Bounds on Unparticles Couplings to Electrons: from Electron g-2 to Positronium Decays
Yi Liao
备注：
v1: 8 pages, 1 figure; v2: proofread version for PRD. (1) Added '(see also [4])' just before eq. (5). (2) Update ref list and change its format, change one PACS number. (3) Minor changes during the course of copyediting, like adding punctuation to eqs, changing hyphenation, etc
Unparticles as suggested recently by Georgi have surprising phenomenological implications, distinctive from any other new physics that we know of. But they must interact very feebly with ordinary matter to have avoided detection thus far. We determine how feebly they can interact with the electron, using the precisely measured quantities in QED: the electron g-2 and the bounds on invisible and exotic positronium decays. The most stringent bound comes from invisible ortho-positronium decays: the effective energy scale entering the vector unparticle-electron interaction must exceed 4 x 10^5 TeV for a scaling dimension 3/2 of the vector unparticle. The lower bounds on scales for other unparticles range from a few tens to a few hundreds TeV. This makes the detection of unparticles challenging in low energy electron systems.
Unparticles as suggested by Georgi are identities that are not constrained by dispersion relations but are governed by their scaling dimension, d. Their coupling to particles can result in macroscopic interactions between matter, that are generally an inverse nonintegral power of distance. This is totally different from known macroscopic forces. We use the precisely measured long-ranged spin-spin interaction of electrons to constrain unparticle couplings to the electron. For 1<d<1.5 the axial vector unparticle coupling is excluded; and for 1<d<1.3 the pseudoscalar and vector couplings are also…
Unparticles ($\U$) interact weakly with particles. The direct signature of unparticles will be in the form of missing energy. We study constraints on unparticle interactions using totally invisible decay modes of $Z$, vector quarkonia $V$ and neutrinos. The constraints on the unparticle interaction scale $Λ_\U$ are very sensitive to the dimension $d_\U$ of the unparticles. From invisible $Z$ and $V$ decays, we find that with $d_\U$ close to 1 for vector $\U$, the unparticle scale $Λ_\U$ can be more than $10^4$ TeV, and for $d_\U$ around 2, the scale can be lower than one TeV. From invisible ne…
We show that when the unparticle sector is coupled to the Standard Model, unparticle excitations can decay to Standard Model particles. This radically modifies the signals of unparticle production. We present a method for the calculation of the decay lifetimes of unparticles. In a particular model, we show that depending on their lifetime, unparticles can manifest themselves through monojets, delayed events or prompt decays.
The decay width of the rare decay Z \to ν\barνγγis strictly constrained from the LEP data. Tensor unparticles provide a tree-level contribution to this rare decay. We have calculated the tensor unparticle contribution to the rare decay Z\to ν\barνγγ. The current experimental limit have been used to constrain unparticle couplings ν\barνZ {U}^{μν} and γγ{U}^{μν}.
We study the production of the vector $U$ -unparticle stuff and a single photon in decays of a dilaton. The signals of an unparticle can be detected through the missing energy and momentum distribution carried away by $U$ once it was produced in radiative decay of a dilaton The continuous energy spectrum of the emitted photons encoding the recoil unparticle can be measured in precision studies of rare decays of the dilaton or Higgs-boson after their discoveres.
We consider a scenario where ultra high energy neutrinos undergo unparticle decay during its passage from its cosmological source to Earth. The idea of unparticle had been first proposed by Georgi by considering the possible existence of an unknown scale invariant sector at high energies and the unparticles in this sector manifest itself below a dimensional transmutation scale $Λ_{\cal U}$. We then explore the possible signature of such decaying neutrinos to unparticles at a square kilometer detector such as IceCube.
We study the decay of a Z' - boson into U -unparticle and a photon. The extended Landau-Yang theorem is used. The clear photon signal would make the decay Z' \rightarrow γU as an additional contribution mode for study of unparticle physics.
We investigate the rare radiative decays of extra gauge neutral bosons. In particular, we established the theoretical predictions for the production of unparticle in decays of $Z^{\prime}$ - bosons. The implementation of our prediction in the analysis at the LHC experiments should be straightforward and lead to more precise determination or limits of unparticle couplings and/or $Z^{\prime}$ couplings and masses.
