Σ+ → pµ+ µ−
Standard Model or New Physics?
Jusak Tandean
National Taiwan University
in collaboration with
XG He & G Valencia
High Energy Physics Seminar
National Tsing Hua University
25 September 2008
Outline of talk
•
•
Introduction
Evaluation of Σ+ → pµ+ µ− within standard model
•
New particle interpretation of HyperCP results
•
Candidate for new particle in NMSSM
•
Testable predictions
•
Conclusions
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
2
Introduction
•
Interesting experimental finding
PHYSICAL REVIEW LETTERS
PRL 94, 021801 (2005)
week ending
21 JANUARY 2005
Evidence for the Decay ! p 8
5
H. K. Park, R. A. Burnstein, A. Chakravorty,5 Y. C. Chen,1 W. S. Choong,2,7 K. Clark,9 E. C. Dukes,10 C. Durandet,10
J. Felix,4 Y. Fu,7 G. Gidal,7 H. R. Gustafson,8 T. Holmstrom,10 M. Huang,10 C. James,3 C. M. Jenkins,9 T. Jones,7
D. M. Kaplan,5 L. M. Lederman,5 N. Leros,6 M. J. Longo,8,* F. Lopez,8 L. C. Lu,10 W. Luebke,5 K. B. Luk,2,7
K. S. Nelson,10 J.-P. Perroud,6 D. Rajaram,5 H. A. Rubin,5 J. Volk,3 C. G. White,5 S. L. White,5 and P. Zyla7
(HyperCP Collaboration)
1
Institute of Physics, Academia Sinica, Taipei 11529, Taiwan, Republic of China
2
University of California, Berkeley, California 94720, USA
3
Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
4
Universidad de Guanajuato, 37000 León, Mexico
5
Illinois Institute of Technology, Chicago, Illinois 60616, USA
6
Université de Lausanne, CH-1015 Lausanne, Switzerland
7
Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
8
University of Michigan, Ann Arbor, Michigan 48109, USA
9
University of South Alabama, Mobile, Alabama 36688, USA
10
University of Virginia, Charlottesville, Virginia 22904, USA
(Received 3 November 2004; published 18 January 2005)
We report the first evidence for the decay ! p from data taken by the HyperCP (E871)
experiment at Fermilab. Based on three observed events, the branching ratio is B ! p 8
8:66:6
5:4 stat 5:5syst 10 . The narrow range of dimuon masses may indicate that the decay
proceeds via a neutral intermediate state, ! pP0 ; P0 ! with a P0 mass of 214:3 8
0:5 MeV=c2 and branching ratio B ! pP0 ; P0 ! 3:12:4
1:9 stat 1:5syst 10 .
DOI: 10.1103/PhysRevLett.94.021801
PACS numbers: 13.30.Ce, 14.20.Jn, 14.80.Mz
•
What’sInthe
up-to-date standard-model
prediction for the decay?
dent on copper targets and momentum selected by a curved
the standard model (SM), the decay !
•
Do the observed 3 events hint at new physics?
calculation
by Bergstrom,
collimator situated in (old
a dipole
magnet (hyperon
magnet).Safadi, Singer, ZPC, 1988)
pl l pll ; l e; can be described as proceeding
The sign of the charged secondary beam was periodically
through a flavor-changing neutral-current (FCNC) interacchanged by reversing the field of the hyperon magnet. We
tion and by internal conversion, as shown in Fig. 1(a)–1(c).
analyzed 2:14 109 triggers from the positive-secondaryBergström et al. [1] argue that in the SM the FCNC
beam data set and 0:37 109 from the negative.
contribution for the decay pll is not dominant. The decay
The signature of the p decay is two unlike-sign
is of interest since it also allows a direct search for a
J Tandean (NTU) pll
NTHU muon
HEP tracks
Seminar,
Septrack
2008originating from a common
and a25
proton
new scalar or vector particle, which could contribute an
3
Standard model calculation
•
(He, JT, Valencia, PRD, 2005)
Long-distance contributions
dominate Σ+ → pµ+ µ− .
