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Hadrons and nuclei

In 2018, the USQCD Collaboration’s Executive Committee organized several subcommittees to recognize future opportunities and formulate possible goals for lattice field theory calculations in several physics areas. The conclusions of these studies, along with community input, are presented in seven white papers. Here, we discuss opportunities for lattice QCD calculations related to the structure and spectroscopy of hadrons and nuclei. An overview of recent lattice calculations of the structure of the proton and other hadrons is presented along with prospects for future extensions. Progress and prospects of hadronic spectroscopy and the study of resonances in the light, strange and heavy quark sectors are summarized. In conclusion recent advances in the study of light nuclei from lattice QCD are addressed and the scope of future investigations that are currently envisioned is outlined.

74 ATOMIC AND MOLECULAR PHYSICS↗

A measurement of the calorimeter response to single hadrons and determination of the jet energy scale uncertainty using LHC Run-1 pp-collision data with the ATLAS detector

A measurement of the calorimeter response to isolated charged hadrons in the ATLAS detector at the LHC is presented. This measurement is performed with 3.2 nb –1 of proton–proton collision data at √s = 7 TeV from 2010 and 0.1 nb –1 of data at √s = 8 TeV from 2012. A number of aspects of the calorimeter response to isolated hadrons are explored. After accounting for energy deposited by neutral particles, there is a 5% discrepancy in the modelling, using various sets of Geant4 hadronic physics models, of the calorimeter response to isolated charged hadrons in the central calorimeter region. The description of the response to anti-protons at low momenta is found to be improved with respect to previous analyses. The electromagnetic and hadronic calorimeters are also examined separately, and the detector simulation is found to describe the response in the hadronic calorimeter well. The jet energy scale uncertainty and correlations in scale between jets of different momenta and pseudorapidity are derived based on these studies. The uncertainty is 2–5% for jets with transverse momenta above 2 TeV, where this method provides the jet energy scale uncertainty for ATLAS.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Global constraint on the jet transport coefficient from single-hadron, dihadron, and γ -hadron spectra in high-energy heavy-ion collisions

Modifications of large transverse momentum single-hadron, dihadron, and γ -hadron spectra in relativistic heavy-ion collisions are direct consequences of parton-medium interactions in the quark-gluon plasma (QGP). The interaction strength and underlying dynamics can be quantified by the jet transport coefficient q ̂ . We carry out the first global constraint on q ̂ using a next-to-leading order pQCD parton model with higher-twist parton energy loss and combining world experimental data on single-hadron, dihadron, and γ -hadron suppression at both RHIC and LHC energies with a wide range of centralities. The global Bayesian analysis using the information field (IF) priors provides the most stringent constraint on q ̂ ( T ) . We demonstrate in particular the progressive constraining power of the IF Bayesian analysis on the strong temperature dependence of q ̂ using data from different centralities and colliding energies. We also discuss the advantage of using both inclusive and correlation observables with different geometric biases. As a verification, the obtained q ̂ ( T ) is shown to describe data on single-hadron anisotropy at high transverse momentum well. Predictions for future jet quenching measurements in oxygen-oxygen collisions are also provided. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Effect of the QCD equation of state and strange hadronic resonances on multiparticle correlations in heavy ion collisions

The QCD equation of state at zero baryon chemical potential is the only element of the standard dynamical framework to describe heavy ion collisions that can be directly determined from first principles. Continuum extrapolated lattice QCD equations of state have been computed using 2+1 quark flavors (up/down and strange) as well as 2+1+1 flavors to investigate the effect of thermalized charm quarks on QCD thermodynamics. Lattice results have also indicated the presence of new strange resonances that not only contribute to the equation of state of QCD matter but also affect hadronic afterburners used to model the later stages of heavy ion collisions. We investigate how these new developments obtained from first principles calculations affect multiparticle correlations in heavy ion collisions. We compare the commonly used equation of state S95n-v1, which was constructed using what are now considered outdated lattice results and hadron states, to the current state-of-the-art lattice QCD equations of state with 2+1 and 2+1+1 flavors coupled to the most upto-date hadronic resonances and their decays. New hadronic resonances lead to an enhancement in the hadronic spectra at intermediate p T . Using an outdated equation of state can directly affect the extraction of the shear viscosity to entropy density ratio, η/s , of the quark-gluon plasma and results for different flow observables. The effects of the QCD equation of state on multiparticle correlations of identified particles are determined for both AuAu √ sNN = 200 GeV and PbPb √ sNN = 5.02 TeV collisions. New insights into the v 2 {2} to v 3 {2} puzzle in ultracentral collisions are found. Flow observables of heavier particles exhibit more non-linear behavior regardless of the assumptions about the equation of state, which may provide a new way to constrain the temperature dependence of η/s .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

