We determine the contribution of long-range pion interactions to the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> dynamics, assuming it is a loosely bound <math><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mo>⁎</mo><mn>0</mn></mrow></msup></math> molecule. Our result is based on the distorted wave Born approximation in non-relativistic quantum mechanics. Despite their long-range nature, we find that pion interactions cannot produce a large and negative effective range. Nonetheless, they introduce imaginary parts. In particular, they contribute to the total decay width of the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> a term associated with, but not precisely corresponding to, the <math><msup><mrow><mi>D</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math> width. Our approach can also be applied to the recently discovered <math><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math> state.

Italy

Angelo Esposito

Davide Germani

France

Alfredo Glioti

Antonio D. Polosa

Switzerland

Riccardo Rattazzi

United States

Michele Tarquini

The role of the pion in the lineshape of the (3872)

We propose antiferromagnets as optimal targets to hunt for sub-MeV dark matter with spin-dependent interactions. These materials allow for multimagnon emission even for very small momentum transfers and are therefore sensitive to dark matter particles as light as the keV. We use an effective theory to compute the event rates in a simple way. Among the materials studied here, we identify nickel oxide (a well-assessed antiferromagnet) as an ideal candidate target. Indeed, the propagation speed of its gapless magnons is very close to the typical dark matter velocity, allowing the absorption of all its kinetic energy, even through the emission of just a single magnon.

Shashin Pavaskar

Optimal antiferromagnets for light dark matter detection

Forthcoming experiments such as Project 8 and Ptolemy aim at investigating with high precision the end point of the tritium <math><mi>β</mi></math>-decay spectrum sensitive to the neutrino mass. In light of this, using the standard parametrization in terms of nuclear polar form factors, we analyze the complete relativistic expression for the spectrum of the <math><mi>β</mi></math> electron emitted by a tritium nucleus. Given the small parameters in the problem, we systematically discuss the approximations that can be made, and present the first two corrections to the standard lowest-order formula. We particularly discuss the case of an initially polarized target, and the consequences on the spectrum as a function of the neutrino mass. We show that, while it induces an angular anisotropy that can be measured by future experiments, such anisotropy cannot be used as an additional handle to constrain the neutrino mass.

Gianluca Cavoto

Guglielmo Papiri

Relativistic corrections to polarized-tritium <math><mi>β</mi></math> decay

Dark matter scattering off a nucleus has a small probability of inducing an observable ionization through the inelastic excitation of an electron, called the Migdal effect. We use an effective field theory to extend the computation of the Migdal effect in semiconductors to regions of small momentum transfer to the nucleus, where the final state of the nucleus is no longer well described by a plane wave. Our analytical result can be fully quantified by the measurable dynamic structure factor of the semiconductor, which accounts for the vibrational degrees of freedom (phonons) in a crystal. We show that, due to the sum rules obeyed by the structure factor, the inclusive Migdal rate and the shape of the electron recoil spectrum is well captured by approximating the nuclei in the crystal as free ions; however, the exclusive differential rate with respect to energy depositions to the crystal depends on the phonon dynamics encoded in the dynamic structure function of the specific material. Our results now allow the Migdal effect in semiconductors to be evaluated even for the lightest dark matter candidates (m  χ  ≳ 1 MeV) that can kinematically excite electrons.

Kim Berghaus

Rouven Essig

Mukul Sholapurkar

The Migdal effect in semiconductors for dark matter with masses below ∼ 100 MeV

It is a common lore that the amplitude for a scattering process involving one soft Nambu-Goldstone boson should scale like an integer power of the soft momentum. We revisit this expectation by considering the <math><mrow><mn>2</mn><mo>→</mo><mn>2</mn></mrow></math> scattering of phonons in solids. We show that, depending on the helicities of the phonons involved in the scattering process, the scattering amplitude may in fact vanish like a fractional power of the soft momentum. This is a peculiarity of the 4-point amplitude, which can be traced back to (1) the (spontaneous or explicit) breaking of Lorentz invariance, and (2) the approximately collinear kinematics arising when one of the phonons becomes soft. Our results extend to the general class of nonrelativistic shift-invariant theories of a vector field.

Norway

Tomáš Brauner

Riccardo Penco

Fractional Soft Limits of Scattering Amplitudes

From a study of the line shape of the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math>, the LHCb collaboration measures a sizeable negative effective range. This cannot be reconciled with a shallow <math><mi>D</mi><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> bound state hypothesis. Based on Weinberg’s compositeness criterion, together with a theorem by Smorodinsky, it follows that the <math><mi>X</mi></math> has to have a compact hidden charm structure interacting with unbound <math><mi>D</mi><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> pairs via short-distance color forces. This conclusion is strengthened by the general pattern recently emerging from exotic mesons.

