Study of K_{S} semileptonic decays and CPT test with the KLOE detector

S tu d y o f K s se m ile p to n ic d eca y s an d C P T t e s t w ith th e K L O E d e te c to r

D a r ia K a m iń sk a o n b e h a lf o f t h e K L O E -2 C o lla b o r a tio n

T he M arian Smoluchowski In stitu te of Physics, Jagiellonian U niversity Łojasiew icza 11, 30-348 K rakow , Poland

E-m ail: d a r ia .k a m in s k a @ d o c to r a l.u j.e d u .p l

A b s t r a c t . Study of sem ileptonic decays of n eu tra l kaons allows to perform a te st of discrete sym m etries, as well as basic principles of th e S tan d a rd Model. In th is p ap e r a general review on dependency betw een charge asym m etry constructed for sem ileptonic decays of short- and long-lived kaons and C P T sym m etry is given. T he cu rrent sta tu s of d eterm in atio n of charge asym m etry for short-lived kaon, obtained by reconstruction of ab o u t 105 K s ^ n e v decays collected a t D A TN E w ith th e K L O E detecto r is also reviewed.

1. I n tr o d u c tio n

D iscrete sym m etries of n a tu re such as charge conjugation (C), p a rity ( P ) or tim e reversal (T ) do not lead to new conserved q u an tities. N evertheless, all of th e m entioned sym m etries plays an im p o rta n t role in particle physics, especially in calculations of th e cross sections and decay rates. W eak in teractio n does not conserve th e C, P , T or com bined C P sym m etry. However, up to now, th ere is no indication of C P T sym m etry violation [1], which would also im ply th e break of L orentz sym m etry [2]. A special role in C P T violation searches plays a n e u tra l kaon system which, due to a sensitivity to a variety of sym m etry violation effects, is one of th e best can d idates for such kind of studies. One of th e possible tests is based on com parison betw een sem ileptonic asy m m etry in K S decays (A S) and th e analogous asy m m etry in K L decays (A L).

2. T e s t o f C P T s y m m e tr y v io la t io n t h r o u g h s e m ile p t o n ic d e c a y s in n e u tr a l kaon s y s te m

2.1. Semileptonic decays in neutral kaon system

N eu tral kaons are th e lightest particles which contain a stran ge quark. O bserved short-lived K S and long-lived Kl are linear com binations of strange eigenstates ( K 0 and K 0):

IK l ) = / 2 ( 1 ? |

V

M

|K s > = / o n 1 I ,2, ((1 + ) | K °) + (1 - CS) |K °)) . V 2(1 + 1 CS 12)

Journal of Physics: Conference Series 631 (2015) 012042 doi:10.1088/1742-6596/631/1/012042

where introduced small param eters eL and es can be rew ritte n to sep arate C P and C P T violation p aram eters eK and óK , respectively:

es = €K + SK, (2)

eL — eK — $K .

In this p ap er a p a rticu la r em phasis will be given to sem ileptonic decays of K -sh ort and K -long states ( Ks/l ^ n e v ). A ccording to Eq. 1, only th e four possible decays of strang e eigenstates should be considered:

K ° ^ n _e+ v, K 0 ^ n + e _ x ,

+ - + (3)

K 0 ^ n + e x, K 0 ^ n e+v.

However, in th e S tan d ard M odel th e decay of K 0 (or K 0) s ta te is associated w ith th e tra n sitio n of th e s q u ark into U q u ark (or s into u) and em ission of th e charged boson. C hange of strangeness (A S ) implies th e corresponding change of electric charge (A Q ) (see F igure 1). This is so called A S — A Q rule. Therefore, decays of K 0 ^ n _ e + v and AT0 ^ n + e _ x are present b u t K 0 ^ n + e _ x and AT0 ^ n _ e + v are forbidden by if A Q — A S .

F ig u r e 1. F eynm an diagram s for K 0 and A'0 sem ileptonic decay.

D ecay am plitudes for sem ileptonic decays of sta te s |K 0} and | A'0) can be w ritte n as follows [3]:

<n_e+v| H weak |K 0) — A + , <n+e_x| H weak |K 0} — A _ , (^)

<n+e_x| H weak |K 0) — A - , <n_e+v| Hweak |kK0} — A + ,

w here th e H weak is th e te rm of H am iltonian corresponding to th e weak in teractio n and A + , A _ , A - , A + p aram etrize th e sem ileptonic decay am plitudes.

