Search for new physics via baryon EDM at LHC
L. Henry, D. Marangotto, A. Merli, N. Neri, J. Ruiz, F. Martinez Vidal
JJanuary 5, 2021 1:56 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in main page 1 Search for new physics via baryon EDM at LHC
L. Henry , D. Marangotto , A. Merli , , N. Neri , , J. Ruiz , F. Martinez Vidal IFIC, Universitat de Val`encia-CSIC, Valencia, Spain INFN Sezione di Milano and Universit`a di Milano, Milan, Italy CERN, Geneva, Switzerland
Permanent electric dipole moments (EDMs) of fundamental particles provide powerfulprobes for physics beyond the Standard Model. We propose to search for the EDM ofstrange and charm baryons at LHC, extending the ongoing experimental program onthe neutron, muon, atoms, molecules and light nuclei. The EDM of strange Λ baryons,selected from weak decays of charm baryons produced in pp collisions at LHC, can bedetermined by studying the spin precession in the magnetic field of the detector trackingsystem. A test of CP T symmetry can be performed by measuring the magnetic dipolemoment of Λ and Λ baryons. For short-lived Λ + c and Ξ + c baryons, to be produced ina fixed-target experiment using the 7 TeV LHC beam and channeled in a bent crys-tal, the spin precession is induced by the intense electromagnetic field between crystalatomic planes. The experimental layout based on the LHCb detector and the expectedsensitivities in the coming years are discussed. Keywords : Baryons (including antiparticles) - Electric and magnetic moments
1. Introduction
The magnetic dipole moment (MDM) and the electric dipole moment (EDM) arestatic properties of particles that determine the spin motion in an external electro-magnetic field, as described by the T-BMT equation .The EDM is the only static property of a particle that requires the violation ofparity ( P ) and time reversal ( T ) symmetries and thus, relying on CP T invariance,the violation of CP symmetry. The amount of CP violation in the weak interactionsof quarks is not sufficient to explain the observed imbalance between matter andantimatter in the Universe. CP-violation in strong interactions is strongly boundedby the experimental limit on the neutron EDM . In the Standard Model (SM),contributions to the EDM of baryons are highly suppressed but can be largelyenhanced in some of its extensions. Hence, the experimental searches for the EDMof fundamental particles provide powerful probes for physics beyond the SM.Since EDM searches started in the fifties , there has been an intense experimen-tal program, leading to limits on the EDM of leptons , neutron , heavy atoms ,proton (indirect from Hg) , and Λ baryon . New experiments are ongoing andothers are planned, including those based on storage rings for muon , protonand light nuclei . Recently we proposed to improve the limit on strange baryonsand extend it to charm and bottom baryons .EDM searches of fundamental particles rely on the measurement of the spinprecession angle induced by the interaction with the electromagnetic field. For a r X i v : . [ h e p - e x ] J a n anuary 5, 2021 1:56 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in main page 2 unstable particles this is challenging since the precession has to take place beforethe decay. A solution to this problem requires large samples of high energy polarizedparticles traversing an intense electromagnetic field.Here we reviewed the unique possibility to search for the EDM of the strange Λ baryon and of the charmed baryons at LHC. Using the experimental upperlimit of the neutron EDM, the absolute value of the Λ EDM is predicted to be < . × − e cm , while the indirect constraints on the charm EDM areweaker, < ∼ . × − e cm . Any experimental observation of an EDM wouldindicate a new source of CP violation from physics beyond the SM. The EDM ofthe long-lived Λ baryon was measured to be < . × − e cm (95% C.L.) in afixed-target experiment at Fermilab . No experimental measurements exist forshort-lived charm baryons since negligibly small spin precession would be inducedby magnetic fields used in current particle detectors.
