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La Fisica dei K a DAΦNE-2
F. Bossi
CSN1, Frascati 14-15 Ottobre 2005
1
Summary of the talk
DAΦNE and KLOE 1999 − 2005
PHYSICS ISSUES AT DAΦNE−2:
• TESTS OF CPT• CHIRAL PERTURBATION THEORY
• SOME PREDICTION OF THE STANDARD MODEL
DETECTOR ISSUES
F. Bossi, CSN1, Frascati 14 Ottobre 2005 2
Some basic concepts (and numbers)
A Φ meson decaying at rest produces pairs of neutral or chargedkaons with branching ratios of ~34% and ~49%,respectively
Daughter particles are monochromatic, Pch ~ 125 MeV/c, Pneu ~ 110 MeV/c
Parity conservation imposes the neutral state to be KSKL
In resonant e+e− collisions, particles fluxes are:
1.5 x 106 K± pairs/pb−1
1. x 106 KS KL pairs/pb−1
F. Bossi, CSN1, Frascati 14 Ottobre 2005 3
A brief history of luminosity
2
DAΦNE performance up to April 2005
Peak Luminosity
Integrated Luminosity
Present day performance
Lpeak ~ 1.4 x 1032 cm−2s−1
Best ∫L dt ~ 200 pb−1/month
Total KLOE ∫L dt ~ 2200 pb−1
(2001,02,04,05) 4
F. Bossi, CSN1, Frascati 14 Ottobre 2005
KLOE papers on K physics
Ks → πeν PLB 535, 37 (02)Ks → ππ PLB 538, 21 (02)
KL → γγ PLB 566, 61 (03)
K± → π±π0π0 PLB 597, 49 (04)
Ks → 3π0 PLB 619, 61 (05)
KL lifetime PLB 626, 15 (05)
KL main BR, Vus Accepted by PLB
K± → µ±ν Accepted by PLB
Plus (at least) as many in preparation
F. Bossi, CSN1, Frascati 14 Ottobre 2005 5
A possible evolution of DAΦNE
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 willdiscuss here, and refer to as DAΦNE-2 is:
A Φ-factory able to deliver 7-10 fb−1 in one year, i.e some 109 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
F. Bossi, CSN1, Frascati 14 Ottobre 2005 6
K Physics issues at DAΦNE-2
What studies can be performed using kaons at DAΦNE-2?:
• Tests of fundamental symmetries (CP, CPT)
• Tests of prediction of Chiral Perturbation Theory
• Tests of prediction of Standard Model
For each of these three topics I will discuss some examples of measurements that can be performed at DAΦNE−2. The list reflects my present personal knowledge of the matter and
must be considered as non-exhaustive
F. Bossi, CSN1, Frascati 14 Ottobre 2005 7
CPT
F. Bossi, CSN1, Frascati 14 Ottobre 2005 8
CPT
In the framework of quantum field theory (QFT), CPTconservation is a theorem. It is consequence of Lorentz
invariance, locality as well as quantum mechanics
The possibility of CPT violation is considered in several theoreticalcontexts that go beyond conventional QFT, for instance in models
of quantum gravity
CPT violation may manifest itself in many subtle ways differentfrom the inequality of particle-antiparticle masses. This is mostly
the realm of Φ-factories
F. Bossi, CSN1, Frascati 14 Ottobre 2005 9
CPT violation: the “standard” path
In the standard description of the neutral K system, a chargeasymmetry in semileptonic KL and KS decays is predicted due to
CP and (possibly) CPT violation
δL = 2Re(εK ) − ∆
δS = 2Re(εK ) + ∆CPT is violated if
δS ≠ δL
The most recent measurement are:
δL = (3322 ± 58 ± 47) x 10−6 KTeV, 02δS = (1.5 ± 10 ± 3) x 10−3 KLOE, ~400 pb−1
F. Bossi, CSN1, Frascati 14 Ottobre 2005 10
Potentialities of DAΦNE-2 for δS
Assuming present detection efficiencies and a modestimprovement in systematic studies, at DAΦNE-2 one could aim at
a total error on δS of order 10-3
B (kG)
Present analysis, MC with detailed field map400 pb−1 MC with LSF=0.5, with uniform axial B field
53 4
0.05
0.1
0.15
0.2
Acc
epta
nce
However it has already beenshown that one can obtainan increase in acceptanceup to a factor of 2 just bylowering the B field to 3
kGauss
With some optimism one can hope to reach a
sensitivity on δS below the 10−3 level
11F. Bossi, CSN1, Frascati 14 Ottobre 2005
CPT and decoherence
It has been suggested that quantum gravity could give rise tomodification of standard QM, observed in decoherence effects
together with CPT violation
This can be observed in deviation of the behaviour of entagledsystems (like KSKL from Φ decays) from the one predicted by
standard QM
F. Bossi, CSN1, Frascati 14 Ottobre 2005 12
CPT and decoherence: the EHNS model
Ellis, Hagelin, Nanopoulos and (independently) Srednicki set up anevolution equation of the neutral K system containing three new
CPT violating parameters α,β,γ with dimensions of energy