It is useful to introduce th e following notation:

A + ( A _ X A*_ - A +

X — , X — , y —--- — ,

A + V A _ J A _ + A + (5)

x ± x* i rA + , ( a _ y i ( )

x ± — 2 — 2 A + V A _ J .

For fu rth e r considerations, rules for applying sym m etry op erato rs to am plitu des of two spin zero system s A and B (and corresponding anti-system s A and B ) could be sum m arized as:

<TB | T H w k T _ 1 |T A ) — « B | T H w k T _ 1 |A })*

(CP B | C P Hwk C P _ 1 1 C P A ) — <B | C P Hwk CP _ 1 1A } (6)

<CPTB |C P T H w k C P T _ |C P T A ) — (<B ^ P T H w k C P T _ 1 |A })*

One ob tain s th e relatio n betw een th e sem ileptonic am plitudes and conservation of a p a rticu la r sym m etry by applying th e presented above rules to th e sta te s presented in Eq. 4. These considerations are sum m arized in Table 1.

T a b le 1. R elatio ns betw een discrete sym m etries and semiletp o n ic am plitudes Conserved q u a n tity R equired relation

A S _ A Q rule C P T sym m etry

C P sym m etry T sym m etry

x _ x _ 0 x _ X*, y _ 0 x _ X, y _ Im (y )

y _ R e(y )

2.2. Charge asym m etry

C harge asy m m etry can be defined for sem ileptonic decays of Ks and K l mesons in th e following way:

a _ r (K s ,L ^ n - e+v) - T (Ks,l ^ n + e - P)

S,L r ( K S,L ^ n - e+v) + r ( K S,L ^ n + e - v) ( ) and can be rew ritte n in term s of p aram eters introduced in Eq. 5:

As,l _ 2 [Re ( e x ) ± R e (5k) — R e (y) ± R e ( x - ) ] . (8) In th a t case, sum and difference of th e A S and A L allow to search for th e C P T sym m etry violation, eith er in th e decay am plitudes th ro u g h th e p a ra m ete r y or in th e m ass m a trix th ro u g h th e p a ra m ete r 5k :

A s + A l _ 4Re(e) — 4R e ( y ) , (9)

A S — Al _ 4R e(5K ) + 4R e (x - ) . 2.3. Experimental verification

T he m easurem ent based on 1.9 millions Kl ^ n e v decays produced in collisions of p ro to n beam w ith a BeO ta rg e t perform ed by K TeV C ollaboration allowed to determ in e A L values [4]:

Al _ (3.322 ± 0.058stat ± 0.047syst) x 10- 3 . (10) At present m ost accu rate m easurem ent of Ks charge asym m etry was conducted by K L O E experim ent. M easurem ent of As was perform ed w ith 0.41 fb -1 to ta l lum inosity d a ta sam ple and th e result is [5]:

A s _ (1.5 ± 9.6stat ± 2.9syst) x 10- 3 . (11) O btained charge asym m etry for Ks decays is consistent in erro r lim its w ith charge asy m m etry for Kl decays. However, th e inaccuracy of Ks d eterm in atio n is m ore th a n two orders of m agn itude bigger th a n th is of th e A L and th e error of A S is d o m inated by a sta tistic a l uncertainty, which is th re e tim es larger th e n system atical one. Therefore, in th is work a new m easurem ent of As

based on aro u n d four tim es bigger d a ta sam ple collected by m eans of th e K L O E d e te c to r in 2004 and 2005, is presented.

3. T h e K L O n g E x p e r im e n t a t D A T N E

K L O E was m ounted a t D A T N E collider in 1999 and collected d a ta durin g two cam paigns in 2001­

2002 and 2004-2005. T he gath ered d a ta sam ple corresponds to th e to ta l lum inosity of 2.5 fb- 1 . E nergy of colliding beam s (e- and e+) was set to th e m ass of 0 meson. D A T N E collider produce

~ 1300 kaon pairs p er second which corresponds to th e lum inosity 5 x 1032 cm - 2 s- 1 . In order to o b tain efficient detection of th e Kl m esons th e K L O E d e te c to r was co n stru cted w ith a view to properties of n e u tra l kaon system . A schem atic cross-section side view of th e K L O E d etecto r is shown in F igure 2. T he m ain com ponents of K L O E are th e cylindrical d rift cham ber and th e

Journal of Physics: Conference Series 631 (2015) 012042 doi:10.1088/1742-6596/631/1/012042

F ig u r e 2. Scheme of th e K L O E d etecto r system . D rift cham ber in th e central p a rt of th e K L O E detecto r is surro u n ded by th e electrom agnetic calorim eter. B o th detecto rs are inserted in a m agnetic field. Figure a d a p te d from [6].

calorim eter, b o th su rrounding th e beam pipe. All elem ents are im m ersed in a 0.52 T m agnetic field created by superconducting coils th a t are placed along th e beam axis.