We consider the unparticle physics introduced by Georgi and show that if the standard model is extended to include a singlet scalar as a dark matter candidate, there is a channel which leads to its decay to photon and unparticle. We calculate the decay rate for this new channel and find a lower bound on unparticle physics scale by demanding the stability of this candidate of the dark matter.
We study effects of unparticle physics on muon g-2 and LFV tau decay processes. LFV interactions between the Standard Model sector and unparticles can explain the difference of experimental value of muon g-2 from the Standard Model prediction. While the same couplings generate LFV tau decay, we found that LFV coupling can be of O(0.1 ... 1) without conflict with experimental bounds of LFV tau decay if the scaling dimension of unparticle operator d_{U} > 1.6.
We predict the contribution of scalar unparticle to the branching ratios of the lepton flavor conserving Z -> l^+ l^- decays and we study the discrepancy between the experimental and the QED corrected standard model branching ratios. We observe that these decays are sensitive to the unparticle scaling dimension d_u for its small values, especially for heavy lepton flavor output.
We study the decay of the standard model Z boson into unparticle plus a single photon through a one-loop process. As in the anomaly type decay, only the axial-vector part of the Z coupling matching with the vector unparticle and/or the vector part of the Z coupling matching with the axial-vector unparticle can give a nonzero contribution to the decay. We show that the photon spectrum terminates at the end point in accord with Yang's theorem. Existing data on single photon production at LEP I is used to constrain the unparticle sector.
The effects of the peculiar CP conserving phases in unparticle propagators are explored. We find that the phases have a great impact on CP-violation. We adopt the decays $B_{d}\to π^{+} π^{-}$ and $B_{d}\to \ell^{-}\ell^{+}$ as the illustrators to demonstrate the influences of these phases on the direct CP asymmetries. In particular, we emphasize that unparticle physics is the only model suggested to date that could give the direct CP asymmetries in $B_d\to \ell^{-} \ell^{+}$ as large as 15%. We also point out that the unparticle phases could be probed in $B\to K^* \ell^{+} \ell^{-}$ decays by…
We study the contribution of the antisymmetric tensor unparticle mediation to the diphoton production rate of the Higgs boson and try to explain the discrepancy between the measured value of the decay width of the discovered new resonance and that of the standard model Higgs boson. We observe that tree level contribution of the antisymmetric unparticle mediation is a possible candidate to explain the measured value of the diphoton decay rate.
Rare (t -> c g g) decay can only appear at loop level in the Standard Model (SM), and naturally they are strongly suppressed. These flavor changing decays induced by the mediation of spin-0 and spin-2 unparticles, can appear at tree level in unparticle physics. In this work the virtual effects of unparticle physics in the flavor-changing (t -> c g g) decay is studied. Using the SM result for the branching ratio of the (t -> c g g) decay, the parameter space of d_U and Lambda_U, where the branching ratio of this decay exceeds the one predicted by the SM, is obtained. Measurement of the branchin…
The decay of the standard model Higgs boson into a single photon and a vector unparticle through a one-loop process is studied. For an intermediate mass Higgs boson, this single photon plus unparticle mode can have a branching ratio comparable with the two-photon discovery mode. The emitted photon has a continuous energy spectrum encoding the nature of the recoil unparticle. It can be measured in precision studies of the Higgs boson after its discovery.
The unparticle is proposed by Georgi as a conceptual new physics beyond the standard model to describe the low energy sector of a nontrivial scale invariant sector of an effective theory. We consider the neutrino decay in unparticle scenario and investigate the effect of such decay for the case of ultra high energy neutrinos from GRB. The effect on the detection yield of these neutrinos are also probed for a kilometer scale ice-Cerenkov detector.
