arXiv subjects

Abhishek Mohapatra

Publications and source records attributed to Abhishek Mohapatra.

At least 19 recordsLinked to original sources

arXiv2026

Open-flavor threshold effects on quarkonium spectrum in the BOEFT

The impact of open-flavor thresholds on the quarkonium spectrum has been a subject of study since the introduction of the Cornell potential and has been quantified through various phenomenological approaches, most notably the $^3P_0$ model. We revisit this problem using the Born--Oppenheimer effective field theory (BOEFT), an effective field theory systematically derived from QCD by exploiting hierarchies of energy scales and symmetries. Within the BOEFT, open-flavor threshold effects emerge from the mixing between quarkonium and tetraquark static potentials sharing the same Born--Oppenheimer quantum numbers. The shapes of the static potentials are constrained by lattice QCD calculations. Furthermore, we account for the distinctive behavior of the BOEFT tetraquark static potentials at short and large distances: at short distances they are repulsive, reflecting the color-octet configuration of the heavy quark-antiquark pair, while at large distances they asymptotically approach heavy-light meson-antimeson thresholds. To quantify threshold effects on the quarkonium spectrum below threshold, we solve a set of coupled Schrödinger equations dictated by the BOEFT, whose only free parameter, the adjoint meson mass, is fixed to the mass of the $χ_{c1}(3872)$ state. These coupled equations are solved both in the spin-isospin averaged threshold limit and, for the first time, including the spin splittings of the physical thresholds. We validate our results by computing the same threshold effects as self-energy corrections to the quarkonium propagator. We compare our predictions with existing experimental data and previous literature. Finally, we provide a field-theoretical interpretation of the pair-creation constant $γ$ appearing in the $^3P_0$ model.

hep-ph↗

arXiv2026

Quarkoniumlike states above open-flavor thresholds in Born-Oppenheimer EFT

Many quarkoniumlike states have been observed above open-flavor thresholds, but their organization and internal structure remain unsettled. We study the isoscalar hidden-charm and hidden-bottom sectors in Born--Oppenheimer effective field theory (BOEFT), between the spin--isospin averaged $S+S$ and $S+P$ thresholds. At leading order, heavy-quark spin decouples, and the quarkonium static potential mixes through string breaking with the lowest tetraquark/open-flavor BO potentials of the same quantum numbers. These potentials are constrained by QCD symmetries, their short- and long-distance behavior, and lattice-QCD data. The only calibrated parameter is the lowest $1^{--}$ adjoint meson mass, fixed from the shallow multiplet associated with the $χ_{c1}(3872)$. Using $T$-matrix, $K$-matrix, and complex-scaling methods, we determine bound states and resonance poles, their masses, pole widths from the included nonstrange $S+S$ channels, normalized pole couplings, and prescription-dependent quarkonium--open-flavor composition measures. Uncoupled hybrid BOEFT multiplets are included as reference levels. The spectrum exhibits a common heavy-quark-spin-symmetry multiplet organization. Most poles are predominantly quarkonium resonances localized at short distances, with the largest open-flavor components closest to threshold. The same equations also generate shallow, spatially extended, open-flavor-dominated states with molecular long-distance characteristics. Their binding energies, radii, and small quarkonium components are highly sensitive to the adjoint meson mass, whereas the higher spectrum is more stable. Together with the hybrid reference levels, the spectrum provides multiplet assignments for most candidates. States not naturally accommodated point to the need for hidden-strange and $S+P$ tetraquark/open-flavor BO sectors and for hybrid--tetraquark and hybrid--quarkonium mixings.

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arXiv2026

Inclusive hadroproduction of $χ_{c1}(3872)$, $X_b$ and pentaquarks

We use the Born--Oppenheimer effective field theory factorization to compute the inclusive production cross sections of the $χ_{c1}(3872)$ and its partner in the bottomonium sector. In the same framework, we compute the production cross sections of the pentaquark states $P_{c\bar{c}}(4312)^+$, $P_{c\bar{c}}(4457)^+$, $P_{c\bar{c}}(4380)^+$ and $P_{c\bar{c}}(4440)^+$ within two possible scenarios for the Born--Oppenheimer potentials. Also for pentaquarks, we extend the results to the bottomonium sector. All our results are genuine predictions that do not involve fits to prompt hadroproduction data.

