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.

France

Taro Kimura

Japan

Go Noshita

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

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.

United States

Tyler Grover

Kory Stiffler

Patrick Vecera

Covariant and manifestly projective invariant formulation of Thomas-Whitehead gravity

Experimental High Energy Physics has entered an era of precision measurements. However, measurements of many of the accessible processes assume that the final states’ underlying kinematic distribution is the same as the Standard Model prediction. This assumption introduces an implicit model-dependency into the measurement, rendering the reinterpretation of the experimental analysis complicated without reanalysing the underlying data. We present a novel reweighting method in order to perform reinterpretation of particle physics measurements. It makes use of reweighting the Standard Model templates according to kinematic signal distributions of alternative theoretical models, prior to performing the statistical analysis. The generality of this method allows us to perform statistical inference in the space of theoretical parameters, assuming different kinematic distributions, according to a beyond Standard Model prediction. We implement our method as an extension to the pyhf software and interface it with the EOS software, which allows us to perform flavor physics phenomenology studies. Furthermore, we argue that, beyond the pyhf or HistFactory likelihood specification, only minimal information is necessary to make a likelihood model-agnostic and hence easily reinterpretable. We showcase that publishing such likelihoods is crucial for a full exploitation of experimental results.

Germany

Lorenz Gärtner

Nikolai Hartmann

Lukas Heinrich

Malin Horstmann

Thomas Kuhr

Méril Reboud

Slavomira Stefkova

United Kingdom

Danny Dyk

Constructing model-agnostic likelihoods, a method for the reinterpretation of particle physics results

Thomas-Whitehead (TW) gravity was recently introduced as a projective gauge theory of gravity over a d-dimensional manifold that embeds reparametrization invariance into the action functional for gravitation through the use of the Thomas-Whitehead connection. The projective invariance in this d-dimensional theory enjoys an intimate relationship with the Virasoro coadjoint elements found in string theory as one of the components of the connection, <math><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>a</mi><mi>b</mi></mrow></msub></mrow></math>, is directly related to the coadjoint elements of the Virasoro algebra. TW gravity exploits projective Gauss-Bonnet terms in the action functional which allows the theory to collapse to Einstein’s theory of general relativity in the limit that <math><msub><mi>D</mi><mrow><mi>a</mi><mi>b</mi></mrow></msub></math> vanishes. In this paper we develop the graded extension of TW gravity, super-TW gravity, in the framework of a DeWitt supermanifold. We construct the Lagrangian for super-TW gravity, give a detailed derivation of the classical field equations, and discuss the graded extension of the projective connection as a prelude to a future understanding of TW-supergravity (which has manifest supersymmetry) and its relationship to the super-Virasoro algebra.

Calvin Mera Sánchez

Vincent G. J. Rodgers

Graded extension of Thomas-Whitehead gravity

However, this changes the interpretation of our results but slightly, because the exact probability distribution of the metric is only important for the choice and interpretation of the stopping criterium of the clustering.

Jason Aebischer

Kilian Lieret

Erratum to: Clustering of   <math> <mover> <mi>B</mi> <mo>¯</mo> </mover> <mo>→</mo> <msup> <mi>D</mi> <mfenced> <mo>∗</mo> </mfenced> </msup> <msup> <mi>τ</mi> <mo>−</mo> </msup> <msub> <mover> <mi>v</mi> <mo>¯</mo> </mover> <mi>τ</mi> </msub> </math>  $$ \overline{B}\to {D}^{\left(\ast \right)}{\tau}^{-}{\overline{v}}_{\tau } $$  kinematic distributions with ClusterKinG

Thomas-Whitehead (TW) gravity is a projectively invariant model of gravity over a d-dimensional manifold that is intimately related to string theory through reparametrization invariance. Unparametrized geodesics are the ubiquitous structure that ties together string theory and higher dimensional gravitation. This is realized through the projective geometry of Tracy Thomas. The projective connection, due to Thomas and later Whitehead, admits a component that in one dimension is in one-to-one correspondence with the coadjoint elements of the Virasoro algebra. This component is called the diffeomorphism field <math><msub><mi>D</mi><mrow><mi>a</mi><mi>b</mi></mrow></msub></math> in the literature. It also has been shown that in four dimensions, the TW action collapses to the Einstein-Hilbert action with cosmological constant when <math><msub><mi>D</mi><mrow><mi>a</mi><mi>b</mi></mrow></msub></math> is proportional to the Einstein metric. These previous results have been restricted to either particular metrics, such as the Polyakov 2D metric, or were restricted to coordinates that were volume preserving. In this paper, we review TW gravity and derive the gauge invariant TW action that is explicitly projectively invariant and general coordinate invariant. We derive the covariant field equations for the TW action and show how fermionic fields couple to the gauge invariant theory. The independent fields are the metric tensor <math><msub><mi>g</mi><mrow><mi>a</mi><mi>b</mi></mrow></msub></math>, the fundamental projective invariant <math><msub><msup><mi>Π</mi><mi>a</mi></msup><mrow><mi>b</mi><mi>c</mi></mrow></msub></math>, and the diffeomorphism field <math><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>a</mi><mi>b</mi></mrow></msub></mrow></math>.

