DIRAC ++

πK-atom (A_πK) is a hydrogen-like atom consisting of K⁺(K⁻) and π⁻(π⁺) mesons. The πK-atom lifetime (ground state 1S), is dominated by the annihilation process into π⁰K⁰. There is a relation between the width of A_πKdecay and S-wave πK scattering lengths for isospin 1/2 and 3/2 [1]:

(1)

Here α is the fine structure constant, µ is the reduced mass of the π^±K^∓system, p^∗is the outgoing π⁰momentum in the πK atom system, and δ_Kaccounts for corrections, due to isospin breaking, at order α and quark mass difference (m_u− m_d).

Prediction of scattering length difference [2] provides an estimation of lifetime of A_πKin ground state to be: τ = (3.5 ± 0.4) × 10⁻¹⁵.

A method of investigation for π⁺π⁻, πK and other atoms, consisted of two oppositely charged mesons, has been proposed in [3]. Pairs of K⁺(K⁻) and π⁻(π⁺) mesons are producing in proton-target interactions. Pairs, which are generated from fragmentation and strong decays (“short-lived” sources), are affected by Coulomb interaction in the final state. Some of them form Coulomb bound states — atoms, other are generated as free pairs (“Coulomb pairs”). Number of produced atoms (N_A) is proportional to a number of “Coulomb pairs” (N_C) with low relative momentum Q in a pair C.M. system: N_A= K · N_C. The coefficient K is calculated with an accuracy better than 1% [4].

If at least one meson is generated from long-lived sources (electromagnetically or weakly decaying mesons or baryons: η, η⁰, K_s⁰, ...), then such pairs (“non-Coulomb pairs”) are not affected by interaction in the final states.

After production, A_πKtravel through the target and could to annihilate into π⁰K⁰, or to be ionised due to interaction with the target matter, producing specific “atomic pairs”. These pairs have small relative momentum (Q < 3 MeV/c) and a number of such pairs n_Acould be measured experimentally. Ratio of “atomic pair” number to a number of atom produced is a breakup probability: P_br(τ) = n_A/N_A= n_A/(K·N_C) [5, 6]. In Fig dependence of A_πKbreakup probability is shown for two nickel target are used in experiment DIRAC for pair laboratory momentum range 5.1÷8.5 GeV/c. Value is averaged, using experimentally measured spectrum of atoms.

References

[1] J. Schweizer, Phys. Lett. B 587, 33 (2004)

[2] J. Bijnens et al., JHEP 0405, 036 (2004)

[3] L. Nemenov, Sov. J. Nucl. Phys. 41, 629 (1985)

[4] L. Afanasyev and O. Voskresenskaya, Phys. Lett. B 453, 302 (1999)

[5] L. Afanasyev and A. Tarasov, Phys. At. Nucl. 59, 2130 (1996) [6] M. Zhabitsky, Phys. At. Nucl. 71, 1040 (2008)

Why SPS?

Experimental data on the πK low-energy phases are absent. The only experimental pion-kaon scattering length measurements have been done with estimation of πK atom lifetime [12]:

, (8)

and [13]:

. (9)

Table 1: Yields of atoms (W_A) and charged particles (W_ch) per one proton nuclear interaction. Values normalized by experimental condition of experiment DIRAC are presented as and , correspondingly. Ratio (W_A/W_ch)^Npresents gain in statistic of atoms for the same background conditions.

θlab	5.7°	4°	2°	0°
E_p	24 GeV	450 GeV	450 GeV	450 GeV
Yield charged particles
W_ch	0.022	0.14	0.50	2.9
	1	6.4	22.7	132
Yield of π⁺π⁻ atoms
W_A × 10⁹	1.94	34.	69.	89.
	1.	17.3	35.4	45.9
(W_A/W_ch)^N	1.	2.4	1.2	0.27
Yield of π⁺K⁻ atoms
W_A × 10⁹	0.217	8.1	16.3	23
	1.	37.5	75.	106.
(W_A/W_ch)^N	1.	10.6	5.8	1.2
Yield of K⁺π⁻ atoms
W_A × 10⁹	0.52	8.5	19.	30.
	1.	16.4	37.6	57.4
(W_A/W_ch)^N	1.	4.9	3.0	0.66

Present experimental accuracy is not sufficient for test of Low Energy QCD prediction. As shown in [14], the number of πK atoms detected per time unit would be increased by a factor of 30 to 40, if the DIRAC experiment could exploit the CERN SPS 450 GeV/c proton beam. Table 1 shows yield of atoms (W_A) and charged particles (W_ch) per one proton-nuclear interaction at different momenta of proton beam (E_p) and angles between proton beam and secondary beam channel (Θ_lab). Values W_A^Nand W_ch^Nshows change relative to experimental conditions of experiment DIRAC. Statistic, taken in certain time, also depends on beam intensity, which is limited by a flux of charged particles through detectors of the setup. Ratio W_A/W_ch)^Nprovides gain from new beam energy and the setup angle for the same beam time.