T he K L O E drift cham ber (DC) is a 3.3 m long cylinder w ith an in tern al and external radii of 25 cm and 2 m, respectively, which allows to register ab o u t 40% of K L decays inside th e cham ber while th e rest reach th e electrom agnetic calorim eter. Between th e endp lates arou n d 12500 sense wires are streched and allows to obtain: a sp atial resolution in th e r, ^ plane b e tte r th a n 200 ^m , a resolution along th e z axis of ^ 2 m m and on th e resolution of th e decay vertex d eterm in atio n of ^ 1 mm. Moreover, th e cu rvature of th e reco n stru cted tracks allows to determ ine th e particle m om entum w ith a relative accuracy of 0.4 %. T he drift cham ber allows to reco nstruct inform ation ab o u t charged particles while th e calorim eter enables recording of b o th charged and n e u tra l particles. T h e K L O E calorim eter has been designed to have an excellent accuracy of energy determ in atio n and tim e resolution:

in order to register th e h its of n e u tra l particles and provide a possibility of th e Tim e of Flight (T O F ) m easurem ent.

a ( E ) _ 5.4%

~ _

Z p

54 ps

at _ — © 140 ps

* v

p

4. R e g is tr a t io n o f t h e 0 ^ KlKs ^ K ^ n e v p r o c e s s e s a t K L O E Ą.I. Preselection

D ue to th e conservation of q u a n tu m num bers du rin g decay of 0 m eson th e n e u tra l kaons are produced in pairs. In general case it is an entangled anti-sym m etric sta te , which p roperties allows to perform a fu nd am en tal tests of Q u an tu m M echanics and Lorentz sym m etry [7]:

|0) = ^ +i ! S |2>(1 + 7 ^ <|K'l® > |Ks( - P ) ) - |Ks(P)) |K L( -p )> ) (13) v 2(1 - £S£L>

where p is a m om entum in th e 0 m eson rest fram e. However, w hen one of th e kaon is d etected a t tim e t > > ts, th e sta te in Eq. 13 factorizes and th e system behaves as if th e initial s ta te was a m ix tu re of |K L(p)> |K S (—p)> and |K S (p)> |K L(-p )> . Hence th e d etectio n of K L a t large distance from In te rac tio n P oint tag s K S s ta te in th e opposite direction. M easurem ent described in this p ap er is based on identification of K s th ro u g h th e detectio n of Kl in teractio n in th e calorim eter.

A sketch of typical signal event is shown in F igure 3(left). Selection of K L cand idates takes into account only clusters w ith high energy deposition and requires th a t th e clu ster is not close to any tra c k reconstru cted in th e d rift cham ber. Also, velocity of n e u tra l particle th a t deposits energy in th is clu ster m ust be close to th e theo retical value of K L m eson velocity in th e 0 m eson rest fram e (0 0.22).

In th e next step, cand id ates for K S m eson decays are selected by selection of two oppositely charged particles w ith track s form ing a vertex close to th e in teraction point (IP):

pvtx < 15 cm, (14)

| Zvtx | < 10 cm,

where pvtx = y/x2tx + y2tx. O btained d istrib u tio n is shown in F igure 3(right). Then, th e rejection of m ain source of background (K S ^ n + n - ) is conducted by applying th e following cuts:

• 70° < a < 175°

w here a is an angle betw een charged secondaries in K S rest fram e. O b tained a d istrib u tio n is shown a t th e left side of Figure 4. In case of th re e bo dy decay (K S ^ n e v ) it is spanned over a large angle range.

• 300 < M inv < 490 MeV

an invariant m ass M inv is calculated using m om enta of th e particles which track s form a vertex assum ing th a t b o th particle were pions. O btain ed M inv d istrib u tio n is shown at th e right side of F igure 4.

B o th tracks reconstructed in th e d rift cham ber m ust be associated w ith neighbouring clusters in calorim eter in order to use Tim e-of-Flight technique.

