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Exploring D0 Mixing: Phenomenology and Measurements from Jožef Stefan Institute Collaborations

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This study examines the intricate behavior of D0 mixing through extensive phenomenological analysis and experimental measurements conducted at the University of Ljubljana and the Jožef Stefan Institute. We present detailed discussions on CP violation states, decay time distributions, and the implications of t-dependent Dalitz analyses. The results shed light on mixing parameters and prospects for future research, providing valuable insight into potential new physics. Our findings contribute significantly to the understanding of D0 dynamics in particle physics.

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Exploring D0 Mixing: Phenomenology and Measurements from Jožef Stefan Institute Collaborations

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  1. D0 Mixing B. Golob University of Ljubljana, Jožef Stefan Institute & Belle Collaboration “Jožef Stefan” Institute University of Ljubljana • Outline • Phenomenology • Measurements • A) Experiments • B)CP states • C) Wrong sign (non-CP) • D) t-dependent Dalitz • E)y(3770) • F) Average of results • 3. Prospects & Summary • A) Mixing param. • B) CPV param. • C) Summary

  2. q2 q1 q2 q1 1. Phenomenology P0 P0 P0 = K0, Bd0, Bs0 and D0 Time evolution flavor states ≠ Heff eigenstates: (defined flavour) (defined m1,2 and G1,2) |x|, |y| << 1 Decay time distribution of experimentally accessible states D0, D0 sensitive to mixing parameters x and y, depending on final state coherent production, V→D0D0

  3. 1. Phenomenology x and y d, s, b d, s, b K+ difficult to estimate DCS SU(3) breaking D0 D0 W+ D0 D0 K- W- I.I. Bigi, N. Uraltsev, Nucl. Phys. B592, 92 (2001); A.F. Falk et al., PRD69, 114021 (2004) unique for D0’s: down q’s loop; mixing: 30 years after discovery The duration of passion is proportionate with the original resistance of the woman. H. de Balzac (1799 -1850)

  4. Vus* 1. Phenomenology K+ CP violation Vcs D0 D0: first two quark generations; CKM elements ≈ real; using CKM unitarity: bellow current exp. sensitivity; signals New Physics K- parameterization: RD ≠1: Cabbibo suppression AD ≠0: CPV in decay AM ≠0: CPV in mixing f ≠0 : CPV in interference

  5. 2. Measurements A) Experiments continuum production s(c c)  1.3 nb (~109 XcYc pairs) e+e-→ y(3770) → D0D0, D+D- (coherent C=-1 state); ~800 pb-1 of data available at y(3770) 2.8x106 D0D0 very diverse exp. conditions c g* General B-factories c D*+ →D0ps+ charge of ps flavor of D0; dM=M(D0ps)-M(D0)  background reduction p*(D*) > 2.5 GeV/c eliminates D0 from b → c

  6. S. Bergman et al., PLB486, 418 (2000) 2. Measurements B) Decays to CP eigenstates D0→ K+K- / p+p-, CP even no CPV: CP|D1> = |D1> t=1/G1; K-p+: mixture of CP states t=f(1/G1,1/G2) + = K+K-/p+p- and K-p+ratio Belle, PRL 98, 211803 (2007), 540fb-1 1stevidence for D0 mixing BaBar, arXiv:0712.2249, 384fb-1

  7. 2. Measurements B) Decays to CP eigenstates CPV t-depedent / t-independent method Belle, PRL 98, 211803 (2007), 540fb-1 t-dependent t-independent similar sensitivity BaBar, arXiv:0712.2249, 384fb-1 Belle, arXiv:0807.0148, 540fb-1 BaBar, PRL 100, 061803 (2007), 386fb-1

  8. D*+→ D0pslow+D0 → D0 → K+p- 2. Measurements C) WS decays (non-CP) DCS decays  interference; t-dependence to separate DCS/mixed likelihood contours d: unknown strong phase DCS/CF 1s 3.9s 1stevidence for D0 mixing 3s CDF, PRL 100, 121802 (2008), 1.5fb-1 BaBar, PRL 98, 211802 (2007), 384fb-1 Belle, PRL 96, 151801 (2006), 400fb-1 5s likelihood contours 95% FC confidence region 1s 3.8s 3s

