We present a model of the dark sector involving Dirac fermion dark matter, with axial coupling to a dark photon which provides a portal to Standard Model particles. In the nonrelativistic limit, this implies that the dominant effective operator relevant to direct detection is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">O</mi><mn>8</mn></msub></math>. The resulting event rate for direct detection is suppressed by either the dark matter velocity or the momentum transfer. In this scenario there are much wider regions of the dark parameter space that are consistent with all of the existing constraints associated with thermal relic density, direct detection, and collider searches.

Australia

X.G. Wang

A.W. Thomas

Relaxed constraints for dark matter with axial coupling to a dark photon

We develop a contour integral formalism for computing the K-theoretic equivariant 3-vertex. Within the Jeffrey-Kirwan (JK) residue framework, we show that, by an appropriate choice of the reference vector, both the equivariant Donaldson-Thomas (DT) and Pandharipande-Thomas (PT) 3-vertices can be extracted from the same integrand. We analyze three distinct limits of the PT 3-vertex, recovering the unrefined topological vertex, the refined topological vertex, and the Macdonald refined topological vertex. Higher-rank extensions of PT counting and the DT/PT correspondence are also explored. From a quantum algebraic perspective, we construct an operator version of the equivariant PT 3-vertex and term it the Pandharipande-Thomas $\textit{qq}$-character. We then discuss its connection with the quantum toroidal $${\mathfrak{g}\mathfrak{l}}_{1}$$ .

France

Taro Kimura

Japan

Go Noshita

Gauge origami and quiver W-algebras. Part IV. Pandharipande-Thomas $\textit{qq}$-characters

We perform a comprehensive global QCD analysis of spin-dependent parton distribution functions (PDFs), combining all available data on inclusive and semi-inclusive deep-inelastic scattering (DIS), as well as inclusive weak boson and jet production in polarized <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi></math> collisions, simultaneously extracting spin-averaged PDFs and fragmentation functions. Including recent Jefferson Lab DIS data at high <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>, together with subleading power corrections to the leading-twist framework, allows us to verify the stability of the PDFs for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>W</mi><mn>2</mn></msup><mo>≥</mo><mn>4</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></math> and quantify the uncertainties on the spin structure functions more reliably. We explore the use of new lattice QCD data on gluonic pseudo-Ioffe time distributions, which, together with jet production and high-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> DIS data, improve the constraints on the polarized gluon PDF. The expanded kinematic reach afforded by the data into the high-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> region allows us to refine the bounds on higher-twist contributions to the spin structure functions, and test the validity of the Bjorken sum rule.

United States

C. Cocuzza

N.T. Hunt-Smith

W. Melnitchouk

N. Sato

Global QCD analysis of spin PDFs in the proton with high-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> and lattice constraints

We revisit the exclusion constraints on the parameters of a narrow dark photon set by direct experimental searches. We investigate how a dark photon with a larger decay width impacts these limits, in particular, in the case where the dark photon also decays into light dark matter. As an example, taking the upper limits on the mixing parameter, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ε</mi></math>, reported by the CMS Collaboration, we find that they could be significantly relaxed. Indeed, even a very modest coupling of the dark photon to dark matter can lead to an increase in the bound on the mixing parameter by an order of magnitude.

J.R. Felix

Relaxing constraints on a broad dark photon

The study of the spectrum of excited states of the nucleon is vital to our understanding of how QCD is realized in the baryon spectrum. Using a simultaneous analysis of the pion nucleon scattering data up to 2 GeV as well as the results of lattice QCD calculations, we obtain new insight into the nature of the Roper resonance as well as the excited states around 1.9 GeV.

S. Owa

D.B. Leinweber

Nucleon resonance structure up to 2 GeV and the nature of the Roper resonance

In the context of future electroweak precision measurements at the Future Circular Lepton Collider (FCC-ee), we consider recent proposals aimed at finding signatures of physics beyond the Standard Model. In particular, we focus on recent novel suggestions for very precise direct measurements of <math altimg='si1.svg'><msub><mrow><mi>&#945;</mi></mrow><mrow><mi mathvariant='normal'>em</mi></mrow></msub><mo stretchy='false'>(</mo><msubsup><mrow><mi>M</mi></mrow><mrow><mi>Z</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo stretchy='false'>)</mo></math>. It is shown that at a level of precision of order <math altimg='si2.svg'><msup><mrow><mn>10</mn></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>5</mn></mrow></msup></math>, the effects of a dark photon may be very significant.

Searching for the dark photon at the Future Circular Lepton Collider

We further develop the BPS/CFT correspondence between quiver W-algebras/ -characters and partition functions of gauge origami. We introduce -characters associated with multi-dimensional partitions with nontrivial boundary conditions which we call Donaldson-Thomas (DT) -characters. They are operator versions of the equivariant DT vertices of toric Calabi-Yau three and four-folds. Moreover, we revisit the construction of the D8 -characters with no boundary conditions and give a quantum algebraic derivation of the sign rules of the magnificent four partition function. We also show that under the proper sign rules, the D6 and D8 -characters with no boundary conditions all commute with each other and discuss its physical interpretation.

Gauge origami and quiver W-algebras. Part III. Donaldson-Thomas

We perform the first global QCD analysis of electron-nucleon deep-inelastic scattering and related high-energy data including the beyond the Standard Model <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> gauge boson, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math>. Contrary to the dark photon case, we find no improvement in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>χ</mi><mn>2</mn></msup></math> relative to the baseline result. The finding allows us to place exclusion limits on the coupling constant of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> with mass in the range <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><msup><mi>Z</mi><mo>′</mo></msup></msub><mo>=</mo><mn>2</mn></math> to 160 GeV.

Constraints on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mi>B</mi><mo>−</mo><mi>L</mi></mrow></msub></math> model from global QCD analysis

We analyze the angular momentum balance for a particle undergoing Thomas precession. The relationships among relativistic torque, the center of mass, and the center of inertia for a spinning particle are clarified. We show that spin precession is accompanied by orbital angular momentum precession, and present examples of the resulting out-of-plane motion.

Canada

Andrzej Czarnecki

Andrei Zelnikov

Thomas precession, relativistic torque, and non-planar orbits

Thomas-Whitehead (TW) gravity is a recently formulated projectively invariant extension of Einstein-Hilbert gravity. Projective geometry was used long ago by Thomas et al. to succinctly package equivalent paths encoded by the geodesic equation. Projective invariance in gravity has further origins in string theory through a geometric action constructed from the method of coadjoint orbits using the Virasoro algebra. A projectively invariant connection arises from this construction, a part of which is known as the diffeomorphism field. TW gravity exploits projective Gauss-Bonnet terms in the action functional to endow the diffeomorphism field with dynamics, while allowing the theory to collapse to general relativity in the limit that the diffeomorphism field vanishes and the connection becomes Levi-Civita. In the original formulation of TW gravity, the diffeomorphism field is projectively invariant but not tensorial and the connection is projectively invariant but not affine. In this paper we reformulate TW gravity in terms of projectively invariant tensor fields and a projectively invariant covariant derivative, derive field equations respecting these symmetries, and show that the field equations obtained are classically equivalent across formulations. This provides a “Rosetta Stone” between this newly constructed covariant and projective invariant formulation of TW gravity and the original formulation that was manifestly projective invariant, but not covariant.