2. Experimental setup
The magnetic and electric dipole moment of a spin-1/2 particle is given (in Gaussianunits) by µ = gµ B s / δ = dµ B s /
2, respectively, where s is the spin-polarizationvector a and µ B = e (cid:126) / (2 mc ) is the particle magneton, with m its mass. The g and d dimensionless factors are also referred to as the gyromagnetic and gyroelectricratios. The experimental setup to measure the change of the spin direction in anelextromagnetic field relies on three main elements:(i) a source of polarized particles whose direction and polarization degree are known;(ii) an intense electromagnetic field able to induce a sizable spin precession angleduring the lifetime of the particle;(iii) the detector to measure the final polarization vector by analysing the angulardistribution of the particle decays. Λ and Λ case Weak decays of heavy baryons (charm and beauty), mostly produced in the for-ward/backward directions at LHC, can induce large longitudinal polarization dueto parity violation. For example, the decay of unpolarized Λ + c baryons to the Λπ + final state , produces Λ baryons with longitudinal polarization ≈ − Λ b → ΛJ/ψ decay where Λ baryons are produced almost 100%longitudinally polarized .The spin-polarization vector s of an ensemble of Λ baryons can be analysedthrough the angular distribution of the Λ → pπ − decay , dNd Ω (cid:48) ∝ α s · ˆ k , (1) a The spin-polarization vector is defined such as s = 2 (cid:104) S (cid:105) / (cid:126) , where S is the spin operator. anuary 5, 2021 1:56 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in main page 3 where α = 0 . ± . is the decay asymmetry parameter. The CP invariancein the Λ decay implies α = − α , where α is the decay parameter of the charge-conjugate decay. The unit vector ˆ k = (sin θ (cid:48) cos φ (cid:48) , sin θ (cid:48) sin φ (cid:48) , cos θ (cid:48) ) indicates themomentum direction of the proton in the Λ helicity frame, with Ω (cid:48) = ( θ (cid:48) , φ (cid:48) ) thecorresponding solid angle. For the particular case of Λ flying along the z axis inthe laboratory frame, an initial longitudinal polarization s , i.e. s = (0 , , s ), and B = (0 , B y , s = s x = − s sin Φ s y = − s dβg sin Φ s z = s cos Φ (2)where Φ = D y µ B β (cid:126) c (cid:112) d β + g ≈ gD y µ B β (cid:126) c with D y ≡ D y ( l ) = (cid:82) l B y dl (cid:48) the integratedmagnetic field along the Λ flight path. The polarization vector precesses in the xz plane, normal to the magnetic field, with the precession angle Φ proportional tothe gyromagnetic factor of the particle. The presence of an EDM introduces a non-zero s y component perpendicular to the precession plane of the MDM, otherwisenot present. At LHCb, with a tracking dipole magnet providing an integrated field D y ≈ ± , the maximum precession angle for particles traversing the entiremagnetic field region yields Φ max ≈ ± π/
4, and allows to achieve about 70% of themaximum s y component. Moreover, a test of CP T symmetry can be performed bycomparing the g and − ¯ g factors for Λ and Λ baryons, respectively, which precess inopposite directions as g and d change sign from particle to antiparticle. Charm baryon case
The Λ + c baryon EDM can be extracted by measuring the precession of the polar-ization vector of channeled particles in a bent crystal. There, a positively-chargedparticle channeled between atomic planes moves along a curved path under the ac-tion of the intense electric field between crystal planes. In the instantaneous restframe of the particle the electromagnetic field causes the spin rotation. The signa-ture of the EDM is a polarization component perpendicular to the initial baryonmomentum and polarization vector, otherwise not present, similarly to the case ofthe Λ baryon.The phenomenon of spin precession of positively-charged particles channeled in abent crystal was firstly observed by the E761 collaboration that measured the MDMof the strange Σ + baryon . The feasibility of the measurement at LHC energiesoffers clear advantages with respect to lower beam energies since the estimatednumber of channeled charm baryons is proportional to γ / , where γ is the Lorentzfactor of the particles .In the limit of large boost with Lorentz factor γ (cid:29)
