A future $ e^+e^- $ collider could run at the $\textit{Z}$-pole to perform important electroweak (EW) precision measurements, but such a run may not be viable for a future muon collider. However, this can be compensated for by measuring other EW processes utilizing the high energy and large luminosity of the muon collider. In this paper, we consider the measurements of the vector boson fusion processes of $ WW/WZ/W\gamma $ to a pair of fermions (along with a $ \nu_{\mu}\bar{\nu}_{\mu} $ or $ \nu_{\mu}\mu^+/\bar{\nu}_{\mu}\mu^- $ pair) at a high-energy muon collider and study their potential for probing EW observables. We consider two run scenarios for the muon collider with center-of-mass energies of 10 and 30 TeV, respectively, and focus on the processes involving $ f=b,c,\tau $ and the dimension-6 operators that directly modify the corresponding fermions coupling to the $ Z/W $ bosons. The invariant mass distribution of the $ f\bar{f} $ pair helps to separate the events from the $ Z/W $ and high-energy resonances, whereas the polar angle of the outing fermion provides additional information. Through a chi-squared analysis on the binned distributions and combining the information from the $\textit{WW}$ and $ WZ/W\gamma $ fusion processes, all relevant Wilson coefficients can be constrained simultaneously. The precision surpasses the current EW measurement constraints and is even competitive with future $ e^+e^- $ colliders. Our analysis can be included in a more complete framework that is required to fully determine the potential of muon colliders in EW precision measurements.

China

Hao-Qiao Li

Hai-Ning Yan

Jiayin Gu

Germany

Xiao-Ze Tan

Probing $\textit{Z}$/$\textit{W}$ pole physics at high-energy muon colliders via vector-boson-fusion processes * Supported by the National Natural Science Foundation of China (NSFC) (12035008, 12375091, 12347171), and the Innovation Program for Quantum Science and Technology (2024ZD0300101). Xiao-Ze Tan also acknowledges the support from Helmholtz – OCPC (Office of China Postdoctoral Council) Postdoctoral Fellowship Program

We study $ \cos2\phi $ azimuthal asymmetry in doubly longitudinally polarized proton-proton Drell-Yan collisions within the transverse momentum dependent factorization framework. The asymmetry arises from the convolution of the longitudinal transversity distribution $ h_{1L}^{\perp} $ for both protons. Using the Bacchetta-Delcarro-Pisano-Radici-Signori parameterization for the nonperturbative Sudakov form factor and the Wandzura-Wilczek approximation for collinear $ h_{1L}^{\perp} $ , we predict the double spin asymmetry $ A_{LL}^{\cos2\phi} $ at RHIC and NICA kinematics. Our results demonstrate sensitivity to sea quark distributions, with the asymmetry reaching up to 25% for maximal sea quark contributions. These predictions highlight the potential of polarized Drell-Yan measurements to probe sea quark dynamics and advance our understanding of nucleon structures.

Hui Li

Ting Hu

Liang-Liang Liu

Xiao-Yu Wang

Zhun Lu

Asymmetry ${{\boldsymbol A}_{\boldsymbol{LL}}^{\bf\cos2\boldsymbol\phi}} $ in the polarized proton-proton Drell-Yan process within TMD factorization * Hui Li is supported by Fundamental Research Program of Shanxi Province (202203021222224) and Natural Science Foundation of Shanxi Normal University (JCYJ2023021). Xiao-Yu Wang is supported by the Natural Science Foundation of Henan Province (242300421377, 232300421140)

We study the transverse momentum ( $p_T$ ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( ${v_2\{2}\}$ , ${v_2\{4\}}$ , and ${\langle v_2\rangle}$ ) and flow fluctuation ( ${\sigma_{v_2}}$ ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation ${\sigma_{v_2}}$ tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( ${v_2\{4\}/v_2\{2\}}$ , $F({v_2})$ ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( ${A_2^f}$ , ${M_2^f}$ ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.

Jie Zhu

Canada

Xiang-Yu Wu

Guang-You Qin

Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscosity * Supported in part by the Natural Science Foundation of China (12225503, 11890710, 11890711, 11935007). Zhu Jie is supported in part by the China Scholarship Council (202306770009). Wu Xiang-Yu is supported in part by the National Science Foundation within the framework of the JETSCAPE collaboration (OAC-2004571) and in part by the Natural Sciences and Engineering Research Council of Canada. Some of the calculations were performed in the Nuclear Science Computing Center at Central China Normal University (NSC$^{3}$), Wuhan, Hubei, China.

We use the spectral lag catalog of 46 short GRBs aggregated by Xiao et al. (Astrophys J Lett 924:L29, 2022), to carry out an independent search for Lorentz invariance violation (LIV). For this purpose, we use a power-law model as a function of energy for the intrinsic astrophysical induced spectral lags. The expansion history of the universe needed for constraining LIV was obtained in a non-parametric method using cosmic chronometers. We use Bayesian model comparison to determine if the aforementioned spectral lags show evidence for LIV as compared to only astrophysically induced lags. We do not find any evidence for LIV, and obtain 95% CL lower limits on the corresponding energy scale to be  $$4 \times 10^{15}$$  <math> <mrow> <mn>4</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>15</mn> </msup> </mrow> </math>   GeV and  $$6.8 \times 10^{9}$$  <math> <mrow> <mn>6.8</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>9</mn> </msup> </mrow> </math>   GeV for the linear and quadratic LIV models respectively. Our results obtained by using the flat  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM model for characterizing the cosmic expansion history are consistent with those obtained using chronometers.