Naively, one expects α,β,γ ~ O(MK2 / MPlank) ~ 10-20 GeV
Peskin and Huet worked out the expression of the usual doubledecay intensity of the KSKL pair from Φ decays in the EHNS
framework
There appear new bizarre terms in the distribution which allow toextract experimentally limits (or measurements) of these new
parameters by proper fitting
F. Bossi, CSN1, Frascati 14 Ottobre 2005 13
Fixing the EHNS parameters
The EHNS parameters have already been constrained byCPLEAR results
α = ( −0.5 ± 2.8) x 10−17 GeVβ = ( 2.5 ± 2.3) x 10−19 GeVγ = ( 1.1 ± 2.5) x 10−21 GeV
KLOE can reach equal sensitivityon β,γ with present data samplejust with the π+π−π+π− channel
14F. Bossi, CSN1, Frascati 14 Ottobre 2005
Fixing the EHNS parameters
With 20 fb−1 one can dramatically improve, especially on βand γ
In the plots below the horizontal line is CPLEAR, VDETmeans σvert = ¼ τS
δ(α/ΓS) δ(β/ΓS) δ(γ/ΓS)
fb−1 fb−1 fb−1
• Present KLOE• KLOE + VDET
15F. Bossi, CSN1, Frascati 14 Ottobre 2005
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 KSKL state from Φ decays does not strictly obey
Bose statistics, thus modifying the final state wave function
І i > = C {( І KS(+)> І KL(−)> − І KL(+)>І KS(−)>) + ω ( І KS(+)> І KS(−)> − І KL(+)>І KL(−)>)}
The complex parameter ω quantifies the departure from Bosestatistics, in a formalism in which the time evolution of the state
is still described by the equations of standard QM
Naively, ІωІ ~ O(MK2 / MPlank ∆Γ)1/2 ~ 10-3 ÷ 10−4
16F. Bossi, CSN1, Frascati 14 Ottobre 2005
Measuring the ω parameter
The parameter ω can be measured by a fit to the decay time distribution of the KSKL pair to 4π
Arg(ω) = 0, ІωІ = 1,2,3 x 10−3
∆t (τS units)
fb−1
• Present KLOE• KLOE + VDET
A. Di Domenico
A. Di Domenico
δ(ω)
17F. Bossi, CSN1, Frascati 14 Ottobre 2005
A note on the previous slides
All our estimates refer to the π+π−π+π− channel only. Further information can be obtained by other decay
channels, to be studied in more detail.
F. Bossi, CSN1, Frascati 14 Ottobre 2005 18
Some fundamental bibliography
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
F. Bossi, CSN1, Frascati 14 Ottobre 2005 19
Chiral Perturbation Theory
F. Bossi, CSN1, Frascati 14 Ottobre 2005 20
Chiral Perturbation Theory
In the limit in which u,d,s are massless the QCD lagrangian isinvariant under SUL(3)xSUR(3). The left-handed world is separate
from the right-handed one: this is chiral symmetry.
The dynamical breaking of this (approximate) symmetry produces8 massless Goldstone bosons to be identified with the π, K, η
One then writes down the most general lagrangian consistent withthe chiral symmetry, and expands it in terms of the momentum of
the involved particles. If momenta are low enough, then: M(p2) > M(p4) > M(p6) …
…and one can perform calculations perturbatively
This is the basic idea of Chiral Perturbation Theory
21F. 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 p2, 12 at order p4…
F. Bossi, CSN1, Frascati 14 Ottobre 2005 22
KS → γγ : a test for ChPT
NA48/1 has measured BR(KS → γγ) = (2.78 ±0.06±0.04)x10−6
This result differs from predictions of ChPT at O(p4) by 30%
A preliminary analysis shows that KLOE can reach a statisticalaccuracy of ~ 4% with the present data sample.
A projection to 20 fb−1 would give an accuracy better than 1%
F. Bossi, CSN1, Frascati 14 Ottobre 2005 23
KS → π+π −π0 : another test for ChPT
ChPT predicts B(Ks → π+π−π0) = (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 εsig ~ 1.3%, S/B ~ 2
AssumingError on BR @ 2 fb−1 (%)
Error on BR @ 20 fb−1 (%)
No further effort madeto reduce background ~ 60% ~ 20%
Further effortscompletely removebackground
~ 40% ~ 12%
24F. Bossi, CSN1, Frascati 14 Ottobre 2005
KS → π+π −π0 as a pedagogical example
This is the typical case where analysis would greatly benefit fromsimple detector upgrades
At least one of the two tracks has low momentum: 65% of signallost only due to acceptance
Acceptance can be increased by the use of a lower B field. Alsothe use of a vertex chamber could definitely help
Both can be useful also for the rejection of the background due topathological charged kaon events
F. Bossi, CSN1, Frascati 14 Ottobre 2005 25
Study of KS → π+π −γ spectrum
Spectrum is distorted wrt topure I.B.
