Standard Model or New Physics?

Transcription

1 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

2 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

3 Introduction Interesting experimental finding PRL 94, (2005) PHYSICAL REVIEW LETTERS week ending 21 JANUARY 2005 Evidence for the Decay! p H. K. Park, 8 R. A. Burnstein, 5 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. Zyla 7 (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, 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 8:6 6:6 5:4 stat 5:5 syst The narrow range of dimuon masses may indicate that the decay proceeds via a neutral intermediate state,! pp 0 ;P 0! with a P 0 mass of 214:3 0:5 MeV=c 2 and branching ratio B! pp 0 ;P 0! 3:1 2:4 1:9 stat 1:5 syst DOI: /PhysRevLett PACS numbers: Ce, Jn, Mz What s the up-to-date standard-model prediction for the decay? In the standard model (SM), the decay! dent on copper targets and momentum selected by a curved pl l pll ;l e; can be described as proceeding collimator situated in (old a dipole calculation magnet (hyperon by Bergstrom, magnet). Safadi, Singer, ZPC, 1988) through a flavor-changing neutral-current (FCNC) interaction and by internal conversion, as shown in Fig. 1(a) 1(c). changed by reversing the field of the hyperon magnet. We The sign of the charged secondary beam was periodically Do the observed 3 events hint at new physics? Bergström et al. [1] argue that in the SM the FCNC analyzed 2: triggers from the positive-secondarybeam data set and 0: from the negative. contribution for the decay pll is not dominant. The decay The signature of the pll is of interest since it also allows a direct search for a p decay is two unlike-sign J Tandean (NTU) NTHUmuon HEPtracks Seminar, and a25 proton Septrack 2008originating from a common 3 new scalar or vector particle, which could contribute an

4 Standard model calculation (He, JT, Valencia, PRD, 2005) Long-distance contributions dominate Σ + pµ + µ. γ µ + µ Σ + p Gauge-invariant amplitude has four form-factors M ( B i B f γ ) = eg F Bf [ iσ µν q µ ( a + bγ5 ) q four-momentum of γ. + (q 2 γ ν q ν q) ( c + dγ 5 )] Bi ε ν Form factors a(q 2 ), b(q 2 ), c(q 2 ), and d(q 2 ) are all complex and get imaginary parts from N 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

5 Long-distance contributions to Σ + pγ Unitarity cut γ Σ + N p Leading-order diagrams for N pγ reactions + γ + γ + γ n p n p n p 0 γ 0 γ p p p 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

6 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 (a) 6 Re a = 6.0 MeV Re b = 13.3 MeV (b) dγ(σ+ pµ + µ ) dq 2 (MeV 1 ) M µµ (MeV) Re a = 11.1 MeV Re b = 7.3 MeV (c) dγ(σ+ pµ + µ ) dq 2 (MeV 1 ) M µµ (MeV) Re a = 7.3 MeV Re b = 11.1 MeV (d) M µµ (MeV) M µµ (MeV) 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

7 Branching ratio in standard model The SM calculation yields the range B ( Σ + pµ + µ ) This agrees well with HyperCP measurement B(Σ + pµ + µ ) = ( ± 5.5 ) 10 8 (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

8 Alternative interpretation of HyperCP results From HK Park s talk (2007) J Tandean (NTU) NTHU HEP Seminar, 25 Sep

9 New particle hypothesis Interpreting their results as hinting at a new particle (X 0 ), HyperCP finds B ( Σ + px 0 pµ + µ ) = ( ± 1.5 ) 10 8 mass m X = (214.3 ± 0.5) MeV This observation implies the particle is short lived, decaying inside detector is narrow, with Γ X 10 7 MeV (Geng & Hsiao, PLB, 2006) 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

10 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

11 Constraints from kaon and B-meson decays E865 at BNL: B(K ± ± A 0 1) (Ma et al., PRL, 2000) NA48: B(K S 0 A 0 1) (Batley et al., PLB, 2004) BABAR & Belle: (Aubert et al., PRL, 2004) B(B X s A 0 1) (Iwasaki et al., PRD, 2005) J Tandean (NTU) NTHU HEP Seminar, 25 Sep