hep-ph↗

arXiv2025

The nature of $χ_{c1}\left(3872\right)$ and $T_{cc}^+\left(3875\right)$

Two decades ago the $χ_{c1}\left(3872\right)$ was discovered in the hadron spectrum with two heavy quarks. The discovery fueled a surge in experimental research, uncovering dozens of so called XYZ exotics states lying outside the conventional quark model, as well as theoretical investigations into new forms of matter, such as quark-gluon hybrids, tetraquarks, pentaquarks, with the potential of disclosing new information about the fundamental strong force. Among the XYZs, the $χ_{c1}\left(3872\right)$ and $T_{cc}^+\left(3875\right)$ stand out for their striking characteristics and unlashed many discussions about their nature. Here, we address this question using the Born--Oppenheimer Effective Field Theory (BOEFT) and show how QCD settles the issue of their composition. Not only we describe well the main features of the $χ_{c1}\left(3872\right)$ and $T_{cc}^+\left(3875\right)$ but obtain also predictions in the bottomonium sector. This opens the way to systematic applications of BOEFT to all XYZs.

hep-ph↗

arXiv2025

Unravelling Pentaquarks with Born--Oppenheimer effective theory

The hidden-charm pentaquark states $P_{c\bar{c}}\left(4312\right)^+$, $P_{c\bar{c}}\left(4380\right)^+$, $P_{c\bar{c}}\left(4440\right)^+$, and $P_{c\bar{c}}\left(4457\right)^+$, all with isospin $I = 1/2$, were discovered by the LHCb collaboration in the decay process $Λ_b^0 \to J/ψp K^-$. Although their quantum numbers remain undetermined, these states have generated significant theoretical interest. We analyze their spectrum and decay patterns-including those of their spin partners-within the Born--Oppenheimer effective field theory (BOEFT), a framework grounded in QCD. At leading order in BOEFT, we identify these pentaquark states as bound states in BO potentials that exhibit at short-distance a repulsive octet behavior and a nonperturbative shift due to the adjoint baryons masses, while asymptotically approaching the $Σ_c\bar{D}$ threshold. We further incorporate ${\cal O}(1/m_Q)$ spin-dependent corrections to compute pentaquark multiplet spin splittings. Based on the spectrum, semi-inclusive decay widths to $J/ψ$ and $η_c$, and the decay width ratios to $Λ_c\bar{D}$ and $Λ_c\bar{D}^*$, we provide the first theoretical predictions for the adjoint baryon masses, which can be confirmed by future lattice QCD studies. Moreover, our analysis supports the quantum number assignments: $J^{P} = (1/2)^-$ for $P_{c\bar{c}}\left(4312\right)^+$, $(3/2)^-$ for $P_{c\bar{c}}\left(4380\right)^+$, $(1/2)^-$ for $P_{c\bar{c}}\left(4457\right)^+$, and $(3/2)^-$ for $P_{c\bar{c}}\left(4440\right)^+$. We also present results for the lowest bottom pentaquarks.

hep-ph↗

arXiv2025

One Born Oppenheimer Effective Theory to rule all Exotics

The discovery of XYZ exotic states in the hadronic sector with two heavy quarks constitute one of the most important open problems in particle theory. In this work, we demonstrate that the QCD derived Born-Oppenheimer effective field theory (BOEFT) framework, provides a systematic framework to describe exotic states of arbitrary composition. The BOEFT construction is based on QCD taking into consideration the scale separation and symmetry of systems containing two heavy quarks. We show the results for the coupled channel Schrödinger equations incorporating nonadiabatic mixing terms that describes exotic states for arbitrary quantum number of the light degrees of freedom: hybrids, tetraquarks, pentaquarks, doubly heavy baryons, and quarkonia at leading order. Additionally, we present the results of the predicted spin-symmetry multiplets, and the expression of the nonperturbative gauge-invariant correlators to be computed on lattice that are required for BOEFT: static energies, generalized Wilson loops, gluelumps, adjoint mesons or baryons, and triplet or sextext mesons or baryons. Moreover, for the static energies, we describe the short-distance behavior based on multipole expansion and the mixing with heavy-light thresholds at long distances based on the conserved quantum numbers.

hep-ph↗

arXiv2024

One Born$-$Oppenheimer Effective Theory to rule them all: hybrids, tetraquarks, pentaquarks, doubly heavy baryons and quarkonium

