It is well-known that the back-to-back (correlation) limit of inclusive quark-antiquark dijet production in unpolarized high energy electron-proton collisions can probe the Weizsäcker-Williams (WW) gluon transverse momentum-dependent distribution (TMD) at small $\textit{x}$ [1, 2]. In this paper, we consider a helicity-dependent version of the same process: we study the double-spin asymmetry for inclusive quark-antiquark dijet production in longitudinally polarized electron-proton scattering at high energies. We show that in the back-to-back limit this process probes the WW gluon $\textit{helicity}$ TMD. Furthermore, we derive the small-$\textit{x}$ evolution equation for the operator related to the WW gluon helicity distribution. We find that in the double-logarithmic approximation and in the large-$\textit{N}$ limit, the small-$\textit{x}$ asymptotics of the WW gluon helicity distribution is governed by exactly the same evolution equation as that for the $\textit{dipole}$ gluon helicity distribution. The longitudinal double-spin asymmetry for inclusive dijet production in the longitudinally polarized electron-proton collisions can thus test the small-$\textit{x}$ helicity evolution equations and facilitate constraining the initial conditions for phenomenology based on these equations.

United States

Yuri Kovchegov

Ming Li

Weizsäcker-Williams gluon helicity distribution and inclusive dijet production in longitudinally polarized electron-proton collisions

<p>Understanding the internal structure of nucleons and nuclei has been a topic of enduring interest in high-energy physics. Gravitational form factors (GFFs) provide an important portal for us to probe the energy-momentum/mass distribution of nucleons and nuclei. This paper presents the study of the photon and gluon momentum GFFs, also known as the A-GFFs, of relativistic hadrons using the Weizsäcker-Williams method. To begin, we express the photon A-GFFs in terms of charge form factors and discuss the corresponding photon radius. Furthermore, an integral relation between the gluon A-GFF and the Laplacian of dipole scattering amplitude is derived in the small-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> framework, and it allows us to unravel the gluon energy momentum distribution inside hadrons through measurements at the upcoming Electron-Ion Collider. In addition, we generalize the analysis to study the A-GFF of nuclei and propose employing the nuclear gluon mean square radius, together with the charge distribution, to constrain the neutron distribution for large nuclei. This work provides an interesting perspective into the fundamental structure of high-energy hadrons.</p>

Hong Kong

China

Yoshikazu Hagiwara

Finland

Xuan-Bo Tong

Bo-Wen Xiao

Understanding gravitational form factors with the Weizsäcker-Williams method

<p>The simplified connection between Standard Model (SM) particles and light dark matter (LDM) can be introduced via spin-0 and spin-1 lepton-specific mediators. Moreover, in a mediator mass range from sub-MeV to sub-GeV, fixed-target facilities such as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>NA</mi><mrow><mn>64</mn><mi>e</mi></mrow></mrow></math>, LDMX, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>NA</mi><mrow><mn>64</mn><mi>μ</mi></mrow></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="normal">M</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math> can potentially probe such particles of the hidden sector via missing energy signatures that are described by the bremsstrahlunglike process involving leptons. We compare the Weizsaker-Williams (WW) approximation and the exact tree-level (ETL) approach for the bremsstrahlunglike mediator production cross section by choosing various parameters of the fixed-target experiments. We show that the relative difference between the total cross sections calculated in the WW and ETL approximation varies from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo><mo>%</mo></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo><mo>%</mo></math> for a muon mode and from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mo>−</mo><mn>20</mn><mo stretchy="false">)</mo><mo>%</mo></math> to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>80</mn><mo stretchy="false">)</mo><mo>%</mo></math> for an electron mode. We argue that the main difference between two approaches for electron beam mode arises from peak forward region of the cross section. We also discuss the impact of parametrization of nuclear and atomic elastic form factors on the total cross section. In particular, we show that the employing different form-factor parametrization can lead to a uncertainty in the cross section at the level of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>≲</mo><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>10</mn><mo stretchy="false">)</mo><mo>%</mo></math>. That study may be helpful for the lepton fixed-target experiments that examine the bremsstrahlunglike production of the DM mediators.</p>