γ∗
Σ+
•
µ+
µ−
p
Gauge-invariant amplitude has four form-factors
M Bi → Bf γ ∗ = −eGF B̄f iσ µν qµ a + bγ5
+ (q 2 γ ν − q ν6 q) c + dγ5 Bi ε∗ν
q four-momentum of γ ∗ .
•
•
Form factors a(q 2 ), b(q 2 ), c(q 2 ), and d(q 2 ) are all complex and
get imaginary parts from N π intermediate states.
a(0) and b(0) contribute to the (on shell) radiative decay
Σ+ → pγ, but c and d do not.
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
4
Long-distance contributions to Σ+ → pγ ∗
•
Unitarity cut
Σ+
•
γ
π
p
N
Leading-order diagrams for N π → pγ ∗ reactions
γ
π+
π0
p
γ
π+
p
n
p
n
γ
π0
p
p
π+
γ
n
p
γ
p
•
Diagrams for imaginary part of amplitude in heavy-baryon case
•
Pole diagrams contributing to the c and d amplitudes
(a)
(b)
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
5
Results in standard model
• Invariant-mass distributions corresponding to the smallest and largest branching
ratios for the (a,b) relativistic and (c,d) heavy baryon cases.
2
Re a = 13.3 MeV
Re b = −6.0 MeV
6
Re a = −6.0 MeV
Re b = 13.3 MeV
(a)
(b)
0
2
220
240
Mµµ (MeV)
260
Re a = 11.1 MeV
Re b = −7.3 MeV
(c)
dΓ(Σ+ →pµ+ µ− )
(MeV−1 )
dq 2
1
1023 ×
1023 ×
dΓ(Σ+ →pµ+ µ− )
(MeV−1 )
dq 2
4
1
2
0
6
220
240
Mµµ (MeV)
260
Re a = −7.3 MeV
Re b = 11.1 MeV
(d)
4
2
0
220
240
Mµµ (MeV)
260
0
220
240
Mµµ (MeV)
260
Each solid curve receives contributions from all form factors.
• Different possible graphs reflect uncertainty in the calculation.
• Not surprisingly, the predicted spectra show no sharp peak anywhere.
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
6
Branching ratio in standard model
•
The SM calculation yields the range
1.6 × 10−8 ≤ B Σ+ → pµ+ µ−
•
≤ 9.0 × 10−8
This agrees well with HyperCP measurement
−8
B(Σ+ → pµ+ µ− ) = 8.6+6.6
−5.4 ± 5.5 × 10
(under the assumption of no new physics).
•
The lower end of the predicted rate leaves room for attributing all
the 3 events observed by HyperCP to new physics.
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
7
Alternative interpretation of HyperCP results
From HK Park’s talk (2007)
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
8
New particle hypothesis
•
•
Interpreting their results as hinting at a new particle (X 0 ),
HyperCP finds
+
∗ B Σ
→ pX 0 → pµ+ µ− = 3.1+2.4
±
1.5
× 10−8
−1.9
∗ mass m
X = (214.3 ± 0.5) MeV
This observation implies the particle
∗ is short lived, decaying inside detector
−7
MeV
∗ is narrow, with Γ
X ∼ 10
+ −
+ −
∗ decays mainly into µ µ , e e , or γγ
∗ does not interact strongly
∗ has effective |∆S| = 1 coupling to d, s quarks
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
(Geng & Hsiao, PLB, 2006)
9
Constraints on new particle with mass 214 MeV
•
The existence of a new particle with such a low mass would be
remarkable, as it would signal the existence of physics beyond the
SM unambiguously.
•
But the new-particle interpretation faces serious challenges:
∗ A new-physics model having a suitable candidate for the
particle and able to explain why it is light.
∗ An explanation of why the particle has not been observed by
other experiments covering the same kinematic range.
∗ Its interactions must produce the rate implied by the
HyperCP observation.