12 Two types of S = 1 contributions Two-quark contributions (He, JT, Valencia, PRD, 2006) L Asd = ic R 2 C L,R are in general unrelated. d(1 + γ 5 )s A ic L 2 d(1 γ 5 )s A H.c. Four-quark contributions, which arise from the combined effects of the usual SM four-quark S = 1 operators and A 0 1 being radiated off one of the light quarks via its flavor-conserving couplings. u s d W A 0 1 u Similarly for a scalar particle. J Tandean (NTU) NTHU HEP Seminar, 25 Sep

13 Hadronic couplings arising from two-quark contributions Chiral Lagrangian techniques can be used to derive the hadronic realization of the sda 0 1 couplings. The resulting Lagrangian L A = b D B {ha, B} + b F B [ha, B] + b 0 h A BB f 2 B 0 h A + c T α h A T α c 0 h A T α T α + H.c. h A = i ( C R ξ hξ + C L ξhξ ) A 0 1 and h = 1 2 ( λ6 + iλ 7 ). Baryon and meson fields are contained in 3 3 matrices B and ξ, and also tensor T µ. Diagrams for Σ pa 0 1 A 0 1 A 0 1 Σ + p Σ + K0 p Similarly for a scalar particle. J Tandean (NTU) NTHU HEP Seminar, 25 Sep

14 Chiral Lagrangians in SM Leading-order strong Lagrangian L s = B iγ µ ( µ B + [ V µ, B ]) m 0 BB + D Bγ µ γ 5 { Aµ, B } + F Bγ µ γ 5 [ Aµ, B ] + b D B {M+, B} + b F B [M+, B] + b 0 M + BB f 2 µ Σ µ Σ f 2 B 0 M + T µ i DT µ + m T T µ T µ + C ( T µ A µ B + BA µ T µ) + c T µ M + T µ c 0 M+ T µ T µ Leading-order weak Lagrangian L w = h D B { ξ hξ, B } + h F B [ ξ hξ, B ] + γ 8 f 2 h µ Σ µ Σ + 2 γ 8 f 2 B 0 hξm+ ξ + h C T µ ξ hξt µ + H.c. J Tandean (NTU) NTHU HEP Seminar, 25 Sep

15 Chiral Lagrangians for four-quark contributions From SM strong and weak chiral Lagrangians, one derives L A s = ( b D B{ M, B } + b F B[ M, B ] + b 0 M BB f 2 B 0 M ) ia 0 1 v L A w = 2 γ 8 f 2 B 0 hξ M ξ ia0 1 + H.c. v M = ξ Mξ ξ M ξ and M = diag ( ) l u ˆm, l d ˆm, l d m s From the coupling of A 0 1 to two gluons via the axial anomaly, ( ) [ L η1 A = 1 2 m 2 η m2 K 1 3 m2 η 1 + f ] 2 A0 1 (2l u + l d ) 6 v A A A 0, η, η 0, η, η 0, η, η Σ + p Σ + Σ + p Σ + p p A A A A K K K 0 0, η, η K K K 0, η, η J Tandean (NTU) NTHU HEP Seminar, 25 Sep

16 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 ± γ 5 )sx: the part without γ 5 contributes significantly to K µ + 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 qq X are related for different (q, q ) sets, experimental data on B X s 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

17 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 H u and H d 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 A 0 1, turns out to be able to play the role of X. The soft-susy-breaking term in the Higgs potential is V soft = m 2 H u H u 2 + m 2 H d H d 2 + m 2 N N 2 ( λa λ H d H u N ka kn 3 + H.c. ) and has a global U(1) symmetry in the limit that A λ, A k 0. (Dobrescu, Matchev, JHEP, 2000) The global U(1) symmetry allows the A 0 1 mass to be naturally, and masses of order 100 MeV are not ruled out. (Dobrescu, PRD, 2001) J Tandean (NTU) NTHU HEP Seminar, 25 Sep

18 A 0 1 in NMSSM In the large-tan β limit (tan β the ratio of VEVs of Higgs doublets) the A 0 1 is mostly the singlet pseudoscalar and couples to SM fields through mixing its squared mass m 2 A = 3k x A k + O(1/ tan β) with x = N 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, L Add = l d m d dγ5 d ia0 1 v, L Al = l d m l lγ5 l ia0 1 v, l d = v δ / ( 2 x ), with v = 246 GeV and δ = (A λ 2kx)/(A λ + kx) the lower bound of l d is l d 0.1 (Hiller, PRD, 2004) and its upper bound l d 1.2. (He, JT, Valencia, PLB, 2005) Therefore the 4-quark contributions are given in terms of l d in the large-tan β limit J Tandean (NTU) NTHU HEP Seminar, 25 Sep

