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