<p>The Lie algebra of symmetries generated by the left-moving current <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>j</mi><mo>=</mo><msub><mrow><mo>∂</mo></mrow><mrow><mo>−</mo></mrow></msub><mi>ϕ</mi></mrow></math> in the two-dimensional (2D) single scalar conformal field theory is infinite dimensional, exhibiting mutually commuting subalgebras. The infinite-dimensional mutually commuting subalgebras define integrable deformations of the 2D single scalar conformal field theory that preserve the Poisson bracket structure. We study these mutually commuting subalgebras, finding general properties that the generators of such a subalgebra must satisfy. Along the way, we derive constraints on integrable equations of the Korteweg–de Vries type. We also confirm that the recently found <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">[</mo><mi>j</mi><mo stretchy="false">]</mo><mo>=</mo><mn>0</mn><mo>,</mo><mo>−</mo><mn>1</mn><mo>,</mo><mo>−</mo><mn>2</mn></math> mutually commuting subalgebras are infinite dimensional.</p>

Taiwan

Lukas W. Lindwasser

Constraining all possible Korteweg–de Vries type hierarchies

A perturbative scheme is applied to calculate corrections to the leading, exponentially small (beyond-all-orders) amplitude of the “trailing” wave asymptotics of weakly localized solitons. The model considered is a Korteweg–de Vries equation modified by a fifth order derivative term, <math><msup><mi>ε</mi><mn>2</mn></msup><msubsup><mo>∂</mo><mi>x</mi><mn>5</mn></msubsup></math> with <math><mi>ε</mi><mo>≪</mo><mn>1</mn></math> (fKdV). The leading order corrections to the tail amplitude are calculated up to <math><mi>O</mi><mo>(</mo><msup><mi>ε</mi><mn>5</mn></msup><mo>)</mo></math>. An arbitrary precision numerical code is implemented to solve the fKdV equation and to check the perturbative results. Excellent agreement is found between the numerical and analytical results. Our work also clarifies the origin of a long-standing disagreement between the <math><mi>O</mi><mo>(</mo><msup><mi>ε</mi><mn>2</mn></msup><mo>)</mo></math> perturbative result of Grimshaw and Joshi [SIAM J. Appl. Math. 55, 124 (1995)] and the numerical results of Boyd [Comput. Phys. 9, 324 (1995)].

Hungary

Gyula Fodor

France

Péter Forgács

Muneeb Mushtaq

Higher order corrections to beyond-all-order effects in a fifth order Korteweg–de Vries equation

Two-dimensional conformal field theories with just Virasoro symmetry are endowed with integrable structure. We review how to construct the integrable charges in a two-dimensional conformal field theory and how to relate them to the charges of quantum sinh-Gordon theory when <math><mi>c</mi><mo>≥</mo><mn>25</mn></math>. We then explicitly calculate the single charge characters in the large <math><mi>c</mi></math> limit for all charges and thereby reveal how their degeneracies grow within one module. This, in particular, allows us to approximate the characters in the limit of small chemical potential, which source the respective charges. The latter gives us insights into possible transformation properties of the characters. We also comment on the full generalized Gibbs ensemble and approximations to pure states.

Germany

Enrico M. Brehm

India

Diptarka Das

Korteweg–de Vries characters in large central charge CFTs

The thermodynamic properties of the Bañados-Teitelboim-Zanelli black hole endowed with Korteweg–de Vries (KdV)-type boundary conditions are reconsidered. This family of boundary conditions is labeled by a non-negative integer <math><mi>n</mi></math>, and gives rise to a dual theory which possesses anisotropic Lifshitz scaling invariance with dynamical exponent <math><mi>z</mi><mo>=</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></math>. We show that from the scale invariance of the action for stationary and circularly symmetric spacetimes, an anisotropic version of the Smarr relation arises. Finally, we analyze the global and local thermal stability of the system and we found that the specific heat of the black hole is positive for all possible values of <math><mi>z</mi></math>, and at the self-dual temperature <math><msub><mi>T</mi><mi>s</mi></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>π</mi></mrow></mfrac><mo>(</mo><mfrac><mn>1</mn><mi>z</mi></mfrac><msup><mo>)</mo><mfrac><mi>z</mi><mrow><mi>z</mi><mo>+</mo><mn>1</mn></mrow></mfrac></msup></math>, there is a Hawking-Page phase transition between the BTZ black hole and thermal <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> spacetime.

Chile

Greece

Cristián Erices

Miguel Riquelme

Pablo Rodríguez

BTZ black hole with Korteweg–de Vries-type boundary conditions: Thermodynamics revisited

In thermal dark matter models, allowing the dark matter candidate to coannihilate with another particle can considerably loosen the relic density constraints on the dark matter mass. In particular, introducing a single strongly interacting coannihilation partner in a dark matter model can bring the upper bound on the dark sector energy scale from a few TeV up to about 10 TeV. While these energies are outside the LHC reach, a large part of the parameter space for such coannihilating models can be explored by future hadron colliders. In this context, it is essential to determine whether the current bounds on dark matter simplified models also hold in non-minimal scenarios. In this paper, we study extended models that include multiple coannihilation partners. We show that the relic density bounds on the dark matter mass in these scenarios are stronger than for the minimal models in most of the parameter space and that weakening these bounds requires sizable interactions between the different species of coannihilation partners. Furthermore, we discuss how these new interactions as well as the additional particles in the models can lead to stronger collider bounds, notably in jets plus missing transverse energy searches. This study serves as a vital ingredient towards the determination of the highest possible energy scale for thermal dark matter models.