Russia

I.V. Voronchikhin

D.V. Kirpichnikov

Implication of the Weizsacker-Williams approximation for the dark matter mediator production

We perform the first convergent Bayesian global fits of 4D Composite Higgs Models with partially-composite third generation quarks and leptons based on the minimal SO(5) → SO(4) symmetry breaking pattern. We consider two models with the τ lepton and its associated neutrino in different representations of SO(5). Fitting each model with a wide array of experimental constraints allows us to analyse the Bayesian evidence and currently-observed fine-tuning of each model by calculating the Kullback-Leibler divergence between their respective priors and posteriors. Notably both models are found to be capable of satisfying all constraints simultaneously at the 3σ level at scales of &lt; 5 TeV. From a Bayesian viewpoint of naturalness the model with leptons in the 14 and 10 representations is preferred over those in the 5 representation due to its lower fine-tuning. Finally, we consider the experimental signatures for the preferred parameters in these models, including lepton partner decay signatures and gluon-fusion produced Higgs signal strengths, and discuss their potential phenomenology at future high-luminosity LHC runs.

United Kingdom

Ethan Carragher

Australia

Kenn Goh

Wei Su

Martin White

Anthony Williams

Extending global fits of 4D Composite Higgs Models with partially composite leptons

SuperWIMPs are extremely weakly interacting massive particles that inherit their relic abundance from late decays of frozen-out parent particles. Within supersymmetric models, gravitinos and axinos represent two of the most well motivated superWIMPs. In this paper we revisit constraints on these scenarios from a variety of cosmological observations that probe their production mechanisms as well as the superWIMP kinematic properties in the early Universe. We consider in particular observables of Big Bang Nucleosynthesis and the Cosmic Microwave Background (spectral distortion and anisotropies), which limit the fractional energy injection from the late decays, as well as warm and mixed dark matter constraints derived from the Lyman- $$\alpha $$  <math> <mi>α</mi> </math>   forest and other small-scale structure observables. We discuss complementary constraints from collider experiments, and argue that cosmological considerations rule out a significant part of the gravitino and the axino superWIMP parameter space.

Meera Deshpande

Jan Hamann

Dipan Sengupta

Yvonne Wong

Revisiting cosmological constraints on supersymmetric SuperWIMPs

In addition to vector (<math><mrow><mi>V</mi></mrow></math>) type new particles extensively discussed previously, both <math><mi>C</mi><mi>P</mi></math>-even (<math><mi>S</mi></math>) and <math><mi>C</mi><mi>P</mi></math>-odd (<math><mi>P</mi></math>) spin-0 dark matter (DM) mediators can couple to muons and be produced in the bremsstrahlung reaction <math><mrow><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>+</mo><mi>N</mi><mo>→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>+</mo><mi>N</mi><mo>+</mo><mi>S</mi><mo>(</mo><mi>P</mi><mo>)</mo></mrow></math>. Their possible subsequent invisible decay into a pair of Dirac DM particles, <math><mi>S</mi><mo>(</mo><mi>P</mi><mo>)</mo><mo>→</mo><mi>χ</mi><mover><mi>χ</mi><mo>¯</mo></mover></math>, can be detected in fixed target experiments through missing energy signature. In this paper, we focus on the case of experiments using high-energy muon beams. For this reason, we derive the differential cross sections involved using the phase space Weiszäcker-Williams approximation and compare them to the exact-tree-level calculations. The formalism derived can be applied in various experiments that could observe muon-spin-0 DM interactions. This can happen in present and future proton beam-dump experiments such as NA62, SHIP, HIKE, and SHADOWS; in muon fixed target experiments as <math><mrow><mi>NA</mi><mrow><mn>64</mn><mi>μ</mi></mrow></mrow></math>, MUonE and M3; in neutrino experiments using powerful proton beams such as DUNE. In particular, we focus on the <math><mrow><mi>NA</mi><mrow><mn>64</mn><mi>μ</mi></mrow></mrow></math> experiment case, which uses a 160 GeV muon beam at the CERN Super Proton Synchrotron accelerator. We compute the derived cross sections, the resulting signal yields and we discuss the experiment projected sensitivity to probe the relic DM parameter space and the <math><mo>(</mo><mi>g</mi><mo>−</mo><mn>2</mn><msub><mo>)</mo><mi>μ</mi></msub></math> anomaly favored region considering <math><msup><mn>10</mn><mn>11</mn></msup></math> and <math><msup><mn>10</mn><mn>13</mn></msup></math> muons on target.

