Enhancements and suppressions of CP violating effect in the nucleons, nuclei, and atoms
Nodoka Yamanaka
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11 pages, 4 figures, short review on the electric dipole moment, proceedings of the 23rd International Spin Symposium (SPIN 2018), September 10-14, 2018
The electric dipole moment (EDM) is a very sensitive probe of CP violation beyond the standard model, and it as been measured in many systems such as atoms, neutrons, etc. The EDM of composite systems may be sensitive to several elementary level CP violating processes, but the theoretical evaluations of the CP violation at different physical (atomic, nuclear, hadronic, elementary) hierarchies are required to unveil them. In this context, we are particularly interested in which CP violating processes are enhanced in a given system, or vice versa. In this proceedings contribution, we will give an overview of the enhancement and suppression of CP violation in processes contributing to the EDMs of composite systems.
We show that the present experimental limits on electron-nucleon interactions that violate both parity and time reversal invariance provide new stringent bounds on the imaginary parts of some of the products of the R-parity violating coupling constants in the R-parity violating Minimal Supersymmetric Standard Model.
We apply the large-$N_c$ expansion to the time-reversal-invariance-violating (TV) nucleon-nucleon potential. The operator structures contributing to next-to-next-to-leading order in the large-$N_c$ counting are constructed. For the TV and parity-violating case we find a single operator structure at leading order. The TV but parity-conserving potential contains two leading-order terms, which however are suppressed by 1/$N_c$ compared to the parity-violating potential. Comparison with phenomenological potentials, including the chiral EFT potential in the TV parity-violating case, leads to large-…
Two-pion exchange parity-violating nucleon-nucleon interactions from recent effective field theories and earlier fully covariant approaches are investigated. The potentials are compared with the idea to obtain better insight on the role of low-energy constants appearing in the effective field theory approach and the convergence of this one in terms of a perturbative series. The results are illustrated by considering the longitudinal asymmetry of polarized protons scattering off protons, $\vec{p}+p -> p+p$, and the asymmetry of the photon emission in radiative capture of polarized neutrons by p…
The effects of charge symmetry breaking in nucleon electromagnetic form factors on parity- violating elastic electron-12C scattering is studied, and found to be much smaller than other known effects. The analysis of a planned experiment is discussed.
We review the area of strange quark contributions to nucleon structure. In particular, we focus on current models of strange quark vector currents in the nucleon and the associated parity-violating elastic electron scattering experiments from which vector- and axial-vector currents are extracted
In this lecture, I review progress made in the calculations of the parity-violating meson-nucleon interaction regions. The underlying framework is the topological chiral soliton model of the nucleon. Emphasis is put on the computation of theoretically and experimentally accessible nuclear parity violating observables. I stress the importance of the interplay of strong and weak interactions which makes this field interesting and challenging. I also discuss recent developments pointing towards the importance of strange quark admixtures in the proton wave function. (Invited talk presented at the …
We address the typical strengths of hadronic parity-violating three-nucleon interactions in "pion-less" Effective Field Theory in the nucleon-deuteron (iso-doublet) system. By analysing the superficial degree of divergence of loop diagrams, we conclude that no such interactions are needed at leading order. The only two linearly independent parity-violating three-nucleon structures with one derivative mix two-S and two-P-half waves with iso-spin transitions Delta I = 0 or 1. Due to their structure, they cannot absorb any divergence ostensibly appearing at next-to-leading order. This observation…
We study the effective $B-L$ violating couplings for scalar and vector leptoquarks which can naturally induce dimension seven $B-L$ violating operators leading to very interesting nucleon decay modes such as $n \rightarrow e^- π^+, e^-K^+,μ^- π^+, μ^-K^+$ and $p \rightarrow νπ^+$. This opens a new window to probe the nature and couplings of the scalar and vector leptoquarks in an ultraviolet model independent way which can provide an orthogonal probe for scalar and vector leptoquark solutions to the recent anomalous $B$-decay data. Furthermore, we also discuss how these $B-L$ violating interac…
We consider the two-nucleon weak interaction with a pionless effective field theory. Dibaryon fields are introduced to facilitate calculations and ensure precision in the initial and final state propagators. Weak interactions are accounted for with the parity-violating dibaryon-nucleon-nucleon vertices, which contain unknown weak dibaryon-nucleon-nucleon coupling constants. We apply the model to the calculation of a parity-violating observable in the neutron-proton capture at threshold. Result is obtained up to the linear order in the unknown dibaryon-nucleon-nucleon coupling constants. We com…
A purely left-chiral model of the weak interactions is used to show that the total parity-violating asymmetry in quark-quark scattering must grow with increasing energy. In the absence of other new physics, non-observation of a large asymmetry can therefore be used to infer an upper bound on the mass scale for new right-chiral weak vector bosons. Applying this idea to actual nucleon-nucleon scattering requires more involved calculations, as the dominant contribution appears to come from a component of diquark-quark scattering related to, but not identical to, wavefunction-mixing. Earlier criti…
Parity violating (PV) contributions due to interference between $γ$ and $Z^0$ exchange are calculated for pion electroproduction off the nucleon. A phenomenological model with effective Lagrangians is used to determine the resulting asymmetry for the energy region between threshold and $Δ(1232)$ resonance. The $Δ$ resonance is treated as a Rarita-Schwinger field with phenomenological $N Δ$ transition currents. The background contributions are given by the usual Born terms using the pseudovector $πN$ Lagrangian. Numerical results for the asymmetry are presented.
