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

In this work, we reconstruct the $\textit{H}$($\textit{z}$) based on observational Hubble data with Artificial Neural Network, then estimate the cosmological parameters and the Hubble constant. The training data we used are covariance matrix and mock $\textit{H}$($\textit{z}$), which are generated based on the real OHD data and Gaussian process. The use of the covariance matrix propagates the correlated uncertainties and improves training efficiency. Using the reconstructed H(z) data, we first determine the Hubble constant and compare it with CMB-based measurements. To constrain cosmological parameters, we sample on the reconstructed data and calculate the corresponding posterior distributions with Markov chain Monte Carlo. Through comprehensive statistical comparisons, we demonstrate that the parameter estimation using reconstructed samples achieves comparable statistical accuracy to the result derived from real OHD data.

Jie-feng Chen

Tong-Jie Zhang

Peng He

Tingting Zhang

Jie Zhang

Estimating cosmological parameters and reconstructing Hubble constant with artificial neural networks: a test with covariance matrix and mock H(z)

We consider extending the Standard Model by an anomaly-free and possibly flavour non-universal $\textit{U}$(1) gauge symmetry, whose breaking gives a $\textit{Z′}$ boson that does not affect electroweak precision observables at tree-level or via 1-loop renormalisation group (RG) running. Provided it does not also couple to electrons, such a $\textit{Z′}$ boson would be largely invisible to an electroweak precision machine like FCC-ee or CEPC (up to small finite 1-loop matching contributions that we quantify). We show that, while this class of $\textit{Z′}$ models can also evade tests of quark flavour violation, the constraint of anomaly-cancellation implies that valence quarks, muons, and taus are all charged under $\textit{U}$(1) , with the up quark charge being necessarily large. The conclusion holds even if one augments the SM by three right-handed neutrinos to try and absorb anomalies. This means such $\textit{Z′}$ bosons cannot simultaneously hide below the TeV scale from $\textit{pp}$ → $\textit{ℓℓ}$ Drell–Yan measurements at the LHC and, even if we entertain esoteric models in which the lepton charges are numerically very small, we cannot escape dijet searches at the LHC. For equitable quark and lepton charges, $\textit{pp}$ → $\textit{ℓℓ}$ already excludes such a $\textit{Z′}$ up to $\textit{M/g}$ ≳ 10 TeV, with a reach of 20 TeV expected by the end of the High-Luminosity LHC. The dijet bounds currently sit around 5 TeV, while sensitivity up to 10 TeV could be achieved at HL-LHC. We thus find an excellent complementarity between FCC-ee and HL-LHC in covering all anomaly-free $\textit{Z′}$ bosons up to several TeV.

Switzerland

Joe Davighi

In search of an invisible $\textit{Z′}$

Dark matter particles could be superheavy (mass $$M_X\gtrsim 10^9~$$ GeV) provided that their lifetime $$\tau _X$$ is extremely long, i.e. greater than $$\simeq 10^{22}~$$ yr. Such stringent constraints on $$\tau _X$$ are generally obtained by limiting the prompt emission of ultrahigh energy ( $$\gtrsim 10^9~$$ GeV) gamma rays and neutrinos from the decay processes to below the corresponding flux upper bounds. In this paper, we show that even more severe bounds can be obtained for $$M_X\gtrsim 10^{13}~$$ GeV from the synchrotron radiation of electron decay byproducts in the Galaxy. We illustrate the power of these constraints using generic Higgs-induced $$h\nu $$ and gauge-induced $$Z\nu /W\ell $$ decay channels, motivated by particle-physics setups invoking right-handed neutrinos. As a concrete benchmark, we consider a superheavy dark-matter candidate within an extended type-I seesaw framework and show that the lower bounds on lifetime can be translated into upper bounds on a mass-mixing parameter $$\delta M$$ , which must satisfy approximately $$\delta M\lesssim 2\times 10^{-17}/[M_X/(10^9~\textrm{GeV})]^{0.5}$$ GeV for $$M_X\gtrsim 10^9$$ GeV. Some implications in the context of inflationary cosmologies are discussed.

