extr.}) \; {mb} \;,$ where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation $t\rightarrow 0$. In addition, the slope of the exponential function describing the elastic cross section at small $t$ is determined to be $B = 19.74 \pm 0.05 \; ({{stat.}}) \pm 0.23 \; ({{syst.}}) \; {GeV}^{-2}$.
The measured total cross section, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The nuclear slope of the differential eslastic cross section at small |t|, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The total elastic cross section and the observed elastic cross section within the fiducial volume.
A measurement of the total $pp$ cross section at the LHC at $\sqrt{s}=7$ TeV is presented. In a special run with high-$\beta^{\star}$ beam optics, an integrated luminosity of 80 $\mu$b$^{-1}$ was accumulated in order to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable $t$. The measurement is performed with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the $|t|$ range from 0.01 GeV$^2$ to 0.1 GeV$^2$ to extrapolate to $|t|\rightarrow 0$, the total cross section, $\sigma_{\mathrm{tot}}(pp\rightarrow X)$, is measured via the optical theorem to be: $$\sigma_{\mathrm{tot}}(pp\rightarrow X) = 95.35 \; \pm 0.38 \; ({\mbox{stat.}}) \pm 1.25 \; ({\mbox{exp.}}) \pm 0.37 \; (\mbox{extr.}) \; \mbox{mb},$$ where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation to $|t|\rightarrow 0$. In addition, the slope of the elastic cross section at small $|t|$ is determined to be $B = 19.73 \pm 0.14 \; ({\mbox{stat.}}) \pm 0.26 \; ({\mbox{syst.}}) \; \mbox{GeV}^{-2}$.
The measured total cross section, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The nuclear slope of the differential eslastic cross section at small |t|, the first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
The Optical Point dsigma/(elastic)/dt(t-->0), the total elastic cross section and the observed elastic cross section within the fiducial volume. The first systematic error accounts for all experimental uncertainties and the second error for the extrapolation t-->0.
Pseudorapidity gap distributions in proton-proton collisions at sqrt(s) = 7 TeV are studied using a minimum bias data sample with an integrated luminosity of 7.1 inverse microbarns. Cross sections are measured differentially in terms of Delta eta F, the larger of the pseudorapidity regions extending to the limits of the ATLAS sensitivity, at eta = +/- 4.9, in which no final state particles are produced above a transverse momentum threshold p_T Cut. The measurements span the region 0 < Delta eta F < 8 for 200 < p_T Cut < 800 MeV. At small Delta eta F, the data test the reliability of hadronisation models in describing rapidity and transverse momentum fluctuations in final state particle production. The measurements at larger gap sizes are dominated by contributions from the single diffractive dissociation process (pp -> Xp), enhanced by double dissociation (pp -> XY) where the invariant mass of the lighter of the two dissociation systems satisfies M_Y <~ 7 GeV. The resulting cross section is d sigma / d Delta eta F ~ 1 mb for Delta eta F >~ 3. The large rapidity gap data are used to constrain the value of the pomeron intercept appropriate to triple Regge models of soft diffraction. The cross section integrated over all gap sizes is compared with other LHC inelastic cross section measurements.
The inelastic cross section differential in the forward rapidity gap size, DELTA(C=RAPGAP) for a maximum observed particle transverse momentum of 200 MeV in the gap.
The inelastic cross section differential in the forward rapidity gap size, DELTA(C=RAPGAP) for a maximum observed particle transverse momentum of 400 MeV in the gap.
The inelastic cross section differential in the forward rapidity gap size, DELTA(C=RAPGAP) for a maximum observed particle transverse momentum of 600 MeV in the gap.
