weak coherent kaon production l. alvarez-ruso 1, j. nieves 1, i. ruiz simo 2, m. valverde 3, m....

Weak Coherent Kaon Production

L. Alvarez-Ruso1, J. Nieves1, I. Ruiz Simo2, M. Valverde3, M. Vicente Vacas1

1. IFIC, Universidad de Valencia2. Universidad de Granada3. RCNP, Osaka

1. IFIC, Universidad de Valencia2. Universidad de Granada3. RCNP, Osaka

L. Alvarez-Ruso1, J. Nieves1, I. Ruiz Simo2, M. Valverde3, M. Vicente Vacas1

Weak Coherent Kaon Production

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

IntroductionQE and 1¼ are the most important (large and relevant for oscillations) (anti)º interaction channels in the few-GeV region, but there are others…Strangeness production:

¢S = 0 e.g.¢S = 1 :

Cabibbo suppressed but with lower thresholds than ¢S = 0

Hyperon e.g.

Kaon:

Background for proton decay p ! º K+

Accessible by Minerºa but also MiniBooNE, T2K, …There is a coherent channel

ºl p(n) ! l¡ K + § +(¤)

¹ºl p! l+ § 0(¤)ºl p ! l¡ K + p

ºl n ! l¡ K 0 p

ºl n ! l¡ K + n

ºl A ! ¹ ¡ K + A

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

IntroductionQE and 1¼ are the most important (large and relevant for oscillations) (anti)º interaction channels in the few-GeV region, but there are others…Strangeness production:

¢S = 0 e.g.¢S = -1 :

Cabibbo suppressed but with lower thresholds than ¢S = 0

antiKaon:

Accessible by Minerºa but also MiniBooNE, T2K, …

Potentially interesting for antiº beams

There is a coherent channel

ºl p(n) ! l¡ K + § +(¤)

¹ºl p ! l+ K ¡ p

¹ºl p ! l+ ¹K 0 n

¹ºl n ! l+ K ¡ n

¹ºl A ! ¹ + K ¡ A

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

The model

1. Microscopic kaon production on the nucleon

2. The coherent reaction

3. Kaon distortion

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

The model

1. Microscopic kaon production on the nucleon Rafi Alam et al.,

PRD82

Includes all terms in SU(3) chiral Lagrangians at leading order

Parameters: f¼ , ¹p and ¹n , D and F (from semileptonic

decays)

A global dipole form factor : F(q2)=(1-q2/M2F)-2 , MF = 1 GeV

Absence of S=1 baryon resonances ) Extended validity of model

CT KP

Cr§, Cr¤ ¼F, ´F

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

The model

1. Microscopic kaon production on the nucleon Rafi Alam et al.,

PRD82

Includes all terms in SU(3) chiral Lagrangians at leading order

A global dipole form factor : F(q2)=(1-q2/M2F)-2 , MF = 1 GeV

(§ 10%)

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

The model

1. Microscopic kaon production on the nucleon Rafi Alam et al.,

PRD82

vs ¢S = 0 from GENIE

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

The model

2. The coherent reaction

Amplitude:

Nuclear current:

¼F, ´F vanish with the sum

initial and final nucleons taken on-shell with averaged momenta:

M =Gp

2sinµc l¹ J ¹

J ¹ =X

i

X

r=p;n

Zd~r ei(~q¡ ~pK )¢~r½r(r)

12

T rh¹u ¡ ¹

i(r) ui

i=CT , K P, Cr¤, Cr§ , ¼F , ´F

~p= ¡ ~p0= (~pK ¡ ~q)=2

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

The model

3. Kaon distortion (with DWBA)

or in the eikonal approximation:

The optical potential:

C=0.13 or 0.114

e¡ i~pK ¢~r ! Á¤out(~pK ;~r) ~pK e¡ i~p¼¢~r ! i ~r Á¤

out(~pK ;~r)³¡ ~r 2 ¡ ~p2

K + 2! K Vopt

´Á¤

out = 0 Ã Klein-Gordon eq.

Á¤out ¼e¡ i~pK ¢~r ¡ i ! K

j ~pK j

R1

zdz0Vopt

2! K Vopt = ¦ (r) = Cm2K

½½0

Cabrera, Vicente Vacas, PRC69

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

ResultsIn the Impulse Approximation:

Very small cross section…

ºl A ! ¹ ¡ K + A

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

ResultsIn the Impulse Approximation:

Very small cross section…

Compare to Coh¼+ (on 12C):

¾(Coh¼+,1 GeV)~ 0.05-0.1 >> ¾ (CohK+,1.35 GeV)~ 0.00014

ºl A ! ¹ ¡ K + A

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

ResultsIn the Impulse Approximation:

Very small cross section… why?

