Sandra Malvezzi I.N.F.N. Milano Recent Results from FOCUS QCD 2005 Conversano June 2005

How charm can still be charming Charm physics is a paradigm of how –precise measurements have led to a revival of the sector New Physics search: Mixing, CPV, rare and forbidden decays Spectroscopy of high-mass states (“the renaissance of spectroscopy”) – sophisticated investigations (typical of a mature field, under study over various decades) Dalitz plot analyses, Semileptonic Form-Factor measurements... have revealed limits in the “standard” approach precisely

QCD effects in charm weak decays can complicate the analysis and the phenomenological interpretation of the results requiring a new direction/approach in the decay dynamics investigation – What experimentalists have learnt so far Goals : –Proper tools for present/future precise high-statistics studies of charm and beauty hadrons –coherent description of FSI in Beauty - Charm decays and & Light hadron sector (hopefully) –Synergy between experimentalists and theorists FOCUS has played a pioneering role in various analyses

Lifetime hep-ex/ A Measurement of the Ds+ Lifetime Mixing hep-ex/ D 0 -D 0 hadronic mixing and DCS decays (the best charm mixing limit from a fixed-target exp) Pentaquark hep-ex/ Pentaquark search (Null) Rare & forbidden decays Semileptonic Hadronic decays (Dalitz plot) Multi-body channels (4,5,6 bodies) Charm Baryons D* spectroscopy hep-ex/ hep-ex/ FOCUS role

Charm lifetimes ( * ) FOCUS (○) PDG 2002  Ds  5074   Bigi Uraltsev (no WA/WX) (different process interference )

Charm mixing circa 2000   2 sigma hints of mixing at few percent level!  (K  ) =  1.34 ps  (KK) =  5.5 ps CP lifetime comparisons Time evolution of wrong-sign D* decay Some intriguing results.....not conclusive!

Mixing circa 2003 It will be interesting to see if mixing does occur at the percent level. B-factories are leading the game Things have come a long way since those heady days...

: data continue.... Belle : hep-ex/ Phys. Lett. B The best mixing limit from a fixed-target experiment: a valuable check More and more stringent limits! FOCUS has the world’s most accurate lifetime measurements and excellent lifetime-resolution. hep-ex/ FOCUS....agrees better with BaBar & Belle than with the old CLEO contour

.....The semileptonic sector Decay dynamics investigation

New results on Our K  spectrum looks like 100% K*(892) This has been known for about 20 years...but a funny thing happened when we tried to measure the form factor ratios by fitting the angular distributions

Decay is very accessible to theory Assuming the K  spectrum contains nothing but K*, the decay rate is straight-foreward

An unexpected asymmetry in the K* decay A 4-body decay requires 5 kinematics variables: 3 angles and 2 masses forward-backward asymmetry in cos below the K* pole but almost none above the pole Sounds like QM interference -15 % F-B asymmetry matches model

Try an interfering spin-0 amplitude will produce 3 interference terms (plus mass terms) Phys.Lett.B535,43, 2002 H 0 (q 2 ), H + (q 2 ), H - (q 2 ) are helicity-basis form factors computable by LQCD...

The S-wave amplitude is about 7% of the K* BW with a 45 o relative phase F-B asymmetry D +  K  is the natural place to study the K  system in the absence of interactions with other hadrons. Due to Watson’s theorem the observed K  phase shift should be the same as those measured in elastic scattering K*  interferes with S- wave K  and creates a forward- backward asymmetry in the K* decay angle with a mass variation due to the varying BW phase

The S & P waves from LASS 892 MeV/c 2 The phase difference between S & P wave at K*(892) pole from LASS is ~ 45 degrees!.  Most information on K -  + scattering comes from the LASS experiment (SLAC, E135) Aston et al., Nucl. Phys. B296 (1988) 493 PWA by LASS

 (900) with no fsi phase shift and with a 100 degree phase shift. cos  v weighted M(K  ), GeV/c 2 A broad Breit-Wigner amplitude ( the controversial  (900))? hep-ex/ Hadronic Mass Spectrum Analysis of D +  K  Decay and Measurementof the K*(892) 0 Mass and Width in FOCUS Additional checks:  (900) is not required

Form Factors The vector and axial form factors are generally parametrized by a pole dominance form Nominal spectroscopic pole masses D+D+ d d uuuu s Two numbers parameterize the decay

Our analysis is the first to include the effects on the acceptance due to changes in the angular distribution brought about by the S-wave interference The inclusion of the S-wave amplitude dramatically improved the quality of the Form-Factor Fit Form -factor lattice calculation (Damir Becirevic ICHEP02) R V = 1.55  0.11 is remarkably close to the FOCUS result. Phys.Lett.B 544(2002) 89