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
10
Constraints from kaon and B-meson decays
•
E865 at BNL:
B(K ± → π ± A01 ) . 8.7 × 10−9
•
NA48:
•
BABAR & Belle:
B(B → Xs A01 ) . 8.0 × 10−7
(Batley et al., PLB, 2004)
B(KS → π
J Tandean (NTU)
(Ma et al., PRL, 2000)
0
A01 )
−9
. 1.8 × 10
NTHU HEP Seminar, 25 Sep 2008
(Aubert et al., PRL, 2004)
(Iwasaki et al., PRD, 2005)
11
Two types of |∆S| = 1 contributions
(He, JT, Valencia, PRD, 2006)
•
Two-quark contributions
LAsd =
iCR ¯
iCL ¯
d(1 + γ5 )s A01 +
d(1 − γ5 )s A01 + H.c.
2
2
CL,R are in general unrelated.
•
Four-quark contributions, which arise from the combined effects of the usual
SM four-quark |∆S| = 1 operators and A01 being radiated off one of the
light quarks via its flavor-conserving couplings.
u
d
A01
W
s
•
u
Similarly for a scalar particle.
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
12
Hadronic couplings arising from two-quark contributions
• Chiral Lagrangian techniques can be used to derive the hadronic realization of the
sdA01 couplings.
• The resulting Lagrangian
LA = bD B̄ {hA , B } + bF B̄ [hA , B ] + b0 hhA i B̄ B +
α
hA
1 2
f B0
2
hhA i
α
+ c T̄ hA Tα − c0 hhA i T̄ Tα + H.c.
= −i CR ξ † hξ † + CL ξhξ A01 and h = 21 λ6 + iλ7 .
• Baryon and meson fields are contained in 3×3 matrices B and ξ, and also tensor
Tµ .
A01
• Diagrams for Σ → pA01
A01
K̄ 0
Σ
+
p
Σ
+
p
• Similarly for a scalar particle.
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
13
Chiral Lagrangians in SM
•
Leading-order strong Lagrangian
Ls = B̄ iγ µ ∂µ B + Vµ , B
− m0 B̄ B
+ D B̄ γ µ γ5 Aµ , B + F B̄ γ µ γ5 Aµ , B
+ bD B̄ {M+ , B} + bF B̄ [M+ , B] + b0 hM+ i B̄ B
+ 41 f 2 ∂ µ Σ† ∂µ Σ + 12 f 2 B0 hM+ i
− T̄ µ i D
6 Tµ + mT T̄ µ Tµ + C T̄ µ Aµ B + B̄Aµ T µ
+ c T̄ µ M+ Tµ − c0 M+ T̄ µ Tµ
•
Leading-order weak Lagrangian
Lw = hD B̄ ξ † hξ, B + hF B̄ ξ † hξ, B
+ γ8 f 2 h ∂µ Σ ∂ µ Σ† + 2γ̃8 f 2 B0 hξM+ ξ †
+ hC T̄ µ ξ † hξTµ + H.c.
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
14
Chiral Lagrangians for four-quark contributions
• From SM strong and weak chiral Lagrangians, one derives
A
Ls =
bD B̄ M̃− , B
+ bF B̄ M̃− , B + b0 M̃− B̄ B +
1 2
2 f B0
M̃−
iA01
v
0
A
2
† iA1
+ H.c.
Lw = 2γ̃8 f B0 hξ M̃− ξ
v
M̃− = ξ † M̃ ξ † − ξ M̃ † ξ and M̃ = diag lu m̂, ld m̂, ld ms
• From the coupling of A01 to two gluons via the axial anomaly,
Lη
1A
2
= − 12 mη −
1
2
2
3 mK
A
−
2
1
3 mπ
#2
f A0
η1 + √ 1 (2lu + ld )
6v
"
A
0
π , η, η
′
π , η, η
p
Σ+
A
0
Σ+
′
0
π , η, η
p
Σ+
Σ+
K
J Tandean (NTU)
p
p
A
A
′
A
A
π
K
K0
π 0 , η, η ′
π
K
K
π
NTHU HEP Seminar, 25 Sep 2008
K
π 0 , η, η ′
π
15
Two- and four-quark contributions
•
The interplay between the 2- and 4-quark contributions makes it possible to
find a desired model
However, it is not easy to devise such a model.
