While often omitted in the SMEFT analyses of electroweak measurements, the electroweak dipole operators of the bottom quark have been found to be important in some cases and are also related to processes involving the top quark. In this paper, we further investigate their effects, focusing on the measurements of the $$ {e}^{+}{e}^{-}\to b\overline{b} $$ process at a future lepton collider. Their linear contributions are suppressed by the bottom mass due to the helicity flip in the interference term with the SM amplitude, leading to a nontrivial interplay between the linear and the quadratic contributions. With two runs at the Z-pole and 240 GeV, the effects of CP-even dipole coefficients can be well separated from the modifications of the SM $$ Zb\overline{b} $$ couplings, while an additional run (e.g. at 360 GeV) is useful for lifting a nontrivial second best-fit point due to the quadratic contributions.

China

Jiayin Gu

Jiayu Guo

Germany

Xiao-Ze Tan

Tracing the bottom electroweak dipole operators at future lepton colliders

Higgs couplings are essential probes for physics beyond the Standard Model (BSM) since they can be modified by new physics, such as through the Higgs portal interaction   <math> <msup> <mfenced> <mi>H</mi> </mfenced> <mn>2</mn> </msup> <mi>O</mi> </math>  $$ {\left|H\right|}^2\mathcal{O} $$ . These modifications influence Higgs interactions via dimension-6 operators of the form (∂|H|2)2 and |H|6, which are generally expected to be of comparable size. This paper discusses a phenomenon of accidental suppression, where the |H|6 coupling is significantly smaller than (∂|H|2)2. This suppression, arising from the truncation of the tree-level effective potential, lacks a clear symmetry explanation but persists in portal models. This paper aims to inspire further studies on additional instances of accidental suppression without symmetry explanations or a general framework to characterize such suppression. We also discuss constraints, at the HL-LHC and future colliders, on the Wilson coefficients of the two dimension-6 operators for various benchmark scenarios of the concrete model.

United States

Yunjia Bao

Zhen Liu

Chi Shu

Lian-Tao Wang

Accidental suppression of Wilson coefficients in Higgs coupling

Parameters in an effective field theory can be subject to certain positivity bounds if one requires a UV completion that obeys the fundamental principles of quantum field theory. These bounds are relatively straightforward at the tree level, but would become more obscure when loop effects are important. Using scalar theories as examples, we carefully exam the positivity bounds in a case where the leading contribution to a forward elastic amplitude arises at the one-loop level, and point out certain subtleties in terms of the implications of positivity bounds on the theory parameter space. In particular, the one-loop generated dimension-8 operator coefficients (that would be positive if generated at the tree level), as well as their β-functions are generally not subject to positivity bounds as they might correspond to interference terms of the cross sections under the optical theorem, which could have either sign. A strict positivity bound can only be implied when all contributions at the same loop order are considered, including the ones from dim-4 and dim-6 operator coefficients, which have important effects at the one-loop level. Our results may have important implications on the robustness of experimental tests of positivity bounds.

Yunxiao Ye

Bin He

Positivity bounds in scalar Effective Field Theories at one-loop level

We apply machine-learning techniques to the effective-field-theory analysis of the e + e  −  → W + W  −  processes at future lepton colliders, and demonstrate their advantages in comparison with conventional methods, such as optimal observables. In particular, we show that machine-learning methods are more robust to detector effects and backgrounds, and could in principle produce unbiased results with sufficient Monte Carlo simulation samples that accurately describe experiments. This is crucial for the analyses at future lepton colliders given the outstanding precision of the e + e  −  → W + W  −  measurement (~ 10 −4 in terms of anomalous triple gauge couplings or even better) that can be reached. Our framework can be generalized to other effective-field-theory analyses, such as the one of e + e  −  →   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> </math>  $$ t\overline{t} $$  or similar processes at muon colliders.

Shengdu Chai

Lingfeng Li

From optimal observables to machine learning: an effective-field-theory analysis of e+e −  → W+W −  at future lepton colliders

By tagging one or two intact protons in the forward direction, it is possible to select and measure exclusive photon-fusion processes at the LHC. The same processes can also be measured in heavy ion collisions, and are often denoted as ultraperipheral collisions (UPC) processes. Such measurements open up the possibility of probing certain dimension-8 operators and their positivity bounds at the LHC. As a demonstration, we perform a phenomenological study on the γγ → ℓ + ℓ  −  processes, and find out that the measurements of this process at the HL-LHC provide reaches on a set of dimension-8 operator coefficients that are comparable to the ones at future lepton colliders. We also point out that the γq → γq process could potentially have better reaches on similar types of operators due to its larger cross section, but a more detailed experimental study is need to estimate the signal and background rates of this process. The validity of effective field theory (EFT) and the robustness of the positivity interpretation are also discussed.