We study the parity-violating pion-nucleon coupling $G_π$ in the framework of a realistic three flavor Skryme model. We find a sizeable enhancement of $G_π\simeq 0.8 ... 1.3 \cdot 10^{-7}$ compared to previous calculations in two-flavor models with vector mesons. This strangeness enhancement stems from induced kaon fields of the chiral soliton and the non-monotoneous dependence on symmetry breaking of the nucleon matrix element of the flavor singlet piece of the operator associated with these induced fields. Both features are sensitive to four quark operators including an $\bar s s$ pair.
Parity-violating (PV) interactions among quarks in the nucleon induce a PV $γNN$ coupling, or anapole moment (AM). We compute electroweak gauge-independent contributions to the AM through ${\cal O}(1/\lamchis)$ in chiral perturbation theory. We estimate short-distance PV effects using resonance saturation. The AM contributions to PV electron-proton scattering slightly enhance the axial vector radiative corrections, R_A^p, over the scale implied by the Standard Model when weak quark-quark interactions are neglected. We estimate the theoretical uncertainty associated with the AM contributions to…
Parity- and time reversal-violating (PVTV) pion-nucleon couplings govern the magnitude of long-range contributions to nucleon and atomic electric dipole moments. When these couplings arise from chiral symmetry-breaking CP-violating operators, such as the QCD $θ$-term or quark chromoelectric dipole moments, one may relate hadronic matrix elements entering the PVTV couplings to nucleon and pion mass shifts by exploiting the corresponding chiral transformation properties at leading order (LO) in the chiral expansion. We compute the higher-order contributions to the lowest order relations arising …
We present a reanalysis of nucleon decay in the context of the R-parity violating MSSM, updating bounds on R-parity violating parameters against recent experimental and lattice results. We pay particular attention to the derivation of these constraints and specifically to the hadronic matrix elements, which usually stand as the limiting factor in order to derive reliable bounds, except for these few channels that have been studied on the lattice.
Axions or similar hypothetical pseudoscalar bosons may have a small CP-violating scalar Yukawa interaction g_s(N) with nucleons, causing macroscopic monopole-dipole forces. Torsion-balance experiments constrain g_p(e) g_s(N), whereas g_p(N) g_s(N) is constrained by the depolarization rate of ultra-cold neutrons or spin-polarized nuclei. However, the pseudoscalar couplings g_p(e) and g_p(N) are strongly constrained by stellar energy-loss arguments and g_s(N) by searches for anomalous monopole-monopole forces, together providing the most restrictive limits on g_p(e) g_s(N) and g_p(N) g_s(N). The…
Deuteron electrodisintegration is described in a relativistic PWIA framework. The reduction to the factorized PWIA, and the effect thereof on the observables accessible in parity-violating scattering, is discussed. The extent to which such relativistic effects may affect the extraction of strangeness nucleon form factors from measurements of the PV asymmetry, is investigated.