19 Two-quark contributions of A 0 1 in NMSSM In certain versions of the NMSSM at large tan β, the couplings C L,R are related by C L = C R m d /m s = 2g A m d /v, corresponding to L Asd = ig A v [ ms d(1 + γ5 )s m d d(1 γ5 )s ] A H.c. This is the case with the NMSSM of Hiller (2004) at large tan β, where C L,R are generated by one-loop diagrams containing charginos and squarks. With suitable modifications, the Hiller model provides an A 0 1 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 with l d = 0.35 Branching ratios of Σ + pa 0 1 (solid curves), K + + A 0 1 (dotted curves), and K S 0 A 0 1 (dashed curves), where horizontal lines indicate HyperCP and kaon bounds g J Tandean (NTU) NTHU HEP Seminar, 25 Sep

20 More general scenario for light A 0 1 in NMSSM Additional one-loop contributions to the sda 0 1 couplings with other SUSY particles in the loop could enlarge the parameter space, making C L,R unrelated. L Asd = ic R 2 d(1 + γ 5 )s A ic L 2 d(1 γ 5)s A H.c. 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 C L and C R can be taken to be independent, to be constrained with data. J Tandean (NTU) NTHU HEP Seminar, 25 Sep

21 Parameter space 1.0 Regions in the (C L +C R, l d ) parameter space allowed by K + + µ + µ (blue) and K S 0 µ + µ (green). The overlap (red) band covers points that satisfy both constraints. l d Regions in the (C L +C R, C L C R ) parameter space reproducing the HyperCP result (yellow) and respecting the K µ + µ bounds (red) for l d = 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 C L,R C L CR C L C R C L C R J Tandean (NTU) NTHU HEP Seminar, 25 Sep

22 Other rare decays with light A 0 1 in NMSSM (He, JT, Valencia, JHEP, 2008) Some other rare decays can help confirm of refute the light-a 0 1 hypothesis S = 1 decays Evaluate K A 0 1 µ + µ and Ω Ξ A 0 1 Ξ µ + µ. They involve both two-quark and four-quark contributions. Flavor-conserving decays Υ(1S) γa 0 1 γµ + µ and φ γa 0 1 γµ + µ. Evaluate η A 0 1 µ + 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

23 K A quark contributions K A 0 1 K K 0 A quark contributions K A 0 1 K K A 0 1 K K A 0 1 K P K A 0 1 K P A 0 1 K P A 0 1 K K P A 0 1 K P P A 0 1 Predicted branching ratios (solid curves) for K L + A 0 1 and K L 0 0 A 0 1 with l d = The dotted curves result from the 2-quark contributions alone, the pink bands indicate the allowed ranges of C L C R, and each green dashed line corresponds to the case of C L,R being related. Being studied by KTeV K L Π Π A K L Π 0 Π 0 A L R J Tandean (NTU) NTHU HEP Seminar, 25 Sep

24 Ω Ξ A 0 1 A 0 1 Two- and four-quark contributions K0 Ω A 0 1 P Ξ Ω Ξ Ξ 12 Predicted branching ratio for l d = A L R The best limit currently available from HyperCP (2003) B(Ω Ξ µ + µ ) < (90%C.L.) SM predicts B SM (Ω Ξ µ + µ ) = (Safadi & Singer, PRD, 1988) The predicted Ω Ξ A 0 1 Ξ µ + µ rate for most of allowed regions is substantially enhanced with respect to the SM rate. J Tandean (NTU) NTHU HEP Seminar, 25 Sep

25 η A 0 1 They are special, involving only flavor-diagonal interactions η A 0 1 η η, η A 0 1 Predicted branching ratio B ( η + A 0 1) = l 2 d for η-η mixing angle θ = The best limit currently available from CELCIUS/WASA collaboration (2008) B(η + µ + µ ) < (90%C.L.) implies loose bound l d < 26. There is room for enhancement over the expected standard-model rate B SM (η + µ + µ ) = ( ) η + µ + µ may be accessible to DAΦNE experiment. (Borasoy, Nissler, EPJA, 2007) J Tandean (NTU) NTHU HEP Seminar, 25 Sep