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 study the radiative lepton flavor violating l_i -> l_j γγdecays in the case that the lepton flavor violation is induced by the scalar unparticle mediation. We restrict the scaling dimension d_u and the scalar unparticle-photon-photon coupling by using the experimental upper limit of the branching ratio of the decay μ-> e γγ. Furthermore, we predict the BRs of the other radiative decays by using the restrictions we get. We observe that the measurements of upper limits of BRs of these decays ensure considerable information for testing the possible signals coming from unparticle physics
The coupling of an unparticle operator O_U to Standard Model particles opens up the possibility of unparticle decays into standard model fields. We study this issue by analyzing the pole structure (and spectral function) of the unparticle propagator, corrected to account for one-loop polarization effects from virtual SM particles. We find that the propagator of a scalar unparticle (of scaling dimension 1 < d_U < 2) with a mass gap m_g develops an isolated pole, m_p^2-i m_p Gamma_p, with m_p^2 < m_g^2 below the unparticle continuum that extends above m_g (showing that the theory would be unstab…
We predict the branching ratios of the lepton flavor violating Higgs decays H^0\rightarrow e^{\pm} μ^{\pm}, H^0\rightarrow e^{\pm} τ^{\pm} and H^0\rightarrow μ^{\pm} τ^{\pm} with the assumption that lepton flavor violation is due to the unparticle mediation. Here, we consider an effective interaction which breaks the conformal invariance after the electroweak symmetry breaking and causes that unparticle becomes massive. The new interaction results in a modification of the mediating unparticle propagator and brings additional contribution to the branching ratios of the lepton flavor violating d…
We study the contribution of the tensor unparticle mediation to the branching ratios of the radiative lepton flavor violating decays and predict a restriction region for free parameters of the scenario by using experimental upper limits. We observe that the branching ratios of the radiative lepton flavor violating decays are sensitive to the fundamental mass scales of the scenario and to the scale dimension of antisymmetric tensor unparticle. We obtain a more restricted set for the free parameters in the case of the μ\rightarrow e γdecay
We investigate the effect of unparticles in the pure annihilation type decays $B^- \to D_s^-ϕ$ and $ D_s^- K^{*0}$. Since these decays have only annihilation contributions their branching ratios are expected to be very small in the standard model and the direct CP asymmetry parameters to be zero. We find that due to the unparticle effect these branching ratios can be significantly enhanced from their standard model values. Furthermore, sizable nonzero direct CP violation could also be possible in these channels due to the presence of intrinsic CP conserving phase in the unparticle propagator.
Recently Georgi has discussed the possible existence of `Unparticles' describable by operators having non-integral scaling dimensions. With the interaction of these with the Standard Model (SM) particles being constrained only by gauge and Lorentz symmetries, it affords a new source for lepton flavour violation. Current and future muon decay experiments are shown to be very sensitive to such scenarios.
We predict the branching ratios of the lepton flavor violating Higgs decays H^0->e^{\pm} μ^{\pm}, H^0-> e^{\pm} τ^{\pm} and H^0->μ^{\pm} τ^{\pm} in the case that the lepton flavor violation is carried by the scalar unparticle mediation. We observe that their branching ratios are strongly sensitive to the unparticle scaling dimension and they can reach to the values of the order of $10^{-4}$, for the heavy lepton flavor case and for the small values of the scaling dimension.
A first result related to a CPT test in the decay of ortho-positronium based on data collected by means of the J-PET detector is already available, and a new test of CP symmetry is under investigation. Both results are based on the determination of angular correlations between momenta of gamma rays and other vector properties of the investigated system. Here, arguments for the possible usage of data collected by the J-PET group to test CPT symmetry within the Standard-Model Extension framework are shortly presented.
We predict the branching ratios of the lepton flavor violating Z boson decays Z\to e^{\pm} μ^{\pm}, Z\to e^{\pm} τ^{\pm} and Z\to μ^{\pm} τ^{\pm} in the case that the lepton flavor violation is carried by the scalar unparticle mediation. We observe that their BRs are strongly sensitive to the unparticle scaling dimension and the branching ratios can reach to the values of the order of 10^{-8}, for the heavy lepton flavor case, for the small values of the scaling dimension.
We predict the branching ratios of the lepton flavor violating radion decays r -> e^{\pm} μ^{\pm}, r -> e^{\pm} τ^{\pm} and r ->μ^{\pm} τ^{\pm} in the framework of the Randall-Sundrum scenario that the lepton flavor violation is carried by the scalar unparticle mediation. We observe that their BRs are strongly sensitive to the unparticle scaling dimension and, for its small values, the branching ratios can reach to the values of the order of 10^{-8}, for the heavy lepton flavor case.