Calculations at O(p4) can lead either to an excess or toa lack of events wrt prediction
at O(p2), BR O(10−6)
Toy MC fit: sensitivity to BR at 10−6 level with 106 events
with Eγ > 20 MeV
Events with 20 fb−1: 107 withEγ > 20 MeV
26F. Bossi, CSN1, Frascati 14 Ottobre 2005
A digression in the η world
It is known that a good Φ-factory is also a reasonable η-factory.
Actually, at present KLOE has the largest η statistics in the world
The η world is largely complementary with the K one in that itaddresses most of the same physics issues.
Tests of C, CP, CPT Tests of ChPT
η → γγγη → π0l+l−
η → ππγ
η → π0γγη → 3πη → ππγ
More on C. Bini’s talk
27F. Bossi, CSN1, Frascati 14 Ottobre 2005
Predictions of the SM
F. Bossi, CSN1, Frascati 14 Ottobre 2005 28
KS → π0π 0π0 : a genuine CP violating decay
MCEff. Stat. =5.3× data
This decay violates CP. SM branching ratio is 2x10−9 χ2
2π
Analysis based on γ countingand kinematic fit on 2π0 and 3π0
hypothesis χ23π
450 pb−1
’01+’02 dataKLOE with 450 pb−1
χ22πB(KS → 3π0) < 1.2 x 10−7 90% CL
based on 2 observed events with anexpected background of 3.1
29
χ23π
F. Bossi, CSN1, Frascati 14 Ottobre 2005
KS → π0π 0π0 : 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 betterassessment 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 laterdiscussion
F. Bossi, CSN1, Frascati 14 Ottobre 2005 30
KS → πeν decays and the ∆S = ∆Q rule
The relevant parameter here is:
Re (x+) ~<e+π−ν | Hwk | K0 >
<e+π−ν | Hwk | K0 >~ 10−6 S.M.
1 + 4 Re(x+) =ΓSΓL
BR(KS → πeν) τL
BR(KL → πeν) τS=
6 10−3
1 10−3 4 10−3
=
These are KLOE measurements
PresentUncertainties20 10−3
@ 20 fb−1 one can reach ~ 2 10−3 in BR(KS → πeν)
F. Bossi, CSN1, Frascati 14 Ottobre 2005 31
Play the same game with muons
Muon semilptonic channel is more difficult:• Lower expected BR ~ 4 x 10−4
• High pollution from ππ events with π decays in flight • More difficult to separate charge states
• 2002 data− MC µ+π− ν− MC ππγ− MC ππ
However, it has never beenmeasured before
KLOE has already a clearsignal and can reach 3%
accuracy with present data
This channel clearly begs formore luminosity
Emiss − Pmiss (πµ hyp) (MeV)32F. Bossi, CSN1, Frascati 14 Ottobre 2005
R = Γ(K± → e± ν) / Γ(K± → µ±ν ) 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 Ke3 decays KLOE can aim at ~ 0.5% @ 20 fb−1
Use of a vertex chamber could greatly improve efficiency
33F. Bossi, CSN1, Frascati 14 Ottobre 2005
Detector Issues
F. Bossi, CSN1, Frascati 14 Ottobre 2005 34
The ingredients of KLOE success
E.M: Calorimeter: Drift Chamber:
Full angular coverageExceptional timing capabilitiesLarge lever arm
Good momentum resolutionLarge tracking volumeMinimization of materials
Excellent e/π separation based on t.o.f.
Good π0 reconstruction capabilities
Full kinematical reconstruction of events
Maximization of efficiency for long-lived particles (K± ,KL)
35F. Bossi, CSN1, Frascati 14 Ottobre 2005
There can be improvements
Still, based on our experience, some possible modificationscan improve KLOE performance
• Use of a lower magnetic field. This can increase acceptancefor several of the above mentioned channels and easepattern recognition
• Insertion of a vertex chamber. At present, first tracking layeris at 30 cm (i.e. 50 τS) 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 improvephoton counting, as well as particle identification.
36F. Bossi, CSN1, Frascati 14 Ottobre 2005
An explicative example from K+K−
Split track Split track, no VTX reconstructed
37F. Bossi, CSN1, Frascati 15 Ottobre 2005
Summary (I)
A high luminosity Φ−factory is a perfect tool to study a widevariety of relevant physics topics in several distinct and
complementary ways
With KLOE we have learned a lot on how to perform thesemeasurements and have solid ideas on the potentialities of our
detector
We have also several ideas on the potential improvements thatcan be done and intend to study in detail the feasibility and
relevance of all of them in the coming months
38F. Bossi, CSN1, Frascati 14 Ottobre 2005
Summary (II)
Upgrades of the detector can likely be of importance for otherimportant studies, which I did not mention previously because
of lack of time and/or because real potentialities have to beunderstood yet:
KS → π0e+e− (π0µ+µ−)
KS → π0 γγ
KS → e+e− (µ+µ−)
KL → γγ
KS lifetimeImproved Vus measurement
39F. Bossi, CSN1, Frascati 14 Ottobre 2005