  9. D0→KSp+p- 2. Measurements D)t-dependent Dalitz analyses different types of interm. states; CF: D0→ K*-p+ DCS: D0→ K*+p- CP: D0→r0 KS if f = f  populate same Dalitz plot; relative phases determined (unlike D0→ K+p-); t-dependence: regions of Dalitz plane→ specific t dependence f(x, y); D0→f access directly x, y l1,2=f(x,y); Belle, PRL 99, 131803 (2007), 540fb-1 D0→f D0→KSp+p- most accurate x

  10. Cleo-c, PRD78, 012001 (2008), 281pb-1 2. Measurements E) y(3770) →D0D0 uncorrelated production at threshold D0D0 in C=-1 state  effective Br’s depending on mixing param.: y, RM=(x2+y2)/2, RDcosd S±: CP eigenstates e-: Xen fit to set of single and double Br’s single D0 reconstr. both D0 reconstr. measured from ST rates Br(D0D0→fi/fj) Br(D0→fi)Br(D0→fj) Br(D0D0→fiX) Br(D0→fi) uncorrelated production (RWS=G(K+p-)/G(K-p+))

  11. Cleo-c, PRD78, 012001 (2008), 281pb-1 2. Measurements DT yields E) y(3770) →D0D0 fit to set of single and double Br’s ST yields M [GeV] 1.83 1.89 1.83 1.89 1.83

  12. 2. Measurements K+K- F) Average of results c2 fit including correlations among measured quantities K+p- RM KSp-p+ d uncertainty CPV c2/n.d.f.=25.3/20 http://www.slac.stanford.edu/xorg/hfag/charm/ and HFAG, arXiv:0808.2268 (x,y)≠(0,0): 9.8s; CP even state heavier and shorter lived; no CPV within 1s

  13. 3. Prospects and summary s(√RDcosd) [10-2] charm A) Mixing parameters Cleo-c results improved signif. with higher stat.; (all estimates based on ) x, y related measurements of similar or better accuracy at Super-B with modest lumin.; d already constrained with reasonable accuracy from combination of x’2, y’, x, y meas.; Cleo-c, PRD78, 012001 (2008), 281pb-1 L [fb-1] 0.5 5.0 0.5 5.0 s(RM) [10-3] charm s(x’2) [10-3] B s(y) [%] charm s(yCP) [%] B Prediction is very difficult, especially of the future. s(x) [%] B s(y) [%] B N. Bohr (1885 - 1962) L [fb-1] L [fb-1] L [ab-1] L [ab-1]

  14. 3. Prospects and summary A) Mixing parameters asymmetric factory at y(3770): for same <Dz> as at U(4S) gb~2 (0.42 at Belle), E(e-/e+)=8 GeV/0.45 GeV (8 GeV/3.5 GeV at Belle); resolution: sresD ~ sresB (bgB/bgD) ~0.3 ps ~tD0 N(S+K-p+, S+e-)~1300 @ 281 pb-1 sy~0.1% with 2 ab-1 (stat. only)

  15. 3. Prospects and summary s(AG) [%] B s(|q/p|) B s(f) [rad] B B) CPV parameters various options at y(3770); decays to same sign CP eigenstates: (assuming no direct CPV) suppressed by RM; not feasible; L [ab-1] >>

  16. 3. Prospects and summary B) CPV parameters various options at y(3770); untagged asymmetry: ACP linear in CPV and mixing param., feasible (stat. only); systematics from charge dependent e asymm.? also possible at B-factories L[fb-1] 1400 1000 600 200 current d >> RD, y uncertainty 300 fb-1 0.2 0.5 0.9 sind

  17. 3. Prospects and summary B) CPV parameters D0D0 in C=+1 state (D0D0 g); tagged asymmetry:

  18. 3. Prospects and summary s(AG) [%] B s(|q/p|) B s(f) [rad] B B) CPV parameters various options at y(3770); CPV in mixing: ACP linear in CPV param., feasible (stat. only); systematics from e- spectrum extrapolation (cancels in ACP)? s(AM)~1% with 300 fb-1 sensitivity better than at Super-B; L [ab-1]

