Theory overview on rare eta decays WASA Jose L. Goity Hampton/JLab BES III KLOE Hadronic Probes of Fundamental Symmetries Joint ACFI-Jefferson Lab Workshop March 6-8, 2014!UMass Amherst
Motivation Main motivation for the workshop The JEF proposal submitted to JLab Hall D (talk by Liping Gan) Physics of the proposal accurate measurement of improve bounds on η π 0 γγ η π 0 π 0 η γγγ and One objective of the workshop is to learn more about the possibilities of searching for BSM effects in the decays η η has been and is investigated in precision experiments at several facilities
The special role of the η Self conjugate meson 0 + Is a Goldstone Boson despite being a little overweight Mostly an octet, but mixes with the The decays η 3π Chiral anomaly in η γγ,... give access to Can we ask more from η? η m u m d m s
Outline η π 0 γγ : generalities other QED mediated decays η π 0 µ + µ, BSM with η Discussion of the two pertinent decays Possible points of discussion η µ + µ η ππ η 3γ
The decay η π 0 γγ Γ Exp =0.35 ± 0.07 ev Has changed significantly over time Challenge for ChPT Ametller et al ( 91) No tree level contributions up to Finite contributions to 1-loop 1-loop contributions are very small Dominant contributions are NLO in ChPT. Must be estimated using models Window into O(p 6 ) ChPT O(p 4 ) O(p 4 ) γγ ηπ 0 = γγ π 0 π 0
M = αω 1 ω 2 1 2 + β ( 1 k 1 ) ( 2 k 2 ) α, β functions of meson masses, M γγ, ω 1 + ω 2 Only known meson decay that proceeds through polarizability pathway one-loop contributions Γ 1 loop =3.9 10 3 ev Estimation of dominant contributions Ametller et al; Ko; Oset et al; Piccioto; Ng & Peters Resonance dominance models ω, ρ, a 0, a 2 η ρ, ω π 0 a 0, a 2
Important constraints from spectrum from Oset et al JEF Left to do More accurate measurement of the spectrum JEF proposal (Liping s talk) Possible improvement of predictions? Possible future access from Lattice QCD? Pion E polarizabilities studied in LQCD: Detmold et al: still large errors Possible interesting point of discussion in workshop...
γγ π 0 π 0 from Hoferichter et al from Oset et al γγ ηπ 0 f 2 (1270) a 0 (980) a 2 (1320) Could it be improved? The expert s review: Hans Bijnens talk
η π 0 µ + µ Current Exp bound Γ PDG (η π 0 µ + µ ) < 6.5 mev Calculation by Ng & Peters η π 0 Γ(η π 0 µ + µ ).6 ±.3µeV Any useful bound on new physics? e.g: heavy scalar µ + µ dγ 1 de π 12π 3 gqs g S M 2 S 2 M η p π 3 M S < g qs g S 13 GeV 10 2 Bound @ EM contribution M S > g qs g S 130 GeV Bound from µ (g 2) g qs,g S M S >g S 240 GeV are likely to be very small
η µ + µ A more sensitive case η µ + µ BR Exp =5.8 ± 0.8 10 6 Theoretically understood at the level of the experimental error: e.g. Luke et al. Bound for a heavy pseudoscalar mass? η P µ + µ δa P = g qp g µp M η F η M 2 P ū µ γ 5 v µ Sensitivity @ exp error M P > g gp g µp 240 GeV Bound from µ (g 2) M P >g µp 240 GeV Contribution from Z0 exchange δbr Z 0 5 10 8 Q: any model BSM that can receive a meaningful bound from η Xµ + µ
BSM Physics The case for it Hierarchy problem quark and lepton masses Mechanism to explain : BAU Dark matter is out there Family problem, or who ordered them? θ QCD 0 axion? Many models motivated by these facts: SUSY, SUGRA, string theory phenomenology, extra dimensions, technicolor, dark matter models,...
