1. 1 La Fisica dei K a DA  NE-2 F. Bossi CSN1, Frascati 14-15 Ottobre 2005

2. 2 F. Bossi, CSN1, Frascati 14 Ottobre 2005 Summary of the talk DA  NE and KLOE 1999  2005 PHYSICS ISSUES AT DA  NE  2: DETECTOR ISSUES TESTS OF CPT CHIRAL PERTURBATION THEORY SOME PREDICTION OF THE STANDARD MODEL

3. 3 F. Bossi, CSN1, Frascati 14 Ottobre 2005 Some basic concepts (and numbers) A  meson decaying at rest produces pairs of neutral or charged kaons with branching ratios of ~34% and ~49%,respectively Daughter particles are monochromatic, P ch ~ 125 MeV/c, P neu ~ 110 MeV/c In resonant e + e  collisions, particles fluxes are: 1.5 x 10 6 K ± pairs/pb  1 1. x 10 6 K S K L pairs/pb  1 Parity conservation imposes the neutral state to be K S K L

4. 4 F. Bossi, CSN1, Frascati 14 Ottobre 2005 A brief history of luminosity 2 DA  NE performance up to April 2005 Peak Luminosity Integrated Luminosity Present day performance L peak ~ 1.4 x 10 32 cm  2 s  1 Best  L dt ~ 200 pb  1 /month Total KLOE  L dt ~ 2200 pb  1 (2001,02,04,05)

5. 5 F. Bossi, CSN1, Frascati 14 Ottobre 2005 KLOE papers on K physics K s   e PLB 535, 37 (02) K s   PLB 538, 21 (02) K L   PLB 566, 61 (03) K±  ±00 K±  ±00 PLB 597, 49 (04) K s  3  0 PLB 619, 61 (05) K L lifetime PLB 626, 15 (05) K L main BR, V us Accepted by PLB K ±   ± Accepted by PLB Plus (at least) as many in preparation

6. 6 F. Bossi, CSN1, Frascati 14 Ottobre 2005 A possible evolution of DA  NE The Laboratory is now studying the possibilty for an upgrade of the present facility There are a few options under consideration. The one that I will discuss here, and refer to as DA  NE-2 is: A  -factory able to deliver 7-10 fb  1 in one year, i.e some 10 9 well tagged kaons of all species after 2-3 years of run I will also assume that the detector to be used is some more or less conservative evolution of KLOE. Therefore almost all of the figures about detection performances are based on measurements on real data

7. 7 F. Bossi, CSN1, Frascati 14 Ottobre 2005 K Physics issues at DA  NE-2 Tests of fundamental symmetries (CP, CPT) Tests of prediction of Chiral Perturbation Theory Tests of prediction of Standard Model What studies can be performed using kaons at DA  NE-2?: For each of these three topics I will discuss some examples of measurements that can be performed at DA  NE  2. The list reflects my present personal knowledge of the matter and must be considered as non-exhaustive

8. 8 F. Bossi, CSN1, Frascati 14 Ottobre 2005 CPT

9. 9 F. Bossi, CSN1, Frascati 14 Ottobre 2005 CPT In the framework of quantum field theory (QFT), CPT conservation is a theorem. It is consequence of Lorentz invariance, locality as well as quantum mechanics The possibility of CPT violation is considered in several theoretical contexts that go beyond conventional QFT, for instance in models of quantum gravity CPT violation may manifest itself in many subtle ways different from the inequality of particle-antiparticle masses. This is mostly the realm of  -factories

10. 10 F. Bossi, CSN1, Frascati 14 Ottobre 2005 CPT violation: the “standard” path In the standard description of the neutral K system, a charge asymmetry in semileptonic K L and K S decays is predicted due to CP and (possibly) CPT violation  L = 2Re(  K )    S = 2Re(  K ) +  CPT is violated if  S ≠  L The most recent measurement are:  S = (1.5 ± 10 ± 3) x 10  3 KLOE, ~400 pb  1  L = (3322 ± 58 ± 47) x 10  6 KTeV, 02