Samuel Brensinger

Kenneth Heitritter

General structure of Thomas-Whitehead gravity

Motivated by the calculation of observables in the decays <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msub><mi>Λ</mi><mi>c</mi></msub><mrow><mo>(</mo><msup><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>±</mo></msup><mo>)</mo></mrow><mo>ℓ</mo><mover><mi>ν</mi><mo>¯</mo></mover></math>, we present a calculation of form factors in the quark model. Our scheme combines a spectroscopic model with the internal wave functions and the Bakamjian-Thomas (BT) relativistic formalism to get the wave functions in motion. In the heavy quark limit, the current matrix elements provide the Isgur-Wise (IW) function. This limit is covariant, satisfies a large set of sum rules, and has been successfully applied to mesons. On the other hand, for baryons, we meet difficulties using standard spectroscopic models. This leads us to propose a phenomenological model, a Q-pointlike-diquark model, nonrelativistic, with harmonic oscillator forces, giving both a reasonable low-lying spectrum and the expected slope of the IW function. To begin, we extract this slope from lattice QCD data and find it to be around <math><msubsup><mi>ρ</mi><mi>Λ</mi><mn>2</mn></msubsup><mo>∼</mo><mn>2</mn></math>, that we use as a guideline. We are not able to reproduce the right <math><msubsup><mi>ρ</mi><mi>Λ</mi><mn>2</mn></msubsup></math> using certain typical standard <math><mrow><mtext>linear</mtext><mo>+</mo><mtext>Coulomb</mtext></mrow></math> potential models, both with three quarks <math><mi>Q</mi><mi>q</mi><mi>q</mi></math> or in a Q-pointlike-diquark picture. These difficulties seem to derive from the high sensitivity of <math><msubsup><mi>ρ</mi><mi>Λ</mi><mn>2</mn></msubsup></math> to the structure of the light quark subsystem in a relativistic scheme. Finally, we present our model, and fixing its parameters to yield the correct spectrum and <math><msubsup><mi>ρ</mi><mi>Λ</mi><mn>2</mn></msubsup><mo>∼</mo><mn>2</mn></math>, we apply it to the calculation of observables. By studying Bjorken sum rule, we show that the inelastic IW function is large, and therefore, the transitions <math><msub><mi>Λ</mi><mi>b</mi></msub><mo>→</mo><msub><mi>Λ</mi><mi>c</mi></msub><mrow><mo>(</mo><msup><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>−</mo></msup><mo>,</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>−</mo></msup><mo>)</mo></mrow><mo>ℓ</mo><mover><mi>ν</mi><mo>¯</mo></mover></math> could be studied at LHCb. Interestingly, some observables in the <math><mi>τ</mi></math> case present zeroes for specific values of <math><msup><mi>q</mi><mn>2</mn></msup></math> that could be tests of the Standard Model.

D. Bečirević

A. Le Yaouanc

V. Morénas

L. Oliver

Heavy baryon wave functions, Bakamjian-Thomas approach to form factors, and observables in <math><mrow><msub><mrow><mi>Λ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>→</mo><msub><mrow><mi>Λ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><msup><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>±</mo></mrow></msup><mo>)</mo><mo>ℓ</mo><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math> transitions

New Physics can manifest itself in kinematic distributions of particle decays. The parameter space defining the shape of such distributions can be large which is chalenging for both theoretical and experimental studies. Using clustering algorithms, the parameter space can however be dissected into subsets (clusters) which correspond to similar kinematic distributions. Clusters can then be represented by benchmark points, which allow for less involved studies and a concise presentation of the results. We demonstrate this concept using the Python package ClusterKinG, an easy to use framework for the clustering of distributions that particularly aims to make these techniques more accessible in a High Energy Physics context. As an example we consider $$ \overline{B}\to {D}^{\left(\ast \right)}{\tau}^{-}{\overline{\nu}}_{\tau } $$ distributions and discuss various clustering methods and possible implications for future experimental analyses.

Clustering of

We compute the elliptic genus of the D1/D7 brane system in flat space, finding a non-trivial dependence on the number of D7 branes, and provide an F-theory interpretation of the result. We show that the JK-residues contributing to the elliptic genus are in one-to-one correspondence with coloured plane partitions and that the elliptic genus can be written as a chiral correlator of vertex operators on the torus. We also study the quantum mechanical system describing D0/D6 bound states on a circle, which leads to a plethystic exponential formula that can be connected to the M-theory graviton index on a multi-Taub-NUT background. The formula is a conjectural expression for higher-rank equivariant K-theoretic Donaldson-Thomas invariants on ℂ 3.