¯
• In most models having dsX
couplings, the 2-quark operators have the
¯
structure d(1 ± γ5 )sX: the part without γ5 contributes significantly to
K → πµ+ µ− leading to couplings that are too small to account for the
HyperCP events.
•
•
In some models, there may be parameter space where the 2- and 4-quark
contributions are comparable and cancel sufficiently to lead to rates within
the kaon and hyperon bounds.
•
However, since in many models the flavor-changing two-quark couplings
q̄q 0 X are related for different (q, q 0 ) sets, experimental data on
B → Xs µ+ µ− also provide stringent constraints.
•
Thus the light (pseudo)scalars in many models, such as the SM and the
two-Higgs-doublet model, are ruled out as candidates to explain the
HyperCP events.
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
16
Any candidate for X?
• The next-to-minimal supersymmetric standard model (NMSSM) is an extension of
the MSSM.
• In the NMSSM, there is a gauge-singlet Higgs field N in addition to the two Higgs
fields Hu and Hd responsible for the up- and down-type quark masses in the
MSSM.
• As a result, the physical spectrum of the NMSSM has 2 additional neutral Higgs
bosons: one a scalar and the other a pseudoscalar.
• The lighter pseudoscalar Higgs boson, the A01 , turns out to be able to play the role
of X.
• The soft-susy-breaking term in the Higgs potential is
Vsoft = m2Hu |Hu |2 + m2Hd |Hd |2 + m2N |N |2 − λAλ Hd Hu N + 13 kAk N 3 + H.c.
and has a global U(1) symmetry in the limit that Aλ , Ak → 0.
(Dobrescu, Matchev, JHEP, 2000)
• The global U(1) symmetry allows the
A01
mass to be naturally, and masses of order
100 MeV are not ruled out.
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
(Dobrescu, PRD, 2001)
17
A01 in NMSSM
•
In the large-tan β limit (tan β the ratio of VEVs of Higgs doublets)
∗
∗
∗
∗
the A01 is mostly the singlet pseudoscalar and couples to SM fields through
mixing
its squared mass m2A = 3k x Ak + O(1/ tan β) with x = hN i
its tree-level couplings to up-type quarks are negligible
its tree-level couplings to down-type quarks and charged leptons can be
described in terms of one parameter,
¯ 5d
LAdd = −ld md dγ
ld = v δ − /
∗
•
√
iA01
,
v
¯ 5`
LA` = −ld m` `γ
iA01
,
v
2 x , with v = 246 GeV and δ− = (Aλ − 2kx)/(Aλ + kx)
the lower bound of ld is |ld | ∼ 0.1
and its upper bound |ld | ∼ 1.2.
(Hiller, PRD, 2004)
(He, JT, Valencia, PLB, 2005)
Therefore the 4-quark contributions are given in terms of ld in the
large-tan β limit
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
18
Two-quark contributions of A01 in NMSSM
• In certain versions of the NMSSM at large tan β, the couplings CL,R are related by
CL = −CR md /ms = −2gA md /v, corresponding to
LAsd =
igA ¯ + γ5 )s − md d(1
¯ − γ5 )s A01 + H.c.
ms d(1
v
• This is the case with the NMSSM of Hiller (2004) at large tan β, where CL,R are
generated by one-loop diagrams containing charginos and squarks.
• With suitable modifications, the Hiller model provides an A01 with the desired
properties: it can evade the K and B bounds, while being responsible for the
HyperCP events.
(He, JT, Valencia, PRL, 2007)
• Including the 4-quark contributions
10-7
with ld = 0.35
+
+
K → π A01 (dotted curves), and
KS → π 0 A01 (dashed curves), where
10-8
B
• Branching ratios of Σ+ → pA01 (solid curves),
10-9
horizontal lines indicate HyperCP and kaon bounds.