The contribution of the R-parity violating minimal supersymmetric Standard model (RPVMSSM) at the one-loop level to the 199Hg atomic electric dipole moment (EDM) through P, CP-odd electron-nucleon (e-N) interaction is calculated. We show that the current experimental data of the 199Hg EDM give tighter constraints on some of the imaginary parts of R-parity violating (RPV) coupling than those currently known. We add also the analysis of the P, CP-odd 4-quark interaction generated by R-parity violating interactions at the one-loop level, and discuss the possibility to constrain them in future exp…
We compute isospin-violating meson-nucleon coupling constants and their consequent charge-symmetry-breaking nucleon-nucleon potentials. The couplings result from evaluating matrix elements of quark currents between nucleon states in a nonrelativistic constituent quark model; the isospin violations arise from the difference in the up and down constituent quark masses. We find, in particular, that isospin violation in the omega-meson--nucleon vertex dominates the class IV CSB potential obtained from these considerations. We evaluate the resulting spin-singlet--triplet mixing angles, the quantiti…
Several experimental investigations have observed parity violation in nuclear systems-a consequence of the weak force between quarks. We apply the $1/N_c$ expansion of QCD to the P-violating T-conserving component of the nucleon-nucleon (NN) potential. We show there are two leading-order operators, both of which affect $\vec{p}p$ scattering at order $N_c$. We find an additional four operators at $O(N_c^0 \sin^2 θ_W)$ and six at $O(1/N_c)$. Pion exchange in the PV NN force is suppressed by $1/N_c$ and $\sin^2 θ_W$, providing a quantitative explanation for its non-observation up to this time. Th…
We analyze parity-violating nucleon-nucleon scattering at energies E<m_π^2/M using the effective field theory appropriate for this regime. The minimal Lagrangian for short-range parity-violating NN interactions is written in an operator basis that encodes the five partial-wave transitions that dominate at these energies. We calculate the leading-order relationships between parity-violating NN asymmetries and the coefficients in the Lagrangian and also discuss the size of sub-leading corrections. We conclude with a discussion of further observables needed to completely determine the leading-ord…
The chiral quark model posits pseudoscalar and vector meson couplings to constituent quarks. The parity violating meson-quark couplings lead to anapole moments and form factors of the nucleons. These arise both as parity violating meson loop fluctuations as well as exchange currents and polarization currents that are induced by the parity violating interaction between quarks. Because of cancellations between the different contributions the magnitude of the calculated anapole moments is only of the order $\sim 10^{-8}$ and is determined mainly by magnitude of the parity-violating meson-nucleon …
Electric dipole moments of atoms can arise from P-odd and T-odd electron--nucleon couplings. This work studies a general class of dimension-six electron--nucleon interactions mediated by Lorentz-violating tensors of ranks ranging from $1$ to $4$. The possible couplings are listed as well as their behavior under C, P, and T, allowing us to select the couplings compatible with electric-dipole-moment physics. The unsuppressed contributions of these couplings to the atom's hamiltonian can be read as equivalent to an electric dipole moment. The Lorentz-violating coefficients' magnitudes are limited…
Experiments with paramagnetic ground or metastable excited states of molecules (ThO, HfF$^+$, YbF, YbOH, BaF, PbO, etc.) provide strong constraints on electron electric dipole moment (EDM) and coupling constant $C_{SP}$ of contact semileptonic interaction. We compute new contributions to $C_{SP}$ arising from the nucleon EDMs due to combined electric and magnetic electron-nucleon interaction. This allows us to improve limits from the experiments with paramagnetic molecules on the $CP$-violating parameters, such as the proton EDM, $|d_p|< 1.1\times 10^{-23} e\cdot $cm, the QCD vacuum angle, $|\…
In the presence of P,T-violating interactions, the exchange of axion-like particles between electrons and nucleons in atoms and molecules induces electric dipole moments (EDMs) of atoms and molecules. We perform calculations of such axion-exchange-induced atomic EDMs using the relativistic Hartree-Fock-Dirac method including electron core polarisation (RPA) corrections. We present analytical estimates to explain the dependence of these induced atomic EDMs on the axion mass and atomic parameters. From the experimental bounds on the EDMs of atoms and molecules, including $^{133}$Cs, $^{205}$Tl, …
Baryon-number-violating nucleon decays in SMEFT extended with a light scalar
State Key Laboratory of Nuclear Physics and Technology, Institute of Quantum Matter, South China Normal University（华南师范大学量子物质研究所核物理与技术国家重点实验室）；Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Guangdong Provincial Key Laboratory of Nuclear Science（广东省基础研究中心物质结构与基本相互作用卓越中心广东省核科学重点实验室）；Sydney Consortium for Particle Physics and Cosmology, School of Physics, The University of New South Wales（新南威尔士大学物理学院悉尼粒子物理与宇宙学联盟）