11. 11 F. Bossi, CSN1, Frascati 14 Ottobre 2005 Potentialities of DA  NE-2 for  S Assuming present detection efficiencies and a modest improvement in systematic studies, at DA  NE-2 one could aim at a total error on  S of order 10 -3 B (kG) Present analysis, MC with detailed field map 400 pb  MC with LSF=0.5, with uniform axial B field 534 0.05 0.1 0.15 0.2 Acceptance However it has already been shown that one can obtain an increase in acceptance up to a factor of 2 just by lowering the B field to 3 kGauss With some optimism one can hope to reach a sensitivity on  S below the 10  3 level

12. 12 F. Bossi, CSN1, Frascati 14 Ottobre 2005 CPT and decoherence It has been suggested that quantum gravity could give rise to modification of standard QM, observed in decoherence effects together with CPT violation This can be observed in deviation of the behaviour of entagled systems (like K S K L from  decays) from the one predicted by standard QM

13. 13 F. Bossi, CSN1, Frascati 14 Ottobre 2005 CPT and decoherence: the EHNS model Ellis, Hagelin, Nanopoulos and (independently) Srednicki set up an evolution equation of the neutral K system containing three new CPT violating parameters , ,  with dimensions of energy Naively, one expects , ,  ~ O (M K 2 / M Plank ) ~ 10 -20 GeV Peskin and Huet worked out the expression of the usual double decay intensity of the K S K L pair from  decays in the EHNS framework There appear new bizarre terms in the distribution which allow to extract experimentally limits (or measurements) of these new parameters by proper fitting

14. 14 Fixing the EHNS parameters The EHNS parameters have already been constrained by CPLEAR results  = (  0.5 ± 2.8) x 10  17 GeV  = ( 2.5 ± 2.3) x 10  19 GeV  = ( 1.1 ± 2.5) x 10  21 GeV KLOE can reach equal sensitivity on ,  with present data sample just with the  +    +   channel F. Bossi, CSN1, Frascati 14 Ottobre 2005

15. 15 (/S)(/S) (/S)(/S) (/S)(/S) fb  1 Present KLOE KLOE + VDET Fixing the EHNS parameters With 20 fb  1 one can dramatically improve, especially on  and  In the plots below the horizontal line is CPLEAR, VDET means  vert = ¼  S F. Bossi, CSN1, Frascati 14 Ottobre 2005

16. 16 CPT and Bose statistics: the BMP model Bernabeu, Mavromatos and Pavassiliou argued that in presence of CPT violation induced by quantum gravity the concept of antiparticle has to be modified. In this case the K S K L state from  decays does not strictly obey Bose statistics, thus modifying the final state wave function І i > = C {( І K S (+)> І K L (  )>  І K L (+)>І K S (  )>) +  ( І K S (+)> І K S (  )>  І K L (+)>І K L (  )>)} The complex parameter  quantifies the departure from Bose statistics, in a formalism in which the time evolution of the state is still described by the equations of standard QM F. Bossi, CSN1, Frascati 14 Ottobre 2005 Naively, І  І ~ O (M K 2 / M Plank  ) 1/2 ~ 10 -3  10  4

17. 17 Measuring the  parameter F. Bossi, CSN1, Frascati 14 Ottobre 2005 The parameter  can be measured by a fit to the decay time distribution of the K S K L pair to 4  Arg(  ) = 0, І  І = 1,2,3 x 10  3  t (  S units) fb  1 Present KLOE KLOE + VDET A. Di Domenico 

18. 18 A note on the previous slides All our estimates refer to the  +    +   channel only. Further information can be obtained by other decay channels, to be studied in more detail. F. Bossi, CSN1, Frascati 14 Ottobre 2005

19. 19 Some fundamental bibliography F. Bossi, CSN1, Frascati 14 Ottobre 2005 1.Hawking, PR D14 (1975) 2460, Comm. Math. Phys. 87 (1982) 395 2.Wald, PR D14 (1975) 2460, Comm. Math. Phys. 87 (1982) 395 3.Ellis et. al, NP B241 (1984) 381; MPL A10 (1995) 425; PRD53 (1996) 3846 4.Huet, Peskin, NP B434 (1995) 3 5.Bernabeu, et al. PRL 92 (2004) 131601, hep-ph/0506025 6.Benatti, Floreanini, NP B511 (1998) 550 7.Bertlmann, Durstberger, Hiesmayr, PR A68 (2003) 012111