  19. 3. Prospects and summary B) CPV parameters s(AD) [%] charm s(AD) [%] B various options at y(3770); direct CPV: ACP linear in CPV param., feasible (stat. only); systematics from e- spectrum extrapolation (cancels in ACP)? sensitivity better than at Super-B; a complete overview of physics cases (for BES-III) can be found in L [fb-1] 0.5 5.0 L [ab-1] K.T. Chao, Y. Wang, editors, arXiv:0809.1869

  20. 3. Prospects and summary C) Summary today: D mixing unambigiously established; x, y ~ O(1%); no CPV asymmetry @ ~0.3%; “tomorrow”: Super-B factory at initial stage s(x), s(y) ~ O( 0.1%) s(ACP) ~ O(0.1%); dKp precisely determined from combination of measurements; RM, y @ charm factory of lower accuracy than @ B factory (unless t-dependent meas. with asymmetric collider); various options for CPV (only few examples shown); several competitive or better, and complementary to B-factory (including D0D0 with C=+1); many other possibilities (Dalitz studies, triple product correlations, T-odd moments, ...)

  21. Systematics bckup Belle, PRL 98, 211803 (2007), 540fb-1 Decays to CP eigenstates scales with MC better detect. (MC) desc. scales with data/MC scales with data/MC scales with data/MC total non-scaling 0.10% 0.06% L0=540 fb-1

  22. Systematics bckup Decays to CP eigenstates s(yCP) [%] s(AG) [%] L [ab-1] L0=540 fb-1

  23. L0=540 fb-1 Systematics bckup t-dependent Dalitz analyses Belle, PRL 99, 131803 (2007), 540fb-1 model dependence [10-4]: Dx                 Dy -10.3           +0.1K*0(1430) DCS/CF -15% + 6.9           -2.5K*2(1430) DCS/CF -30% -1.6 -0.9 K*(1410) DCS & CF -20% -5.1 -4.1G(q2) const. --------------------------------- +10+6        Total model dep. -14-8 experimental: Dx           Dy +7.6         -7.8               p* variation -5.6         -5.7  Dalitz pdf for bkg. from different t bins ----------------------- +9+8 Total experimental-7          -12 better underst. of DCS/CF; arbitrary ½ of uncertainty taken as non-scaling ±8 ± 4.3 model non-scaling scales with data/MC ±6 ±6 exp. non-scaling ±10 ±7 total non-scaling

  24. L0=540 fb-1 Systematics bckup t-dependent Dalitz analyses model dependence: D|q/p|Df [rad] ±0.08 ±0.06 experimental: D|q/p|Df [rad]+0.06 +0.06           p* variation +0.03 -0.05bkg. decay t parameters ±0.08 ±0.06 model non-scaling scales with data/MC scales with data/MC ±0.08 ±0.06 total non-scaling

  25. Systematics bckup t-dependent Dalitz analyses s(x) [%] s(y) [%] s(|q/p|) s(f) [rad] L [ab-1] L0=540 fb-1

  26. L0=400 fb-1 Systematics bckup WS decays (non-CP) Belle, PRL 96, 151801 (2006), 400fb-1 ssyst(1-dim) = 0.75 sstat Dx’2 [sstat]Dy’ [sstat] ±0.44 ±0.44        p* variation ±0.26 ±0.26 fixed decay-t parameters ±0.26 ±0.26st effect on fractions scales with data/MC scales with data scales with data ±0.48 ±0.48 total non-scaling assumed same fraction of scaling/non-scaling systematics as for x’2

  27. Systematics bckup WS decays (non-CP) s(x’2) [10-3] s(y’) [%] L [ab-1] L0=400 fb-1

  28. L0=281 pb-1 Systematics bckup y(3770) →D0D0 Cleo-c, PRD78, 012001 (2008), 281pb-1 assume sensitivity on y is mainly due to S±e- RDcosd is mainly due to S±K-p+ RM is mainly due to K-p+K-p+ calculate fraction of non-scaling syst. on DT yields in total relative error: S±e- (y) s(non-scaling)/s(total)=15% extrap. of e- momentum S±K-p+ (RDcosd) s(non-scaling)/s(total)=15% FSR, sideband subtr. K-p+K-p+ (RM) s(non-scaling)/s(total)=2.4% FSR