Switzerland

H. Sieber

D. V. Kirpichnikov

I. V. Voronchikhin

P. Crivelli

S. N. Gninenko

M. M. Kirsanov

JINR

N. V. Krasnikov

Spain

L. Molina-Bueno

S. K. Sekatskii

Probing hidden sectors with a muon beam: Implication of spin-0 dark matter mediators for the muon (<math><mrow><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math>) anomaly and the validity of the Weiszäcker-Williams approach

In [1], we performed the first complete computation of the back-to-back inclusive dijet cross-section in Deeply Inelastic Scattering (DIS) at small x Bj to next-to-leading order (NLO) in the Color Glass Condensate effective field theory (CGC EFT). We demonstrate here that for dijets with relative transverse momentum P ⊥ and transverse momentum imbalance q ⊥, to leading power in q ⊥/P ⊥, the cross-section for longitudinally polarized photons can be fully factorized into the product of a perturbative impact factor and the non-perturbative Weizsäcker-Williams (WW) transverse momentum dependent (TMD) gluon distribution to NLO accuracy. The impact factor can further be expressed as the product of a universal soft factor which resums Sudakov double and single logs in P ⊥/q ⊥ and a coefficient function given by a remarkably compact analytic expression. We show that in the CGC EFT the WW TMD satisfies a kinematically constrained JIMWLK renormalization group evolution in rapidity. This factorization formula is valid to all orders in Q  s /q ⊥ for q ⊥, Q  s  ≪ P ⊥, where Q  s  is the semi-hard saturation scale that grows with rapidity.

France

Paul Caucal

Farid Salazar

Björn Schenke

Poland

Tomasz Stebel

Raju Venugopalan

Back-to-back inclusive dijets in DIS at small x: gluon Weizsäcker-Williams distribution at NLO

The <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production originating from elastic and inelastic photoproduction processes in <math><mrow><mi>p</mi><mtext>−</mtext><mi>p</mi></mrow></math> collisions at LHC energies is investigated, where the fragmentation processes are involved. An exact treatment is performed, which adopts the Martin-Ryskin method to weight the contribution from different channels, and can return to Weizsäcker-Williams approximation (WWA) when <math><msup><mi>Q</mi><mn>2</mn></msup><mo>→</mo><mn>0</mn></math>. The relevant kinematical relations are also achieved. We present a comprehensive analysis for the feature of WWA by comparing with the exact treatment. The results are expressed in <math><msup><mi>Q</mi><mn>2</mn></msup></math>, <math><mi>y</mi></math>, <math><mi>z</mi></math>, <math><msub><mi>p</mi><mi>T</mi></msub></math>, and <math><msub><mi>y</mi><mi>r</mi></msub></math> (rapidity) distributions, and the total cross sections are also estimated. The numerical results indicate that the incoherent-photon emission can provide a meaningful contribution to elastic photoproduction, and starts to play a very important role in the inelastic processes. The photoproduction and fragmentation processes can improve the contribution of <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production in <math><mrow><mi>p</mi><mtext>−</mtext><mi>p</mi></mrow></math> collisions at LHC energies. Moreover, the WWA is only effective in very restricted domains, and the exact treatment is needed to deal accurately with the <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> photoproduction, which can naturally avoid double counting and WWA errors.