In a special run of the LHC with $\beta^\star = 2.5~$km, proton-proton elastic-scattering events were recorded at $\sqrt{s} = 13~$TeV with an integrated luminosity of $340~\mu \textrm{b}^{-1}$ using the ALFA subdetector of ATLAS in 2016. The elastic cross section was measured differentially in the Mandelstam $t$ variable in the range from $-t = 2.5 \cdot 10^{-4}~$GeV$^{2}$ to $-t = 0.46~$GeV$^{2}$ using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section $\sigma_{\textrm{tot}}$, parameters of the nuclear slope, and the $\rho$-parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit $t \rightarrow 0$. These parameters are determined from a fit to the differential elastic cross section using the optical theorem and different parameterizations of the $t$-dependence. The results for $\sigma_{\textrm{tot}}$ and $\rho$ are \begin{equation*} \sigma_{\textrm{tot}}(pp\rightarrow X) = \mbox{104.7} \pm 1.1 \; \mbox{mb} , \; \; \; \rho = \mbox{0.098} \pm 0.011 . \end{equation*} The uncertainty in $\sigma_{\textrm{tot}}$ is dominated by the luminosity measurement, and in $\rho$ by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.
The measured total cross section. The systematic uncertainty includes experimental and theoretical uncerainties.
The measured total cross section. The systematic uncertainty includes experimental and theoretical uncerainties.
The rho-parameter, i.e. the ratio of the real to imaginary part of the elastic scattering amplitude extrapolated to t=0. The systematic uncertainty includes experimental and theoretical uncerainties.
A comparison is made of the low-mass three-meson systems (πππ), (Kππ), (π K K ) and ( K K K ) diffractively produced in the reaction meson + proton → three mesons + proton. Several striking similarities and a few important differences are observed: (i) the reactions are consistent with the assumption that the three mesons decay entirely into a 0 − meson and a 0 + , 1 − or 2 + resonance; (ii) the three-meson mass spectra have a peak ≈ 250 MeV above the effective threshold M eff of the dominant decay mode and then fall off approximately as (mass) −3 ;(iii) the average spin 〈 J 〉 = 0.55 + 1.1 Q eff , where Q eff = M - M eff ; (iv) the average orbital angular momentum 〈 l 〉 increases according to 〈 l 〉 = 0.75 Q eff ; (v) the three-meson states are produced dominantly in unnatural spin-parity states and no evidence for their being resonant is found; (vi) the only natural spin-parity states found are the well-established 2 + resonances A 2 and K ∗ (1420); they have similar properties to the non-resonant unnatural parity states except for a dip at t = 0 in the dσ/d t distributions; (vii) both the unnatural and natural spin-parity states are produced mostly by an exchange of natural parity; (viii) there is evidence for two types of production mechanism with different polarization properties, one approximately conserving helicity in the t -channel and the other in the s -channel.
No description provided.
Results are presented on elastic scattering of 10.1 GeV/ c K − mesons on protons, based on a sample of 16 261 kinematically-fitted bubble-chamber events. The differential cross section is given over the | t |- range of 0.06 to 2.5 GeV 2 and is fitted with the expressions a e bt , A e Bt + Ct 2 and ( P e Qt + Re St ) over various intervals of t . The results are compared with those of other experiments at nearby energies. Upper limits of | α | < 0.28 and σ B < 0.4 μ b (both at a 90% confidence level) are given for the ratio of real to imaginary part of the forward-scattering amplitude and the backward-elastic-scattering cross section, respectively.
No description provided.
ERROR INCLUDES STATISTICAL ERROR AND ERROR IN TOTAL CROSS SECTION USED FOR NORMALIZATION. EXTRAPOLATION OF D(SIG)/DT TO T=0 PROVIDES ABOUT 0.5 PCT UNCERTAINTY.
NO BACKWARD EVENTS OBSERVED. LARGEST ANGLE EVENT SEEN WAS AT 64 DEG (-T = 2.33 GEV**2).
We report on the measurement of the reaction e+e−→e+e− with a large—solid-angle electromagnetic shower detector at center-of-mass energies s=13 and 17 GeV. Comparison of our results with predictions of quantum electrodynamics shows excellent agreement in both the angular distribution and energy dependence. Values of cutoff parameters are also given.
No description provided.
We present measurements of the αα elastic scattering differential cross section at √ s = 126 GeV in the range 0.05 ⩽ ‖ t ‖
ERRORS ARE STATISTICAL ONLY.
EXPONENTIAL FIT TO CROSS SECTION BELOW T = 0.075 GEV**2.
Results are presented onK+p elastic scattering and on the reactionK+p→K+pπ+π− at 70 GeV/c. For the
.