Probing positivity at the LHC with exclusive photon-fusion processes

CERN

Carlotta Accettura

United Kingdom

Dean Adams

Rohit Agarwal

Claudia Ahdida

Italy

Chiara Aimè

Nicola Amapane

David Amorim

Paolo Andreetto

Fabio Anulli

Robert Appleby

Artur Apresyan

Aram Apyan

France

Sergey Arsenyev

Pouya Asadi

Egypt

Mohammed Mahmoud

Aleksandr Azatov

John Back

Lorenzo Balconi

Laura Bandiera

Roger Barlow

Nazar Bartosik

Emanuela Barzi

Fabian Batsch

Matteo Bauce

J. Berg

Andrea Bersani

Alessandro Bertarelli

Alessandro Bertolin

Kevin Black

Fulvio Boattini

Alex Bogacz

Maurizio Bonesini

Bernardo Bordini

Salvatore Bottaro

Luca Bottura

Alessandro Braghieri

Marco Breschi

Natalie Bruhwiler

Xavier Buffat

Laura Buonincontri

Philip Burrows

Graeme Burt

Dario Buttazzo

Barbara Caiffi

Marco Calviani

Simone Calzaferri

Daniele Calzolari

Rodolfo Capdevilla

Christian Carli

Fausto Casaburo

Massimo Casarsa

Luca Castelli

Maria Catanesi

Lorenzo Cavallucci

Gianluca Cavoto

Spain

Francesco Celiberto

Luigi Celona

Alessandro Cerri

Gianmario Cesarini

Cari Cesarotti

Portugal

Grigorios Chachamis

Antoine Chance

Switzerland

Siyu Chen

Yang-Ting Chien

Mauro Chiesa

Anna Colaleo

Francesco Collamati

Gianmaria Collazuol

Marco Costa

Nathaniel Craig

Camilla Curatolo

Canada

David Curtin

Giacomo Molin

Magnus Dam

Heiko Damerau

Sridhara Dasu

Jorge Blas

Stefania Curtis

Ernesto Matteis

Stefania Rosa

Jean-Pierre Delahaye

Dmitri Denisov

Türkiye

Haluk Denizli

Christopher Densham

Radovan Dermisek

Luca Luzio

Elisa Meco

Biagio Micco

Keith Dienes

Eleonora Diociaiuti

Tommaso Dorigo

Alexey Dudarev

Robert Edgecock

Filippo Errico

Marco Fabbrichesi

Stefania Farinon

Anna Ferrari

Jose Somoza

Netherlands

Frank Filthaut

Davide Fiorina

Erratum: Towards a muon collider

A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.

Towards a muon collider

The <math><mi>W</mi></math>-boson mass measurement recently reported by the CDF-II experiment exhibits a significant deviation from both the Standard Model prediction and previous measurements. There is also a long-standing deviation between the Standard Model prediction of the forward-backward asymmetry of the bottom quark (<math><msubsup><mi>A</mi><mi>FB</mi><mrow><mn>0</mn><mo>,</mo><mi>b</mi></mrow></msubsup></math>) and its measurement at the LEP experiment. The beautiful mirror model, proposed to resolve the <math><msubsup><mi>A</mi><mi>FB</mi><mrow><mn>0</mn><mo>,</mo><mi>b</mi></mrow></msubsup></math> discrepancy, introduces vectorlike quarks that modify the <math><mi>W</mi></math>-boson mass at the one-loop level. In this study, we find an interesting region in the model parameter space that could potentially explain both discrepancies, which puts the new quarks in the multi-TeV region. This region is mostly consistent with current LHC bounds from direct searches and Higgs coupling measurements, but will be thoroughly probed at the high-luminosity LHC. As such, the beautiful mirror model as an explanation of the <math><msub><mi>m</mi><mi>W</mi></msub></math> and <math><msubsup><mi>A</mi><mi>FB</mi><mrow><mn>0</mn><mo>,</mo><mi>b</mi></mrow></msubsup></math> discrepancies could be confirmed or falsified in the near future.

