Charge Symmetry Breaking in pn dπ 0

Transcription

1 Charge Symmetry Breaking in n dπ 0 reniy Filin Helmholtz-Intitut für Strahlen- und Kernhyik (Theorie), Univerität Bonn, Bonn, Germany Intitute for Theoretical and Exerimental Phyic, ocow, Ruia In collaboration with V. Baru, E. Eelbaum, J. Haidenbauer, C. Hanhart,. Kudryavtev and U.-G. eißner ESO010 Friday, June 11-th, Parallel Seion C1 Phy.Lett.B681:43-47,009

2 Introduction Charge ymmetry Invariance under u and d quark exchange aroximate ymmetry of QCD Exlicitly broken by quark ma difference and electromagnetic effect Charge ymmetry breaking () ha numerou manifetation. We conider following two: eutron-roton ma difference: δ m = m m = m + = 1.93 ev n δ δ m Cro ection aymmetry in n dπ 0 and contribute indeendently δ m δ m Our goal: Study in n dπ 0 to extract individual contribution δ m and which rovide imortant connection to other low energy rocee through the chiral ymmetry. δ m

3 Obervation in n dπ 0 Differential cro ection exanded in Legendre olynomial d σ ( θ ) = P1(co θ ) + P(co θ ) + σ = 4π 0 dω If charge ymmetry i exact the differential cro ection of n dπ 0 i ymmetric about θ=90 in C frame (i.e. 1 0) ny aymmetry ( 1 0) i due to effect Exerimentally oberved value i forward-backward aymmetry fb fb = 1 fb = [17 ± 8(y.) ± 5.5(tat.)] 10 ex 4 Kinetic energy of incident neutron T = Lab Exce energy ev ev Oer et al. (003) TRIUF

4 Effective Field Theory of π Hybrid aroach Weinberg (199) 1. Calculate tranition (roduction) oerator. Convolute with non-erturbative wave function Production oerator Chiral erturbation theory i ued to calculate Exanion of conit of irreducible grah = + + Secial ower counting for π due to large tranferred momentum m ~ π Exanion arameter: π Cohen et al. (1996); Hanhart et al. (000) χ = ~ Λ ChPT m π Λ ChPT ~ m ~1GeV

5 Leading Order Effect in n dπ 0 ear threhold there are two nonzero contribution to 1 : -wave -wave -wave -wave 1 + LO ( S S D ) + Re , 1 3S1, 1P1 3S1, * 1 3 LO t leading order only firt tye hould be conidered: Ioin conerving () amlitude calculated u to and including LO by Baru, Eelbaum, Haidenbauer, Hanhart, Kudryavtev, Lenky, eißner (009) See talk by V. Baru In thi work we tudy amlitude at LO: o LO contribution

6 Leading Order mlitude Effective chiral Lagrangian at LO Ioin conerving term: L = π τ σ π + (0) δ m δ m δ m term: L = τ3 τ ππ 3 ( τ3π τ ππ 3 ) + 4Fπ 4Fπ δ m = m m = δ m + δ m n WT (0) 1 g τ ( π) + 4Fπ Fπ Leading order contribution to 1P1 3S1, Diagram (a) wa conidered in reviou tudie Kolck, ikanen, iller (000) Bolton, iller (009) (a)

7 Leading Order mlitude Effective chiral Lagrangian at LO Ioin conerving term: L = π τ σ π + WT (0) 1 g τ ( π) + 4Fπ Fπ (0) δ m δ m δ m term: L = τ3 τ ππ 3 ( τ3π τ ππ 3 ) + 4Fπ 4Fπ δ m = m m = δ m + δ m n Leading order contribution to 1P1 3S1, Diagram (a) wa conidered in reviou tudie Kolck, ikanen, iller (000) Bolton, iller (009) (a) (b) We howed that recattering diagram (b) alo contribute to LO amlitude due to time deendence of WT vertex ( π )

8 ew Leading Order Contribution to ω 1 ω Weinberg Tomozawa oerator i time deendent 1 LWT = τ ( π π) 4F π ππ vertex i roortional to the zeroth comonent of ion (b) Diagram (b) in article bai: 0 π n V 1 ( ) abc c = ω + ω ε τ 4F π WT 1 0 π n π m π m n π 1 mn + π π + 1 m + π (b 1 ) n n (b ) V 3 i δ m + for diagram (b 1) WT = π 3 4 Fπ δ m π for diagram (b ) Recattering diagram give δ m contribution to LO amlitude

9 fb at LO. Dicuion and Reult = 1P1 3S1, δ m δ m + δ m 3 δ m + δ m ( 1 3S1, ) Re + 1S0 3S1, D 1P1 3S1, 1 3 -wave amlitude from Baru et al. (009)

10 fb at LO. Dicuion and Reult = 1P1 3S1, δ m δ m + δ m 3 δ m + δ m ( 1 3S1, ) Re + 1S0 3S1, D 1P1 3S1, 1 3 -wave amlitude from Baru et al. (009) 0 i related to total cro ection σ=4π 0. recie value extracted from ionic deuterium lifetime exeriment (π - d nn) Strauch et al., PSI (009) 0 = μb fb 4 δ m ( ) 10 ev 1 = = ± 0

11 fb at LO. Dicuion and Reult = 1P1 3S1, δ m δ m + δ m 3 δ m + δ m ( 1 3S1, ) Re + 1S0 3S1, D 1P1 3S1, 1 3 -wave amlitude from Baru et al. (009) 0 i related to total cro ection σ=4π 0. recie value extracted from ionic deuterium lifetime exeriment (π - d nn) Strauch et al., PSI (009) 0 = μb fb 4 δ m ( ) 10 ev 1 = = ± 0 Our reult: Cottingham um rule: Lattice QCD: m fb = [17 ± 8(y.) ± 5.5(tat.)] 10 ex 4 δ = 1.5 ± 0.8(ex.) ± 0. 5(th.) ev ( ) δ m =. 0± 0. 3 ev δ m =.6 ± 0.57 ± 0.4 ± 010. ev tatitic Gaer, Leutwyler (198) int u Oer et al. (003) TRIUF chiral extraol. PLQCD (007)

12 Summary and Outlook Comlete leading order calculation of effect in n dπ 0 ew LO effect dicovered Strong neutron-roton ma difference extracted from aymmetry data δ = 1.5 ± 0.8(ex.) ± 0. 5(th.) ev m ( ) greent with Cottingham um rule and lattice QCD Outlook Comlete LO calculation required to confirm theoretical uncertainty (loo, LEC, etc.) dd απ 0 can hel to conain arameter in LO calculation Stehenon et al. (003), Gårdetig et al. (004); ogga et al.(006), Foneca et al.(009)