.
INTEGRATION OVER RANGE OF ABS(T) FROM 0 TO 1 GEV.
We report the first observation of diffractively produced W bosons. In a sample of W -> e nu events produced in p-barp collisions at sqrt{s}=1.8 TeV, we find an excess of events with a forward rapidity gap, which is attributed to diffraction. The probability that this excess is consistent with non-diffractive production is 1.1 10^{-4} (3.8 sigma). The relatively low fraction of W+Jet events observed within this excess implies that mainly quarks from the pomeron, which mediates diffraction, participate in W production. The diffractive to non-diffractive W production ratio is found to be R_W=(1.15 +/- 0.55)%.
No description provided.
We present results from a measurement of double diffraction dissociation in $\bar pp$ collisions at the Fermilab Tevatron collider. The production cross section for events with a central pseudorapidity gap of width $\Delta\eta^0>3$ (overlapping $\eta=0$) is found to be $4.43\pm 0.02{(stat)}{\pm 1.18}{(syst) mb}$ [$3.42\pm 0.01{(stat)}{\pm 1.09}{(syst) mb}$] at $\sqrt{s}=1800$ [630] GeV. Our results are compared with previous measurements and with predictions based on Regge theory and factorization.
Cross sections for double diffractive production.
We have studied the reactions e + e − → e + e − , e + e − → γγ , e + e − → μ + μ − , and e + e − → τ + τ − in the centre-of-mass (CM) energy range from 39.8 to 45.2 GeV using the CELLO detector at PETRA. Upper limits on the partial widths for new spin 0 bosons with masses both within and above the energy range covered are determined. No evidence for contributions of such new particles has been observed up to the highest PETRA energies in a model independent way. Under the assumptions of recently suggested models relating the existence of spin 0 bosons to the radiative width Γ τ of the Z 0 we exclude such bosons at the 95% confidence level for masses below the Z 0 -mass if Γ τ > 20 MeV.
No description provided.
Figure actually gives the 95 PCT CL upper limits of the coupling constants for each process as a function of the mass of the intermediate spin zero boson.
The differential cross sections of the reactions e + e − → e + e − and e + e − → λλ are measured at energies between 33.0 and 36.7 GeV. The results agree with the predictions of quantum electrodynamics. A comparison with the standard model of electroweak interaction yields sin 2 θ W = 0.25 ± 0.13.
No description provided.
No description provided.
Differential cross sections fore+e−→e+e−, τ+, τ- measured with the CELLO detector at\(\left\langle {\sqrt s } \right\rangle= 34.2GeV\) have been analyzed for electroweak contributions. Vector and axial vector coupling constants were obtained in a simultaneous fit to the three differential cross sections assuming a universal weak interaction for the charged leptons. The results,v2=−0.12±0.33 anda2=1.22±0.47, are in good agreement with predictions from the standardSU(2)×U(1) model for\(\sin ^2 \theta _w= 0.228\). Combining this result with neutrino-electron scattering data gives a unique axial vector dominated solution for the leptonic weak couplings. Assuming the validity of the standard model, a value of\(\sin ^2 \theta _w= 0.21_{ - 0.09}^{ + 0.14}\) is obtained for the electroweak mixing angle. Additional vector currents are not observed (C<0.031 is obtained at the 95% C.L.).
No description provided.
We measured the elastic scattering of αα at s = 126 GeV and of α p at s = 89 GeV . For αα , the differential cross section d σ /d t has a diffractive pattern minima at | t | = 0.10 and 0.38 GeV 2 . At small | t | = 0.05−0.07 GeV 2 , this cross section behaves like exp[(100 ± 10) t ]. Extrapolating a fit to the data to the optical point, we obtained for the total cross section α tot ( αα ) = 250 ± 50 mb and an integrated elastic cross section σ e1 ( αα ) = 45 ± mb. Another method of estimating σ tot ( αα ), based on measuring the interaction rate, yielded 295 ± 40 mb. For α p, d σ /d t has aminimum at | t | = 0.20 GeV 2 , and for 0.05 < | t | < 0.18 GeV 2 behaves like exp[(41 ± 2) t ]. Extrapolating this slope to | t | = 0, we found σ tot ( α p) = 130 ± 20 and σ e1 ( α p) = 20 ± 4mb. Results on pp elastic scattering at s = 63 GeV agree with previous ISR experiments.