Zhi-Lei Ma

Zhun Lu

Jia-Qing Zhu

Li Zhang

Elastic and inelastic <math><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></math> photoproduction in <math><mrow><mi>p</mi><mtext>−</mtext><mi>p</mi></mrow></math> collisions at LHC energies: Features of the Weizsäcker-Williams approximation

Current interpretations of the LHC results on two Higgs doublet models (2HDM) underestimate the sensitivity due to neglecting higher order effects. In this work, we revisit the impact of these effects using the current cross-section times branching ratio limits of the  $$A\rightarrow hZ, H \rightarrow VV$$  <math> <mrow> <mi>A</mi> <mo>→</mo> <mi>h</mi> <mi>Z</mi> <mo>,</mo> <mi>H</mi> <mo>→</mo> <mi>V</mi> <mi>V</mi> </mrow> </math>   and  $$H\rightarrow hh$$  <math> <mrow> <mi>H</mi> <mo>→</mo> <mi>h</mi> <mi>h</mi> </mrow> </math>   channels. With a degenerate heavy Higgs mass  $$m_\varPhi $$  <math> <msub> <mi>m</mi> <mi>Φ</mi> </msub> </math>  , we find that the LHC searches gain sensitivity to the small  $$\tan \beta $$  <math> <mrow> <mo>tan</mo> <mi>β</mi> </mrow> </math>   region after including loop corrections, even close to  $$\cos (\beta -\alpha )=0$$  <math> <mrow> <mo>cos</mo> <mo>(</mo> <mi>β</mi> <mo>-</mo> <mi>α</mi> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </math>   which is not reachable at tree level for all types of 2HDM. For a benchmark point with  $$m_\varPhi =300$$  <math> <mrow> <msub> <mi>m</mi> <mi>Φ</mi> </msub> <mo>=</mo> <mn>300</mn> </mrow> </math>   GeV,  $$\tan \beta &lt;1.8(1.2)$$  <math> <mrow> <mo>tan</mo> <mi>β</mi> <mo>&lt;</mo> <mn>1.8</mn> <mo>(</mo> <mn>1.2</mn> <mo>)</mo> </mrow> </math>   can be probed for the Type-I(II) 2HDM model for  $$\cos (\beta -\alpha )=0$$  <math> <mrow> <mo>cos</mo> <mo>(</mo> <mi>β</mi> <mo>-</mo> <mi>α</mi> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </math>  . When the deviation from  $$\cos (\beta -\alpha )=0$$  <math> <mrow> <mo>cos</mo> <mo>(</mo> <mi>β</mi> <mo>-</mo> <mi>α</mi> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </math>   is larger, the region for which current searches have exclusion potential becomes larger.

Canada

Yongcheng Wu

Exploring the low  $$\tan \beta $$  <math> <mrow> <mo>tan</mo> <mi>β</mi> </mrow> </math>   region of two Higgs doublet models at the LHC

The Scotogenic Model is one of the most minimal models to account for both neutrino masses and dark matter (DM). In this model, neutrino masses are generated at the one-loop level, and in principle, both the lightest fermion singlet and the lightest neutral component of the scalar doublet can be viable DM candidates. However, the correct DM relic abundance can only be obtained in somewhat small regions of the parameter space, as there are strong constraints stemming from lepton flavour violation, neutrino masses, electroweak precision tests and direct detection. For the case of scalar DM, a sufficiently large lepton-number-violating coupling is required, whereas for fermionic DM, coannihilations are typically necessary. In this work, we study how the new scalar singlet modifies the phenomenology of the Scotogenic Model, particularly in the case of scalar DM. We find that the new singlet modifies both the phenomenology of neutrino masses and scalar DM, and opens up a large portion of the parameter space of the original model.