arXiv subjects

Eric Braaten

Publications and source records attributed to Eric Braaten.

At least 37 records · Page 2Linked to original sources

arXiv2019

Production of $X(3872)$ Accompanied by a Pion in $B$ Meson Decay

If the $X(3872)$ is a weakly bound charm-meson molecule, it can be produced by the creation of $D^{*0} \bar{D}^0$ or $D^{0} \bar{D}^{*0}$ at short distances followed by the formation of the bound state from the charm-meson pairs. It can also be produced by the creation of $D^{*} \bar{D}^*$ at short distances followed by the rescattering of the charm mesons into $X π$. We use results of a previous isospin analysis of $B$ meson decays into $K D^{(*)} \bar D^{(*)}$ to estimate the short-distance amplitudes for creating $D^* \bar D^*$. We use an effective field theory for charm mesons and pions called XEFT to calculate the amplitudes for rescattering of $D^{*} \bar{D}^*$ into $X π$ with small relative momentum. The $Xπ$ invariant mass distribution is predicted to have a narrow peak near the $D^{*} \bar{D}^*$ threshold from a charm-meson triangle singularity. We estimate the branching fractions into the peak from the triangle singularity for the decays $B^0 \to K^+ X π^-$ and $B^+ \to K^0 X π^+$.

hep-ph↗

arXiv2019

Estimates of the $X(3872)$ Cross Section at a Hadron Collider

The claim that the $X(3872)$ meson cannot be a charm-meson molecule because its prompt production cross section at hadron colliders is too large is based on an upper bound in terms of a cross section for producing charm-meson pairs. Assuming $X$ is sufficiently weakly bound, we derive an equality between the $X$ cross section and a charm-meson pair cross section that takes into account the threshold enhancement from the $X$ resonance. The cross section for producing $X$ is equal to that for producing $D^{*0} \bar{D}^0$ integrated up to a relative momentum $k_\mathrm{max} = 7.7\,γ_X$, where $γ_X$ is the binding momentum of $X$. We also derive an order-of-magnitude estimate of the $X$ cross section in terms of a naive charm-meson pair cross section that does not take into account the threshold enhancement, such as that produced by a Monte Carlo event generator. The cross section for producing $X$ can be approximated by the naive cross section for producing $D^{*0} \bar{D}^0$ integrated up to a relative momentum $k_\mathrm{max}$ of order $(m_π^2 γ_X)^{1/3}$. The estimates of the prompt $X$ cross section at hadron colliders are consistent with the cross sections observed at the Tevatron and the LHC.

hep-ph↗

arXiv2019

Production of $X(3872)$ Accompanied by a Soft Pion at Hadron Colliders

If the $X(3872)$ is a weakly bound charm-meson molecule, it can be produced by the creation of $D^{*0} \bar{D}^0$ or $D^{0} \bar{D}^{*0}$ at short distances followed by the formation of the bound state from the charm-meson pair. The $X$ can also be produced by the creation of $D^* \bar{D}^*$ at short distances followed by the rescattering of the charm-meson pair into $X π$. At a high-energy hadron collider, the prompt cross section from this mechanism has a narrow peak in the $X π$ invariant mass distribution near the $D^* \bar D^*$ threshold from a charm-meson triangle singularity. An order-of-magnitude estimate of the ratio of the cross section for producing the peak in the $X π^\pm$ distribution to the cross section for producing $X$ without an accompanying pion suggests that the peak may be observable at the LHC.

hep-ph↗

arXiv2019

Triangle Singularity in the Production of $X(3872)$ and a Photon in $e^+e^-$ Annihilation

If the $X(3872)$ is a weakly bound charm-meson molecule, it can be produced in $e^+ e^-$ annihilation by the creation of $D^{*0} \bar D^{*0}$ from a virtual photon followed by the rescattering of the charm-meson pair into $X$ and a photon. A triangle singularity produces a narrow peak in the cross section for $e^+ e^- \to X γ$ about 2.2 MeV above the $D^{*0} \bar{D}^{*0}$ threshold. We predict the normalized cross section in the region near the peak. The peak from the triangle singularity may be observable by the BESIII detector.