1, the precession angle Φ, anuary 5, 2021 1:56 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in main page 4 y zx s Λ c+ p TargetProduction plane yx s Λ c+ Bent crystal Φ B * E * z θ C y z Fig. 1. (Left) Production plane of the Λ + c baryon defined by the proton and the Λ + c momenta.The initial polarization vector s is perpendicular to the production plane, along the y axis, dueto parity conservation in strong interactions . (Right) Deflection of the baryon trajectory andspin precession in the yz and xy plane induced by the MDM and the EDM, respectively. The red(dashed) arrows indicate the (magnified) s x spin component proportional to the particle EDM.Φ is the MDM precession angle and θ C is the crystal bending angle. E ∗ and B ∗ are the intenseelectromagnetic field in the particle rest frame which induce spin precession. shown in Fig. 1, induced by the MDM is Φ ≈ g − γθ C , (3)where g is the gyromagnetic factor, θ C = L/ρ is the crystal bending angle, L isthe circular arc of the crystal and ρ the curvature radius .In presence of a non-zero EDM, the spin precession is no longer confined to the yz plane, originating a s x component proportional to the particle EDM represented bythe red (dashed) arrows in (Right) Fig. 1. The polarization vector, after channelingthrough the crystal is s = s x ≈ s dg − − s y ≈ s cos Φ s z ≈ s sin Φ , (4)where Φ is given by Eq. (3). The MDM and EDM information can be extractedfrom the measurement of the spin polarization of channeled baryons at the exit ofthe crystal, via the study of the angular distribution of final state particles. For Λ + c decaying to two-body final states such as f = ∆ ++ K − , pK ∗ , ∆(1520) π + andΛ π − , the angular distribution is described by Eq. 1. A Dalitz plot analysis wouldprovide the ultimate sensitivity to the EDM measurement.The initial polarization s would require in principle the measurement of the an-gular distribution for unchanneled baryons. In practice this is not required since themeasurement of the three components of the final polarization vector for channeledbaryons allows a simultaneous determination of g, d and s , up to discrete ambi-guities. These can be solved exploiting the dependence of the angular distributionwith the Λ + c boost γ , as discussed in Ref. . anuary 5, 2021 1:56 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in main page 5
3. Sensitivity studies3.1. Λ and Λ case The number of Λ particles produced can be estimated as N Λ = 2 L σ qq f ( q → H ) B ( H → ΛX (cid:48) ) B ( Λ → pπ − ) B ( X (cid:48) → charged) , (5)where L is the total integrated luminosity, σ qq ( q = c, b ) are the heavy quarkproduction cross sections from pp collisions at √ s = 13 TeV , and f is thefragmentation fraction into the heavy baryon H . In Table 1 the dominant Table 1. Dominant Λ production mechanisms from heavy baryon decays and estimated yieldsproduced per fb − at √ s = 13 TeV, shown separately for SL and LL topologies. The Λ baryonsfrom Ξ − decays, produced promptly in the pp collisions, are given in terms of the unmeasuredproduction cross section.SL events N Λ / fb − ( × ) LL events, Ξ − → Λπ − N Λ / fb − ( × ) Ξ c → ΛK − π + Ξ c → Ξ − π + π + π − Λ + c → Λπ + π + π − Ξ c → Ξ − π + Ξ + c → ΛK − π + π + Ξ + c → Ξ − π + π + Λ + c → Λπ + Λ + c → Ξ − K + π + Ξ c → ΛK + K − (no φ ) 0.2 Ξ c → Ξ − K + Ξ c → Λφ ( K + K − ) 0.1 Prompt Ξ − . × σ pp → Ξ − [ µ b] production channels and the estimated yields