Axis error includes +- 15/15 contribution.
Axis error includes +- 15/15 contribution.
METHOD 1 FOR SIG IS USING OPTICAL THEOREM. METHOD 2 FOR SIG IS BASED ON THE MEASURED LUMINOSITY-MONITOR CROSS SECTIONS.
None
THESE DATA ARE TABULATED IN THE RECORD OF THE PUBLISHED VERSION.
DIVIDE BY 20 TO GET MB/GEV**2.
FROM QUADRATIC EXPONENTIAL FITS TO D(SIG)/DT FOR -T = 0 TO 1.4 GEV**2. SYSTEMATIC ERRORS INCLUDED.
We are reporting on a new determination of sin 2 ϑ w from the ratio of v μ e to v e scattering cross sections. A new detector designed for this purpose was exposed tothe Wide Band Neutrino Beamof the 450 GeV (CERN SPS. An analysis of data taken in 1987 and 1988 is presented based on 762 v μ e and 1017 v e events. From the ratio of σ( v μ e ) to σ( v μ e ) we determined sin 2 ϑ w =0.233±0.012 ( stat ) ± 0.008 ( syst ) without radiative correction. With radiative correction for m t = m H =100 GeV we find sin 2 ϑ w =0.232±0.012( stat )±0.008( syst ).
Data without electroweak radiative corrections.
Data corrected for electroweak radiative effects with TOP and HIGGS masses 100 GeV.
We report on a study of the differential cross section d σ /d y for the processes of elastic ν μ - and ν μ - electron scattering. The data on which this analysis is based were recorded between 1987 and 1990 with the CHARM II detector in the wide band neutrino beam at the CERN-SPS. For the first time the shapes of these y -distributions have been determined in a model-independent way. A fit to the data yields for the squares of the neutral coupling constants the ratio g R 2 / g L 2 =0.60 ± 0.19 (stat.) ± 0.09 (syst.).
Cross sections in arbitrary units.
Cross sections in arbitrary units.
Value of SIN2TW obtained from data.
We have performed the most comprehensive resonance-model fit of $\pi^-\pi^-\pi^+$ states using the results of our previously published partial-wave analysis (PWA) of a large data set of diffractive-dissociation events from the reaction $\pi^- + p \to \pi^-\pi^-\pi^+ + p_\text{recoil}$ with a 190 GeV/$c$ pion beam. The PWA results, which were obtained in 100 bins of three-pion mass, $0.5 < m_{3\pi} < 2.5$ GeV/$c^2$, and simultaneously in 11 bins of the reduced four-momentum transfer squared, $0.1 < t' < 1.0$ $($GeV$/c)^2$, are subjected to a resonance-model fit using Breit-Wigner amplitudes to simultaneously describe a subset of 14 selected waves using 11 isovector light-meson states with $J^{PC} = 0^{-+}$, $1^{++}$, $2^{++}$, $2^{-+}$, $4^{++}$, and spin-exotic $1^{-+}$ quantum numbers. The model contains the well-known resonances $\pi(1800)$, $a_1(1260)$, $a_2(1320)$, $\pi_2(1670)$, $\pi_2(1880)$, and $a_4(2040)$. In addition, it includes the disputed $\pi_1(1600)$, the excited states $a_1(1640)$, $a_2(1700)$, and $\pi_2(2005)$, as well as the resonancelike $a_1(1420)$. We measure the resonance parameters mass and width of these objects by combining the information from the PWA results obtained in the 11 $t'$ bins. We extract the relative branching fractions of the $\rho(770) \pi$ and $f_2(1270) \pi$ decays of $a_2(1320)$ and $a_4(2040)$, where the former one is measured for the first time. In a novel approach, we extract the $t'$ dependence of the intensity of the resonances and of their phases. The $t'$ dependence of the intensities of most resonances differs distinctly from the $t'$ dependence of the nonresonant components. For the first time, we determine the $t'$ dependence of the phases of the production amplitudes and confirm that the production mechanism of the Pomeron exchange is common to all resonances.