The discovery of XYZ exotic states in the hadronic sector with two heavy quarks, represents a significant challenge in particle theory. Understanding and predicting their nature remains an open problem. In this work, we demonstrate how the Born$-$Oppenheimer (BO) effective field theory (BOEFT), derived from Quantum Chromodynamics (QCD) on the basis of scale separation and symmetries, can address XYZ exotics of any composition. We derive the Schrödinger coupled equations that describe hybrids, tetraquarks, pentaquarks, doubly heavy baryons, and quarkonia at leading order, incorporating nonadiabatic terms, and present the predicted multiples. We define the static potentials in terms of the QCD static energies for all relevant cases. We provide the precise form of the nonperturbative low-energy gauge-invariant correlators required for the BOEFT: static energies, generalized Wilson loops, gluelumps, and adjoint mesons. These are to be calculated on the lattice and we calculate here their short-distance behavior. Furthermore, we outline how spin-dependent corrections and mixing terms can be incorporated using matching computations. Lastly, we discuss how static energies with the same BO quantum numbers mix at large distances leading to the phenomenon of avoided level crossing. This effect is crucial to understand the emergence of exotics with molecular characteristics, such as the $χ_{c1}(3872)$. With BOEFT both the tetraquark and the molecular picture appear as part of the same description.

hep-ph↗

arXiv2024

Born-Oppenheimer Potentials for $SU(3)$ Gauge Theory

We develop parameterizations of 8 of the lowest Born-Oppenheimer potentials for quarkonium hybrid mesons as functions of the separation $r$ of the static quark and antiquark sources. The parameters are determined by fitting results calculated using pure $SU(3)$ lattice gauge theory. The parameterizations have the correct limiting behavior at small $r$, where the potentials form multiplets associated with gluelumps. They have the correct limiting behavior at large $r$, where the potentials form multiplets associated with excitations of a relativistic string. There is a narrow avoided crossing in the small-$r$ region between two potentials with the same Born-Oppenheimer quantum numbers.

hep-ph↗

arXiv2022

Heavy hybrid decays to quarkonia

The decay rates of the XYZ exotics discovered in the heavy quarkonium sector are crucial observables for identifying the nature of these states. Based on the framework of nonrelativistic effective field theories, we calculate the rates of semi-inclusive decays of heavy quarkonium hybrids into conventional heavy quarkonia. We compute them at leading and subleading power in the inverse of the heavy-quark mass, extending and updating previous results. We compare our predictions with experimental data of inclusive decay rates for candidates of heavy quarkonium hybrids.

hep-ph↗

arXiv2021

Masses of Doubly Heavy Tetraquarks with Error Bars

In the heavy-quark limit, the two heavy quarks in a doubly heavy baryon or a doubly heavy tetraquark are bound by their color-Coulomb potential into a compact diquark. The doubly heavy hadrons are related by the approximate heavy-quark--diquark symmetry of QCD to the heavy hadrons obtained by replacing the heavy diquark by a heavy antiquark. Effective field theories can be used to expand the masses of singly heavy hadrons and doubly heavy hadrons in inverse powers of the heavy quark masses. The coefficients in the expansions for doubly heavy tetraquarks can be determined from those for heavy mesons, heavy baryons, and doubly heavy baryons using heavy-quark--diquark symmetry. We predict the masses of the ground-state doubly heavy tetraquarks with error bars using as inputs the masses of heavy mesons and heavy baryons measured in experiments and the masses of doubly heavy baryons calculated using lattice QCD. The only doubly heavy tetraquarks predicted to be stable with respect to strong decays are $bb$ tetraquarks with light flavor $\bar u \bar d$, $\bar s \bar u$ and $\bar s \bar d$.

hep-ph↗

arXiv2020

Operator Counting and Soft Blocks in Chiral Perturbation Theory

Chiral perturbation theory (ChPT) is a low-energy effective field theory of QCD and also a nonlinear sigma model based on the symmetry breaking pattern ${\rm SU}(N_f)\times {\rm SU}(N_f)\to {\rm SU}(N_f)$. In the limit of massless $N_f$ quarks, we enumerate the independent operators without external sources in ChPT using an on-shell method, by counting and presenting the soft blocks at each order in the derivative expansion, up to ${\cal O}(p^{10})$. Given the massless on-shell condition and total momentum conservation, soft blocks are homogeneous polynomials of kinematic invariants exhibiting the Adler's zero when any external momentum becomes soft and vanishing. In addition, soft blocks are seeds for recursively generating all tree amplitudes of Nambu-Goldstone bosons without recourse to ChPT, and in one-to-one correspondence with the "low energy constants" which are the Wilson coefficients. Relations among operators, such as those arising from equations of motion, integration-by-parts, hermiticity, and symmetry structure, manifest themselves in the soft blocks in simple ways. We find agreements with the existing results up to NNNLO, and make a prediction at N$^4$LO.