The LHCb Collaboration has recently measured the difference of time-integrated $CP$ asymmetry in $D^{0}\rightarrow K^{+}K^{-}$ and $D^{0}\rightarrow π^{+}π^{-}$ decays, more precisely. The reported value is $ ΔA_{CP}=-0.10 \pm 0.08 (\text{stat}) \pm 0.03 (\text{syst})\% $ which indicates no evidence for $CP$ violation. We consider the possible unparticle physics contribution in this quantity and by using the LCHb data try to constrain the parameter space of unparticle stuff.
We investigate the lepton flavor violation decays of vector mesons in the scenario of the unparticle physics by considering the constraint from $μ-e$ conversion. In unparticle physics, the predictions of LFV decays of vector mesons depend strongly on the scale dimension $d_{\mathcal{U}}$. The predictions of LFV decays of vector mesons can reach the detective sensitivity in experiment in region of $3\le d_{\mathcal{U}}\le 4$, while the prediction of $μ-e$ conversion rate can meet the experimental upper limit. For the searching of the lepton flavor violation processes of charged lepton sector in…
We analyze the inclusive decay mode $B\to X_s+{\rm Missing Energy}$ in the unparticle model, where an unparticle can also serve as the missing energy. We use the Heavy Quark Effective Theory in the calculation. The analytical result of the decay width in the free quark limit and that of the differential decay rate to the order of $1/m_b^2$ are presented. Numerical results of the inclusive mode show interesting differences from those of the exclusive modes. Near the lower endpoint region, the $d_{\mathcal U}<2$ unparticle has very different behavior from the Standard Model particles.
We discuss properties of hypothetical scale invariant (unparticle) matter by viewing it as a tower of massive particles. We show how peculiar properties of unparticles emerge in the limit when the mass spacing parameter Delta vanishes. We explain why unparticle cannot decay in this limit and how, for finite Delta, the decays manifest themselves in a relation between the reconstructed invariant mass and vertex displacement. We describe a model field theory in AdS5 which explicitly implements the deconstruction procedure by truncating the extra dimension to size of order 1/Delta.
Following Georgi's unparticle scheme, we examine the effective couplings between neutrinos and unparticle operators. As an immediate consequence, neutrinos become unstable and can decay into the unparticle stuff. Assuming the dimension transmutation scale is around $Λ^{}_{\cal U} \sim 1 ~{\rm TeV}$, we implement the cosmological limit on the neutrino lifetime to constrain the neutrino-unparticle couplings for different scaling dimensions $d$. In addition, provided that the electron-unparticle coupling is restricted due to the precise measurement of the anomalous magnetic moment of electron, we…
We study unparticle physics effects in (Lambda_b -> Lambda + missing energy) decay with polarized $Λ_b$ and $Λ$ baryons. The sensitivity of the branching ratio of this decay and polarizations of (Lambda_b) and (Lambda) baryons on the scale dimension d_U and effective cut-off parameter (Lambda_U) are discussed.
Corrections $\sim α^2 $ to the positronium decay rate, induced by one--loop vacuum polarization diagram, are calculated. Their relative values are $0.4468(3)(α/π)^2$ for para- and $0.960(3)(α/π)^2$ for orthopositronium.
Recently H. Georgi has introduced an unparticle $\unpart$ in order to describe the low energy physics of a nontrivial scale invariant sector of an effective theory. In this work we have explored the phenomenology of an unparticle using the lepton flavour violating decay $μ^{-}\to e^{-} e^{+} e^{-}$, and found that the branching ratio of this decay is strongly dependent on the scaling dimension.
Relativistic corrections to the positronium decay rate are calculated. They are close to $40(α/π)^2$ and $46(α/π)^2$ for singlet and triplet states respectively.
In this work we study the flavor changing neutral current(FCNC) decays of the top quark, $t\to cγ$ and $t\to c g$. The Standard Model, predictions for the branching ratios of these decays are about $\sim 5\times 10^{-14}$, and $\sim 1\times 10^{-12}$, respectively. The recent study presented by the ATLAS Collaboration gives a sensitivity on these branching ratios about $\sim 10^{-5}$ at $%95$ C.L. The parameter space of $λ$, $Λ$, and $d$ where the branching ratios of $t\to cγ$ and $t\to c g$ decays exceed these predictions is obtained.