France

Olivier Deligny

Constraints on superheavy dark matter decaying into $$h\nu $$ , $$Z\nu $$ and $$W\ell $$

In the minimal gauged <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">B</mi><mo stretchy="false">−</mo><mi mathvariant="normal">L</mi></mrow></math> extension of the Standard Model, we demonstrate that PeV-scale dark matter (DM) and the baryon asymmetry of the Universe (BAU) can be simultaneously explained through the three right-handed neutrinos (RHNs) present in the theory. The DM candidate undergoes rare decay into light neutrinos, providing an explanation for the observed IceCube events, while the other two RHNs generate the BAU via leptogenesis. The breaking of gauge symmetry gives rise to detectable gravitational waves (GWs) from decaying cosmic strings (CS), making this framework testable at several future GW detectors—despite being beyond the reach of conventional collider experiments due to the extremely weak gauge coupling. The symmetry-breaking scale establishes a connection between particle masses, couplings, and the GW spectrum, offering a unified and predictive scenario.

India

Basabendu Barman

Japan

Arindam Das

South Korea

Suruj Jyoti Das

Sweden

Marco Merchand

Hunting for heavy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> with IceCube neutrinos and gravitational waves

A measurement is presented of the cross section in proton-proton collisions for the production of two <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math> bosons and one <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> boson. It is based on data recorded by the CMS experiment at the CERN LHC at center-of-mass energies <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn></math> and 13.6 TeV, corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>200</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. Events with four charged leptons (electrons or muons) in the final state are selected. Both nonresonant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi><mi>W</mi><mi>Z</mi></math> production and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>H</mi></math> production, with the Higgs boson decaying into two <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math> bosons, are reported. For the first time, the two processes are measured separately in a simultaneous fit. Combining the two modes, signal strengths relative to the standard model (SM) predictions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>0.75</mn><mrow><mo>−</mo><mn>0.29</mn></mrow><mrow><mo>+</mo><mn>0.34</mn></mrow></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>1.74</mn><mrow><mo>−</mo><mn>0.60</mn></mrow><mrow><mo>+</mo><mn>0.71</mn></mrow></msubsup></math> are measured for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn></math> and 13.6 TeV, respectively. The observed (expected) significance for the triboson signal is 3.8 (2.5) standard deviations for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo><mn>13.6</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math>, thus providing the first evidence for triboson production at this center-of-mass energy. Combining the two modes and the two center-of-mass energies, the inclusive signal strength relative to the SM prediction is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mn>1.03</mn><mrow><mo>−</mo><mn>0.28</mn></mrow><mrow><mo>+</mo><mn>0.31</mn></mrow></msubsup></math>, with an observed (expected) significance of 4.5 (5.0) standard deviations.

Armenia

A. Hayrapetyan

V. Makarenko

A. Tumasyan

Austria

W. Adam

J.W. Andrejkovic

L. Benato

T. Bergauer

K. Damanakis

M. Dragicevic

C. Giordano

P.S. Hussain

M. Jeitler

N. Krammer

A. Li

D. Liko

I. Mikulec

J. Schieck

R. Schöfbeck

D. Schwarz

M. Shooshtari

M. Sonawane

W. Waltenberger

C.E. Wulz

Belgium

T. Janssen

H. Kwon

D. Ocampo Henao

T. Van Laer

P. Van Mechelen

J. Bierkens

N. Breugelmans

J. D’Hondt

S. Dansana

A. De Moor

M. Delcourt

F. Heyen

Y. Hong

P. Kashko

S. Lowette

I. Makarenko

D. Müller

J. Song

S. Tavernier

M. Tytgat

G.P. Van Onsem

S. Van Putte

D. Vannerom

B. Bilin

B. Clerbaux

A.K. Das

I. De Bruyn

G. De Lentdecker

H. Evard

L. Favart

P. Gianneios

A. Khalilzadeh

F.A. Khan

A. Malara

M.A. Shahzad

L. Thomas

M. Vanden Bemden

C. Vander Velde

P. Vanlaer

F. Zhang

M. De Coen

D. Dobur

G. Gokbulut

J. Knolle

L. Lambrecht

D. Marckx

K. Skovpen

N. Van Den Bossche

J. van der Linden

J. Vandenbroeck

L. Wezenbeek

S. Bein

A. Benecke

A. Bethani

G. Bruno

A. Cappati

J. De Favereau De Jeneret

C. Delaere

A. Giammanco

A.O. Guzel

V. Lemaitre

J. Lidrych

P. Malek

P. Mastrapasqua

S. Turkcapar

Brazil

G.A. Alves

M. Barroso Ferreira Filho

E. Coelho

C. Hensel

T. Menezes De Oliveira

C. Mora Herrera

P. Rebello Teles

M. Soeiro

E.J. Tonelli Manganote

A. Vilela Pereira

W.L. Aldá Júnior

H. Brandao Malbouisson

Measurement of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi><mi>W</mi><mi>Z</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>H</mi></math> Production Cross Sections at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn></math> and 13.6 TeV