hep-ph↗

arXiv2019

Perturbative Corrections to Heavy Quark-Diquark Symmetry Predictions for Doubly Heavy Baryon Hyperfine Splittings

Doubly heavy baryons $\left(QQq\right)$ and singly heavy antimesons $\left(\bar{Q}q\right)$ are related by the heavy quark-diquark (HQDQ) symmetry because in the $m_Q \to \infty$ limit, the light degrees of freedom in both the hadrons are expected to be in identical configurations. Hyperfine splittings of the ground states in both systems are nonvanishing at $O(1/m_Q)$ in the heavy quark mass expansion and HQDQ symmetry relates the hyperfine splittings in the two sectors. In this paper, working within the framework of Non-Relativistic QCD (NRQCD), we point out the existence of an operator that couples four heavy quark fields to the chromomagnetic field with a coefficient that is enhanced by a factor from Coulomb exchange. This operator gives a correction to doubly heavy baryon hyperfine splittings that scales as $1/m_Q^2 \times α_S/r$, where $r$ is the separation between the heavy quarks in the diquark. This correction can be calculated analytically in the extreme heavy quark limit in which the potential between the quarks in the diquark is Coulombic. In this limit, the correction is $O(α_s^2/m_Q)$ and comes with a small coefficient. For values of $α_s$ relevant to doubly charm and doubly bottom systems, the correction to the hyperfine splittings in doubly heavy baryons is only a few percent or smaller. We also argue that nonperturbative corrections to the prediction for the hyperfine splittings are suppressed by $Λ^2_{\rm QCD}/m_Q^2$ rather than $Λ_{\rm QCD}/m_Q$. Corrections should be $\approx 10\%$ in the charm sector and smaller in heavier systems.

hep-ph↗

arXiv2019

Double Heavy baryons and Corrections to Heavy Quark-Diquark Symmetry Prediction for Hyperfine Splitting

In the $m_Q\rightarrow\infty$ limit, the hyperfine splittings in the ground state doubly heavy baryons $\left(QQq\right)$ and single heavy antimesons $(\bar{Q}q)$ are related by heavy quark-diquark symmetry (HQDQ) as the light degrees of freedom in both the hadrons are expected to have identical configurations. In this article, working within the framework of nonrelativistic QCD (NRQCD), we study the perturbative and nonperturbative corrections to the HQDQ symmetry hyperfine splitting relation that scale as ${\cal O}\left(α_s^2\right)$ and $Λ_{\rm QCD}^2/m_Q^2$ respectively. In the extreme heavy quark limit, the perturbative corrections to hyperfine splitting of doubly charm or bottom baryons are a few percent or smaller. The nonperturbative corrections to hyperfine splitting are of order $10\%$ in the case of doubly charm baryons and $1\%$ or smaller in doubly bottom baryons.

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

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↗

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↗

arXiv2016

Nonrelativistic Effective Field Theory for Axions

Axions can be described by a relativistic field theory with a real scalar field $ϕ$ whose self-interaction potential is a periodic function of $ϕ$. Low-energy axions, such as those produced in the early universe by the vacuum misalignment mechanism, can be described more simply by a nonrelativistic effective field theory with a complex scalar field $ψ$ whose effective potential is a function of $ψ^*ψ$. We determine the coefficients in the expansion of the effective potential to fifth order in $ψ^*ψ$ by matching low-energy axion scattering amplitudes. In order to describe a Bose-Einstein condensate of axions that is too dense to expand the effective potential in powers of $ψ^*ψ$, we develop a sequence of systematically improvable approximations to the effective potential that include terms of all orders in $ψ^*ψ$.

hep-ph↗

arXiv2016

Emission of Photons and Relativistic Axions from Axion Stars

The number of nonrelativistic axions can be changed by inelastic reactions that produce photons or relativistic axions. Any odd number of axions can annihilate into two photons. Any even number of nonrelativistic axions can scatter into two relativistic axions. We calculate the rate at which axions are lost from axion stars from these inelastic reactions. In dilute systems of axions, the dominant inelastic reaction is axion decay into two photons. In sufficiently dense systems of axions, the dominant inelastic reaction is the scattering of four nonrelativistic axions into two relativistic axions. The scattering of odd numbers of axions into two photons produces monochromatic radio-frequency signals at odd-integer harmonics of the fundamental frequency set by the axion mass. This provides a unique signature for dense systems of axions, such as a dense axion star or a collapsing dilute axion star.

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