4.2. K S ^ n e v events identification

T he T im e of F light technique aim s a t rejection of th e background, which a t th is stage of analysis is due to K S ^ n + n - events, and at identification of th e final charge sta te s (n ± e T). For each particle, th e difference St betw een th e m easured tim e of associated clu ster (tc1) and expected tim e of flight is calculated assum ing a given m ass hypothesis, m x:

d t(m x ) = t c; — -,

C P (m x) ’ (15)

0 (m x ) = T P T S I '

Journal of Physics: Conference Series 631 (2015) 012042 doi:10.1088/1742-6596/631/1/012042

F ig u r e 3. Left: Transverse view of exem plary signal event. T h e Ks is identified using th e Kl in teractio n in th e calorim eter. In th e next step two oppositely charged particle tracks are selected which form a vertex n ear th e in teractio n point. B oth tracks m ust be associated w ith th e colorim eter clusters. R ight: M onte C arlo sim ulation of transversal and longitudinal coordinates of vertex position for Ks ^ n e v events. D ashed line represents applied cuts which preserves

^ 95% of th e signal.

F ig u r e 4. Left: Sim ulated d istrib u tio n of angle betw een charged secondaries in Ks rest fram e.

Right: Sim ulated d istrib u tio n of invariant m ass calculated und er assum ption th a t b o th registered p articles were pions. In b o th figures solid and dashed histogram s represents all events and sem ileptonic decays, respectively. V ertical dashed lines represent cuts described in tex t.

w here L is a to ta l length of p article tra je c to ry and P is particle m om entum . For fu rth e r consideration it is useful to introduce th e difference of 5t (m a) and 5t (m b):

d5t,ab _ 5t(m a )i — 5t(m 6)2. (16)

F ig u r e 5. Sim ulated d istrib u tio n s of tim e differences dót,ne vs dót,en defined in Eq. 18 for K S ^ n e v events (left) and background events (right), once th e St,nn cu t has been applied. T he regions delim its by th e dashed lines are selected. In case of en (ne) th e dót,en (dSt,ne) variable acquires value close to zero.

where suffix 1 and 2 refers to th e first and second particle according to th e ordering determ ined by th e recon struction procedure.

Tw o cu ts are fu rth e r applied. For th e first cut, b o th particles are assum ed to be pions and d6t,nn is calculated. For K S ^ n n events th is value is around zero and th is fraction of events could be rejected by requiring:

|d5t,nn I > 1.5 ns. (17)

T hen, for surviving events, th e pion-electron hypothesis is tested:

dót,ne = St(m-K)i - St(me)2. (18)

d5t,en = ^t(m e)i - 5 t(m n)2.

If a m ass assum ption is correct th e n one of th e variables above should be close to zero. T he o b tained M onte C arlo d istrib u tio n s for K S ^ n ± e T v and background events are presented in F igure 5. Hence, th e following cu t is applied:

Id5t,en I < 1.3 ns A d5t,ne < - 3 .4 ns

or (19)

d6t,en > 3.4 ns A |d£t,ne| < 1.3 ns

T he above requirem ent ensures th a t th e possibility of m isidentification of charged particles from signal events is equal to 10-4 only.

O b tain ed distrib u tio n s for sim ulated d a ta and experim ental K L O E d a ta are shown in F igure 6 (top). T he M onte C arlo sim ulation indicates th e signal position around th e point (0,0) while th e background location is spread at th e corners of th e obtained d istrib u tio n . D ue to th a t an additio nal T O F cu t is applied by selecting events w ithin th e circle in th e St (e) vs St (n)

Journal of Physics: Conference Series 631 (2015) 012042 doi:10.1088/1742-6596/631/1/012042

...

>.5 -2 -1.5 -1 -0 .5 0 0.5 1 1.5 2

F ig u r e 6. D istrib u tio n s of th e tim e difference for pion m ass hypothesis (% (n)) versus th e tim e difference for electron m ass hypothesis (5t (e)) for experim ental d a ta (top-left), to ta l MC events (to p -righ t), MC K S ^ n e v events (bo ttom -left) and MC background events (b o tto m -rig h t).

E vents w ithin th e circle are retained for fu rth er analysis.

plane, as shown in F igure 6. This cut allows to preserve 94% of th e rem aining signal and control th e num ber of selected background events for norm alization. T he d istrib u tio n of th e difference betw een th e m issing energy and m om entum ( A E ( n ,e ) ) shows th e rem aining background com ponents (see Figure 7). B ased on an integ rated lum inosity of 1.7fb-1 around 105 of K S ^ n e v decays were recon stru cted and will be used to determ in e th e charge asym m etry and branching ratio for Ks sem ileptonic decays. A prelim inary analysis shows a p o ten tial of reaching a two tim es b e tte r sta tistic a l erro r d eterm in atio n w ith a sam ple four tim es bigger th a n th e previous K L O E analysis. T he analysis is still in progress and p relim inary results will be available soon.