0.2
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
0.4
0.6
107 gA
0.8
1
19
More general scenario for light A01 in NMSSM
•
Additional one-loop contributions to the sdA01 couplings with
other SUSY particles in the loop could enlarge the parameter
space, making CL,R unrelated.
LAsd =
iCR ¯
iCL ¯
0
0
d(1 + γ5 )s A1 +
d(1 − γ5 )s A1 + H.c.
2
2
•
Loops containing gluinos and neutralinos have been shown to
produce this decoupling.
(Gao, Li, Li, Zhang, EPJC, 2008)
•
This opens up the possibility of satisfying the kaon bounds in the
absence of the 4-quark contributions.
Thus CL and CR can be taken to be independent, to be
constrained with data.
•
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
20
Parameter space
1.0
• Regions in the (CL +CR , ld ) parameter
space allowed by K + → π + µ+ µ− (blue)
and KS → π 0 µ+ µ− (green).
The overlap (red) band covers points
that satisfy both constraints.
ld
0.5
0.0
-0.5
-1.0
-1.0
-0.5
0.0
10 HCL + CRL
0.5
1.0
10
15
10
5
0
10
10 HCL - CRL
• Regions in the (CL +CR , CL −CR )
parameter space reproducing the
HyperCP result (yellow) and
respecting the K → πµ+ µ−
bounds (red) for ld = 0.35.
The overlap (black) areas cover
points satisfying both the hyperon
and kaon constraints, and the
unshaded (white) region on the
vertical band corresponds to the
case of related CL,R .
-5
-10
-15
-1.0
-0.5
0.0
10 HCL + CRL
0.5
1.0
10
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
21
Other rare decays with light A01 in NMSSM
•
•
•
•
(He, JT, Valencia, JHEP, 2008)
Some other rare decays can help confirm of refute the light-A01
hypothesis
|∆S| = 1 decays
0
+ −
∗ Evaluate K̄ → ππA
and
1 → ππµ µ
−
− 0
− + −
Ω → Ξ A1 → Ξ µ µ .
∗ They involve both two-quark and four-quark contributions.
Flavor-conserving decays
0
+ −
∗ Υ(1S) → γA
and φ → γA01 → γµ+ µ− .
1 → γµ µ
0
+ −
∗ Evaluate η → ππA
1 → ππµ µ
∗ They help test the hypothesis independently of the details of
the flavor-changing sector.
They can be searched for in ongoing experiments.
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
22
K → ππA01
π
2-quark
contributions
K̄
π
4-quark
contributions
π
A01
π
A01
π
A01
K̄
K̄
π
K̄
K̄
P
A01
P
K̄
π
A01
CL,R being related.
A01
5
0.6
8
0.4
8
+ -
A01
6
0.8
0.2
0.0
-15
P
π
4
3
2
1
-10
-5
0
5
10 HCL - CRL
10
Being studied by KTeV.
P
K̄
1.0
10 ´ BHKL ® Π Π A10 L
2-quark contributions alone, the pink
bands indicate the allowed ranges of
CL −CR , and each green dashed
line corresponds to the case of
P
π
• Predicted branching ratios (solid
curves) for KL → π + π − A01 and
KL → π 0 π 0 A01 with ld = 0.35.
π
K̄
K̄
π
• The dotted curves result from the
π
π
P
A01
π
π
K̄
J Tandean (NTU)
A01
π
π
K̄
K̄
π
•
K̄ 0
K̄
π
K̄
•
π
A01
10 ´ BHKL ® Π0 Π0 A01 L
•
NTHU HEP Seminar, 25 Sep 2008
10
15
0
-15
-10
-5
0
5
10 HCL - CRL
10
15
10
23
Ω− → Ξ− A01
A01
•
Two- and four-quark
contributions
A01
K̄ 0
Ω−
Ξ∗−
Ω−
Ξ−
P
Ξ−
12
10
6
Predicted branching ratio
for ld = 0.35
10 ´ BHW- ® X- A01 L
•
8
6
4
2
0
-15
-10
-5
0
10 HCL - CRL
5
10
15
10
•
•
•
The best limit currently available from HyperCP (2003)
B(Ω− → Ξ− µ+ µ− ) < 6.1 × 10−6 (90%C.L.)