are summarised. Only the decayswhere it is experimentally possible to determine the production and decay vertexof the Λ are considered. Overall, there are about 1 . × Λ baryons per fb − produced directly from heavy baryon decays (referred hereafter as short-lived, or SLevents), and 3 . × from charm baryons decaying through an intermediate Ξ − particle (long-lived, or LL events). The yield of Λ baryons experimentally availablecan then be evaluated as N reco Λ = (cid:15) geo (cid:15) trigger (cid:15) reco N Λ , where (cid:15) geo , (cid:15) trigger and (cid:15) reco arethe geometric, trigger and reconstruction efficiencies of the detector system. Thegeometric efficiency for SL topology has been estimated to be about 16% using aMonte Carlo simulation of pp collisions at √ s = 13 TeV and the decay of heavyhadrons.To assess the EDM sensitivity, pseudo-experiments have been generated usinga simplified detector geometry that includes an approximate LHCb magnetic fieldmapping . Λ baryons decaying towards the end of the magnet provide most ofthe sensitivity to the EDM and MDM, since a sizeable spin precession could hap-pen. The decay angular distribution and spin dynamics have been simulated usingEq. (1) and the general solution as a function of the Λ flight length , respectively.For this study the initial polarization vector s = (0 , , s ), with s varying between20% and 100%, and factors g = − . and d = 0, were used. Each generatedsample was fitted using an unbinned maximum likelihood method with d , g and s as free parameters. The d -factor uncertainty scales with the number of events N reco Λ anuary 5, 2021 1:56 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in main page 6 and the initial longitudinal polarization s as σ d ∝ / ( s (cid:112) N reco Λ ). The sensitivitysaturates at large values of s , as shown in (Left) Fig. 2, and it partially relaxes therequirements on the initial polarizations. Similarly, (Right) Fig. 2 shows the ex-pected sensitivity on the EDM as a function of the integrated luminosity, summingtogether SL and LL events, assuming global trigger and reconstruction efficiency (cid:15) trigger (cid:15) reco of 1% (improved LHCb software-based trigger and tracking for the up-grade detector ) and 0.2% (current detector ), where the efficiency estimatesare based on a educated guess. An equivalent sensitivity is obtained for the gy-romagnetic factor. Therefore, with 8 fb − a sensitivity σ d ≈ . × − couldbe achieved (current detector), to be compared to the present limit, 1 . × − .With 50 fb − (upgraded detector) the sensitivity on the gyroelectric factor canreach ≈ × − . s d s Error of d ) -1 (fb L d s - · x+y = 0.2% trigger e reco e = 1% trigger e reco e Fig. 2. (Left) Dependence of the Λ gyroelectric factor uncertainty with the initial polarization for N reco Λ = 10 events, and (Right) as a function of the integrated luminosity assuming reconstructionefficiency of 0.2% and 1%. Charm baryon case
We propose to search for charm baryon EDMs in a dedicated fixed-target experimentat the LHC to be installed in front of the LHCb detector. The target should beattached to the crystal to maximize the yield of short-lived charm baryons to bechanneled. The rate of Λ + c baryons produced with 7 TeV protons on a fixed targetcan be estimated as dN Λ + c dt = FA σ ( pp → Λ + c X ) N T , (6)where F is the proton rate, A the beam transverse area, N T the number of targetnucleons, and σ ( pp → Λ + c X ) is the cross-section for Λ + c production in pp interactionsat √ s = 114 . N T = N A ρAT A N /A T , where N A is the Avogadro number, ρ ( T ) is the target density(thickness), and A T ( A N ) is the atomic mass (atomic mass number). For ourestimates we consider a target of tungsten thick T = 0 . ρ = anuary 5, 2021 1:56 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in main page 7 .