  29. d bckup y(3770) →D0D0 • constraints • average • direct meas. • (fit w/o external input) cosd 1.0 0.5 0 -0.5 -1.0 1 0 -1 y’ measured y’=ycosd-xsind [%] d measured 0 1 2 3 4 5 d [rad] 0 1 2 3 4 5 d [rad]

  30. q2 q1 Introduction bckup History observation of K0: 1950 (Caltech) mixing in K0: 1956 (Columbia) observation of Bd0: 1983 (CESR) mixing in Bd0: 1987 (Desy) observation of Bs0: 1992 (LEP) mixing in Bs0: 2006 (Fermilab) observation of D0: 1976 (SLAC) mixing in D0: 2007 (KEK, SLAC) (evidence of) Mixing phenomena in course of life neutral meson P0 can transform into anti-meson P0 P0 = K0, Bd0, Bs0 and D0 6 years 4 years 14 years 31 years c quark t quark mass q2 q1 P0 P0 ???? ????

  31. Introduction bckup Central Drift Chamber e+ 3.5 GeV 3(4) layer Si det. e- 8 GeV Aerogel Cherenkov (n=1.015- 1.030) m and KL Counter (14/15 layers RPC+Fe) 1.5T SC solenoid EM calorimeter CsI (16X0) tracking s(pt)/pt= 0.2% √(pt2+2.5) PID e(K±) ~ 85%e(p±→K±)  10% for p < 3.5 GeV/c

  32. Introduction bckup BaBar detector at SLAC gb=0.56 Integrated luminosity: Ldt  500 fb-1 tracking s(pt)/pt= 0.45%+0.13%pt PID 3.4 s K/p separation for p < 3.5 GeV/c

  33. e- ID Had. ID tracking Introduction bckup Cleo-c detector at CESR e+e-→ y(3770) → D0D0, D+D- (coherent C=-1 state); analogous to B-factory with e+e-→ BB @ U(4S); symmetric; also higher energy, above DD* or DsDs threshold; ~572 pb-1 of data available at y(3770) 2.0x106 D0D0, 1.6x106 D+D- charm-factory; also upgraded BES at BEPCII Cleo-c, hep-ex/0606016 s [GeV]

  34. Intrrduction bckup CDF 3.5 fb-1 on tape s(D0; pt>5.5 GeV,|y|<1)≈13 mb 50x109 D0’s ds(D0)/dpt [nb/GeV]

  35. diagonal elem.: P0 P0 (including decays) non-diagonal elem.: P0 P0 Phenomenology bckup Time evolution eigenvalues: P1,2 evolve in time according to m1,2 and G1,2:

  36. Vuj* Vci* Vcj Vui u c W+ D0 D0 d, s, b d, s, b W- u c K+ D0 D0 K- Phenomenology bckup x and y in SM 2nd order perturb.: short distance: |x| ~ O(10-5) G. Burdman, I. Shipsey, Ann.Rev.Nucl.Sci. 53, 431 (2003) DCS SU(3) breaking absorptive part (real interm. states)  y dispersive part (off-shell interm. states)  x long distance: |x|, |y| ~ O(10-2) I.I. Bigi, N. Uraltsev, Nucl. Phys. B592, 92 (2001); A.F. Falk et al., PRD69, 114021 (2004) D0 mixing: rare process in SM; possible contrib. from NP

  37. Phenomenology bckup Oscillations measurable rates:

  38. Phenomenology bckup probab. to observe an initially produced X0 as X0 after time t probab. to observe an initially produced X0 as X0 after time t Oscillations ~ Bs0 more difficult to observe oscillations within t visually unobservable deviation from pure exponential

  39. PRL96, 151801 (2006), 400 fb-1 x’2 < 0.72 ·10-3 -0.99% < y’ < 0.68% no signif. CPV K+p- bckup 95% C.L. (x’2, y’) contour frequentist, FC ordering Results: RD = (3.64 ± 0.17 ) ·10-3 x’2 = (0.18 ±0.210.23) · 10-3 y’= (0.6 ±4.03.9) · 10-3 AD = (23 ± 47) ·10-3 AM = (670 ± 1200) ·10-3 no CPV CPV • CPV allowed: • separate D0 and D0 tags • (x’2,y’,RD) → (x’±2, y’±,RD±) (0,0) lies on 96.1% C.L. contour largest syst. due to p*(D*) selection