Netherlands

Sonia Hedri

Maikel Vries

Cornering colored coannihilation

Solitary waves propagation of baryonic density perturbations, ruled by the Korteweg–de Vries equation in a mean-field quark–gluon plasma model, are investigated from the point of view of the theory of information. A recently proposed continuous logarithmic measure of information, called configurational entropy, is used to derive the soliton width, defining the pulse, for which the informational content of the soliton spatial profile is more compressed, in the Shannon's sense.

Brazil

A. Goncalves da Silva

Roldão da Rocha

Information-entropic analysis of Korteweg–de Vries solitons in the quark–gluon plasma

We perform a general study of the relic density and LHC constraints on simplified models where the dark matter coannihilates with a strongly interacting particle X. In these models, the dark matter depletion is driven by the self-annihilation of X to pairs of quarks and gluons through the strong interaction. The phenomenology of these scenarios therefore only depends on the dark matter mass and the mass splitting between dark matter and X as well as the quantum numbers of X. In this paper, we consider simplified models where X can be either a scalar, a fermion or a vector, as well as a color triplet, sextet or octet. We compute the dark matter relic density constraints taking into account Sommerfeld corrections and bound state formation. Furthermore, we examine the restrictions from thermal equilibrium, the lifetime of X and the current and future LHC bounds on X pair production. All constraints are comprehensively presented in the mass splitting versus dark matter mass plane. While the relic density constraints can lead to upper bounds on the dark matter mass ranging from 2 TeV to more than 10 TeV across our models, the prospective LHC bounds range from 800 to 1500 GeV. A full coverage of the strongly coannihilating dark matter parameter space would therefore require hadron colliders with significantly higher center-of-mass energies.

Anna Kaminska

Jose Zurita

Simplified phenomenology for colored dark sectors

Simplified models of the dark matter (co)annihilation mechanism predict striking new collider signatures untested by current searches. These models, which were codified in the coannihilation codex, provide the basis for a dark matter (DM) discovery program at the Large Hadron Collider (LHC) driven by the measured DM relic density. In this work, we study an exemplary model featuring s -channel DM coannihilation through a scalar diquark mediator as a representative case study of scenarios with strongly interacting coannihilation partners. We discuss the full phenomenology of the model, ranging from low energy flavor constraints, vacuum stability requirements, and precision Higgs effects to direct detection and indirect detection prospects. Moreover, motivated by the relic density calculation, we find significant portions of parameter space are compatible with current collider constraints and can be probed by future searches, including a proposed analysis for the novel signature of a dijet resonance accompanied by missing transverse energy (MET). Our results show that the 13 TeV LHC with 100 fb −1 luminosity should be sensitive to mediators as heavy as 1 TeV and dark matter in the 400-500 GeV range. The combination of searches for single and paired dijet peaks, non-resonant jets + MET excesses, and our novel resonant dijet + MET signature have strong coverage of the motivated relic density region, reflecting the tight connections between particles determining the dark matter abundance and their experimental signatures at the LHC.

Malte Buschmann

Jia Liu

Xiao-Ping Wang

Felix Yu

José Zurita

Hunting for dark matter coannihilation by mixing dijet resonances and missing transverse energy

We present a general classification of simplified models that lead to dark matter (DM) coannihilation processes of the form DM + X → SM 1 + SM 2 , where X is a coannihilation partner for the DM particle and SM 1 , SM 2 are Standard Model fields. Our classification also encompasses regular DM pair annihilation scenarios if DM and X are identical. Each coannhilation scenario motivates the introduction of a mediating particle M that can either belong to the Standard Model or be a new field, whereby the resulting interactions between the dark sector and the Standard Model are realized as tree-level and dimension-four couplings. We construct a basis of coannihilation models, classified by the SU(3) C × SU(2) L × U(1) Y quantum numbers of DM, X and M. Our main assumptions are that dark matter is an electrically neutral color singlet and that all new particles are either scalars, Dirac or Majorana fermions, or vectors. We illustrate how new scenarios arising from electroweak symmetry breaking effects can be connected to our electroweak symmetric simplified models. We offer a comprehensive discussion of the phenomenological features of our models, encompassing the physics of thermal freeze-out, direct and indirect detection constraints, and in particular searches at the Large Hadron Collider (LHC). Many novel signatures that are not covered in current LHC searches are emphasized, and new and improved LHC analyses tackling these signatures are proposed. We discuss how the coannihilation simplified models can be used to connect results from all classes of experiments in a straightforward and transparent way. This point is illustrated with a detailed discussion of the phenomenology of a particular simplified model featuring leptoquark-mediated dark matter coannihilation.

Michael Baker

Joachim Brod

Joachim Kopp

Andrea Thamm

The coannihilation codex

The robustness of translating effective operator constraints to BSM theories crucially depends on the mass and coupling of BSM particles. This is especially relevant for hadron colliders where the partonic centre of mass energy is around the typical energy scales of natural BSM theories. The caveats in applying the limits are discussed using Z ′ and G ′ models, illustrating the effects for a large class of models. This analysis shows that the applicability of effective operators mainly depends on the ratio of the transfer energy in the events and the mass scale of the full theory. Moreover, based on these results a method is developed to recast existing experimental limits on four-quark effective operators to the full theory parameter space.

Four-quark effective operators at hadron colliders