FCC-hh: The Hadron Collider

Particle physics has arrived at an important moment of its history. The discovery of the Higgs boson, with a mass of 125 GeV, completes the matrix of particles and interactions that has constituted the “Standard Model” for several decades. This model is a consistent and predictive theory, which has so far proven successful at describing all phenomena accessible to collider experiments. However, several experimental facts do require the extension of the Standard Model and explanations are needed for observations such as the abundance of matter over antimatter, the striking evidence for dark matter and the non-zero neutrino masses. Theoretical issues such as the hierarchy problem, and, more in general, the dynamical origin of the Higgs mechanism, do likewise point to the existence of physics beyond the Standard Model. This report contains the description of a novel research infrastructure based on a highest-energy hadron collider with a centre-of-mass collision energy of 100 TeV and an integrated luminosity of at least a factor of 5 larger than the HL-LHC. It will extend the current energy frontier by almost an order of magnitude. The mass reach for direct discovery will reach several tens of TeV, and allow, for example, to produce new particles whose existence could be indirectly exposed by precision measurements during the earlier preceding e+e– collider phase. This collider will also precisely measure the Higgs self-coupling and thoroughly explore the dynamics of electroweak symmetry breaking at the TeV scale, to elucidate the nature of the electroweak phase transition. WIMPs as thermal dark matter candidates will be discovered, or ruled out. As a single project, this particle collider infrastructure will serve the world-wide physics community for about 25 years and, in combination with a lepton collider (see FCC conceptual design report volume 2), will provide a research tool until the end of the 21st century. Collision energies beyond 100 TeV can be considered when using high-temperature superconductors. The European Strategy for Particle Physics (ESPP) update 2013 stated “To stay at the forefront of particle physics, Europe needs to be in a position to propose an ambitious post-LHC accelerator project at CERN by the time of the next Strategy update”. The FCC study has implemented the ESPP recommendation by developing a long-term vision for an “accelerator project in a global context”. This document describes the detailed design and preparation of a construction project for a post-LHC circular energy frontier collider “in collaboration with national institutes, laboratories and universities worldwide”, and enhanced by a strong participation of industrial partners. Now, a coordinated preparation effort can be based on a core of an ever-growing consortium of already more than 135 institutes worldwide. The technology for constructing a high-energy circular hadron collider can be brought to the technology readiness level required for constructing within the coming ten years through a focused R&D programme. The FCC-hh concept comprises in the baseline scenario a power-saving, low-temperature superconducting magnet system based on an evolution of the Nb3Sn technology pioneered at the HL-LHC, an energy-efficient cryogenic refrigeration infrastructure based on a neon-helium (Nelium) light gas mixture, a high-reliability and low loss cryogen distribution infrastructure based on Invar, high-power distributed beam transfer using superconducting elements and local magnet energy recovery and re-use technologies that are already gradually introduced at other CERN accelerators. On a longer timescale, high-temperature superconductors can be developed together with industrial partners to achieve an even more energy efficient particle collider or to reach even higher collision energies.The re-use of the LHC and its injector chain, which also serve for a concurrently running physics programme, is an essential lever to come to an overall sustainable research infrastructure at the energy frontier. Strategic R&D for FCC-hh aims at minimising construction cost and energy consumption, while maximising the socio-economic impact. It will mitigate technology-related risks and ensure that industry can benefit from an acceptable utility. Concerning the implementation, a preparatory phase of about eight years is both necessary and adequate to establish the project governance and organisation structures, to build the international machine and experiment consortia, to develop a territorial implantation plan in agreement with the host-states’ requirements, to optimise the disposal of land and underground volumes, and to prepare the civil engineering project. Such a large-scale, international fundamental research infrastructure, tightly involving industrial partners and providing training at all education levels, will be a strong motor of economic and societal development in all participating nations. The FCC study has implemented a set of actions towards a coherent vision for the world-wide high-energy and particle physics community, providing a collaborative framework for topically complementary and geographically well-balanced contributions. This conceptual design report lays the foundation for a subsequent infrastructure preparatory and technical design phase.