Real and imaginary parts of the normalized transition amplitudes $\mathcal{T}_a$ of the 14 selected partial waves in the 1100 $(m_{3\pi}, t')$ cells (see Eq. (12) in the paper). The wave index $a$ represents the quantum numbers that uniquely define the partial wave. The quantum numbers are given by the shorthand notation $J^{PC} M^\varepsilon [$isobar$] \pi L$. We use this notation to label the transition amplitudes in the column headers. The $m_{3\pi}$ values that are given in the first column correspond to the bin centers. Each of the 100 $m_{3\pi}$ bins is 20 MeV/$c^2$ wide. Since the 11 $t'$ bins are non-equidistant, the lower and upper bounds of each $t'$ bin are given in the column headers. The transition amplitudes define the spin-density matrix elements $\varrho_{ab}$ for waves $a$ and $b$ according to Eq. (18). The spin-density matrix enters the resonance-model fit via Eqs. (33) and (34). The transition amplitudes are normalized via Eqs. (9), (16), and (17) such that the partial-wave intensities $\varrho_{aa} = |\mathcal{T}_a|^2$ are given in units of acceptance-corrected number of events. The relative phase $\Delta\phi_{ab}$ between two waves $a$ and $b$ is given by $\arg(\varrho_{ab}) = \arg(\mathcal{T}_a) - \arg(\mathcal{T}_b)$. Note that only relative phases are well-defined. The phase of the $1^{++}0^+ \rho(770) \pi S$ wave was set to $0^\circ$ so that the corresponding transition amplitudes are real-valued. In the PWA model, some waves are excluded in the region of low $m_{3\pi}$ (see paper and [Phys. Rev. D 95, 032004 (2017)] for a detailed description of the PWA model). For these waves, the transition amplitudes are set to zero. The tables with the covariance matrices of the transition amplitudes for all 1100 $(m_{3\pi}, t')$ cells can be downloaded via the 'Additional Resources' for this table.
Decay phase-space volume $I_{aa}$ for the 14 selected partial waves as a function of $m_{3\pi}$, normalized such that $I_{aa}(m_{3\pi} = 2.5~\text{GeV}/c^2) = 1$. The wave index $a$ represents the quantum numbers that uniquely define the partial wave. The quantum numbers are given by the shorthand notation $J^{PC} M^\varepsilon [$isobar$] \pi L$. We use this notation to label the decay phase-space volume in the column headers. The labels are identical to the ones used in the column headers of the table of the transition amplitudes. $I_{aa}$ is calculated using Monte Carlo integration techniques for fixed $m_{3\pi}$ values, which are given in the first column, in the range from 0.5 to 2.5 GeV/$c^2$ in steps of 10 MeV/$c^2$. The statistical uncertainties given for $I_{aa}$ are due to the finite number of Monte Carlo events. $I_{aa}(m_{3\pi})$ is defined in Eq. (6) in the paper and appears in the resonance model in Eqs. (19) and (20).
We study the spin-exotic $J^{PC} = 1^{-+}$ amplitude in single-diffractive dissociation of 190 GeV$/c$ pions into $\pi^-\pi^-\pi^+$ using a hydrogen target and confirm the $\pi_1(1600) \to \rho(770) \pi$ amplitude, which interferes with a nonresonant $1^{-+}$ amplitude. We demonstrate that conflicting conclusions from previous studies on these amplitudes can be attributed to different analysis models and different treatment of the dependence of the amplitudes on the squared four-momentum transfer and we thus reconcile their experimental findings. We study the nonresonant contributions to the $\pi^-\pi^-\pi^+$ final state using pseudo-data generated on the basis of a Deck model. Subjecting pseudo-data and real data to the same partial-wave analysis, we find good agreement concerning the spectral shape and its dependence on the squared four-momentum transfer for the $J^{PC} = 1^{-+}$ amplitude and also for amplitudes with other $J^{PC}$ quantum numbers. We investigate for the first time the amplitude of the $\pi^-\pi^+$ subsystem with $J^{PC} = 1^{--}$ in the $3\pi$ amplitude with $J^{PC} = 1^{-+}$ employing the novel freed-isobar analysis scheme. We reveal this $\pi^-\pi^+$ amplitude to be dominated by the $\rho(770)$ for both the $\pi_1(1600)$ and the nonresonant contribution. We determine the $\rho(770)$ resonance parameters within the three-pion final state. These findings largely confirm the underlying assumptions for the isobar model used in all previous partial-wave analyses addressing the $J^{PC} = 1^{-+}$ amplitude.