SM predicts
BSM (Ω− → Ξ− µ+ µ− ) = 6.6 × 10−8
(Safadi & Singer, PRD, 1988)
The predicted Ω → Ξ
→ Ξ µ µ rate for most of allowed regions is
substantially enhanced with respect to the SM rate.
J Tandean (NTU)
−
−
A01
− + −
NTHU HEP Seminar, 25 Sep 2008
24
η → ππA01
•
They are special, involving only
flavor-diagonal interactions
π
η
π
A01
π
η, η ′
η
A01
π
•
Predicted branching ratio
B η → π + π − A01 = 5.4 × 10−7 ld2
for η-η 0 mixing angle θ = −19.7◦ .
•
The best limit currently available from CELCIUS/WASA collaboration (2008)
B(η → π + π − µ+ µ− ) < 3.6 × 10−4 (90%C.L.)
implies loose bound |ld | < 26.
•
•
There is room for enhancement over the expected standard-model rate
−9
BSM (η → π + π − µ+ µ− ) = 7.5+4.5
(Borasoy, Nissler, EPJA, 2007)
−2.7 × 10
η → π + π − µ+ µ− may be accessible to DAΦNE experiment.
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
25
New constraint from CLEO
•
arXiv:0807.1427v1 [hep-ex]
CLNS 08/2033
CLEO 08-16
[hep-ex] 9 Jul 2008
Searh for Light CP-odd Higgs in Radiative Deays of (1S)
W. Love,1 V. Savinov,1 H. Mendez,2 J. Y. Ge,3 D. H. Miller,3 I. P. J. Shipsey,3 B. Xin,3
G. S. Adams,4 M. Anderson,4 J. P. Cummings,4 I. Danko,4 D. Hu,4 B. Moziak,4
J. Napolitano,4 Q. He,5 J. Insler,5 H. Muramatsu,5 C. S. Park,5 E. H. Thorndike,5
F. Yang,5 M. Artuso,6 S. Blusk,6 S. Khalil,6 J. Li,6 R. Mountain,6 S. Nisar,6
6
K. Randrianarivony,6 N. Sultana,6 T. Skwarniki,
S. Stone,6 J. C. Wang,6 L. M. Zhang,6
Abstrat
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D. L. Hartill,12 B. K.more
Heltsley,
D. Hertz,12 J. M.
Hunt,
J. Our
Kandaswamy,
12
12
noD.evidene
for a12Higgs
with a mass
of 214 MeV
to u+ger,
.12 Existene
of suh12 a
L. Kreinik,
V. E.state
Kuznetsov,
J. Ledoux,
H.deaying
Mahlke-Kr
D. Mohapatra,
12
12
12
state
as an explanation
for 3 12+D.!Riley,
p+ 12 events,
+Sado,
masses
P. U.wasE.previously
Onyisi,12 proposed
J. R. Patterson,
D. Peterson,
A. Ryd,having
A. J.
12 the kinemati
12
12
13
13
13
just
above
observed
by the HyperCP
experiment.
Our results
onstrain
X. Shi,
S. Stroiney,12 threshold,
W. M. Sun,
T. Wilksen,
S. B. Athar,
R. Patel,
J. Yelton,
14
NMSSM
models.
P. Rubin,
B. I. Eisenstein,15 I. Karliner,15 S. Mehrabyan,15 N. Lowrey,15 M. Selen,15
E. J. White,15 J. Wiss,15 R. E. Mithell,16 M. R. Shepherd,16 D. Besson,17 T. K. Pedlar,18
D. Cronin-Hennessy,19 K. Y. Gao,19 J. Hietala,19 Y. Kubota,19 T. Klein,19 B. W. Lang,19
R. Poling,19 A. W. Sott,19 P. Zweber,19 S. Dobbs,20 Z. Metreveli,20 K. K. Seth,20
A. Tomaradze,20 J. Libby,21 L. Martin,21 A. Powell,21 G. Wilkinson,21 and K. M. Eklund22
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
26
Detour
• The 4-quark contribution to Σ+ → pA01
M4q (Σ+ → pA01 ) =
f ld
2v
−bπ + bη cθ + bη0 sθ ip̄ Apπ0 − Bpπ0 γ5 Σ+
has a sign ambiguity because Apπ0 and Bpπ0 are extracted from the data on nonleptonic
decay Σ+ → pπ 0 up to an overall sign.