In the present work we study the effects of an unparticle $\unpart$ as the possible source of missing energy in the decay $B \to K (K^*) + {\rm missing energy}$. We find that the dependence of the differential branching ratio on the $K$($K^*$)-meson's energy in the presence of the vector unparticle operators is very distinctive from that of the SM. Moreover, in using the existing upper bound on $B \to K (K^*) + {\rm missing energy}$ decays, we have been able to put more stringent constraints on the parameters of unparticle stuff.
We have investigated the effects of unparticles in decays $B \to l ν$. It is found that the direct CP violation in the decays, which is zero in SM, can show up due to the CP conserving phase intrinsic in unparticle physics. For $l=τ$, the direct CP asymmetry can reach 30% for the scalar unparticle contribution, and 100% for the longitudinal vector unparticle contribution under the constraints of ${\rm Br}(B\toτν)$ and $νe$ elastic scattering. If both unparticle-lepton coupling universality and unparticle-quark coupling universality are assumed the constraint from $Br(π\to μν)$ leads that the d…
We analyze the branching ratio and spectrum for the decay mode $K^+ \toπ^++{\not}E$(missing energy) in the unparticle model, where an unparticle can also serve as the missing energy. A vector unparticle can even mediate the $K^+ \to π^+ +ν\barν$, resulting complicated interference with the Standard Model.
Positronium, the electron-positron bound state, is described to a good approximation by pure QED. The states of positronium have definite values of C and P. Consequently, positronium is an attractive system for the investigation of possible violations of the discrete symmetries in the leptonic sector. We discuss signals for CP and CPT violation in the decay of spin-polarized orthopositronium and show where such correlations might arise in the context of the Standard-Model Extension.
According to the standard model, the Cabibbo-favored (CF) decays are $CP$ conserve at tree level. Observation of any finite $CP$ asymmetry can be received as a signal of new physics. In CF charm meson decays, $ D^0 \rightarrow K^- π^+ $ and $ D^+ \rightarrow K_s^0 π^+ $, the following experimental values for their $CP$ asymmetry are reported, respectively: ($0.3 \pm 0.7$) % and ($-0.41 \pm 0.09$) %. The value of the later can be attributed to the mixing of $ K^0 $ and $ \overline{K^0} $, however, its contribution is about ($-0.332 \pm 0.006 $) %. In this paper, we use these experimental result…
The recent measurement on the decay constant of $D_s$ shows a discrepancy between theory and experiment. We study the leptonic and semileptonic decays of $D$ and $D_s$ simultaneously within the standard model by employing a lightfront quark model. There is space by tuning phenomenological parameters which can explain the "$f_{D_s}$ puzzle" and do not contradict other experiments on the semileptonic decays. We also investigate the leptonic decays of D and $D_{s}$ with a new physics scenario, unparticle physics. The unparticle effects induce a constructive interference with the standard model co…
With rapid growth of the database of the BES III and the proposed super flavor factory, measurement on the rare $ψ(2S)$ decays may be feasible, especially the weak decays into baryon final states. In this work we study the decay rate of $ψ(2S)$ to $Λ_c+\overline{Σ^+}$ in the SM and physics beyond the SM (here we use the unparticle model as an example). The QPC model is employed to describe the creation of a pair of $q\bar q$ from vacuum. We find that the rate of $ψ(2S)\rightarrow Λ_c+\overline{Σ^+}$ is at order of $10^{-10}$ in the SM, whereas the contribution of the unparticle is too small to…
We examine the effects of an unparticle $\mathcal{U}$ as a possible source of missing energy in the p-wave decays of $B$ meson. The dependence of the differential branching ratio on the $K_{0}^{\ast}(K_{1}) -$% meson's energy is discussed in the presence of scalar and vector unparticle operators and significant deviation from the standard model value is found after addition of these operators. Finally, we have shown the dependence of branching ratio for the above said decays on the parameters of the unparticle stuff like the effective couplings, cutoff scale $Λ_{% \mathcal{U}}$ and the scale d…
Interest has been directed recently towards low energy implications of a non-trivial conformal sector of an effective field theory with an IR fixed point (Λ), manifest in terms of ``unparticles'' with bizarre properties. We re-examine the implications of the limits on decay lifetimes of solar neutrinos for unparticle interactions. We study in detail the fundamental parameter space (Λ, M) and derive bounds on the energy scale M characterizing the new physics. We work strictly within the framework where conformal invariance holds down to low energies. We first assume that couplings of the unpart…
We rederive here in a simple and transparent way the master formula for the dominant part of large relativistic corrections to the positronium decay rate.