Results for the spin-exotic $1^{-+}1^+[\pi\pi]_{1^{-\,-}}\pi P$ wave from the free-isobar partial-wave analysis performed in the first $t^\prime$ bin from $0.100$ to $0.141\;(\text{GeV}/c)^2$. The plotted values represent the intensity of the coherent sum of the dynamic isobar amplitudes $\{\mathcal{T}_k^\text{fit}\}$ as a function of $m_{3\pi}$, where the coherent sums run over all $m_{\pi^-\pi^+}$ bins indexed by $k$. These intensity values are given in number of events per $40\;\text{MeV}/c^2$ $m_{3\pi}$ interval and correspond to the orange points in Fig. 8(a). In the "Resources" section of this $t^\prime$ bin, we provide the JSON file named <code>transition_amplitudes_tBin_0.json</code> for download, which contains for each $m_{3\pi}$ bin the values of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, their covariances, and further information. The data in this JSON file are organized in independent bins of $m_{3\pi}$. The information in these bins can be accessed via the key <code>m3pi_bin_<#>_t_prime_bin_0</code>. Each independent $m_{3\pi}$ bin contains <ul> <li>the kinematic ranges of the $(m_{3\pi}, t^\prime)$ cell, which are accessible via the keys <code>m3pi_lower_limit</code>, <code>m3pi_upper_limit</code>, <code>t_prime_lower_limit</code>, and <code>t_prime_upper_limit</code>.</li> <li>the $m_{\pi^-\pi^+}$ bin borders, which are accessible via the keys <code>m2pi_lower_limits</code> and <code>m2pi_upper_limits</code>.</li> <li>the real and imaginary parts of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which are accessible via the keys <code>transition_amplitudes_real_part</code> and <code>transition_amplitudes_imag_part</code>, respectively.</li> <li>the covariance matrix of the real and imaginary parts of the $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>covariance_matrix</code>. Note that this matrix is real-valued and that its rows and columns are indexed such that $(\Re,\Im)$ pairs of the transition amplitudes are arranged with increasing $k$.</li> <li>the normalization factors $\mathcal{N}_a$ in Eq. (13) for all $m_{\pi^-\pi^+}$ bins, which are accessible via the key <code>normalization_factors</code>.</li> <li>the shape of the zero mode, i.e., the values of $\tilde\Delta_k$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>zero_mode_shape</code>.</li> <li>the reference wave, which is accessible via the key <code>reference_wave</code>. Note that this is always the $4^{++}1^+\rho(770)\pi G$ wave.</li> </ul>
Results for the spin-exotic $1^{-+}1^+[\pi\pi]_{1^{-\,-}}\pi P$ wave from the free-isobar partial-wave analysis performed in the second $t^\prime$ bin from $0.141$ to $0.194\;(\text{GeV}/c)^2$. The plotted values represent the intensity of the coherent sum of the dynamic isobar amplitudes $\{\mathcal{T}_k^\text{fit}\}$ as a function of $m_{3\pi}$, where the coherent sums run over all $m_{\pi^-\pi^+}$ bins indexed by $k$. These intensity values are given in number of events per $40\;\text{MeV}/c^2$ $m_{3\pi}$ interval and correspond to the orange points in Fig. 15(a) in the supplemental material of the paper. In the "Resources" section of this $t^\prime$ bin, we provide the JSON file named <code>transition_amplitudes_tBin_1.json</code> for download, which contains for each $m_{3\pi}$ bin the values of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, their covariances, and further information. The data in this JSON file are organized in independent bins of $m_{3\pi}$. The information in these bins can be accessed via the key <code>m3pi_bin_<#>_t_prime_bin_1</code>. Each independent $m_{3\pi}$ bin contains <ul> <li>the kinematic ranges of the $(m_{3\pi}, t^\prime)$ cell, which are accessible via the keys <code>m3pi_lower_limit</code>, <code>m3pi_upper_limit</code>, <code>t_prime_lower_limit</code>, and <code>t_prime_upper_limit</code>.