20. 20 F. Bossi, CSN1, Frascati 14 Ottobre 2005 Chiral Perturbation Theory

21. 21 F. Bossi, CSN1, Frascati 14 Ottobre 2005 Chiral Perturbation Theory In the limit in which u,d,s are massless the QCD lagrangian is invariant under SU L (3)xSU R (3). The left-handed world is separate from the right-handed one: this is chiral symmetry. The dynamical breaking of this (approximate) symmetry produces 8 massless Goldstone bosons to be identified with the , K,  One then writes down the most general lagrangian consistent with the chiral symmetry, and expands it in terms of the momentum of the involved particles. If momenta are low enough, then: M (p 2 ) > M (p 4 ) > M (p 6 ) … This is the basic idea of Chiral Perturbation Theory …and one can perform calculations perturbatively

22. 22 F. Bossi, CSN1, Frascati 14 Ottobre 2005 ChPT: the pros and the cons Thus chiral symmetry is: A true/direct consequence of QCD A rigorous way to calculate in the low energy region On the other hand, the effective ChPT lagrangian leaves a number of free parameters to be determined experimentally, that increase with the order to which the lagrangian is computed Thus, the higher you go with the power of p, the higher is the number of the number measurement you need to fix the theory 2 at orderd p 2, 12 at order p 4 …

23. 23 F. Bossi, CSN1, Frascati 14 Ottobre 2005 NA48/1 has measured BR(K S   ) = (2.78 ±0.06±0.04)x10  6 This result differs from predictions of ChPT at O(p 4 ) by 30% A preliminary analysis shows that KLOE can reach a statistical accuracy of ~ 4% with the present data sample. A projection to 20 fb  1 would give an accuracy better than 1% K S   : a test for ChPT

24. 24 F. Bossi, CSN1, Frascati 14 Ottobre 2005 K S   +    0 : another test for ChPT ChPT predicts B(K s   +    0 ) = (2.4 ± 0.7)x10  7 The present experimental value (3.3 +1.1  0.9 ) x10  7 is the average of three different measurement each individually precise at ~ 40% A preliminary KLOE analysis obtains  sig ~ 1.3%, S/B ~ 2 Assuming Error on BR @ 2 fb  1 (%) Error on BR @ 20 fb  1 (%) No further effort made to reduce background ~ 60% ~ 20% Further efforts completely remove background ~ 40% ~ 12%

25. 25 F. Bossi, CSN1, Frascati 14 Ottobre 2005 K S   +    0 as a pedagogical example This is the typical case where analysis would greatly benefit from simple detector upgrades At least one of the two tracks has low momentum: 65% of signal lost only due to acceptance Acceptance can be increased by the use of a lower B field. Also the use of a vertex chamber could definitely help Both can be useful also for the rejection of the background due to pathological charged kaon events

26. 26 F. Bossi, CSN1, Frascati 14 Ottobre 2005 Study of K S   +    spectrum Calculations at O(p 4 ) can lead either to an excess or to a lack of events wrt prediction at O(p 2 ), BR O(10  6 ) Spectrum is distorted wrt to pure I.B. Toy MC fit: sensitivity to BR at 10  6 level with 10 6 events with E  > 20 MeV Events with 20 fb  1 : 10 7 with E  > 20 MeV

27. 27 A digression in the  world It is known that a good  -factory is also a reasonable  -factory. Actually, at present KLOE has the largest  statistics in the world The  world is largely complementary with the K one in that it addresses most of the same physics issues. Tests of C, CP, CPT Tests of ChPT       0 l + l        0    3     More on C. Bini’s talk F. Bossi, CSN1, Frascati 14 Ottobre 2005

28. 28 F. Bossi, CSN1, Frascati 14 Ottobre 2005 Predictions of the SM

29. 29 F. Bossi, CSN1, Frascati 14 Ottobre 2005 K S   0  0  0 : a genuine CP violating decay MC Eff. Stat. = 5.3  data 450 pb - 1 ’01+’02 data 2222 2222 2323 2323 This decay violates CP. SM branching ratio is 2x10  9 Analysis based on  counting and kinematic fit on 2  0 and 3  0 hypothesis KLOE with 450 pb  1 B(K S  3  0 ) < 1.2 x 10  7 90% CL based on 2 observed events with an expected background of 3.1