India

Shantanu Desai

Rajdeep Agrawal

Haveesh Singirikonda

Search for Lorentz invariance violation using Bayesian model comparison applied to Xiao et al. GRB spectral lag catalog

Anomalies from the LHCb lepton flavour universality and Fermilab muon anomalous magnetic moment show tantalizing hints of possible new physics from the lepton sectors. Due to its large mass and shorter lifetime than muon, the tau lepton is believed to couple more to possible new physics beyond the Standard Model. Traditionally, tau leptons are probed through their decay products due to tau’s short lifetime. On the other hand, at a high energy scale, a large fraction of tau leptons could be boosted to a much longer lifetime and fly a visible distance from several centimetres up to kilometer length scale yet very informative to new physics beyond the standard model or high energy cosmic rays. In this article, we investigate rare, yet promising, tau-physics phenomena, where long-lived taus are exploited either as a microscope (for the measurement of tau’s anomalous magnetic moment to an unprecedented level of accuracy) or as a macroscope (for the detection of 1 TeV to 1 PeV cosmic neutrinos).

Qiang Li

Sitian Qian

Zhe Guan

Sen Deng

Yunxuan Song

Tianyu Mu

Jie Xiao

Tianyi Yang

Siguang Wang

Yajun Mao

Meng Lu

Zhengyun You

Boosted Tau Lepton as a Microscope and Macroscope

The LHCb Collaboration recently gave an update on testing lepton flavour universality with B + → K +ℓ+ℓ − , in which a 3.1 standard deviations from the standard model prediction was observed. The g-2 experiment also reports a 3.3 standard deviations from the standard model on muon anomalous magnetic moment measurement. These deviations could be explained by introducing new particles including leptoquarks. In this paper, we show the possibility to search for heavy spin-1 leptoquarks at a future TeV scale muon collider by performing studies from three channels: 1) same flavour final states with either two bottom or two light quarks, 2) different flavour quark final states, and 3) a so-called “VXS” process representing the scattering between a vector boson and a leptoquark to probe the coupling between leptoquark and tau lepton. We conclude that a 3 TeV muon collider with 3 ab −1 of integrated luminosity is already sufficient to cover the leptoquark parameter space in order to explain the LHCb lepton flavour universality anomaly.

Congqiao Li

Fanqiang Meng

Searching for heavy leptoquarks at a muon collider

Measuring longitudinally polarized vector boson scattering in, e.g., the <math><mi>Z</mi><mi>Z</mi></math> channel is a promising way to investigate the unitarization scheme from the Higgs and possible new physics beyond the Standard Model. However, at the LHC, it demands the end of the high-luminosity-LHC lifetime luminosity, <math><mrow><mn>3000</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math>, and advanced data analysis technique to reach the discovery threshold due to its small production rates. Instead, there could be great potential at future colliders. In this paper, we perform a Monte Carlo study and examine the projected sensitivity of longitudinally polarized <math><mi>Z</mi><mi>Z</mi></math> scattering at a TeV scale muon collider. We conduct studies at 14 and 6 TeV muon colliders respectively and find that a 5 standard deviation discovery can be achieved at a 14 TeV muon collider, with <math><mn>3000</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> of data collected. While a 6 TeV muon collider can already surpass high-luminosity LHC, reaching 2 standard deviations with around <math><mrow><mn>4</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>ab</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math> of data. The effect from lepton isolation and detector granularity is also discussed, which may be more obvious at higher energy muon colliders, as the leptons from longitudinally polarized <math><mrow><mi>Z</mi></mrow></math> decays tend to be closer.

Longitudinally polarized <math><mi>Z</mi><mi>Z</mi></math> scattering at a muon collider

An electron-muon collider with an asymmetric collision profile targeting multi-ab-1 integrated luminosity is proposed. This novel collider, operating at collision energies of, e.g., 20–200 GeV, 50–1000 GeV, and 100–3000 GeV, would be able to probe charged lepton flavor violation and measure Higgs boson properties precisely. The collision of an electron and muon beam leads to less physics background compared with either an electron-electron or a muon-muon collider, since electron-muon interactions proceed mostly through higher-order vector boson fusion and vector boson scattering processes. The asymmetric collision profile results in collision products that are boosted towards the electron beam side, which can be exploited to reduce beam-induced background from the muon beam to a large extent. With this in mind, one can imagine a lepton collider complex, starting from colliding order 10 GeV electron and muon beams for the first time in history and to probe charged lepton flavor violation, then to be upgraded to a collider with 50-100 GeV electron and 1-3 TeV muon beams to measure Higgs properties and search for new physics and finally to be transformed to a TeV-scale muon-muon collider. The cost should vary from order 100 million to a few billion dollars, corresponding to different stages, which make the funding situation more practical.

Andrew Michael Levin

Antonios Agapitos

The Physics Case for an Electron-Muon Collider