hep-ph↗

arXiv2019

Branching Fractions of the $X(3872)$

The recoil momentum spectrum from the decay $B^+ \to K^+ +\mathrm{anything}$ has recently been measured by the BaBar collaboration. The spectrum has a peak with invariant mass near the mass of the $X(3872)$ meson. The preliminary measurement by the BaBar collaboration implies that its branching fraction into $J/ψ\, π^+π^-$ is about 4\%. We emphasize that this is the branching fraction for the entire resonance feature from $B^+$-to-$K^+$ transitions, which includes a $D^{*0} \bar D^0$ and $D^0 \bar D^{*0}$ threshold enhancement as well as a possible bound state below the threshold or a virtual state. If the $X$ is a bound state of charm mesons, its branching fraction into $J/ψ\, π^+π^-$ should be considerably larger than that of the $X$ resonance feature. We use measurements of branching ratios of the $X$ to put an upper bound on this branching fraction of 33\%. We also constrain the parameters of the simplest plausible model for the line shapes of the $X$ using the precise measurement of the resonance energy of the $X$ and an estimate of the branching fraction into $D^0 \bar D^0 π^0$ and $D^0 \bar D^0γ$ from the $X$ resonance feature from $B^+$-to-$K^+$ transitions.

hep-ph↗

arXiv2019

Dark Matter Bound States from Three-Body Recombination

The small-scale structure problems of the universe can be solved by self-interacting dark matter that becomes strongly interacting at low energies. A particularly predictive model is resonant short-range self-interactions, with a dark-matter mass of about 19 GeV and a large S-wave scattering length of about 17 fm. Such a model makes definite predictions for the few-body physics of weakly bound clusters of the dark-matter particles. We calculate the production of two-body bound clusters by three-body recombination in the early universe under the assumption that the dark matter particles are identical bosons, which is the most favorable case for forming larger clusters. The fraction of dark matter in the form of two-body bound clusters can increase by as much as 4 orders of magnitude when the dark-matter temperature falls below the binding energy, but its present value remains less than 10^(-6).

hep-ph↗

arXiv2018

Loss of Conformality in Efimov Physics

The loss of conformal invariance in Efimov physics is due to the merger and disappearance of an infrared and an ultraviolet fixed point of a three-body renormalization group flow as the spatial dimension $d$ is varied. In the case of identical bosons at unitarity, it is known that there are two critical dimensions $d_{\rm 1}=2.30$ and $d_{\rm 2}=3.76$ at which there is loss of conformality. For $d d_{\rm 2}$, the beta function of the three-body coupling has real roots which correspond to infrared and ultraviolet fixed points. The fixed points merge and disappear into the complex plane at the critical dimensions $d_1$ and $d_2$. For $d_{\rm 1}<d<d_{\rm 2}$, the beta function has complex roots and the renormalization group flow for the three-body coupling constant is a limit cycle.

cond-mat.quant-gas↗

arXiv2018

Production of dark-matter bound states in the early universe by three-body recombination

The small-scale structure problems of the universe can be solved by self-interacting dark matter that becomes strongly interacting at low energy. A particularly predictive model for the self-interactions is resonant short-range interactions with an S-wave scattering length that is much larger than the range. The velocity dependence of the cross section in such a model provides an excellent fit to self-interaction cross sections inferred from dark-matter halos of galaxies and clusters of galaxies if the dark-matter mass is about 19 GeV and the scattering length is about 17 fm. Such a model makes definite predictions for the few-body physics of weakly bound clusters of the dark-matter particles. The formation of the two-body bound cluster is a bottleneck for the formation of larger bound clusters. We calculate the production of two-body bound clusters by three-body recombination in the early universe under the assumption that the dark matter particles are identical bosons, which is the most favorable case. If the dark-matter mass is 19 GeV and the scattering length is 17 fm, the fraction of dark matter in the form of two-body bound clusters can increase by as much as 4 orders of magnitude when the dark-matter temperature falls below the binding energy, but its present value remains less than 10^(-6). The present fraction can be increased to as large as 10^(-3) by relaxing the constraints from small-scale structure and decreasing the mass of the dark matter particle.

hep-ph↗

arXiv2018

Axion Stars

The particle that makes up the dark matter of the universe could be an axion or axion-like particle. A collection of axions can condense into a bound Bose-Einstein condensate called an axion star. It is possible that a significant fraction of the axion dark matter is in the form of axion stars. This would make some efforts to identify the axion as the dark matter particle more challenging, but it would also open up new possibilities. We summarize the basic properties of isolated axion stars, which can be gravitationally bound or bound by self-interactions. Axions are naturally described by a relativistic field theory with a real scalar field, but low-energy axions can be described more simply by a classical nonrelativistic effective field theory with a complex scalar field.

hep-ph↗

arXiv2018

Gluon fragmentation into quarkonium at next-to-leading order using FKS subtraction