On the base of experimental data, estimation [15] of a time needed for measurement with statistical accuracy for existed DIRAC setup and beam condition (Nickel target only) has been done and results are presented in Table 2: here Mod1 is for DIRAC setup at E_p= 450 GeV beam (small modification due to another geometry of secondary particle beam); Mod2 is for essentially modified DIRAC setup at 450 GeV beam with higher intensity (I_B). It is assumed that at 450 GeV beam setup would obtain 3000 spills (4.5s) per day.

• Expected statistic of πK atomic pairs: n_A≈ 13000.

• Statistical accuracy of πK scattering length difference: ∼ 5%.

• Expected systematic error: ∼ 2%.

• Expected statistic of π⁺π⁻atomic pairs: n_A≈ 400000.

• Statistical accuracy of π⁺π⁻scattering length difference: ∼ 0.7%.

• Expected systematic error: ∼ 2%.

Table 2: Estimation of time needed for measurement with statistical accuracy for present DIRAC setup and beam condition, and for versions Mod1 and Mod2, modified for proton beam energy Ep = 450 GeV and intensity IB (proton per second). Angle between primary and secondary beams θlab and solid angle of secondary beam aperture are presented. It is assumed, that at 450 GeV beam the setup would obtain 3000 spills (4.5s) per day.

Setup	E_p	I_b	θlab	Solid angle	Beam time	Run time
	GeV	p/s		sr	s	months	%
Existed	24	2.7 · 10¹¹	5.7	1.2 · 10⁻³	1.2 · 10⁶	14.5	43.
Mod1	450	1.0 · 10¹¹	4.0	0.6 · 10⁻³	5.5 · 10⁶	13.6	5.
Mod2	450	1.0 · 10¹²	4.0	0.6 · 10⁻³	6.5 · 10⁵	1.6	5.

References

[1] V. Bernard et al., Phys. Rev. D 43, (1991) 2757.

[2] A. Roessl, Nucl. Phys. B 555, (1999) 507.

[3] J. Bijnens et al., JHEP 0405, (2004) 036.

[4] P. Buttiker et al., Eur. Phys. J. C 33, (2004) 409.

[5] S.R. Beane et al., Phys. Rev. D 77, (2008) 094507.

[6] C.B. Lang et al., Phys. Rev. D 86, (2012) 054508.

[7] K. Sasaki et al., Phys. Rev. D 89, (2014) 054502.

[8] T. Janowski et al., PoS LATTICE2014 (2015) 080.

[9] S.R. Beane et al., Phys. Rev. D 74 (2006) 114503.

[10] Z. Fu, Phys. Rev. D 85 (2012) 074501.

[11] K. Sasaki et al., Phys. Rev. D 89 (2014) 054502.

[12] B. Adeva et al., Phys. Lett. B 735, (2014) 288.

[13] B. Adeva et al., arXiv:1707.02184 [hep-ex].

[14] O. Gorchakov and L. Nemenov, J. Phys. G: Nucl. Part. Phys. 43 (2016) 095004.

[15] V. Yazkov, DN-2016-05 (DN = DIRAC Note), http://cds.cern.ch/record/2207227

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Setup

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Detectors

Setup element (number planes)	Aperture	Occupancy	X0	Resolution
	Aperture	Occupancy	X0	Coordinate	Time
	cm	s−1 · cm−2	%	µm	ns
1. Target Station 2. Vacuum system 3. Vertex detector (2 ÷ 4)	7.6 × 7.6	(5 ÷ 20) · 10⁵	0.7 ÷ 1.5	50 ÷ 100	0.2 ÷ 0.4
4. RICH?	9.0 × 9.0	(4 ÷ 16) · 10⁵	< 5		< 1
5. SFD (3)	10. × 10.	(3 ÷ 12) · 10⁵	2.7	60 ÷ 130	0.4
6. Vacuum system 7. Iron shielding wall 8. Spectrometer magnet	155 × 50
9. Downstream Tracker (2 × 8)	75 ÷ 110×44	(1 ÷ 10) · 10⁴	4 ÷ 8	< 80
10.Vertical Hodoscope (2 × 1 ÷ 2)	112 × 44	(1 ÷ 8) · 10⁴			< 0.7
11. Horizontal Hodoscope (2)	115 × 44	(1 ÷ 8) · 10⁴			< 0.5
12.Heavy Gas Cherenkov detector (2)	30 × 49	(1 ÷ 8) · 10⁴			< 1.0
13.Nitrogen Cherenkov detector (2)	90 × 50	(1 ÷ 10) · 10³			< 1.0
14.Nitrogen Cherenkov detector (2)	37 × 53	(1 ÷ 8) · 10⁴			< 1.0
15.PreShower detector (2)	148 × 60	(1 ÷ 8) · 10³			< 1.0
16.PreShower detector (2)	56 × 60	(5 ÷ 40) · 10³			< 1.0

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Plans

These results have been presented on Physics Beyond Colliders Workshop and are under consideration of PBC Committee as DIRAC++. Work under LOI for experiment at 450 Gev proton beam is started.

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