26 New constraint from CLEO arxiv: v1 [hep-ex] ÄÆË ¼»¾¼ Ä Ç ¼ ¹½ Ë Ö ÓÖ Ä Ø È¹Ó À Ò Ê Ø Ú Ý Ó ½Ëµ [hep-ex] 9 Jul 2008 Ϻ ÄÓÚ ½ κ Ë Ú ÒÓÚ ½ Àº Å Ò Þ ¾ º º º Àº Å ÐÐ Ö Áº Ⱥ º Ë Ô Ý º Ò º ˺ Ñ Åº Ò Ö ÓÒ Âº Ⱥ ÙÑÑ Ò Áº Ò Ó º ÀÙ º ÅÓÞ Âº Æ ÔÓÐ Ø ÒÓ Éº À º ÁÒ Ð Ö Àº ÅÙÖ Ñ Ø Ù º ˺ È Ö º Àº Ì ÓÖÒ º Ò Åº ÖØÙ Ó Ëº Ð٠˺ à РРº Ä Êº ÅÓÙÒØ Ò Ëº Æ Ö Ãº Ê Ò Ö Ò Ö ÚÓÒÝ Æº ËÙÐØ Ò Ìº Ë Û ÖÒ ØÖ Ø Ëº ËØÓÒ Âº º Ï Ò Äº ź Ò Ï º Ö ÓÒÚ Ò ÓÖ ÒÓÒ¹ËŹРº Ò ÖÓ È¹Ó Åº Ù ÖÓÚ Ò À Ó ÓÒ º Ä ÒÓÐÒ ¼ Ⱥ Æ Âº Ê Ñ Ö ½µ Û Ø Ñ ¼ ¾Ñ Ò Ö Ø Ú Ý Ó º ź Ò Ö Ãº Ϻ Û Ö Âº Ê Êº º Ö Ö ½¼ ½ Ø ½Ëµ Ù Ò ¾½º Å ½Ëµ Ñ ÓÒ Ö ØÐÝ ÔÖÓ Ù Ò Ìº Ö Ù ÓÒ ½¼ ÒÒ Ð Ø ÓÒº º Ï Ì Ø Ú Ð ½¼ ÒÚ Ø Ø ¼ Àº ÎÓ Ð ½¼ ź º Ï Ø Ò ½¼ º ĺ ÊÓ Ò Ö ½½ º Ⱥ Ð Ü Ò Ö ½¾ º º Ð ½¾ ½ Ò ¼ ½ Ý ÒÒ Ð º ÆÓ Ò ÒØ Ò Ð ÓÙÒ º Ï Ó Ø Ò ÙÔÔ Ö Ð Ñ Ø Âº ÓÒ º Ø Ù Ó Õ ½¾ ÔÖÓ ÙØ Ó Êº ½Ëµ ÖÐ ½¾ ĺ ¼ ½µ Ð ½¾ Ò ¼ ʺ ˺ Ð ½¾ ĺ ÓÒ ½¾ ʺ Ö Ý ½¾ ½ µ ÓÖ ¼ ½ µº ÇÙÖ Ö ÙÐØ Ëº Ö Ïº ÐÑÓ Ø Ö Ý ½¾ ØÛÓ º ÓÖ Ö Äº À ÖØ ÐÐ ½¾ Ó Ñ Ò ØÙ º ú ÑÓÖ À ÐØ Ð Ý ½¾ ØÖ Ò ÒØ º Ø Ò À ÖØÞ ½¾ ÔÖ Ú Ó٠º ź ÙÔÔ Ö ÀÙÒØ ½¾ Ð Ñ Ø º º ÇÙÖ Ã Ò Û ÑÝ ½¾ Ø ÔÖÓÚ ÒÓ º Ú Ò Äº ÃÖ Ò ½¾ ÓÖ À κ º Ø Ø ÃÙÞÒ Ø ÓÚ ½¾ Û Ø Ñ Âº Ä ÓÙÜ ½¾ Ó ¾½ Å ÎÀº Ý Ò Å Ð ¹ÃÖĐÙ Ö ½¾ ØÓ º Ü Ø Ò º ÅÓ Ô ØÖ ½¾ Ó Ù Ø Ø Èº ͺ Û º ÔÖ Ú ÓÙ ÐÝ ÇÒÝ ½¾ ÔÖÓÔÓ Âº ʺ È ØØ Ö ÓÒ ½¾ Ò ÜÔÐ Ò Ø ÓÒ º È Ø Ö ÓÒ ½¾ ÓÖ º Ê Ð Ý ½¾ Ô Ú ÒØ º ÊÝ ½¾ Ú Ò º º Ë Ó«½¾ Ñ Ù Ø º Ë ½¾ ÓÚ Ëº Ø ËØÖÓ Ò Ý ½¾ Ò Ñ Ø Ø Ö ÓРϺ ź ËÙÒ ½¾ Ó ÖÚ Ìº Ï Ð Ò ½¾ Ý Ø ÀÝÔ Ö È Ëº º Ø Ö ½ ÜÔ Ö Ñ Òغ ʺ È Ø Ð ½ ÇÙÖ Ö ÙÐØ Âº ÐØÓÒ ½ ÓÒ ØÖ Ò ÆÅËËŠȺ ÊÙ Ò ½ ÑÓ Ð º º Áº Ò Ø Ò ½ Áº à ÖÐ Ò Ö ½ ˺ Å Ö Ý Ò ½ ƺ ÄÓÛÖ Ý ½ ź Ë Ð Ò ½ º º Ï Ø ½ º Ï ½ ʺ º Å Ø ÐÐ ½ ź ʺ Ë Ô Ö ½ º ÓÒ ½ ̺ ú È Ð Ö ½ º ÖÓÒ Ò¹À ÒÒ Ý ½ ú º Ó ½ º À Ø Ð ½ º ÃÙ ÓØ ½ ̺ ÃÐ Ò ½ º Ϻ Ä Ò ½ ʺ ÈÓÐ Ò ½ º Ϻ ËÓØØ ½ Ⱥ Û Ö ½ ˺ Ó ¾¼ º Å ØÖ Ú Ð ¾¼ ú ú Ë Ø ¾¼ º ÌÓÑ Ö Þ ¾¼ º Ä Ý ¾½ ĺ Å ÖØ Ò ¾½ º ÈÓÛ ÐÐ ¾½ º Ï Ð Ò ÓÒ ¾½ Ò Ãº ź ÐÙÒ ¾¾ J Tandean (NTU) NTHU HEP Seminar, 25 Sep