Accommodating the CDF <math><mi>W</mi></math>-boson mass measurement in the beautiful mirror model

Qiyu Sha

Abdualazem Fadol

Fangyi Guo

Gang Li

Yaquan Fang

Xinchou Lou

Erratum: Probing Higgs CP properties at the CEPC in the  $${e}^{+} {e}^{-} \rightarrow {Z H}\rightarrow {l}^{+} {l}^{-}{H}$$  <math> <mrow> <msup> <mrow> <mi>e</mi> </mrow> <mo>+</mo> </msup> <msup> <mrow> <mi>e</mi> </mrow> <mo>-</mo> </msup> <mo>→</mo> <mrow> <mi>ZH</mi> </mrow> <mo>→</mo> <msup> <mrow> <mi>l</mi> </mrow> <mo>+</mo> </msup> <msup> <mrow> <mi>l</mi> </mrow> <mo>-</mo> </msup> <mi>H</mi> </mrow> </math>   using optimal variables

In the Circular Electron Positron Collider (CEPC), a measurement of the Higgs CP mixing through  $$e^{+} e^{-} \rightarrow Z H \rightarrow l^{+} l^{-}(e^{+} e^{-} /\mu ^{+} \mu ^{-}) H(\rightarrow b \bar{b} / c \bar{c} / g g)$$  <math> <mrow> <msup> <mi>e</mi> <mo>+</mo> </msup> <msup> <mi>e</mi> <mo>-</mo> </msup> <mo>→</mo> <mi>Z</mi> <mi>H</mi> <mo>→</mo> <msup> <mi>l</mi> <mo>+</mo> </msup> <msup> <mi>l</mi> <mo>-</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>e</mi> <mo>+</mo> </msup> <msup> <mi>e</mi> <mo>-</mo> </msup> <mo>/</mo> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> <mo>)</mo> </mrow> <mi>H</mi> <mrow> <mo>(</mo> <mo>→</mo> <mi>b</mi> <mover> <mrow> <mi>b</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mo>/</mo> <mi>c</mi> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mo>/</mo> <mi>g</mi> <mi>g</mi> <mo>)</mo> </mrow> </mrow> </math>   process is presented, with  $$5.6\ \text{ ab}^{-1}$$  <math> <mrow> <mn>5.6</mn> <mspace width="4pt"></mspace> <mspace width="0.333333em"></mspace> <msup> <mtext>ab</mtext> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math>    $$e^{+} e^{-}$$  <math> <mrow> <msup> <mi>e</mi> <mo>+</mo> </msup> <msup> <mi>e</mi> <mo>-</mo> </msup> </mrow> </math>   collision data at the center-of-mass energy of  $$240\ \textrm{GeV}$$  <math> <mrow> <mn>240</mn> <mspace width="4pt"></mspace> <mtext>GeV</mtext> </mrow> </math>  . In this study, the CP-violating parameter  $$\tilde{c}_{Z \gamma }$$  <math> <msub> <mover> <mi>c</mi> <mo>~</mo> </mover> <mrow> <mi>Z</mi> <mi>γ</mi> </mrow> </msub> </math>   is constrained between the region of  $$ -0.30$$  <math> <mrow> <mo>-</mo> <mn>0.30</mn> </mrow> </math>   and 0.27 and  $$\tilde{c}_{Z Z}$$  <math> <msub> <mover> <mi>c</mi> <mo>~</mo> </mover> <mrow> <mi>ZZ</mi> </mrow> </msub> </math>   between  $$-0.06$$  <math> <mrow> <mo>-</mo> <mn>0.06</mn> </mrow> </math>   and 0.06 at  $$68\%$$  <math> <mrow> <mn>68</mn> <mo>%</mo> </mrow> </math>   confidence level. This study demonstrates the great potential of probing Higgs CP properties at the CEPC.

Probing Higgs CP properties at the CEPC in the  $$e^{+} e^{-} \rightarrow Z H \rightarrow l^{+} l^{-}H$$  <math> <mrow> <msup> <mi>e</mi> <mo>+</mo> </msup> <msup> <mi>e</mi> <mo>-</mo> </msup> <mo>→</mo> <mi>Z</mi> <mi>H</mi> <mo>→</mo> <msup> <mi>l</mi> <mo>+</mo> </msup> <msup> <mi>l</mi> <mo>-</mo> </msup> <mi>H</mi> </mrow> </math>   using optimal variables