Decay dynamics investigation..cont’d.....The hadronic sector – Dalitz-plot analysis of D decays

Dalitz Analysis of Heavy Flavour Decays Powerful tool! –It provides a “complete observation” of the decay –Everything could be in principle measured from the dynamical features of the HF decay mechanism –Relative importance of non-spectator processes up to the CP-violating phases, mixing, etc –Just recall  from B o  and   from B   D(*)K  We have already learnt a lot about charm

Recent articles (the Dalitz-plot revenge) hep-ex/ Searches for CP violation and  S-wave in the Dalitz Plot analysis of D 0  +  +  0 (CLEO) hep-ex/ Search for D 0 - D 0 Mixing in the Dalitz Plot Analysis of D 0  K S 0  +  - (CLEO) hep-ex/ Measurement of  in B   D(*)K  decays with a Dalitz analysis of D  K S 0  +  - (BaBar) hep-ex/ Measurement of  3 with Dalitz Plot Analysis of B   D(*)K  Decay (Belle) hep-ex/ Measurement of CP-Violating Asymmetries in B 0  (  ) 0 Using a Time-Dependent Dalitz Plot Analysis ( BaBar) Sophisticated studies both in charm & beauty

I will Address key issues of the Heavy Flavour Dalitz analysis –Formalization problems Failure of the traditional “isobar” model Need for the K-matrix approach –Implications for the future Dalitz analyses in the B-sector Discuss these issues in the context of the recent D s +, D +  +  -  + Dalitz analysis we performed in FOCUS

Formalization Problems The problem is to write the propagator for the resonance r –For a well-defined wave with specific isospin and spin (IJ) characterized by narrow and well- isolated resonances, we know how. r r | 1 2 3

the propagator is of the simple Breit-Wigner type traditional isobar model Spin 0 Spin 1 Spin 2 the decay amplitude is the decay matrix element

when the specific IJ–wave is characterized by large and heavily overlapping resonances (just as the scalars!), the problem is not that simple. where K is the matrix for the scattering of particles 1 and 2. In this case, it can be demonstrated on very general grounds that the propagator may be written in the context of the K-matrix approach as Indeed, it is very easy to realize that the propagation is no longer dominated by a single resonance but is the result of a complicated interplay among resonances. i.e., to write down the propagator we need to know the related scattering K-matrix In contrast

What is K-matrix? It follows from S-matrix and, because of S-matrix unitarity, it is real Viceversa, any real K-matrix would generate an unitary S-matrix This is the real advantage of the K-matrix approach: –It (heavily) simplifies the formalization of any scattering problem since the unitarity of S is automatically respected. E.P.Wigner, Phys. Rev. 70 (1946) 15 S.U. Chung et al. Ann. Physik 4 (1995) 404

From Scattering to Production Thanks to I.J.R. Aitchison (Nucl. Phys. A189 (1972) 514), the K-matrix approach can be extended to production processes In technical language, –From –To The P-vector describes the coupling at the production with each channel involved in the process –In our case the production is the D decay

K-Matrix Picture of D +  +  -  + Describes coupling of resonances to D Known from Scattering Data Beside restoring the proper dynamical features of the resonances, it allows for the inclusion of all the knowledge coming from scattering experiments: enormous amount of results and science!

F or a single pole problem, far away of any threshold, K-matrix amplitude reduces to the standard BW formula The two descriptions are equivalent In all the other cases, the BW representation is not any more valid (limit of the traditional isobar model!!!) The most severe problem is that it does not respect unitarity Add BW Add K Add BW Add K The Unitarity circle Adding BWs ala “traditional Isobar Model” –Breaks the Unitarity –Heavily modify the phase motion!

The decay amplitude may be written, in general, as a coherent sum of BW terms for waves with well-isolated resonances plus K-matrix terms for waves with overlapping resonances. Can safely say that in general K-matrix formalization is just required by scalars (J=0), whose general form is Summarizing

Where can we get a reliable  S-wave scattering parametrization from? In other words, we need to know K to proceed. A global fit to (all) the available data has been performed *  p    0 n,  n,  ’n, |t|  0.2 (GeV/c 2 ) GAMS *  p     n, 0.30  |t|  1.0 (GeV/c 2 ) GAMS * BNL *  p -  KKn CERN-Munich :         * Crystal Barrel * * * pp             pp       ,     ,    pp         K + K -  , K s K s  , K +  s   np       -,        K s K -  , K s K s  -  - p    0 n, 0  |t|  1.5 (GeV/c 2 ) E852 * At rest, from liquid At rest, from gaseous At rest, from liquid “ K-matrix analysis of the 00++-wave in the mass region below 1900 MeV’’ V.V Anisovich and A.V.Sarantsev Eur.Phys.J.A16 (2003) 229

is the coupling constant of the bare state  to the meson channel describe a smooth part of the K-matrix elements suppresses the false kinematical singularity at s = 0 near the  threshold and is a 5x5 matrix (i,j=1,2,3,4,5) 1=  2= 3=4  4= 5= A&S An impressive amount of data is well described in terms of 5 poles