</li> <li>the $m_{\pi^-\pi^+}$ bin borders, which are accessible via the keys <code>m2pi_lower_limits</code> and <code>m2pi_upper_limits</code>.</li> <li>the real and imaginary parts of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which are accessible via the keys <code>transition_amplitudes_real_part</code> and <code>transition_amplitudes_imag_part</code>, respectively.</li> <li>the covariance matrix of the real and imaginary parts of the $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>covariance_matrix</code>. Note that this matrix is real-valued and that its rows and columns are indexed such that $(\Re,\Im)$ pairs of the transition amplitudes are arranged with increasing $k$.</li> <li>the normalization factors $\mathcal{N}_a$ in Eq. (13) for all $m_{\pi^-\pi^+}$ bins, which are accessible via the key <code>normalization_factors</code>.</li> <li>the shape of the zero mode, i.e., the values of $\tilde\Delta_k$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>zero_mode_shape</code>.</li> <li>the reference wave, which is accessible via the key <code>reference_wave</code>. Note that this is always the $4^{++}1^+\rho(770)\pi G$ wave.</li> </ul>
Results for the spin-exotic $1^{-+}1^+[\pi\pi]_{1^{-\,-}}\pi P$ wave from the free-isobar partial-wave analysis performed in the third $t^\prime$ bin from $0.194$ to $0.326\;(\text{GeV}/c)^2$. The plotted values represent the intensity of the coherent sum of the dynamic isobar amplitudes $\{\mathcal{T}_k^\text{fit}\}$ as a function of $m_{3\pi}$, where the coherent sums run over all $m_{\pi^-\pi^+}$ bins indexed by $k$. These intensity values are given in number of events per $40\;\text{MeV}/c^2$ $m_{3\pi}$ interval and correspond to the orange points in Fig. 15(b) in the supplemental material of the paper. In the "Resources" section of this $t^\prime$ bin, we provide the JSON file named <code>transition_amplitudes_tBin_2.json</code> for download, which contains for each $m_{3\pi}$ bin the values of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, their covariances, and further information. The data in this JSON file are organized in independent bins of $m_{3\pi}$. The information in these bins can be accessed via the key <code>m3pi_bin_<#>_t_prime_bin_2</code>. Each independent $m_{3\pi}$ bin contains <ul> <li>the kinematic ranges of the $(m_{3\pi}, t^\prime)$ cell, which are accessible via the keys <code>m3pi_lower_limit</code>, <code>m3pi_upper_limit</code>, <code>t_prime_lower_limit</code>, and <code>t_prime_upper_limit</code>.</li> <li>the $m_{\pi^-\pi^+}$ bin borders, which are accessible via the keys <code>m2pi_lower_limits</code> and <code>m2pi_upper_limits</code>.</li> <li>the real and imaginary parts of the transition amplitudes $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which are accessible via the keys <code>transition_amplitudes_real_part</code> and <code>transition_amplitudes_imag_part</code>, respectively.</li> <li>the covariance matrix of the real and imaginary parts of the $\{\mathcal{T}_k^\text{fit}\}$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>covariance_matrix</code>. Note that this matrix is real-valued and that its rows and columns are indexed such that $(\Re,\Im)$ pairs of the transition amplitudes are arranged with increasing $k$.</li> <li>the normalization factors $\mathcal{N}_a$ in Eq. (13) for all $m_{\pi^-\pi^+}$ bins, which are accessible via the key <code>normalization_factors</code>.</li> <li>the shape of the zero mode, i.e., the values of $\tilde\Delta_k$ for all $m_{\pi^-\pi^+}$ bins, which is accessible via the key <code>zero_mode_shape</code>.</li> <li>the reference wave, which is accessible via the key <code>reference_wave</code>. Note that this is always the $4^{++}1^+\rho(770)\pi G$ wave.</li> </ul>
Forum