Self-energy corrections of order O(alpha^2) to the parapositronium and orthopositronium decay rates are calculated. Numerical values of the corresponding coefficients are B_p=-3.74, B_o=2.02.
We investigate the implication of unparticle physics on the B_{u,d}\to (π, K) πdecays under the constraints of the B_{d,s}-\bar B_{d,s} mixing. We found that not only the unparticle parameters that belong to the flavor changing neutral current (FCNC) processes but also scaling dimension d_{\UP} could be constrained by the B_{d,s}-\bar B_{d,s} mixing phenomenology. Employing the minimum χ^2 analysis to the B_{u,d}\to (π, K) πdecays with the constraints of B_{d,s} mixing, we find that the puzzle of large branching ratio for B_{d}\to π^0 π^0 and the discrepancy between the standard model estimati…
We study the effect of unparticle stuff on $B_s - \bar{B}_s$ mixing and consider possible implications of it for the decaymodes $B_s \to J/ψϕ$ and $ϕϕ$. We find that due to the new contributions from the unparticles the $B_s - \bar{B}_s$ mixing phase could be observable at the LHC along with the possible sizable CP asymmetry parameters $S_{ψϕ(ϕϕ)}$ in $B_s \to J/ψϕ(ϕϕ)$ decay modes.
We briefly review the theoretical and experimental results concerning decays of positronium. Possible solutions of the "orthopositronium lifetime puzzle" are discussed. Positronium annihilation into neutrinos is examined and disagreement is found with previously published results.
We investigate the invisible decay of positronium to probe the fermionic light dark matter mediated by the dark $Z$ boson. Too tiny is the invisible decay rate of positronium through weak interaction in the standard model to be detected in the experiment. We show that it can be enhanced to be observed in the future if the dark matter is lighter than the electron in the dark $Z$ model. We also compute the relic abundance of such light dark matter and discuss the Big Bang Nucleosynthesis constraint with an alternative thermal history scenario.
We construct the propagator for a free fermionic unparticle field from basic considerations of scale and Lorentz invariance. The propagator is fixed up to a normalization factor which is required to recover the result of a free massless fermion field in the canonical limit of the scaling dimension. Two new features appear compared to the bosonic case. The propagator contains both γand non-γterms, and there is a relative phase of π/2 between the two in the time-like regime for arbitrary scaling dimension. This should result in additional interference effects on top of the one known in the boson…
We establish irrational constants, that contribute to the positronium lifetime at $O(α)$ and $O(α^2)$ order. In particular we show, that a new type of constants appear, which are not related to Euler--Zagier sums or multiple $ζ$ values.
Whether in the Standard Model or beyond it, neutrinos contribute to the invisible decay mode of orthopositronium but practically not at all to that of parapositronium. Although this remark does not resolve the orthopositronium decay puzzle, it allows for upper bounds to be set on neutrino magnetic moments.
Unparticle contributions to the recently measured decay mode $B_s\toμ^+μ^-$ are analyzed. We consider only the scalar unparticles because vector unparticles are expected to provide negligible contributions. Assuming that the relevant coupling constants are real, we present allowed regions of coupling constants and the scaling dimension of the scalar unparticle. While the measured value of the branching ratio is very close to the standard model predictions, one cannot exclude the possible contributions from unparticles.
We compute O(alpha^3 ln alpha) corrections to the decay rates of para- and orthopositronium into two and three photons, respectively. For this calculation we employ the nonrelativistic QED regularized dimensionally and we explain how in this framework the logarithms of the fine structure constant can be extracted.
We make an evaluation of the lepton flavor violating (LFV) decays $τ\to \ell (V^0, P^0)$, where $\ell=e$ or $μ$ and $V^0(P^0)$ is a neutral vector (pseudo-scalar) meson, in the context of unparticle physics. The constraints are investigated systematically on the related coupling parameters from all the available experimental data, and the parameter values are specified appropriately. The results show that whereas over the whole parameter space allowed by experiments all the $τ\to \ell P^0$ modes have a branching ratio too small to be measurable experimentally, in a large subspace as observed a…