27 Detour The 4-quark contribution to Σ + pa 0 1 M 4q (Σ + pa 0 1 ) = f l ( ) ( ) d b + b 2v η c θ + b η s θ i p Ap 0 B p 0γ 5 Σ + has a sign ambiguity because A p 0 and B p 0 are extracted from the data on nonleptonic decay Σ + p 0 up to an overall sign. With the opposite relative sign of the 2- and 4-quark contributions to Σ + pa C L C R C L C R 10 8 K L Π Π A C L C R 10 8 K L Π 0 Π 0 A C L C R J Tandean (NTU) NTHU HEP Seminar, 25 Sep

28 CLEO s constraint on A 0 1 Branching ratios of Σ + pa 0 1 (solid curves), K + + A 0 1 (dotted curves), and K S 0 A 0 1 (dashed curves) as functions of C L + C R. Horizontal lines indicate HyperCP and kaon bounds CLEO (2008) reported B ( ) Υ(1S) γa 0 1 < at 90% C.L., which implies l d < 0.16 This squeezes the parameter space for the scenario with C L,R being related, but not completely yet L R L R J Tandean (NTU) NTHU HEP Seminar, 25 Sep

29 Absence of four-quark contributions for l d = 0 If C L,R are not related, the experimental bounds can be satisfied even in the absence of the 4-quark contributions C L CR l d K L Π Π A l d K L Π 0 Π 0 A l d C L C R l d C L C R C L C R 10 6 A C L C R J Tandean (NTU) NTHU HEP Seminar, 25 Sep

30 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 m µµ 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 A 0 1, that could have the desired mass and satisfy all the experimental constraints. Additional rare decays can help confirm or refute this hypothesis: K A 0 1, Ω Ξ A 0 1. Some other rare decays can test the hypothesis independently of the flavor-changing sector: Υ(1S) γa 0 1, φ γa 0 1, η A 0 1. J Tandean (NTU) NTHU HEP Seminar, 25 Sep