  40. Belle, PRL 99, 131803 (2007), 540fb-1 KSp+p- bckup K*X(1400)+ Dalitz projection of fit K*(892)+ r/w K*(892)- test of S-wave pp contr. (f0, s1,2): K-matrix formalism Results (fit fractions, phases) in agreement with (measurement of f3) PRD73, 112009 (2006)

  41. Belle, PRL 99, 131803 (2007), 540fb-1 KSp+p- bckup D0→ KSp+p- model dependence [10-4]: Dx                 Dy -10.3           +0.1K*0(1430) DCS/CF -15% + 6.9           -2.5K*2(1430) DCS/CF -30% -1.6 -0.9 K*(1410) DCS & CF -20% -5.1 -4.1G(q2) const. --------------------------------- +10+6        Total model dep. -14-8 experimental: Dx           Dy +7.6         -7.8               p* variation -5.6         -5.7  Dalitz pdf for bkg. from different t bins ----------------------- +9+8 Total experimental-7          -12 Largest systematics observed discrepancy from input in MC statistical uncertainty: s(x)=29x10-4 s(y)=24x10-4

  42. Belle, PRL 99, 131803 (2007), 540fb-1 KSp+p- bckup D0→ KSp+p- efficiency and resol. in M(pp) rnd ps bkg.: Prnd [(1-fw) M(m-2,m+2,t) +fwM(m+2,m-2,t)] R(t) fw from fit to Q side band: fw= 0.452 ± 0.005 diff. w.r.t. fw=0.5 in systematic error comb. bkg.: Pcmb  B(m-2,m+2) * ([ d(t) + Exp(t) ]R’(t) parameters from fit to Dalitz and t distrib. of M(KSp+p- ) sideband (systematics: Dalitz distrib. in different t intervals)

  43. K+p-p0 bckup BaBar, arXiv:0807.4567, 384fb-1

  44. K+p-p0 bckup BaBar, arXiv:0807.4567, 384fb-1 D0→K+p-p0 separate WS/RS Dalitz distributions; t-distrib. analogous to D0 →K+ p-; RS t-integrated Dalitz analysis; WS Dalitz analysis; no mixing point 0.8% C.L. BaBar, Lepton Photon 07, 384fb-1 dKpp: unknown strong phase shift DCS/CF

  45. K-p+ K+K-/ p+p- bckup Belle, PRL 98, 211803 (2007), 540fb-1 Fit simultaneous binned likelihood fit to K+K-/K-p+/p+p- decay-t, common free yCP R : ideally each si Gaussian resol. term with fraction fi; : described by 3 Gaussians  event-by-event st trec-tgen/st parameters of R depend slightly on data taking conditions t = 408.7±0.6 fs

  46. K+K-/ p+p- bckup Belle, PRL 98, 211803 (2007), 540fb-1 equal t0 assumption DyCP=t0CP - t0Kp / tKp from MC cocktail, including running periods with slight misalign. of SVD

  47. K+K-/ p+p-CPV bckup Decays to CP eigenstates CPV with adec<<1: Belle, PRL 98, 211803 (2007), 540fb-1 t-dependent BaBar, arXiv:0712.2249, 384fb-1 ACPpp ACPKK t-integrated ACPmeas =Aep + AFB + ACPf Aep: comparison of tagged/untagged (D*+→D0p+),D0→K-p+ AFB: asymmetric f(cosqCMS) BaBar, PRL 100, 061803 (2007), 386fb-1 |cosqCMS| |cosqCMS| AFBpp AFBKK Belle, arXiv:0807.0148, 540fb-1 |cosqCMS| |cosqCMS|

  48. y(3770) →D0D0 bckup D0, D0 in anti-symmetric state

  49. Average bckup Average of results inputs http://www.slac.stanford.edu/xorg/hfag/charm/ and HFAG, arXiv:0808.2268

  50. Average bckup http://www.slac.stanford.edu/xorg/hfag/charm/ and HFAG, arXiv:0808.2268 c2 of fit

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