25 g / cm. The rate of Λ + c particles channeled in the bent crystal and reconstructedin the LHCb detector is estimated as dN reco Λ + c dt = dN Λ + c dt B ( Λ + c → f ) ε CH ε DF ( Λ + c ) ε det , (7)where B ( Λ + c → f ) is the branching fraction of Λ + c decaying to f , ε CH is the efficiencyof channeling Λ + c inside the crystal, ε DF ( Λ + c ) is the fraction of Λ + c decaying after thecrystal and ε det is the efficiency to reconstruct the decays. A 6.5 TeV proton beamwas extracted from the LHC beam halo by channeling protons in bent crystals .A beam with intensity of 5 × proton/s, to be directed on a fixed target, isattainable with this technique .The Λ + c cross section is estimated from the total charm production cross sec-tion , rescaled to √ s = 114 . √ s , and Λ + c fragmentation function to be σ Λ + c ≈ . µ b, compatible with theoretical predic-tions .The channeling efficiency in silicon crystals, including both channeling angularacceptance and dechanneling effects, is estimated to be ε CH ≈ − , while thefraction of Λ + c baryons decaying after the crystal is ε DF ( Λ + c ) ≈ γ =1000 and 10 cm crystal length. The geometrical acceptance for Λ + c → pK − π + decaying into the LHCb detector is ε geo ≈
25% according to simulation studies.The LHCb software-based trigger for the upgrade detector is expected to haveefficiency for charm hadrons comparable to the current high level trigger , i.e. ε trigger ≈ ε track ≈
34% for a Λ + c decay with three charged particles. The detectorreconstruction efficiency, ε det = ε geo ε trigger ε track , is estimated to be ε det ( pK − π + ) ≈ . × − for Λ + c → pK − π + decays.Few Λ + c decay asymmetry parameters α f are known. At present, they canbe computed from existing Λ + c → pK − π + amplitude analysis results yielding α ∆ ++ K − = − . ± .
30 for the Λ + c → ∆ ++ K − decay .For the sensitivity studies we assume s = 0 . g − / .
3, accordingto experimental results and available theoretical predictions, respectively, quoted inRef. . The d and g − θ C , γ .Given the estimated quantities we obtain dN recoΛ + c /dt ≈ . × − s − = 21 . − for Λ + c → ∆ ++ K − . A data taking of 1 month will be sufficient to reach a sensitivityof σ δ = 1 . × − on the Λ + c EDM. Therefore, a measurement of Λ + c EDM isfeasible in Λ + c quasi two-body decays at LHCb.The dependence of the sensitivity to Λ + c EDM and MDM as a function of thenumber of incident protons on the target is shown in Fig. 3. The same techniquecould be applied to any other heavy charged baryon, for instance containing b quark. The production rate is lower than Λ + c and the estimates have been studiedand discussed in Ref. . anuary 5, 2021 1:56 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in main page 8 ) · Number of protons on target (0 2 4 6 8 10 ) - · ( d s · Number of protons on target (0 2 4 6 8 10 ) - · ( g s Fig. 3. Dependence of the (Left) d and (Right) g uncertainties for the Λ + c baryon, reconstructedin the ∆ ++ K − final state, with the number of protons on target. One month of data takingcorresponds to 1 . × incident protons (dashed line), according to the estimated quantities.
4. Conclusions
The unique possibility to search for the EDM of strange and charm baryons atLHC is discussed, based on the exploitation of large statistics of baryons with largeLorentz boost and polarization. The Λ strange baryons are selected from weakcharm baryon decays produced in pp collisions at ≈
14 TeV center-of-mass energy,while Λ + c charm baryons are produced in a fixed-target experiment to be installedin the LHC, in front of the LHCb detector. Signal events can be reconstructedusing the LHCb detector in both cases. The sensitivity to the EDM and the MDMof the strange and charm baryons arises from the study of the spin precession inintense electromagnetic fields. The long-lived Λ precesses in the magnetic field of thedetector tracking system. Short-lived charm baryons are channeled in a bent crystalattached to the target and the intense electric field between atomic planes inducesthe spin precession. Sensitivities for the Λ EDM at the level of 1 . × − e cmcan be achieved using a data sample corresponding to an integrated luminosity of50 fb − to be collected during the LHC Run 3. A test of CP T symmetry can beperformed by measuring the MDM of Λ and Λ baryons with a precision of about4 × − on the g factor. The EDM of the Λ + c can be searched for with a sensitivityof 2 . × − e cm in 11 days of data taking. The proposed experiment would allowabout two orders of magnitude improvement in the sensitivity for the Λ EDM andthe first search for the charm baryon EDM, expanding the search for new physicsthrough the EDM of fundamental particles.
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