It is known that limits on baryon-violating nucleon decays do not, in general, imply corresponding suppression of $n - \bar n$ transitions. In the context of a model with fermions propagating in higher dimensions, we investigate a related question, namely the implications of limits on $ΔL=-1$ proton and bound neutron decays mediated by four-fermion operators for rates of nucleon decays mediated by $k$-fermion operators with $k =6$ and $k=8$. These include a variety of nucleon and dinucleon decays to dilepton and trilepton final states with $ΔL=-3, \ -2, \ 1$, and $2$. We carry out a low-energy…
The basic facts of charge symmetry breaking (CSB) phenomena are reviewed. The relevance of CSB to parity-violating electron-proton scattering experiments that seek to extract strange elastic form factors is discussed. Experimentalists have stated and written that the current uncertainty in our knowledge of CSB limits the ability to push further on the strange form factors. I discuss recent calculations using relativistic chiral perturbation theory and realistic values of strong coupling constants which show that the uncertainties due to lack of knowledge of CSB are at least ten times smaller t…
The consequences of the charge symmetry breaking effects of the mass difference between the up and down quarks and electromagnetic effects for searches for strangeness form factors in parity violating electron scattering from the proton are investigated. The formalism necessary to identify and compute the relevant observables is developed by separating the Hamiltonian into charge symmetry conserving and breaking terms. Using a set of SU(6) non-relativistic quark models, the effects of the charge symmetry breaking Hamiltonian are considered for experimentally relevant alues of the momentum tran…
The electric dipole moment (EDM) of an atom could arise also from $P$-odd and $T$-odd electron-nucleon couplings. In this work we investigate a general class of dimension-$6$ electron-nucleon ($e$-$N$) nonminimal interactions mediated by Lorentz-violating (LV) tensors of rank ranging from $1$ to $4$. The possible couplings are listed as well as their behavior under $C$, $P$ and $T$, allowing us to select the couplings compatible with EDM physics. The unsuppressed contributions of these couplings to the atom's Hamiltonian can be read as EDM-equivalent. The LV coefficients' magnitudes are limite…
The extraction of the strangeness form factors from parity violating elastic electron-proton scattering is sensitive to the electromagnetic form factors at low Q^2. We provide parameterizations for the form factors and uncertainties, including the effects of two-photon exchange corrections to the extracted EM form factors. We study effect of the correlations between different form factors, in particular as they impact the parity violating asymmetry and the extraction of the strangeness form factors. We provide a prescription to extract the strangeness form factors from the asymmetry that provi…
In high energy nuclear collisions, the Glauber model is commonly used to evaluate $J/ψ$ suppression due to inelastic interaction with colorless bound nucleons. This requires an effective value for the $J/ψ$-nucleon absorption cross section which is larger than theoretically expected. On the other hand, multiple nucleon-nucleon collisions mediated by color exchange interactions, excite their color degrees of freedom. We investigate the importance of this effect and conclude that the related corrections are important to explain the effective value extrapolated from experiment.
It is shown that in the experiments for search of EDM of an electron (atom, molecule) the T-odd magnetic moment induced by an electric field and the T-odd electric dipole moment induced by a magnetic field will be also measured. It is discussed how to distinguish these contributions.
We show that grand unified theories based on SO(10) generate naturally the next-to-leading baryon number violating operators of dimension seven. These operators, which violate B-L, lead to unconventional decays of the nucleon such as n -> e^-K^+, e^- π^+ and p -> νπ^+. In two-step breaking schemes of non-supersymmetric SO(10), nucleon lifetime for decays into these modes is found to be within reach of experiments. We also identify supersymmetric scenarios where these decays may be accessible, consistent with gauge coupling unification. Further, we show that the (B-L)-asymmetry generated in the…
It has been shown that CP violating electron-nucleon and nucleon-nucleon interactions can induce atomic electric dipole moments and are therefore constrained from experimental data. We show that using the experimental upper bounds on neutron and electron electric dipole moments, one can also obtain constraints, in some cases better ones, on these interactions. In addition stringent constraints can also be obtained for muon-quark and tauon-quark four-fermion CP violating interactions, which cannot be constrained from atomic electric dipole moment experiments.