A&S T-matrix poles and couplings This set of poles and couplings coherently describes the  scattering.  a  object is already included....as very well known it is not a simple narrow BW Can we fit our D data??

Yield D + = 1527  51 S/N D + = 3.64 FOCUS D +   +  +  - analysis Sideband Signal PLB 585 (2004) 200

C.L fit 7.7 % K-matrix fit results Low mass projection High mass projection decay channel phase (deg) fit fractions (%) Reasonable fit with no retuning of the A&S K-matrix. No new ingredient (resonance) required not present in the scattering!

With  Without  C.L. ~ 7.5% Isobar analysis of D +   +  +  would instead require a new scalar meson:  C.L. ~ m = 442.6± 27.0 MeV/c  = ± 65.5 MeV/c

What about  -meson then? Can conclude that –Do not need anything more than what is already in the  S-wave phase- shift to explain the main feature of D  3  Dalitz plot Or, if you prefer, –Any  -like object in the D decay should be consistent with the same  - like object measured in the  scattering. Note: B   D(*)K  Dalitz plot analysis –The model used for the D 0  K s  +  - decay is one of the main sources of systematics –Two “ad hoc” scalar states  1 and  2 to describe excess of events not reproduced by “established” resonances.

FOCUS D s +   +  +  - analysis Observe: f 0 (980) f 2 (1270) f 0 (1500) Sideband Signal Yield D s + = 1475  50 S/N D s + = 3.41 PLB 585 (2004) 200

C.L fit 3 % Low mass projection High mass projection decay channel phase (deg) fit fractions (%) No three-body non-resonant contribution K-matrix fit results

Just by a simple insertion of KK -1 in the decay amplitude F We can view the decay as consisting of an initial production of the five virtual states , KK,   ’  and 4  which then scatter via the physical T-matrix into the final state. The Q-vector contains the production amplitude of each virtual channel in the decay Even more: from P to Q-vector

Q-vector for D s S-wave dominated by an initial production of  and KK-bar states The two peaks of the ratios correspond to the two dips of the  normalizing modulus, while the two peaks due to the K-matrix singularities, visible in the normalization plot, cancel out in the ratios. The normalizing  modulus Ratio of moduli of Q-vector amplitudes

Q-vector for D + The same! –s-wave dominated by an initial production of   and KK-bar states

The resulting picture The S-wave decay amplitude primarily arises from a ss-bar contribution such as that produced by –Cabibbo favored weak diagram for D s –One of the two possible singly Cabibbo suppressed diagram for D +. For the D +. the ss-bar contribution competes with a dd-bar contribution.. The measured fit fractions seems to confirm this picture –S-wave decay fraction, 87% for D s and only 56% for D + –The dd-bar contribution in D + case evidently prefers to couple to a vector state like  (770), that alone accounts for about 30% of the decay.

Conclusions Systematic investigation of charm decay dynamics is giving interesting results in both semileptonic and hadronic sectors Dalitz plot analysis is and will be a crucial tool to extract physics from the HF decays –Nevertheless, to fully exploit this unlimited potential a systematic revision of the amplitude formalization is required FOCUS has applied the K-matrix approach for the first time to the HF sector –Its application has been decisive in clearing up a situation which recently became quite fuzzy and confusing: new “ad hoc” resonances were required to understand data K-matrix allows for a rigorous coupled-channel analysis –This will be the further step in the Dalitz analysis of HF decays D +, D + s  f 0  amplitudes can feed both 3  and KK 

Conclusions...cont’d Strong dynamics effects in D-decays now seem under control and fully consistent with those measured by light-quark experiments. The new scenario is very promising for the future measurements of the CP violating phases in the B sector, where a proper description of the different amplitudes is essential. FOCUS is now sudying the D +  K -  +  + –High statistics sample –Test of the model –Quasi two-body process or multi-body process ?

FOCUS D +  K -     events Low momentum  combination High momentum  combination (GeV 2 ) The first charm Dalitz analysis – MK1 (1977) D +  K  “...consistent with a phase space Dalitz distribution.”

The future 1 node 2 nodes! We can learn even about D* states !!

