CP/CPT Violation in Charm

Transcription

1 CP/CPT Violation in Charm Kevin Stenson Vanderbilt University Heavy Quarks & Leptons 22 Vietri sul Mare, Salerno, Italy May 28 31, 22 Talk Outline I. Quick CP violation recap II. Blurb about E791, FOCUS, & CLEO experiments III. Recent direct CP violation search results IV. A search for CPT violation V. Summary & Future

2 CP violation generalities Three types of CP violation 1 CP violation in mixing (indirect) 2 CP violation in decay (direct) 3 CP violation in decay/mixing interference (indirect or direct) Current Status Experimentally, charm mixing is small CP violation in mixing or interference is small Standard Model predictions for all types of charm CP violation are well below current sensitivities Some Standard Model extensions predict direct CP violation up to 1% (almost within reach) Large window for new physics

3 CP violation generalities Direct CP violation Only type of CP violation possible for charged mesons Requires two decay terms with different CP violating (weak) and different CP conserving (strong) phases Differing strong phases comes from final state interactions In Standard Model differing weak phases often come from tree level and penguin diagrams Measure: A CP Γ(D f) Γ(D f) Γ(D f) + Γ(D f) In fixed-target experiments (E791 & FOCUS), production asymmetries require normalizing by another (copious) mode, assumed to have no CP violation. Procedure also reduces systematic errors.

4 E791: The usual suspects 5 GeV π beam on nucleon target Took data at Fermilab FOCUS: 18 GeV γ beam on nucleon target Took data at Fermilab Target Silicon Targets Silicon Microstrips Trigger Counters Beam Direction Target Region Outer Electromagnetic P.W.C.'s Calorimeter Magnet Outer Muon R.P.C.'s Cerenkov Counter Inner Electromagnetic Calorimeter P.W.C. E831 Fcus Hadron Calorimeter Spectrometer Muon Hodoscope Beam Direction Straw Tubes Trigger P.W.C. Hodoscope Cerenkov Counters Magnet Trigger Hodoscope Beam Calorimeter Muon Filter CLEO: Symmetric e + e at Υ(4S) Most data from CLEO II.V (1996 9)

5 D + K Sh + FOCUS Branching Ratio Measurements: D + BR FOCUS PDG Average Γ(K π + ) Γ(K π + π + ) (3.6±.46±.58)% (32.±4.)% Γ(K K + ) Γ(K π + π + ) (6.4±.35±.35)% (7.7±2.2)% Γ(K K + ) Γ(K π + ) (19.96±1.2±1.6)% (26.3±3.5)% Direct CP Violation search: Measure A CP = η(d+ K s h + ) η(d K s h ) η(d + K s h + ) + η(d K s h ) Normalize to another mode to account for production asymmetries CP Asymmetry FOCUS A CP (KS π+ ) w.r.t. K π + π + ( 1.6±1.5±.9)% A CP (KS K+ ) w.r.t. K π + π + (6.9±6.±1.8)% A CP (KS K+ ) w.r.t. KS π+ (7.1±6.1±1.4)%

6 CP violation search in D π + π, K + K decays Use D + D π + decays to distinguish D from D A CP (%) A CP (%) A CP (KK) =.1% ± 1.7% Average A CP (ππ) = 2.1% ± 2.6% Average E791(98) FOCUS() CLEO(2) Yield(D +D K K + ) = 2463±65 CLEO Yield(D +D π π + ) = CLEO 93±37 Expt A CP (KK) (%) A CP (ππ) (%) E791(98) 1. ± 4.9 ± ± 7.8 ± 3. FOCUS().1 ± 2.2 ± ± 3.9 ± 2.5 CLEO(2). ± 2.2 ± ± 3.2 ±.8

7 CP violation in three-body decays Can look for CP violation integrated over phase space Can look for CP violation via effective two-body decays by cutting on resonances Can fit D and D Dalitz plots separately and compare magnitudes and phases (most sensitive) A CP for D + K K + π +, π π + π + E791 FOCUS A CP (K K + π + ) ( 1.4 ± 2.9)% (.6 ± 1.1 ±.5)% A CP (φπ + ) ( 2.8 ± 3.6)% Dalitz analyses A CP (K K + ) ( 1. ± 5.)% in A CP (π + π π + ) ( 1.7 ± 4.2)% progress

8 FOCUS D + K K + π + preliminary analysis Mode Fraction (%) Phase ( ) K (892)K ± 1.1 (fixed) a (98)π ± ± 5 φ(12)π ± ± 6 f 2 (127)π +.7 ±.2 12 ± 7 f (137)π ± ± 6 K (141)K ± ± 6 K(143)K ± ± 4 φ(168)π ±.5 7 ± 9 m(k π + ) m(k K + ) 2 Yield: 6848 ± ΚΚπ X mass projection Y mass projection m(kk) 2 m(kπ) 2 Will look for direct CP violation by comparing D + & D Dalitz plots