When the cross section of J/psi production is considered varying with the energy of the nucleon-nucleon interaction the production of J/psi in pA and AA collisions has been studied using FRITIOF Model. The calculation shows that the cross section of J/psi production "per nucleon-nucleon collision" decreases with increasing mass number and centrality as a consequence of continuous energy loss of the projectile nucleons to the target nucleons in their successive binary nucleon-nucleon collisions . We have compared our model predictions with the experimental data of J/psi production.
We present a comprehensive study of two-boson exchange (TBE) corrections in parity-violating electron-proton elastic scattering. Within a hadronic framework, we compute contributions from box (and crossed box) diagrams in which the intermediate states are described by nucleons and Delta baryons. The Delta contribution is found to be much smaller than the nucleon one at backward angles (small epsilon), but becomes dominant in the forward scattering limit (epsilon -> 1), where the nucleon contribution vanishes. The dependence of the corrections on the input hadronic form factors is small for Q^2…
In high energy nuclear collisions, the conventional Glauber model is commonly used to evaluate the contribution to $J/ψ$ suppression originating from the inelastic interaction with colorless bound nucleons. This requires an effective value for the $J/ψ$-nucleon absorption cross section which is larger than theoretically expected. On the other hand, multiple nucleon-nucleon collisions mediated by color exchange interactions, excite their color degrees of freedom. We investigate the importance of this effect and find that these excited states provide a larger cross section for $J/ψ$ absorption. …
The existence of permanent electric dipole moments (EDMs) and magnetic quadrupole moments (MQMs) violate both time reversal invariance ($T$) and parity ($P$). Following the $CPT$ theorem they also violate combined $CP$ symmetry. Nuclear EDM are completely screened in atoms and molecules while interaction between electrons and MQM creates atomic and molecular EDM which can be measured and used to test CP-violation theories. Nuclear MQM are produced by the nucleon-nucleon $T,P$-odd interaction and by nucleon EDM. In this work we study the effect of enhancement of the nuclear MQM due to the nucle…
We calculate the parity-violating nucleon-nucleon potential in heavy-baryon chiral perturbation theory up to the next-to-next-to-leading order. The one-pion exchange comes in the leading order and the next-to-next-to-leading order consists of two-pion-exchange and the two-nucleon contact terms. In order to investigate the effect of the higher order contributions, we calculate the parity-violating asymmetry in $\vec{n} p \to d γ$ at the threshold. The one-pion dominates the physical observable and the two-pion contribution is about or less than 10% of the one-pion contribution.
We study baryon number violating nucleon decays induced by unparticle interactions with the standard model particles. We find that the lowest dimension operators which cause nucleon decays can arise at dimension 6 + (d_s-3/2) with the unparticles being a spinor of dimension d_s=d_\U +1/2. For scalar and vector unparticles of dimension d_\U, the lowest order operatoers arise at 6+d_\U and 7+d_\U dimensions,respectively. Comparing the spinor unparticle induced n \to O^s_\U and experimental bound on invisible decay of a neutron from KamLAND, we find that the scale for unparticle physics is requir…
We provide a consistent and complete calculation of the electric dipole moments of the deuteron, helion, and triton in the framework of chiral effective field theory. The CP-conserving and CP-violating interactions are treated on equal footing and we consider CP-violating one-, two-, and three-nucleon operators up to next-to-leading-order in the chiral power counting. In particular, we calculate for the first time EDM contributions induced by the CP-violating three-pion operator. We find that effects of CP-violating nucleon-nucleon contact interactions are larger than those found in previous s…
The relations between the value of T- and P-violating correlations in neutron scattering and different models of CP violation are discussed. It is shown that a specific structure of CP-odd interactions gives the possibility to obtain the essential information about CP-odd interaction at the quark-gluon level from nuclear experimental data. The up-to-date estimations for CP- violating nucleon coupling constants show that CP violation in neutron scattering is sensitive to many models of CP violation.