A E(n,e)[M eV]

F ig u r e 7. D istrib u tio n of A E (n , e) — E miss — p miss for all selected events after norm alization procedure.

5. K L O E -2 P r o j e c t

D A T N E collider in previous years was a d a p te d to increased delivered lum inosity by in stallatio n of th e new in teractio n region based on th e C rabbed W aist com pensation to g eth er w ith large Piw inski angle [10]. Those changes should increase by factor of th ree th e am ount of th e delivered lum inosity w ith respect to th e perform ance reached before. Together w ith th e u pgrade of th e K L O E d e te c to r th is will allow to collect by K LO E-2 project th e o rder of 10 fb _ 1 of in tegrated lum inosity. T he d e te c to r itself was equipped w ith crystal (CCALT) [11] and tile (QCA LT) [12]

calorim eters which covers th e low po lar angles and improve th e detection of th e photons th a t are com ing from Kl decays in th e d rift cham ber, respectively. Also, th ere were m ounted th e two pairs of sm all angle tagging devices th a t allows to detect th e low (Low Energy Tagger [13]) and high (High E nergy Tagger [14]) energy e+ e_ originated from e+ e_ ^ e + e _ X reactions.

However, th e especially im p o rta n t for studies of C P T sym m etry violation th ro u g h sem ileptonic decays in n e u tra l kaons is precise reco nstruction of tracks m om enta and v ertex reconstruction close to th e In teractio n P o in t. This will be provided by In ner Tracker d e te c to r m ade o u t in a novel G EM technology [15]. Those upgrades will also im prove th e sensitivity of C P T and Lorentz invariance tests, which were presented by th e K L O E experim ent and becam e th e m ost precise m easurem ent of th e C P T violating param eters A a ^ for n e u tra l kaons in th e S tan d ard M odel E xtension (SM E) [16]. M easured values of A a ^ cu rren tly have a precision of 10_18 GeV and are pro portion al to th e p a ra m ete r óK [17, 18, 19].

It should be em phasised th a t K LO E-2 aim s to significantly im prove th e sensitivity of tests of discrete sym m etries, th ro u g h studies of K s charge asym m etry or q u a n tu m in terferom etry effects in th e kaon decays, beyond th e presently achieved results.

Journal of Physics: Conference Series 631 (2015) 012042 doi:10.1088/1742-6596/631/1/012042

A c k n o w le d g m e n ts

We w arm ly th a n k our form er K L O E colleagues for th e access to th e d a ta collected during th e K L O E d a ta tak in g cam paign. We th a n k th e D A $ N E tea m for th e ir efforts in m ain tain ing low background running conditions and th e ir collaboration du ring all d a ta taking. We w ant to th a n k our technical staff: G .F. F ortugno and F. Sborzacchi for th eir dedication in ensuring efficient op eratio n of th e K L O E com puting facilities; M. Anelli for his continuous a tte n tio n to th e gas system and d e te c to r safety; A. B alla, M. G a tta , G.

C orradi and G. P ap alin o for electronics m aintenance; M. Santoni, G. Paoluzzi and R.

Rosellini for general d e te c to r sup p ort; C. Piscitelli for his help du rin g m ajo r m aintenance periods. This work was su p p o rted in p a rt by th e E U In teg rated In fra stru c tu re In itiativ e H adro n Physics P ro je c t un d er co n tract num ber R II3-C T - 2004-506078; by th e E u ropean Com m ission u nder th e 7th Fram ew ork P rog ram m e th ro u g h th e ‘R esearch In fra stru c tu re s’ action of th e ‘C ap acities’ Program m e, Call: FP7-IN FR A ST R U C T U R E S-2008-1, G ran t A greem ent No. 227431; by th e Polish N atio n al Science C entre th ro u g h th e G ran ts No. D EC - 2 0 1 1 /0 3 /N /S T 2 /0 2 6 4 1 , 2 0 1 1 /0 1 /D /S T 2 /0 0 7 4 8 , 2 0 1 1 /0 3 /N /S T 2 /0 2 6 5 2 , 2 0 1 3 /0 8 /M /S T 2 /0 0323, D E C -2 0 1 4 /1 2 /S /S T 2 /0 0 4 5 9 , 2 0 1 3 /1 1 /B /S T 2 /0 4 2 4 5 and by th e F o un datio n for Polish Science th ro u g h th e M PD program m e and th e project H O M IN G PLU S B IS/2 01 1-4/3 .

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