43 PARTICLE ACCELERATORS↗

HE-LHC: The High-Energy Large Hadron Collider

Particle physics has arrived at an important moment of its history. The discovery of the Higgs boson, with a mass of 125 GeV, completes the matrix of particles and interactions that has constituted the “Standard Model” for several decades. This model is a consistent and predictive theory, which has so far proven successful at describing all phenomena accessible to collider experiments. However, several experimental facts do require the extension of the Standard Model and explanations are needed for observations such as the abundance of matter over antimatter, the striking evidence for dark matter and the non-zero neutrino masses. Theoretical issues such as the hierarchy problem, and, more in general, the dynamical origin of the Higgs mechanism, do likewise point to the existence of physics beyond the Standard Model. This report contains the description of a novel research infrastructure based on a high-energy hadron collider, which extends the current energy frontier by almost a factor 2 (27 TeV collision energy) and an integrated luminosity of at least a factor of 3 larger than the HL-LHC. In connection with four experimental detectors, this infrastructure will deepen our understanding of the origin of the electroweak symmetry breaking, allow a first measurement of the Higgs self-coupling, double the HL-LHC discovery reach and allow for in-depth studies of new physics signals arising from future LHC measurements. This collider would directly produce particles at significant rates at scales up to 12 TeV. The project re-uses the existing LHC underground infrastructure and large parts of the injector chain at CERN. This particle collider would succeed the HL-LHC directly and serve the world-wide physics community for about 20 years beyond the middle of the 21st century. The European Strategy for Particle Physics (ESPP) update 2013 stated “To stay at the forefront of particle physics, Europe needs to be in a position to propose an ambitious post-LHC accelerator project at CERN by the time of the next Strategy update”. The FCC study has implemented the ESPP recommendation by developing a vision for an “accelerator project in a global context”. This document describes the detailed design and preparation of a construction project for a post-LHC circular high-energy hadron collider “in collaboration with national institutes, laboratories and universities worldwide”, and enhanced by a strong participation of industrial partners. Now, a coordinated preparation effort can be based on a core of an ever-growing consortium of already more than 135 institutes worldwide. The technology for constructing a High-Energy LHC can be brought to the technology readiness level required for construction within the coming ten years through a committed and focused R&D programme. The concept comprises a power-saving, low-temperature superconducting magnet system based on an evolution of the Nb3Sn technology pioneered at the HL-LHC, an energy-efficient cryogenic refrigeration infrastructure based on a neon-helium (Nelium) light gas mixture, a high-reliability and low loss cryogen distribution infrastructure based on Invar, high-power distributed beam transfer using superconducting elements and local magnet energy recovery and re-use technologies that are already gradually introduced at other CERN accelerators. Re-use of the LHC underground civil infrastructure worth about 500 million CHF at the time of its construction, extension of the surface sites and use of the existing injector chain that also serve for a concurrently running physics programme are levers to come to a sustainable research infrastructure at the energy frontier. Strategic R&D for HE-LHC aims at minimising construction cost and energy consumption, while maximising the socio-economic impact. It needs to mitigate technology-related risks and ensure that industry can benefit from an acceptable economic utility. Concerning the implementation, a preparatory phase of about eight years is both necessary and adequate to establish the project governance and organisation structures, to build the international machine and experiment consortia, to develop a territorial implantation plan considering the constraints emerging from using the existing infrastructure and the host states’ requirements, optimising the use of land, resources and preparing the construction project. Such a large-scale, international fundamental research infrastructure, tightly involving industrial partners and providing training at all education levels, will be a strong motor of economic and societal development in all participating nations. The FCC study has implemented a set of actions towards a coherent vision for the world-wide high-energy and particle physics community, providing a collaborative framework for topically complementary and geographically well-balanced contributions. This conceptual design report lays the foundation for a subsequent infrastructure preparatory and technical design phase.