We consider charge-symmetry violations in the nucleon-nucleon force which result from isospin-violating meson-baryon coupling constants. The vector mesons are assumed to couple to the nucleon's electromagnetic current, which we decompose into isoscalar and isovector quark components. We compute these currents in the context of a constituent quark model. The isospin violations in the meson-baryon couplings arise from the difference in the up and down constituent quark masses. We show that class IV charge-symmetry-breaking potentials arise in the resulting $ω$ and $ρ$ exchange contributions to t…
We construct the complete effective chiral pion-nucleon Lagrangian in the presence of virtual photons to one loop. As an application, we consider strong and electromagnetic isospin violation for scattering of neutral pions off nucleons. We show that for the scattering lengths these isospin violating terms are of the same size as the purely hadronic ones. We also analyze isospin-violating effects for the $σ$--term. These can be as large as 10% for the absolute value but are negligible for the shift to the Cheng-Dashen point.
The form factor of the parity and time-reversal violating (PTV) pion-nucleon interaction is calculated from one-loop vertex diagrams. The degrees of freedom included in the effective lagrangian are nucleons, pions, $η$, $ρ$ and $ω$ mesons. We show that by studying the form factor one can constrain the PTV meson-nucleon coupling constants. We evaluate the mean square radius associated with the PTV $πN N$ vertex. Using the mean square radius, we estimate the effect of the PTV $πN N$ vertex on the neutron electric dipole moment, and find a very small correction. We also extract the renormalisatio…
We consider the prospects for studying spin-independent isospin-violating dark matter-nucleon interactions with neutrinos from dark matter annihilation in the Sun, with a focus on IceCube/DeepCore (IC/DC). If dark matter-nucleon interactions are isospin violating, IC/DC's reach in the spin-independent cross section may be competitive with current direct detection experiments for a wide range of dark matter masses. We also compare IC/DC's sensitivity to that of next generation argon, germanium, neon and xenon based detectors.
The measurement of parity violation in the helicity dependence of electron-nucleon scattering provides unique information about the basic quark structure of the nucleons. In this review, the general formalism of parity-violating electron scattering is presented, with emphasis on elastic electron-nucleon scattering. The physics issues addressed by such experiments is discussed, and the major goals of the presently envisioned experimental program are identified. %General aspects of the experimental technique are reviewed and A summary of results from a recent series of experiments is presented a…
The symmetries of the Standard Model dictate that for very low energies, where nucleon dynamics can be described in terms of a pionless effective field theory, the leading-order parity-violating nucleon-nucleon Lagrangian contains five independent unknown low-energy constants (LECs). We find that imposing the approximate symmetry of QCD that appears when the number of colors N(c) becomes large reduces the number of independent LECs to two at leading order in the combined pionless effective field theory and large-N(c) expansions. We also find a relation between the two isoscalar LECs in the lar…
We construct realistic supergravity models where supersymmetry breaking arises from the $D$-terms of an anomalous $U(1)$ gauge symmetry broken at the Planck scale. The model has the attractive feature that the gaugino masses, the $A$ and $B$ terms and the mass splittings between the like-charged squarks of the first two generations compared to their average masses are all suppressed. As a result, the electric dipole moment of the neutron as well as the flavor changing neutral current effects are predicted to be naturally small. These models predict naturally the expected value of the $μ$-term …
We motivate lattice QCD studies of the parity-violating pion-nucleon coupling constant and extend flavor-conserving hadronic parity-violation from QCD to partially-quenched QCD. The parity-violating pion-nucleon coupling and the anapole form factor (and moment) of the proton are computed to one-loop order in the partially-quenched chiral expansion. For the parity-violating pion-nucleon interaction, we include the contributions from total derivative operators necessary to match the kinematics that will be used in lattice simulations.
An effective field theory program to analyze and interpret hadronic parity violation in two-, three-, and few-nucleon systems is described. Observables can be parameterized in terms of five low-energy constants, which have to be determined from experimental input. Results for parity-violating observables in the two- and three-nucleon sectors are presented, including a discussion of the relevance of parity-violating three-nucleon interactions.