Luciano Maiani

Alessandro Pilloni

Verónica Riquer

From the line shape of the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> to its structure

Ultraperipheral heavy ion collisions constitute an ideal setup to look for exotic hadrons because of their low event multiplicity and the possibility of an efficient background rejection. We propose to look for four-quark states produced by photon-photon fusion in these collisions at the center-of-mass energy per nucleon pair <math><msqrt><msub><mi>s</mi><mi>NN</mi></msub></msqrt><mo>=</mo><mn>5.5</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>. In particular, we focus on those states that would represent a definite smoking gun for the compact tetraquark model. We show that the <math><mi>X</mi><mo>(</mo><mn>6900</mn><mo>)</mo></math>, a likely <math><mi>c</mi><mi>c</mi><mover><mi>c</mi><mo>¯</mo></mover><mover><mi>c</mi><mo>¯</mo></mover></math> compact state, is a perfect candidate for this search, and estimate a production cross section ranging from around 250 nb to 1150 nb, depending on its quantum numbers. Furthermore, we discuss the importance of ultraperipheral collisions to the search for the scalar and tensor partners of the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> predicted by the diquarkonium model, and not yet observed. The completion of such a flavor-spin multiplet would speak strongly in favor of the compact tetraquark model.

Claudio Andrea Manzari

Antonio Davide Polosa

Hunting for tetraquarks in ultraperipheral heavy ion collisions

The structure of exotic resonances that do not trivially fit the usual quark model expectations has been a matter of intense scientific debate during the last two decades. A possible way of estimating the size of these states is to study their behavior when immersed in QCD matter. Recently, LHCb has measured the relative abundance of the exotic  $$X(3872)$$  <math> <mrow> <mi>X</mi> <mo>(</mo> <mn>3872</mn> <mo>)</mo> </mrow> </math>   over the ordinary  $$\psi (2S)$$  <math> <mrow> <mi>ψ</mi> <mo>(</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> </math>  . We use the comover interaction model to study the yield of a compact  $$X(3872)$$  <math> <mrow> <mi>X</mi> <mo>(</mo> <mn>3872</mn> <mo>)</mo> </mrow> </math>  . To confirm the reliability of the model in high-multiplicity pp collisions, we describe the suppression of excited over ground  $$\Upsilon $$  <math> <mi>Υ</mi> </math>   states. With this at hand, we show that the size of the compact  $$X(3872)$$  <math> <mrow> <mi>X</mi> <mo>(</mo> <mn>3872</mn> <mo>)</mo> </mrow> </math>   would be slightly larger than that of the  $$\psi (2S)$$  <math> <mrow> <mi>ψ</mi> <mo>(</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> </math>  . If the  $$X(3872)$$  <math> <mrow> <mi>X</mi> <mo>(</mo> <mn>3872</mn> <mo>)</mo> </mrow> </math>   is instead assumed to be a meson molecule of large size, we argue that its evolution in QCD matter should be described via a coalescence model, as suggested by data on deuteron production. We show that the predictions of this model for the  $$X(3872)$$  <math> <mrow> <mi>X</mi> <mo>(</mo> <mn>3872</mn> <mo>)</mo> </mrow> </math>   are in contrast with data.

Spain

Elena Ferreiro

Antonio Polosa

Carlos Salgado

The nature of X(3872) from high-multiplicity pp collisions

We present the analysis of a new signature for light dark matter detection with superfluid <math><mrow><mmultiscripts><mrow><mi>He</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>4</mn></mrow></mmultiscripts></mrow></math>: the emission of three phonons. We show that, in a region of mass below the MeV, the kinematics of this process can offer a way to reconstruct the dark matter interaction vertex while providing background rejection via coincidence requirements and directionality. We develop all the theoretical tools to deal with such an observable, and compute the associated differential distributions.

Germany

Israel

Andrea Caputo

Fulvio Piccinini

Giuseppe Rossi

Directional detection of light dark matter from three-phonon events in superfluid <math><mrow><mmultiscripts><mrow><mi>He</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>4</mn></mrow></mmultiscripts></mrow></math>

We present a relativistic effective field theory for the interaction between acoustic and gapped phonons in the limit of a small gap. We show that, while the former are the Goldstone modes associated with the spontaneous breaking of spacetime symmetries, the latter are pseudo-Goldstones associated with some (small) explicit breaking. We hence dub them “pseudoacoustic” phonons. In this first investigation, we build our effective theory for the cases of one and two spatial dimensions, two atomic species, and assuming large distance isotropy. As an illustrative example, we show how the theory can be applied to compute the total lifetime of both acoustic and pseudoacoustic phonons. This construction can find applications that range from the physics of bilayer graphene to sub-GeV dark matter detectors.

Emma Geoffray

Japan

Tom Melia

Effective field theory for acoustic and pseudoacoustic phonons in solids