We present the calculation at next-to-leading order (NLO) in alpha_s of the fragmentation function of a gluon into heavy quarkonium in the color-octet spin-singlet S-wave channel. To calculate the real NLO corrections, we adapt a subtraction scheme introduced by Frixione, Kunszt, and Signer. Ultraviolet and infrared divergences in the real NLO corrections are calculated analytically by evaluating the phase-space integrals of the subtraction terms using dimensional regularization. The subtracted phase-space integrals are then evaluated in 4 space-time dimensions. The divergences in the virtual NLO corrections are also calculated analytically. After renormalization, all the divergences cancel. The NLO corrections significantly increase the fragmentation probability for a gluon into the spin-singlet quarkonium states eta_c and eta_b.

hep-ph↗

arXiv2018

Classical Nonrelativistic Effective Field Theories for a Real Scalar Field

A classical nonrelativistic effective field theory for a real Lorentz-scalar field $ϕ$ is most conveniently formulated in terms of a complex scalar field $ψ$. There have been two derivations of effective Lagrangians for the complex field $ψ$ in which terms in the effective potential were determined to order $(ψ^* ψ)^4$. We point out an error in each of the effective Lagrangians. After correcting the errors, we demonstrate the equivalence of the two effective Lagrangians by verifying that they both reproduce $T$-matrix elements of the relativistic real scalar field theory and by also constructing a redefinition of the complex field $ψ$ that transforms terms in one effective Lagrangian into the corresponding terms of the other.

hep-ph↗

arXiv2018

Zero-Range Effective Field Theory for Resonant Wino Dark Matter III. Annihilation Effects

Near a critical value of the wino mass where there is a zero-energy S-wave resonance at the neutral-wino-pair threshold, low-energy winos can be described by a zero-range effective field theory (ZREFT) in which the winos interact nonperturbatively through a contact interaction and through Coulomb interactions. The effects of wino-pair annihilation into electroweak gauge bosons are taken into account through the analytic continuation of the real parameters for the contact interaction to complex values. The parameters of ZREFT can be determined by matching wino-wino scattering amplitudes calculated by solving the Schrödinger equation for winos interacting through a real potential due to the exchange of electroweak gauge bosons and an imaginary potential due to wino-pair annihilation into electroweak gauge bosons. ZREFT at leading order gives an accurate analytic description of low-energy wino-wino scattering, inclusive wino-pair annihilation, and a wino-pair bound state. ZREFT can also be applied to partial annihilation rates, such as the Sommerfeld enhancement of the annihilation rate of wino pairs into monochromatic photons.

hep-ph↗

arXiv2018

Zero-Range Effective Field Theory for Resonant Wino Dark Matter II. Coulomb Resummation

Near a critical value of the wino mass where there is a zero-energy S-wave resonance at the neutral-wino-pair threshold, low-energy winos can be described by a zero-range effective field theory (ZREFT) in which the winos interact nonperturbatively through a contact interaction and charged winos also have electromagnetic interactions. At energies near the wino-pair thresholds, the Coulomb interaction from photon exchange between charged winos must also be treated nonperturbatively. The parameters of ZREFT can be determined by matching wino-wino scattering amplitudes calculated by solving the Schrödinger equation for winos interacting through a potential due to the exchange of electroweak gauge bosons. With Coulomb resummation, ZREFT at leading order gives a good description of the low-energy two-body observables for winos.

hep-ph↗

arXiv2017

Zero-Range Effective Field Theory for Resonant Wino Dark Matter I. Framework

The most dramatic "Sommerfeld enhancements" of neutral-wino-pair annihilation occur when the wino mass is near a critical value where there is a zero-energy S-wave resonance at the neutral-wino-pair threshold. Near such a critical mass, low-energy winos can be described by a zero-range effective field theory in which the winos interact nonperturbatively through a contact interaction. The effective field theory is controlled by a renormalization-group fixed point at which the neutral and charged winos are degenerate in mass and their scattering length is infinite. The parameters of the zero-range effective field theory can be determined by matching wino-wino scattering amplitudes calculated by solving the Schrödinger equation for winos interacting through a potential due to the exchange of weak gauge bosons. If the wino mass is larger than the critical value, the resonance is a wino-pair bound state. The power of the zero-range effective field theory is illustrated by calculating the rate for formation of the bound state in the collision of two neutral winos through the emission of two soft photons.