This study investigates neutral triple gauge couplings (nTGCs) through <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>Z</mi></math> production at future electron-positron colliders. The impact of beam polarization on the cross section is analyzed. We compare the signals and backgrounds for five different <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>Z</mi></math> decay channels and present our event selection strategies for future <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> colliders. The expected coefficient constraints for all decay channels are provided, and final expected constraints are derived by combining results from the different decay patterns. Our analysis indicates that future electron-positron colliders will have significantly enhanced detection capabilities for nTGCs compared to the current LHC experiments, with expected improvements in constraints by 1 to 2 orders of magnitude.

United States

Yu-Chen Guo

Man-Qi Ruan

Ji-Chong Yang

Chun-Jing Pan

Search for neutral triple gauge couplings with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mi>Z</mi></math> production at future electron-positron colliders

We investigate new contributions to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mi>Z</mi><mi>Z</mi></math> vertex from the flavor changing neutral current (FCNC) involving the Higgs and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> bosons. Our calculations reveal that the form factors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>h</mi><mn>2</mn><mi>V</mi></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>h</mi><mn>3</mn><mi>V</mi></msubsup></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>V</mi><mo>=</mo><mi>H</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math>) can be induced through these couplings, and we present our results in terms of the Passarino-Veltman scalar functions. Using the current limits on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mover accent="true"><mi>t</mi><mo stretchy="false">¯</mo></mover><mi>c</mi></math> couplings, we determine that the new contributions to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-conserving form factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>h</mi><mn>2</mn><mi>V</mi></msubsup></math> are small compared to the Standard Model (SM) predictions. However, for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-violating form factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>h</mi><mn>3</mn><mi>V</mi></msubsup></math>, the contributions can reach values as high as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math>, 5 orders of magnitude larger than in the SM. Furthermore, we examine how these results influence the left-right asymmetries in the processes <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>H</mi><mo>*</mo></msup><mo stretchy="false">→</mo><mi>Z</mi><mi>Z</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>*</mo></msup><mo stretchy="false">→</mo><mi>Z</mi><mi>H</mi></math>. Our findings suggest that significant deviations from SM predictions may occur when considering FCNC contributions.

Mexico

A.I. Hernández-Juárez

R. Gaitán

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> violation in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mi>Z</mi><mi>Z</mi></math> vertex and left-right asymmetries

This paper investigates the production of Z bosons in proton-lead collisions at a center of mass energy of <math altimg='si8.svg'><mrow><msqrt><mi>s</mi></msqrt><mo linebreak='goodbreak'>=</mo><mn>8.16</mn></mrow></math> TeV, utilizing various transverse momentum dependent parton distribution functions (TMDs), including the leading order Martin-Ryskin-Watt (LO-MRW), next-to-leading order MRW (NLO-MRW), and parton branching (PB) approaches. By comparing theoretical predictions with experimental data from the CMS collaboration, we assess the performance of these TMD models across different kinematic regions. Our analysis reveals that while both LO-MRW and NLO-MRW models generally align well with experimental data, the LO-MRW model tends to overestimate in certain kinematic regions. The NLO-MRW model, with its strong ordering constraint, provides better agreement in these areas. This study highlights the impact of different impositions of angular and strong ordering constraints in the LO-MRW and NLO-MRW approaches in describing Z boson production.

Iran

S. Rezaie

Türkiye

K. Azizi

Z boson production in proton-lead collisions: A study utilizing MRW nuclear TMDs

The occurrence of a topological phase transition can be demonstrated by a direct observation of a change in the topological invariant. For holographic topological semimetals, a topological Hamiltonian method needs to be employed to calculate the topological invariants due to the strong coupling nature of the system. We calculate the topological invariants for the holographic Weyl semimetal and the holographic Weyl-$\textit{Z}$ semimetal, which correspond to the chiral charge and the spin-Chern number, respectively. This is achieved by probing fermions within the system and deriving the topological Hamiltonian from the zero-frequency Green’s function. In both cases, we have identified an effective band structure characterized by an infinite number of Weyl or $\textit{Z}$ nodes, a distinctive feature of holographic systems different from weakly coupled systems. The topological invariants of these nodes are computed numerically and found to be nonzero, thereby confirming the topologically nontrivial nature of these nodes.

Xiantong Chen

Xuanting Ji

Ya-Wen Sun

Topological invariant for holographic Weyl-$\textit{Z}$