30. 30 F. Bossi, CSN1, Frascati 14 Ottobre 2005 K S   0  0  0 : perspectives Background mostly due to photon clusters double splittings Preliminary studies show that there is room for “algorithmic” improvements in background rejection without losses in signal efficiency Study of the entire KLOE data set crucial for a better assessment of the real potentialities of the analysis but… …there are hints that @ 20 fb  1 one can reach ~ 5 x 10  9 With KLOE as it is now. Can we do better than that? see later discussion

31. 31 F. Bossi, CSN1, Frascati 14 Ottobre 2005 K S   e decays and the  S =  Q rule The relevant parameter here is: Re (x + ) ~ ~ 10  6 S.M. 1 + 4 Re(x + ) = SS LL BR(K S   e )  L BR(K L   e )  S = 6 10  3 1 10  3 4 10  3 = These are KLOE measurements Present Uncertainties 20 10  3 @ 20 fb  1 one can reach ~ 2 10  3 in BR(K S   e )

32. 32 F. Bossi, CSN1, Frascati 14 Ottobre 2005 Play the same game with muons Muon semilptonic channel is more difficult: Lower expected BR ~ 4 x 10  4 High pollution from  events with  decays in flight More difficult to separate charge states 2002 data  MC      MC   MC  E miss  P miss (  hyp) (MeV) However, it has never been measured before KLOE has already a clear signal and can reach 3% accuracy with present data This channel clearly begs for more luminosity

33. 33 F. Bossi, CSN1, Frascati 14 Ottobre 2005 R =  (K ±  e ± ) /  (K ±   ± ) and new physics This ratio is a sensitive probe for new physics effects ( see G. Isidori’s talk ) Standard Model Prediction: R = (2.472 ±0.001) x 10  5 NA48/2 Preliminary 05: R = (2.416 ±0.049) x 10  5 NA48/2 can reach ~ 1% precision with present data Scaling from measured efficiencies for K e3 decays KLOE can aim at ~ 0.5% @ 20 fb  1 Use of a vertex chamber could greatly improve efficiency

34. 34 F. Bossi, CSN1, Frascati 14 Ottobre 2005 Detector Issues

35. 35 F. Bossi, CSN1, Frascati 14 Ottobre 2005 E.M: Calorimeter: Full angular coverage Exceptional timing capabilities Large lever arm Drift Chamber: Good momentum resolution Large tracking volume Minimization of materials Good  0 reconstruction capabilities Excellent e/  separation based on t.o.f. Full kinematical reconstruction of events Maximization of efficiency for long-lived particles (K ±,K L ) The ingredients of KLOE success

36. 36 F. Bossi, CSN1, Frascati 14 Ottobre 2005 There can be improvements Still, based on our experience, some possible modifications can improve KLOE performance Use of a lower magnetic field. This can increase acceptance for several of the above mentioned channels and ease pattern recognition Insertion of a vertex chamber. At present, first tracking layer is at 30 cm (i.e. 50  S ) from the I.P. Try some z coordinate reconstruction in the drift chamber. Pattern recognition would benefit of it. Increase calorimeter’s readout granularity. Can improve photon counting, as well as particle identification.

37. 37 F. Bossi, CSN1, Frascati 15 Ottobre 2005 An explicative example from K + K  Split track Split track, no VTX reconstructed

38. 38 F. Bossi, CSN1, Frascati 14 Ottobre 2005 Summary (I) A high luminosity  factory is a perfect tool to study a wide variety of relevant physics topics in several distinct and complementary ways With KLOE we have learned a lot on how to perform these measurements and have solid ideas on the potentialities of our detector We have also several ideas on the potential improvements that can be done and intend to study in detail the feasibility and relevance of all of them in the coming months

39. 39 F. Bossi, CSN1, Frascati 14 Ottobre 2005 Summary (II) Upgrades of the detector can likely be of importance for other important studies, which I did not mention previously because of lack of time and/or because real potentialities have to be understood yet: K S   0 e + e  (  0  +   ) K S   0  K S  e + e  (  +   ) K S lifetime Improved V us measurement K L  