• With the opposite relative sign of the 2- and 4-quark contributions to Σ+ → pA01
15
10
6
5
0.4
8
-5
0.6
8
+ -
0
10 ´ BHKL ® Π0 Π0 A01 L
10 ´ BHKL ® Π Π A10 L
0.8
10
10 HCL - CRL
1.0
5
-10
-15
-1.0
0.2
-0.5
0.0
10 HCL + CRL
10
J Tandean (NTU)
0.5
1.0
0.0
-15
4
3
2
1
-10
-5
0
5
10 HCL - CRL
10
NTHU HEP Seminar, 25 Sep 2008
10
15
0
-15
-10
-5
0
5
10 HCL - CRL
10
15
10
27
CLEO’s constraint on A01
• Branching ratios of Σ+ → pA01 (solid
• Horizontal lines indicate HyperCP and
kaon bounds.
ld = 0.35
10-7
10-8
B
curves), K + → π + A01 (dotted curves),
and KS → π 0 A01 (dashed curves) as
functions of CL + CR .
10-9
• CLEO (2008) reported
< 2.3 × 10
0.0
0.2
10 HCL + CRL
0.4
0.6
0.8
10
−6
ld = 0.15, with 2Q-4Q in S+
at 90% C.L., which implies
ld < 0.16
-7
10
• This squeezes the parameter space for
the scenario with CL,R being related,
but not completely yet.
10-8
B
B Υ(1S) →
γA01
10-9
0.0
0.2
10 HCL + CRL
0.4
0.6
0.8
10
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
28
Absence of four-quark contributions for ld = 0
ld = 0
15
If CL,R are not related, the experimental
bounds can be satisfied even in the absence
of the 4-quark contributions.
10
5
10 HCL - CRL
0
10
•
-5
-10
ld = 0
ld = 0
6
10 ´ BHKL ® Π0 Π0 A01 L
0.8
0.6
8
0.4
0.2
-0.5
0.0
10 HCL + CRL
0.5
1.0
10
4
3
2
ld = 0
12
1
10
-10
-5
0
5
10 HCL - CRL
10
15
0
-15
-10
-5
0
5
10 HCL - CRL
10
10
15
6
10
10 ´ BHW- ® X- A10 L
0.0
-15
-15
-1.0
5
8
+ -
10 ´ BHKL ® Π Π A10 L
1.0
8
6
4
2
0
-15
-10
-5
0
10 HCL - CRL
5
10
15
10
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
29
Conclusions
•
The decay Σ+ → pµ+ µ− within the SM is long-distance dominated, and
the predicted rate is in the right range to explain the HyperCP observation.
•
Within the SM, the predicted mµµ distribution does not have any sharp
peaks, and so it is unlikely to find all 3 events clustered at the same mass.
•
Current constraints allow for an explanation of the 3 events with a new
particle as long as its effective flavor-changing coupling is mostly
pseudoscalar (or axial vector) and smaller for b → s transitions than what
naive scaling from s → d transitions (with CKM angles) would predict.
•
•
•
The NMSSM has a CP -odd Higgs boson, the A01 , that could have the
desired mass and satisfy all the experimental constraints.
Additional rare decays can help confirm or refute this hypothesis:
K → ππA01 , Ω− → Ξ− A01 .
Some other rare decays can test the hypothesis independently of the
flavor-changing sector: Υ(1S) → γA01 , φ → γA01 , η → ππA01 .
J Tandean (NTU)
NTHU HEP Seminar, 25 Sep 2008
30