We continue our study of fractionally charged particles (FCPs)—particles carrying electric charge a multiple of <math altimg='si44.svg'><mrow><mi>e</mi><mo linebreak='goodbreak'>/</mo><mn>6</mn></mrow></math>. Discovering an FCP would inform us about both Standard Model physics (what the true gauge group and the one-form global symmetry are) and Beyond the Standard Model physics (ruling out many unified theories), which makes them a high-stakes target for collider searches. Here we find that with two FCPs there are vastly richer phenomenologies compared to the single-particle extensions we previously studied. Stringent constraints on colored FCPs can be dramatically weakened when decays are open; conversely the cross sections of the least visible species can be enlarged by up to <math altimg='si45.svg'><mrow><mo>&#8764;</mo><msup><mn>10</mn><mn>3</mn></msup></mrow></math>, increasing their discovery potential enormously at the LHC and milliQan. Overall, these simple models motivate performing searches for FCPs produced along with jets or leptons, and highlight &#8216;free&#8217; discovery potential in reanalyzing existing missing-energy datasets for low-quality tracks.

United States

Seth Koren

Adam Martin

Phenomenology of fractionally charged particles: Two reps are better than one

In this paper we study non-factorizable $$ \mathcal{N} $$ = 1 superamplitudes for massive chiral superstates. We demonstrate how little group scaling and the supersymmetric Ward identities determine the form of non-factorizable massless superamplitudes, then extrapolate to massive superamplitudes by requiring they reduce to the massless form when we send all masses to zero. This technique does not depend on whether or not the superstates are self-conjugate (so that the fermionic components are either Dirac or Majorana) or whether the superamplitude is dressed with a form-factor.

Antonio Delgado

China

Runqing Wang

Non-factorizable superamplitudes for massive $$ \mathcal{N} $$ = 1 superstates

<p>We formalize energy-scaling arguments in the standard model effective field theory (SMEFT) to estimate the effects of operators up to dimension ten. Our approach relies on weakly coupled UV completions with no presumed large hierarchies between the Wilson coefficients. We introduce a classification based on the number of external legs and an energy-counting parameter. We establish a dual expansion in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>v</mi><mo>/</mo><mi mathvariant="normal">Λ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>E</mi><mo>/</mo><mi mathvariant="normal">Λ</mi></math>. Extending to four-, five-, and six-particle vertices, our framework highlights energy-enhanced operators that dominate high-energy processes at the High Luminosity-Large Hadron Collider. This organization streamlines experimental analyses to only include operators with energetic impact in their analyses and enhances the discoverability of new physics within the SMEFT framework.</p>

Benoît Assi

Energy-enhanced expansion of the standard model effective field theory

We investigate the impact of dimension-8 operators on $\textit{W}$ $\textit{W}$ production at the LHC for the incoming gluon-gluon channel. To this end, we have identified all dimension-8 CP-even operators contributing to the process in question, and computed the corresponding tree-level helicity amplitudes for fully-leptonic decays of the $\textit{W}$ bosons. These are implemented in the program MCFM-RE, which automatically incorporates the effect of a jet-veto to reduce the otherwise overwhelming $$ t\overline{t} $$ background. We find that, unless we break the hierarchy of the effective field theory (EFT), the interference of the dimension-8 operators with the Standard Model is negligible across the considered distributions. This justifies including the square of dimension-6 operators when performing EFT fits with this channel. We then present new constraints on CP-even and CP-odd dimension-6 operators within the EFT regime. Lastly, we postulate a scenario in which the hierarchy of the EFT is broken, justified by the strong constraints on dimension-6 operators from existing on-shell Higgs data. In this scenario, we discuss the constraints that can be reasonably set on CP-even dimension-8 operators with current and future data. We remark that the effect of the jet-veto on the ability to constrain new physics in the $\textit{W}$ $\textit{W}$ channel is quite dramatic and must be properly taken into account.

United Kingdom

Daniel Gillies

Andrea Banfi

Matthew Lim

Dimension-8 operators in $\textit{W}$

<p>We present analytical expressions for the transverse momentum dependent (unintegrated) gluon and quark densities in a proton derived at leading order of QCD running coupling and valid at both small and large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>. The calculations are performed using the Kimber-Martin-Ryskin/Watt-Martin-Ryskin prescription (in both differential and integral formulations) with different treatment of kinematical constraint, which reflects the angular and strong ordering conditions for parton emissions. As an input, the analytical solution of QCD evolution equations for conventional (collinear) parton distributions is applied, where the valence and nonsinglet quark parts obey the Gross-Llewellyn-Smith and Gottfried sum rules, and momentum conservation for the singlet quark and gluon densities is taken into account. Several phenomenological parameters are extracted from the combined fit to precision data on the proton structure function <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> collected by the BCDMS, H1, and ZEUS Collaborations, comprising a total of 933 points from 5 datasets. Comparison with the numerical results obtained by other groups is presented, and the phenomenological application to the inclusive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-jet production at the LHC is given.</p>

JINR

A.V. Kotikov

Russia

A.V. Lipatov

Updating TMD parton densities in a proton within the Kimber-Martin-Ryskin approach

Romania

Victor E. Ambrus

France

Maxim N. Chernodub

Corrigendum to “Acceleration as a circular motion along an imaginary circle: Kubo-Martin-Schwinger condition for accelerating field theories in imaginary-time formalism” [Physics Letters B 855 (2024) 138757/PLB 138795]