43 PARTICLE ACCELERATORS↗

Hadronization of quarks and correlated di-hadron production in hard scattering

Understanding the dynamics of partons in general, and non perturbative sea, in particular, will be crucial for the understanding of strong interactions. Correlations of the spin of the target or/and the momentum and the spin of quarks, combined with final state interactions define the azimuthal distributions of produced particles. Production of correlated hadron pairs, in addition, will play an increasingly important role in the interpretation of pion electroproduction data in general, and hadronization process of quarks, in particular. More significant, than originaly anticipated, fraction of pions coming from correlated di-hadrons, indicated by recent CLAS12 measurements, and supported by various realistic models describing the hadronization process, may have a significant impact on various aspects of data analysis, including the modeling, composition, and interpretation of semi-inclusive DIS data, as well as calculations of radiative corrections. Studies of the nucleon structure beyond the traditional leading twist and current fragmentation of inclusive hadrons, provide qualitatively new tools to study the nucleon structure and extension of large x region well covered by JLab, to large Q2 at the EIC where it will be very important in interpretation of the data from JLab.

Avakian, Harut↗

Anomalous correlation between hadron and electromagnetic particles in hadron and gamma-ray families

Correlations between hadrons and electromagnetic particles were studied in the hadron-gamma families observed in the Chacaltaya emulsion chamber experiment. It is found that there exist a number of hadrons which associate electromagnetic showers in extraordinarily close vicinity. The probability to have such a large number of hadrons associating electromagnetic showers, expected from background calculation, is found to be negligibly small and it means there exists anomalous correlation between hadrons and electromagnetic particles in the characteristic spread of atmospheric electromagnetic cascade.

Tamada, M.↗

System-size dependence of the hadronic rescattering effect at energies available at the CERN Large Hadron Collider

The first measurements of K * ( 892 ) 0 resonance production as a function of charged-particle multiplicity in Xe-Xe collisions at s N N = 5.44 TeV and p p collisions at s = 5.02 TeV using the ALICE detector are presented. The resonance is reconstructed at midrapidity ( | y | < 0.5) using the hadronic decay channel K * 0 → K ± π ∓ . Measurements of transverse-momentum integrated yield, mean transverse-momentum, nuclear modification factor of K * 0 , and yield ratios of resonance to stable hadron ( K * 0 / K ) are compared across different collision systems ( p p , p -Pb, Xe-Xe, and Pb-Pb) at similar collision energies to investigate how the production of K * 0 resonances depends on the size of the system formed in these collisions. The hadronic rescattering effect is found to be independent of the size of colliding systems and mainly driven by the produced charged-particle multiplicity, which is a proxy of the volume of produced matter at the chemical freeze-out. In addition, the production yields of K * 0 in Xe-Xe collisions are utilized to constrain the dependence of the kinetic freeze-out temperature on the system size using the hadron resonance gas–partial chemical equilibrium model. ©2024 CERN, for the ALICE Collaboration 2024 CERN

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Studies of granularity of a hadronic calorimeter for tens-of-TeV jets at a 100 TeV $pp$ collider

Jet substructure variables for hadronic jets with transverse momenta in the range from 2.5 TeV to 20 TeV were studied using several designs for the spatial size of calorimeter cells. The studies used the full Geant4 simulation of calorimeter response combined with realistic reconstruction of calorimeter clusters. In most cases, the results indicate that the performance of jet-substructure reconstruction improves with reducing cell size of a hadronic calorimeter from Δ η × Δ = 0.087×0.087, which are similar to the cell sizes of the calorimeters of LHC experiments, by a factor of four, to 0.022×0.022.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Direct Observation of Quark-Hadron Duality in the Free Neutron {ital F}{sub 2} Structure Function

Using the recently published data from the BONuS(Barely Off-shell Nucleon Structure) experiment at Jefferson Lab, which utilized a spectator tagging technique to extract the inclusive electron-free neutron scattering cross section, we obtain the first direct observation of quark-hadron duality in the neutron F-2 structure function. The data are used to reconstruct the lowest few (N = 2, 4, and 6) moments of F-2 in the three prominent nucleon resonance regions, as well as the moments integrated over the entire resonance region. Comparison with moments computed from global parametrizations of parton distribution functions suggest that quark-hadron duality holds locally for the neutron in the second and third resonance regions down to Q(2) approximate to 1 GeV2, with violations possibly up to 20% observed in the first resonance region.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Hadronic production of W and Z bosons at large transverse momentum

