Weak Coherent Kaon Production L. Alvarez-Ruso 1, J. Nieves 1, I. Ruiz Simo 2, M. Valverde 3, M. Vicente Vacas 1 1.IFIC, Universidad de Valencia 2.Universidad

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


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


The model

1. Microscopic kaon production on the nucleon

2. The coherent reaction

3. Kaon distortion


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


The model


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%)


The model


PRD82

vs ¢S = 0 from GENIE


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


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


ResultsIn the Impulse Approximation:

Very small cross section…

ºl A ! ¹ ¡ K + A



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



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



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



Very small cross section… why? because K is heavy

ºl A ! ¹ ¡ K + A



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

Sensitive to the nuclear density distribution

ºl A ! ¹ ¡ K + A


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)


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


ResultsWith Kaon distortion. Kaon momentum distributions:



Eikonal approximation breaks down at low |pK|



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

LAR et al., PRC


ResultsWith Kaon distortion. Angular distributions:


ResultsWith Kaon distortion. Angular distributions:


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


The model



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


The model



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

¹ºl A ! ¹ + K ¡ A


Results


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 §*


The model

3. antiKaon distortion (with DWBA)


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


out(~pK ;~r)³¡ ~r 2 ¡ ~p2

K + 2! K Vopt

´Á¤


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


The model

3. antiKaon distortion (with DWBA)


Very different interaction vs Kaon case:


out(~pK ;~r)³¡ ~r 2 ¡ ~p2

K + 2! K Vopt

´Á¤


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


ResultsWith antiKaon distortion. Momentum distributions:


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

Documents

Weak Coherent Kaon Production L. Alvarez-Ruso 1, J. Nieves 1, I. Ruiz Simo 2, M. Valverde 3, M. Vicente Vacas 1 1.IFIC, Universidad de Valencia 2.Universidad