9 CLEO CP violation search in D K π + π A CP = MD 2 MD 2 M 2 D M 2 d DP D = ( 3.1 ± 8.6)% (not optimized to measure A CP ) Mode Fraction (%) Phase ( ) ρ(77)k 78.8 ± 2.3 (fixed) K (892)π ± ± 4 K (892)π 12.7 ± 1. ± 4 ρ(17)k 5.7 ± ± 7 K(143)π 4.1 ± ± 7 K(143)π ±.9 56 ± 7 K (168)π 1.3 ±.4 13 ± 11 NR 7.5 ± ± 7 Yield(D +D K π + π ) = CLEO 6837

10 CPT Violation Point particle Lorentz invariant field theories CPT invariance Some Standard Model extensions need not be Lorentz-invariant Example: strings are not point particles can elude requirement Start with more fundamental theory operating at, e.g., M P lank At current energies have spontanteous symmetry breaking in which vacuum acquires quantities oriented in 4-D violates particle Lorentz invariance (although not observer Lorentz invariance) One could find evidence for strings by precision tests of CPT and/or Lorentz invariance should search for CPT violation and Lorentz violation Limits have been set using neutral K and B mesons (mixing interferometry) No limits yet from charm system

11 Mostly follow formalism developed by Kostelecký (hep-ph/1412) Standard effective Hamiltonian is rewritten: Λ = M 1 2 iγ Λ = 1 ( ) U + ξ V W 2 λ 1 V W U ξ where U, V, W, ξ are complex and λ = M i Γ/2 The time-dependant right-sign D f decay probability, P f (t) = 1 2 F 2 e [( Γt 1+ ξ 2) cosh Γ + ( 1 ξ 2) cos M 2R(ξ) sinh Γ + 2I(ξ) sin M ] The time-dependant D f decay probability P f (t) is P f (t) with ξ ξ and F F Form the asymmetry for right-sign decays: A CPT (t) = P f (t) P f(t) P f (t) + P f (t) = 2R(ξ) sinh Γt 2I(ξ) sin Mt ( 1+ ξ 2 ) cosh Γt + ( 1 ξ 2) cos Mt Taylor expand sin, sinh, cos, cosh to 1st order and use standard mixing variables x M/Γ, y Γ/2Γ. Then: A CPT (t) [R(ξ) y I(ξ) x)] Γt

12 CPT formalism continued... From above, A CPT (t) [R(ξ) y I(ξ) x)] Γt Experimentally, A CPT (t ) = N D (t ) N D (t ) N D (t )+N D (t ) Slope of distribution gives [R(ξ) y I(ξ) x] Lorentz invariance violating parameters In CPT and Lorentz violating extensions, CPT violating parameters (ξ) depend on lab momentum, orientation, and sidereal time Wind up with flavor dependant Lorentz violating coupling coefficients For FOCUS (a forward, fixed-target experiment): ξ(ˆt,p) = γ(p) [ a + β a λ Z cos χ+β sin χ( a Y sin Ωˆt + a X cos Ωˆt) ] Ω (ˆt) sidereal frequency (time) X, Y, Z non-rotating coordinates; Z along Earth s rotation axis λ = (x iy)γ γ(p) = 1 + p 2 D /M D 2 β = 1, χ = 53 for FOCUS

13 Events / 4 MeV/c 2 CPT Violation preliminary results FOCUS R(ξ)y I(ξ)x =.83±.65±.41 Limits depend on mixing parameters Example: x=, y =1% R(ξ) =.83 ±.65 ±.41 Lorentz invariance violating parameters: Still under study Expect limits on a +.6 a Z, a X, & a Y in range of 1 15 GeV Yield(D ) = ± 145 Yield(D ) = ± 152 A CPT R(ξ) (arbitrary units) non-zero slope CPT violation t (ps) M(K π + ) GeV/c M(K + π ) GeV/c Greenwich Mean Sidereal Time (hours)

14 Summary of CP (& CPT) violation searches A CP mode E791(98) (%) FOCUS(,2) (%) CLEO(1,2) (%) D K K + 1. ± 4.9 ± ± 2.2 ± 1.5. ± 2.2 ±.8 D π π ± 7.8 ± ± 3.9 ± ± 3.2 ±.8 D π π.1 ± 4.8 D KS K S 23 ± 19 D KS π.1 ± 1.3 D + KS π+ 1.6 ± 1.5 ±.9 D + KS K+ 6.9 ± 6. ± 1.8 D K π + π 3.1 ± 8.6 (DP) D + K K + π ± ± 1.1 ±.5 D + φπ ± 3.6 D + K K + 1. ± 5. D + π π + π ± 4.2 First CPT violation search in charm from FOCUS (preliminary) R(ξ) y I(ξ) x =.83 ±.65 ±.41

15 Future of CP violation searches in charm Short term: < 1 year FOCUS is working on Dalitz analyses of 3-body D + decays such as D + K K + π + and D + π π + π + CLEO is working on Dalitz analyses of 3-body D decays such as D K S π+ π, D π π + π, D K S π π plus D + modes Belle and BaBar will improve on current limits? Medium term: 1 5 years CLEO-c will be collecting 3 million DD events at the ψ(377) Belle and BaBar will continue to provide excellent results Longer term: > 5 years BTeV at the Fermilab Tevatron (pp) will likely be the first experiment to reconstruct 1 billion charm decays