ºl A ! ¹ ¡ K + A

d¾d ¹ dE ¹ d K

» F 2(j~q¡ ~pK j) ; j~q¡ ~pK j > q0 ¡ j~pK j =q

m2K + ~p2

K ¡ j~pK j

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

ResultsIn the Impulse Approximation:

Very small cross section… why? because K is heavy

ºl A ! ¹ ¡ K + A

d¾d ¹ dE ¹ d K

» F 2(j~q¡ ~pK j) ; j~q¡ ~pK j > q0 ¡ j~pK j =q

m2K + ~p2

K ¡ j~pK j

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

ResultsIn the Impulse Approximation:

Very small cross section… why? because K is heavy

ºl A ! ¹ ¡ K + A

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

ResultsIn the Impulse Approximation:

Very small cross section… why? because K is heavy )

Sensitive to the nuclear density distribution

ºl A ! ¹ ¡ K + A

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

ResultsIn the Impulse Approximation. Contribution from different mechanisms:

ºl A ! ¹ ¡ K + A

CT is the largest contribution, followed by Cr¤Interference stronger than in the free case

Rafi Alam et al., PRD82 (2010)

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

ResultsIn the Impulse Approximation. Contribution from different mechanisms:

ºl A ! ¹ ¡ K + A

CT is the largest contribution, followed by Cr¤Interference stronger than in the free case

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

ResultsWith Kaon distortion. Kaon momentum distributions:

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

ResultsWith Kaon distortion. Kaon momentum distributions:

Eikonal approximation breaks down at low |pK|

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

ResultsWith Kaon distortion. Kaon momentum distributions:

Eikonal approximation breaks down at low |pK|, unlike in Coh¼

LAR et al., PRC

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

ResultsWith Kaon distortion. Angular distributions:

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

ResultsWith Kaon distortion. Angular distributions:

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

The model

Coherent K- production with antineutrinos

Elementary interaction: Rafi Alam et al., PRD 85

Direct terms with strange baryons (¤, §, §*(1385)) in the intermediate state

¹ºl A ! ¹ + K ¡ A

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

The model

Coherent K- production with antineutrinos

Elementary interaction: Rafi Alam et al., PRD 85

N-§*(1385) transition: C3V, C4V, C5V, C3A, C4A, C5A, C6A ff related to those of N-¢(1232) using SU(3) symmetry

In particular: C5A(0) Ã off-diagonal G-T

¹ºl A ! ¹ + K ¡ A

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

The model

Coherent K- production with antineutrinos

Elementary interaction: Rafi Alam et al., PRD 85

Small contribution from §*(1385): it is below K production threshold

¹ºl A ! ¹ + K ¡ A

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

Results

Coherent K- production with antineutrinos

In the Impulse Approximation. Contribution from different mechanisms:

¹ºl A ! ¹ + K ¡ A

Rafi Alam et al., PRD85 (2012)

Largest contribution from CTStrong destructive interference(Relatively) large §*

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

The model

3. antiKaon distortion (with DWBA)

The optical potential:

K-p interaction dominated by ¤(1405) resonance

¤(1405) dynamically generated by s-wave meson-baryon rescattering in coupled channels

Dressing of meson propagators (1p1h, ¢h)

Self consistent treatment of antiK

e¡ i~pK ¢~r ! Á¤out(~pK ;~r) ~pK e¡ i~p¼¢~r ! i ~r Á¤

out(~pK ;~r)³¡ ~r 2 ¡ ~p2

K + 2! K Vopt

´Á¤

out = 0 Ã Klein-Gordon eq.

2! K Vopt = ¦ (r) Ramos, Oset, NPA 671 (2000)

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

The model

3. antiKaon distortion (with DWBA)

The optical potential:

Very different interaction vs Kaon case:

e¡ i~pK ¢~r ! Á¤out(~pK ;~r) ~pK e¡ i~p¼¢~r ! i ~r Á¤

out(~pK ;~r)³¡ ~r 2 ¡ ~p2

K + 2! K Vopt

´Á¤

out = 0 Ã Klein-Gordon eq.

2! K Vopt = ¦ (r) Ramos, Oset, NPA 671 (2000)

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

ResultsWith antiKaon distortion. Momentum distributions:

March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski

Conclusions

(anti)Neutrino induced coherent (anti)kaon production has

been studied

Microscopic production mechanism based on SU(3)chiral

Lagrangians

Coherent sum over all (noninteracting) nucleons

DWIA for the outgoing (anti)kaon by solving the KG eq. with

a realistic density-dependent potential

Small cross sections are obtained due to:

Small (Cabibbo suppressed) c. s. on nucleons

Large momentum transferred to the nucleus because of the

large kaon mass

Destructive interference

Kaon distortion (stronger for K- as expected)

Eikonal approximation is wrong at low momenta