Effective Theory for BSM Physics L(M W )=L SM + L 5 + L 6 + L n = 1 Λ n 4 NP i C (n) i O (n) i Composite operators respect SM gauge symmetries L(Λ QCD )=L QCD + L QED + L W eak + L BSM Bases of composite operators up to dim 6 Grzadkowski et al For sensitivity to BSM physics the structure of operators is key; some hadronic matrix elements need to be estimated and at some point evaluated using LQCD... already possible for known nonleptonic decays
Dim 6 Operators Operators not giving FCNC (MFV models) Array of fields in family multiplets Q L, U R, D R, L L, R, ν R U(N f ) 6 symmetry group U(N f ) 6 SU c (3) SU L (2) U Y (1) singlet operators will not give FCNC Operators built with products of bilinears of the most general forms: Q L γ µ λ c T f Q L, Ū R γ µ λ c U R, DR γ µ λ c U R, λ c color matrices; T f flavor matrices Only permitted the combinations with quarks and leptons: Q L γ µ Q L LL γ µ L L and other flavor and chirality combinations Effects of these operators are non observable in FCNC decays; observable in the purely leptonic decays of the,... but also contributes!... η Z 0 I think this is important point of discussion
Search strategy for NP; look at quantities which Vanish at tree level in the SM Are calculable (finite) at 1-loop level in SM EW precision observables fixed by EW symmetry FCNC (GIM) CPV B, L violation EDMs (g-2)s etc
Low energy SM tests and searches BSM K 0 µ + µ : GIM B B mixing : t quark The newest test of FCNC B s µ + µ Very suppressed and reliably calculable in SM Buras et al Measured by LHCb Constrains MSSM Isidori et al. Future Tight constraints on extra scalar particles
from Cirigliano & Ramsey-Musolf...if only suppression is by the scale of new physics Example with precision EW physics PDG
Symmetry tests with η decays π 0, η, η are the only self conjugated light mesons Test sources for FC non violating physics Most sensitive to SM C violation SM CPV is very suppressed Main disadvantage: short lifetimes Bounds on BSM physics of various kinds
η ππ CP violating; current bound EW contribution Flavor conserving CP violation: requires second order weak interaction π η K S, K L O =( ~ d )( ~ ) (s ~ u )(u ~ d ) ((8f)»=1/2), π 02 2(sL,p dr, ) ) (ql, p ql, ) Oi ((8~), AI = 1/2), Q=XC)d~S BR Exp (η ππ) < 10 5 G 2 F Os 02 5(sL,p~dr, ) (sl,p~sl, ) ((27), AI = 1/2), 04 (sr, p dr, )(ur, p ur, ) + (sr, p ur, )(ul, p dl, ) (sl,p~dr, )(dl, p dr, ) ((27), AI = 3/2), Os = (sr'yy. ~ dl) ) qr'yp~ qr ((8),DI = 1/2), g=tcqcs~s O s = (sl,+~dl, ) ) qrqij, qr g='clqeg) S calculation: Jarlskog & Shabalin ((8), WI = 1/2). BR EW (η ππ) 10 27
θ QCD contribution Γ θ (η ππ) = g θ 2 16πM η 1 4 M 2 π M 2 η g θ = θ M π 2 (cos θ η η 2 sin θ η η ) 8Fπ Γ θ (η ππ) 100 θ 2 kev n EDM θ < 1.5 10 10 Guo & Meissner BR θ < 1.6 10 18
BSM physics: What is needed for a possibly observable effect? A 12 orders of magnitude enhancement: Spontaneous CP violation Estimate in Weinberg s model φ 1 φ 2 Order of magnitude estimate by Jarlskog & Shabalin BR SCPV (η ππ) 10 15 A question for the workshop: Is there any other model BSM that could give even larger contributions?
η γγγ CP conserving mode H eff = g η3γ η F µν F νρ F µ ρ In SM need for one W in Feynman diagram Back of the envelope order of magnitude estimate Loop contribution estimate: only short distances γ Dicus A e3 G F F η k 3 M 2 W η W γ γ Γ(η 3γ) M η A 2 (8π) 3 10 23 ev BR 10 26
Enhancement via a 1 (1260) η a 1 A e3 G F F η g a1 γγ k 3 M 2 a 1 Γ a1 g 2 a 1 γγ 10 15 ev BR g 2 a 1 γγ 10 18 Expect CPV η 3γ to be significantly smaller Q: is η 3γ a good place to look for new physics? what new physics could a BR > 10 6 constrain? A point of discussion which seems interesting.
Possible points for discussion What possible non FC NP could be constrained with eta decays?. Any specific models? Update on experimental BRs achievable in present and proposed experiments. QCD physics: impact the JEF experiment would have for understanding Other decays not addressed: anomalous CV in η π 0 µ + µ @ O(α) lepton family violation η π 0 γγ η µ + e & µ e + η π + π γ