BACKUP SLIDES My backup

What do you learn from Dalitz plots? Bands indicate resonance contributions For spinless parents, the number of nodes in the band give you the resonance spin Look at the  band Interference pattern gives relative phases and amplitudes Look at the D+ K* band pattern of asymmetry Isobar model: Add up BW ’ s with angular factors broad states Nearly all charm analyses use the isobar model:

For a two-body decay CP violation on the Dalitz plot A tot A tot = g 1 M 1 e i  1 + g 2 M 2 e i  2 CP conjugate A tot A tot = g 1 M 1 e i  1 + g 2 M 2 e i  2 **  i  i = strong phase CP asymmetry: a CP = 2Im(g 2 g 1 *) sin(  1 -  2 )M 1 M 2 |g 1 | 2 M 1 2 +|g 2 | 2 M Re(g 2 g 1 *)cos(  1 -  2 )M 1 M 2 |A tot | 2 - |A tot | 2 |A tot | 2 + |A tot | 2 = 2 different amplitudes strong phase-shift

FULL OBSERVATION Dalitz plot = FULL OBSERVATION of the decay COEFFICIENTS and PHASES for each amplitude Measured phase :  =  +  CP conserving CP violating CP conjugate  =   =  -   =  -  E831 a CP =0.006±0.011±0.005 Measure of direct CP violation: D   K  K   asymmetrys in decay rates of D   K  K    CP violation & Dalitz analysis

D s, D +  KK  D s +  K + K   + D +  K + K   +

K + K   projectionK    projection Yield D + = 7106  92 S/N D + = 8.62 Decay Fraction and phases K*(892) = 20.7  1.0 % (0 fixed)  (1020) = 27.8  0.7 % (243.1  5.2)° K*(1410) = 10.7  1.9 % (-47.4  4.9)  ° K * (1430) = 66.5  6.0 % (61.8  3.8)° f 0 (1370) = 7.0  1.1 % (60.0  5.3) ° a 0 (980) = 27.0  4.8 % (145.6  4.3)° f 2 (1270) = 0.8  0.2 % (11.6  7.0) °  (1680) = 1.6  0.4 % (-74.3  7.5) ° Preliminary

phi(1020) K*(1430) a0(980)K1(1410) f2(1270) f0(1370)phi(1680)         K*(1430) phi(1020) a0(980) K1(1410) f2(1270) f0(1370) phi(1680)       , D +, D - Coefficients: D ±, D +, D - D ±, D +, D - Phases: D ±, D +, D - Preliminary! No evidence of CPV K-matrix approach to improve the quality of the analysis

FSI effect Watson’s theorem : weak amplitudes are relatively real; however complex phases can be introduced by final state interaction

Interference term of and a nearly constant amplitude

Rare & forbidden decays FOCUS improved 8 results by a factor of 1.7 –14 CDF Br(D 0  +  - )<2.4 90% C.L. is the best limit for this mode (65 pb -1 data) CDF and D0 can trigger on dimuons  promising Cleo-c sensitivity Phys.Lett. B572 (2003) 21

The best mixing limit from a fixed-target experiment, a valuable check on those results Phys. Lett. B agrees better with BaBar & Belle than with the old CLEO contour (0.381  ) % (0.429   0.027) % (FOCUS) FOCUS has the world’s most accurate lifetime measurements and excellent ifetime-resolution.

Additional more recent studies Search for other resonant contributions in the K  spectrum – <1.6 % at 90 % C.L – <1.9 % at 90 % C.L Deeper investigation of the non-resonant amplitude –Non-resonant component fitted to an effective range model of the form cot  LASS =1/ap * + bp * /2 a=4.03  1.72  0.06 GeV -1 b=1.29  0.63  0.67 GeV -1 NR contribution of 5.30  – 0.51 % angular distribution consistent with the effective-range scalar non- resonant phase shift obtained by LASS (Watson)  excluded from further considerations. Hadronic decay D +  K -  +  + will complete the K  analysis ( see the end of this talk) hep-ex/

New measurement of the D s +    ff According to flavor SU(3) symmetry the form factor ratios r v and r 2 describing D +  K 0    should be close to D s +    since the only difference is a spectator quark d replaced with a s Lattice gauge calculations : max diff= 10% Experiment : – r v OK – r 2 inconsistent (3.3 . hep-ex/

S-wave interference in  K*   data ccbar mc events  cos  V data NO evidence for s-wave interference in Ds  

D s +    Form Factor results 1.Most precise measurement to date 2.very consistent with D +  K 0    3.very consistent with theoretical expectation

A&S K-matrix poles, couplings etc.