We propose a modified factorization formalism in quantum chromodynamics for hadronic production of W and Z bosons at large transverse momentum p T . When p T is much larger than the invariant mass Q of the vector boson, this new factorization formalism systematically resums the large fragmentation logarithms, α s m ln m ( p T 2 / Q 2 ) , to all orders in the strong coupling α s . Using our modified factorization formalism, we present the next-to-leading-order (NLO) predictions for W and Z boson production at high p T at the CERN Large Hadron Collider and at a future 100 TeV proton-proton collider. Our NLO results are about 5% larger in normalization, and they reflect improved convergence and moderate reduction of the scale variation compared to the NLO predictions derived in a conventional fixed-order perturbative expansion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Probing Strangeness Hadronization with Event-by-Event Production of Multistrange Hadrons

This Letter presents the first measurement of event-by-event fluctuations of the net number (difference between the particle and antiparticle multiplicities) of multistrange hadrons Ξ − and $\overline{Ξ}$ + and its correlation with the net-kaon number using the data collected by the ALICE Collaboration in pp, p-Pb, and Pb-Pb collisions at a center-of-mass energy per nucleon pair $\sqrt{s_{NN}}$ = 5.02 TeV. The statistical hadronization model with a correlation over three units of rapidity between hadrons having the same and opposite strangeness content successfully describes the results. On the other hand, string-fragmentation models that mainly correlate strange hadrons with opposite strange quark content over a small rapidity range fail to describe the data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for invisible decays of the Higgs boson produced in association with a hadronically decaying vector boson in pp collisions at √s = 8 with the ATLAS detector

A search for Higgs boson decays to invisible particles is performed using 20.3 fb⁻¹ of pp collision data at a centre-of-mass energy of 8 TeV recorded by the ATLAS detector at the Large Hadron Collider. The process considered is Higgs boson production in association with a vector boson (V = W or Z) that decays hadronically, resulting in events with two or more jets and large missing transverse momentum. No excess of candidates is observed in the data over the background expectation. The results are used to constrain V H production followed by H decaying to invisible particles for the Higgs boson mass range 115 < m H < 300 GeV. The 95 % confidence-level observed upper limit on σ VH × BR(H → inv.) varies from 1.6 pb at 115 GeV to 0.13 pb at 300 GeV. Assuming Standard Model production and including the gg → H contribution as signal, the results also lead to an observed upper limit of 78% at 95% confidence level on the branching ratio of Higgs bosons decays to invisible particles at a mass of 125 GeV.

43 PARTICLE ACCELERATORS↗

Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra

The QCD light-front Hamiltonian equation H L F Ψ = M 2 Ψ derived from quantization at fixed LF time τ = t + z / c provides a causal, frame-independent method for computing hadron spectroscopy as well as dynamical observables such as structure functions, transverse momentum distributions, and distribution amplitudes. The QCD Lagrangian with zero quark mass has no explicit mass scale. de Alfaro, Fubini, and Furlan (dAFF) have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the dAFF procedure to the QCD light-front Hamiltonian, it leads to a color-confining potential κ 4 ζ 2 for mesons, where ζ 2 is the LF radial variable conjugate to the q q ¯ invariant mass squared. The same result, including spin terms, is obtained using light-front holography, the duality between light-front dynamics and A d S 5 , if one modifies the A d S 5 action by the dilaton e κ 2 z 2 in the fifth dimension z . When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions provide a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons and a universal Regge slope. The pion q q ¯ eigenstate has zero mass at m q = 0 . The superconformal relations also can be extended to heavy-light quark mesons and baryons. This approach also leads to insights into the physics underlying hadronization at the amplitude level. I will also discuss the remarkable features of the Poincaré invariant, causal vacuum defined by light-front quantization and its impact on the interpretation of the cosmological constant. AdS/QCD also predicts the analytic form of the nonperturbative running coupling α s ( Q 2 ) ∝ e - Q 2 / 4 κ 2 . The mass scale κ underlying hadron masses can be connected to the parameter Λ M S ¯ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling α s ( Q 2 ) defined at all momenta. One obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. Finally, I address the interesting question of whether the momentum sum rule is valid for nuclear structure functions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for charged Higgs bosons decaying via H ± → τ ± ν in fully hadronic final states using pp collision data at s $$ \sqrt{s} $$ = 8 TeV with the ATLAS detector