We study Higgs boson production via vector boson fusion at the LHC, focusing on the process $\textit{pp}$ → $\textit{H}$ + $\textit{jj}$ and capturing the leading energy-enhanced contributions within the Standard Model Effective Field Theory (SMEFT) up to order 1$\textit{/}$Λ . Employing energy-scaling arguments, we predict the magnitude of each higher-dimensional operator’s contribution. Utilizing the geometric formulation of SMEFT, our analysis incorporates dimension-eight operators not previously considered. We find that the kinematics of vector boson fusion — characterized by two highly forward jets — tend to suppress contributions from higher-dimensional operators, requiring a lower scale Λ for SMEFT effects to become observable. This suggests that the SMEFT remains valid for lower Λ than expected. Combined with the fact that LEP constrains the dimension-six operators with the most considerable impact on vector boson fusion, a regime exists where dimension-eight operators can have significant effects. In many cases, these dimension-eight operators also influence associated production processes like $\textit{pp}$ → $\textit{HV}$($\textit{jj}$), though differences in analysis cuts and kinematics mean this is not always the case. Our findings provide insights that could refine the search for SMEFT signals in collider experiments.

Energy-enhanced dimension eight SMEFT effects in VBF Higgs production

In this paper we develop a semi-standard Young tableau (SSYT) approach to construct a basis of non-factorizable superamplitudes in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 massless supersymmetry. This amplitude basis can be directly translated to a basis for higher dimensional supersymmetric operators, yielding both the number of independent operators and their form. We deal with distinguishable (massless) chiral/vector superfields at first, then generalize the result to the indistinguishable case. Finally, we discuss the advantages and disadvantages of this method compared to the previously studied Hilbert series approach.

Basis for non-factorizable superamplitudes in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supersymmetry

In this paper, we address the reduced beauty cross section [<math><msubsup><mi>σ</mi><mi>red</mi><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math>] and the beauty structure function [<math><msubsup><mi>F</mi><mn>2</mn><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math>], to study the beauty content of a proton. We calculate <math><msubsup><mi>σ</mi><mi>red</mi><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> and <math><msubsup><mi>F</mi><mn>2</mn><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> in the <math><msub><mi>k</mi><mi>t</mi></msub></math>-factorization formalism by using the integral form of the Kimber-Martin-Ryskin and Martin-Ryskin-Watt unintegrated parton distribution function (KMR and MRW-UPDF) with the angular ordering constraint (AOC) and the <math><mi>M</mi><mi>M</mi><mi>H</mi><mi>T</mi><mn>2014</mn></math> <math><mi>P</mi><mi>D</mi><mi>F</mi></math> set as the input. Recently Guiot and van Hameren demonstrated that the upper limit, <math><msub><mi>k</mi><mi>max</mi></msub></math>, of the transverse-momentum integration performed in the <math><msub><mi>k</mi><mi>t</mi></msub></math>-factorization formalism should be almost equal to <math><mi>Q</mi></math>, where <math><mi>Q</mi></math> is the hard scale, otherwise it leads to an overestimation of the proton structure function [<math><msub><mi>F</mi><mn>2</mn></msub><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math>]. In the present work, we show that <math><msub><mi>k</mi><mi>max</mi></msub></math> cannot be equal to <math><mi>Q</mi></math> at low and moderate energy region, and also by considering the gluon and quark contributions to the same perturbative order and a physical gauge for the gluon, i.e., <math><msup><mi>A</mi><mi>μ</mi></msup><msubsup><mi>q</mi><mi>μ</mi><mo>′</mo></msubsup><mo>=</mo><mn>0</mn></math> in the calculation of <math><msubsup><mi>F</mi><mn>2</mn><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> in the <math><msub><mi>k</mi><mi>t</mi></msub></math>-factorization formalism, we do not encounter any overestimation of the theoretical predictions due to different choices of <math><msub><mi>k</mi><mi>max</mi></msub><mo>&gt;</mo><mi>Q</mi></math>. Finally, the resulted <math><msubsup><mi>σ</mi><mi>red</mi><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> and <math><msubsup><mi>F</mi><mn>2</mn><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> are compared to the experimental data and the theoretical predictions. In general, the extracted <math><msubsup><mi>σ</mi><mi>red</mi><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> and <math><msubsup><mi>F</mi><mn>2</mn><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> based on the KMR and MRW approaches are in perfect agreement with the experimental data and theoretical predictions at high energies, but at low and moderate energies, the one developed from the KMR approach has better consistency than that of the MRW approach.

Iran

N. Olanj

Phenomenological investigation of the beauty content of a proton in the framework of <math><msub><mi>k</mi><mi>t</mi></msub></math>-factorization using Kimber-Martin-Ryskin and Martin-Ryskin-Watt unintegrated parton distributions

We discuss the imaginary-time formalism for field theories in thermal equilibrium in uniformly accelerating frames. We show that under a Wick rotation of Minkowski spacetime, the Rindler event horizon shrinks to a point in a two-dimensional subspace tangential to the acceleration direction and the imaginary time. We demonstrate that the accelerated version of the Kubo-Martin-Schwinger (KMS) condition implies an identification of all spacetime points related by integer-multiple rotations in the tangential subspace about this Euclidean Rindler event-horizon point, with the rotational quanta defined by the thermal acceleration, <math><mi>α</mi><mo>=</mo><mi>a</mi><mo>/</mo><mi>T</mi></math>. In the Wick-rotated Rindler hyperbolic coordinates, the KMS relations reduce to standard (anti-)periodic boundary conditions in terms of the imaginary proper time (rapidity) coordinate. Our findings pave the way to study, using first-principle lattice simulations, the Hawking-Unruh radiation in geometries with event horizons, phase transitions in accelerating Early Universe and early stages of quark-gluon plasma created in relativistic heavy-ion collisions.

Victor E. Ambruş

Acceleration as a circular motion along an imaginary circle: Kubo-Martin-Schwinger condition for accelerating field theories in imaginary-time formalism