hep-ph↗

arXiv2017

Conformality Lost in Efimov Physics

A general mechanism for the loss of conformal invariance is the merger and disappearance of an infrared fixed point and an ultraviolet fixed point of a renormalization group flow. We show explicitly how this mechanism works in the case of identical bosons at unitarity as the spatial dimension $d$ is varied. For $d$ between the critical dimensions $d_{\rm 1}=2.30$ and $d_{\rm 2}=3.76$, there is loss of conformality as evidenced by the Efimov effect in the three-body sector. The beta function for an appropriate three-body coupling is a quadratic polynomial in that coupling. For $d d_{\rm 2}$, the beta function has two real roots that correspond to infrared and ultraviolet fixed points. As $d$ approaches $d_{\rm 1}$ from below and as $d$ approaches $d_{\rm 2}$ from above, the fixed points merge and disappear into the complex plane. For $d_{\rm 1}<d<d_{\rm 2}$, the beta function has complex roots and the renormalization group flow for the three-body coupling is a limit cycle.

cond-mat.quant-gas↗

arXiv2017

Effective field theory for resonant wino dark matter

Enhancements in WIMP annihilation rates have been identified with a nonperturbative "Sommerfeld enhancement" arising from the exchange of light mediators. At certain critical values of the WIMP mass, the enhancement is increased dramatically due to a zero-energy resonance at the WIMP-pair threshold. For masses near these critical values, WIMP scattering processes are accurately described by an effective field theory where WIMPs have nonperturbative zero-range contact interactions. The effective field theory is controlled by a renormalization-group fixed point at which the WIMPs are degenerate in mass and their scattering length is infinite. If the WIMPs can exchange massless mediators, the resulting long-range interaction must also be treated nonperturbatively. We develop an effective field theory for SU(2)-triplet dark matter, which have short-range weak and long-range electromagnetic interactions. We refer to these dark matter particles as winos. The long-range Coulomb interaction between charged winos is resummed to all orders. The parameters of the effective field theory can be determined by matching wino-wino scattering amplitudes calculated by solving the Schrödinger equation with a potential describing exchange of electroweak gauge bosons. With Coulomb resummation, the effective field theory at leading order gives a good description of the low-energy two-body observables for winos.

hep-ph↗

arXiv2017

Mass Dependence of Higgs Production at Large Transverse Momentum through a Bottom Quark Loop

In the production of the Higgs through a bottom-quark loop, the transverse momentum distribution of the Higgs at large $P_T$ is complicated by its dependence on two other important scales: the bottom quark mass $m_b$ and the Higgs mass $m_H$. A strategy for simplifying the calculation of the cross section at large $P_T$ is to calculate only the leading terms in its expansion in $m_b^2/P_T^2$. In this paper, we consider the bottom-quark-loop contribution to the parton process $q\bar{q}\to H+g$ at leading order in $α_s$. We show that the leading power of $1/P_T^2$ can be expressed in the form of a factorization formula that separates the large scale $P_T$ from the scale of the masses. All the dependence on $m_b$ and $m_H$ can be factorized into a distribution amplitude for $b \bar b$ in the Higgs, a distribution amplitude for $b \bar b$ in a real gluon, and an endpoint contribution. The factorization formula can be used to organize the calculation of the leading terms in the expansion in $m_b^2/P_T^2$ so that every calculation involves at most two scales.

hep-ph↗

arXiv2017

Mass Dependence of Higgs Production at Large Transverse Momentum

The transverse momentum distribution of the Higgs at large $P_T$ is complicated by its dependence on three important energy scales: $P_T$, the top quark mass $m_t$, and the Higgs mass $m_H$. A strategy for simplifying the calculation of the cross section at large $P_T$ is to calculate only the leading terms in its expansion in $m_t^2/P_T^2$ and/or $m_H^2/P_T^2$. The expansion of the cross section in inverse powers of $P_T$ is complicated by logarithms of $P_T$ and by mass singularities. In this paper, we consider the top-quark loop contribution to the subprocess $q\bar{q}\to H+g$ at leading order in $α_s$. We show that the leading power of $1/P_T^2$ can be expressed in the form of a factorization formula that separates the large scale $P_T$ from the scale of the masses. All the dependence on $m_t$ and $m_H$ can be factorized into a distribution amplitude for $t \bar t$ in the Higgs, a distribution amplitude for $t \bar t$ in a real gluon, and an endpoint contribution. The factorization formula can be used to simplify calculations of the $P_T$ distribution at large $P_T$ to next-to-leading order in $α_s$.

hep-ph↗