The results of a search for charged Higgs bosons decaying to a τ lepton and a neutrino, H ± → τ ± ν, are presented. The analysis is based on 19.5 fb –1 of proton-proton collision data at √s = 8 TeV collected by the ATLAS experiment at the Large Hadron Collider. Charged Higgs bosons are searched for in events consistent with top-quark pair production or in associated production with a top quark, depending on the considered H ± mass. The final state is characterized by the presence of a hadronic τ decay, missing transverse momentum, b-tagged jets, a hadronically decaying W boson, and the absence of any isolated electrons or muons with high transverse momenta. The data are consistent with the expected background from Standard Model processes. A statistical analysis leads to 95% confidence-level upper limits on the product of branching ratios Β(t → bH ± ) × Β(H ± → τ ± ν), between 0.23% and 1.3% for charged Higgs boson masses in the range 80-160GeV. It also leads to 95% confidence-level upper limits on the production cross section times branching ratio, σ(pp → tH ± + X) × Β(H ± → τ ± ν), between 0.76 pb and 4.5 fb, for charged Higgs boson masses ranging from 180 GeV to 1000 GeV. In the context of different scenarios of the Minimal Supersymmetric Standard Model, these results exclude nearly all values of tan β above one for charged Higgs boson masses between 80 GeV and 160 GeV, and exclude a region of parameter space with high tan β for H ± masses between 200 GeV and 250 GeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Measurements of branching fractions of leptonic and hadronic $ D_s^{+} $ meson decays and extraction of the $ D_s^{+} $ meson decay constant

We present measurements of absolute branching fractions of hadronic and lep-tonic \( D_s^{+} \) decays to K - K + π + , \( {{\overline{K}}^0} \) K + , ηπ + , μ + ν μ and τ + ν τ and report a search for the leptonic \( D_s^{+} \) → e + ν e decays. The results are obtained from a data sample of 913 fb -1 collected at or near the \( \varUpsilon \) (4 S ) and \( \varUpsilon \) (5 S ) resonances with the Belle detector at the KEKB asymmetric-energy e + e - collider. The branching fractions of hadronic decays are measured to be $$ \begin{array}{*{20}{c}} {\mathcal{B}\left( {D_s^{+}\ \to\ {K^{-}}{K^{+}}{\pi^{+}}} \right) = \left( {5.06\pm 0.15\pm 0.21} \right)\%,} \\ {\mathcal{B}\left( {D_s^{+}\ \to\ {{\overline{K}}^0}{K^{+}}} \right) = \left( {2.95\pm 0.11\pm 0.09} \right)\%,} \\ {\mathcal{B}\left( {D_s^{+}\ \to\ \eta {\pi^{+}}} \right) = \left( {1.82\pm 0.14\pm 0.07} \right)\%,} \\ \end{array} $$ where the first and second uncertainties are statistical and systematic, respectively. The branching fractions of leptonic decays are measured to be $$ \begin{array}{*{20}{c}} {\mathcal{B}\left( {D_s^{+}\ \to\ {\mu^{+}}{\nu_{\mu }}} \right)=\left( {0.531\pm 0.028\pm 0.020} \right)\%,} \\ {\mathcal{B}\left( {D_s^{+}\to {\tau^{+}}{\nu_{\tau }}} \right)=\left( {5.70\pm 0.21_{-0.30}^{-0.31 }} \right)\%,} \\ \end{array} $$ which are combined to determine the \( D_s^{+} \) meson decay constant $$ {f_{{{D_s}}}}=\left( {255.5\pm 4.2\pm 5.1} \right)\ \mathrm{MeV}. $$ We find no significant signal for \( D_s^{+} \) → e + ν e decays and set an upper limit of \( \mathcal{B}\left( {D_s^{+}\ \to\ {e^{+}}{\nu_e}} \right) \) < 1 . 0(0 . 83) × 10 -4 at 95% (90%) confidence level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